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1. 2 Figure 1 Phasor diagram Suppose that we locally generate another signal vo uo t Ao cos 2m fet 00 2 We want to adjust the local phase o t 27 fet 09 t to that of the input 2m fet 0 t Note we have assumed that v and have the same nominal carrier frequency fe This entails no loss of generality because any difference in instantaneous frequency be included in 00 2 The situation is pictured in Figure 1 The phasor Vo t makes an angle o t with the positive real axis and V t makes an angle 1 with the axis The two phasors rotate with instantaneous frequencies Dd 148 Qn dt 1 400 001 40 Qn dt On dt Ideally the two phasors should coincide at every time t the misalignment is described by the phase error 0 t Silt t 0 t 00 Phase Locked Loop 3 We can adjust e t to 0 by an automatic control system if we can gener ate a control signal as a function of 0 t One way to do this is to multiply the two signals vi t vo t 2n fet 94 cos 2m fet 00 6 cos 6 t 80 2 4 Ai cos 4m fet 0 t Oo t The first term is what we want it provides measure of the phase differ ence Since 0 and 69 are slowly varying with respect to fe the second term is a narrowband signal at 2 2 which be removed by a low pass filter There is however one difficulty Because
2. Hint I suggest using the VPULSE part in PSpice to generate the sampling waveform You need to specify the rise time and fall time of this square wave You can also specify a maximum time step in the Analysis Setup Your PAM signal will probably look spikey This is caused partly by how you adjust the rise and fall times relative to the maximum step size You can reduce this effect but you may not be able to eliminate it by making the maximum step size small relative to the rise and fall times of the sampling waveform Of course the smaller you make the step size the longer the simulation will take As the engineer on this project you will have to reach a reasonable compromise 5 The message x t can be recovered from the PAM signal by ideal low pass filtering This is explained in Couch and in lecture Of course we do not have an ideal LPF Suppose that we recover the sinusoidal signal from the PAM signal in Item 3 by means of a non ideal low pass filter To be exact we shall use the Sallen Key circuit from Laboratory 3 with R 30kQ and 0 01 uF which result in 6dB break frequency of 530Hz Calculate and plot the signal and its amplitude spectrum at the filter output Again you should use Mathcad or Matlab The demodulated output of the filter will not be precisely the sinu soidal message that you started with there will be some other fre quency components present In other words the demodulated output sign
3. X2 X4 j Ro X4 Barkhausen criterion implies first that the loop phase shift be zero in this case X1 X3 0 Then we have M A X1 Xa or since 4 1 Barkhausen criterion also implies that L 1 and so X4 must have the same sign i e they must be the same kind of reactance either inductive or capacitive It follows that X1 must be the other type of reactance If and are capacitors and is an inductor the circuit is called Colpitts oscillator if and are inductors and is L Appendix 11 a capacitor the circuit is called a Hartley oscillator Other combinations are also used For example if 21 and Z are capacitors and 23 is a series combination of an inductor and a capacitor then the circuit is called a Clapp oscillator Remark Transistor versions of the Colpitts and Hartley oscillators are possible see Section 12 3 in Sedra Smith Qualitatively the operation of the circuits is the same as the op amp versions but the detailed analysis is more difficult for two reasons First the low input impedance of the tran sistor shunts 21 and so the equation for the loop gain is more complicated Second if the frequency of oscillation is beyond the audio range the simple h parameter model is not valid and the hybrid 7 model of the transistor must be used 3 3
4. idea of sampling is simple take samples of signal at discrete time instants and if the samples are enough in time the signal can be reconstructed at least approximately by interpolating between the samples The famous sampling theorem tells us precisely how close is close enough if the samples occur at a rate at least twice the highest frequency contained in the signal then the signal can be exactly reconstructed from its samples by passing the sampled signal through an ideal lowpass filter whose bandwidth is equal to the highest frequency contained in the signal The sampling theorem implies the trade off that we always face in analog to digital conversion we want closely spaced samples but the more closely they are spaced the more samples we need and hence the more memory we need to hold them In most practical problems memory is the critical limitation Hence we usually start not by specifying the sampling rate but by specifying the total number of samples that we will take this is the record length We then select or more accurately the oscilloscope selects the appropriate sampling rate for the signal Note how the sampling trade off appears now with a fixed record length we will only acquire a short time duration of a rapidly varying signal while we will acquire a longer duration of a slowly varying signal The Agilent 54622D has a maximum sampling rate of 200 Msamples sec for one channel and 100
5. sin 6 t 27 0o t sin belt The output vo t is the convolution of v a t and h t aus h t sin 0 r VCO is defined by t t 2n Kyvy t 2n K Ka f h t 0 Finally 0 t 0 t 00 2 and so 09 t 6 t 0 5 600 0 t iik h t sin and so we have the dynamic equation for the phase error t i nk Ka h t sin 1 control system diagrammed in Figure 3 obeys this dynamic equation This control system is the equivalent model of the PLL that we were looking for The phase detector multiplier and LPF of Figure 2 is replaced by a subtractor and sinusoidal nonlinearity and the VCO is replaced by an integrator The phases 0 t and 09 t appear explicitly in this model Note that the model is independent of fe referring to the phasor diagram of Figure 1 this model describes the relative motion of the two phasors We have obtained a model describing the PLL in terms of 0 and 99 but we have introduced a new problem the sinusoidal nonlinearity makes an exact analysis very difficult We shall therefore have to content ourselves with an approximate analysis of the equivalent model Phase Locked Loop 6 0 0 va t Loop filter v2 t mee Kasin 8 A t n f AL 0 Figure 3 An e
6. Verify that the filter is a bandpass filter the input is the current into the filter and the output is the voltage across it and that its resonant frequency is the carrier frequency Simulate the circuit of Figure 1 Run the simulation for a long enough time that the of the output voltage will be accurate Reasonable values for the amplitudes of the sinusoids are 0 8 V for the message and 1 0 V for the carrier Display the FFT of the output voltage include the printout in your notebook Lab 6 2 R1 10k DANA 46 Carrier 200kHz R4 1k m Figure 1 AM Modulator Lab 6 3 6 Your FFT should show an AM signal at 200 kHz with the sideband lines 30kHz above and below But you will also see other smaller components What is their origin Two hints What is the frequency response of your bandpass filter Is the diode ezactly square law device Calculate how many dB below the carrier line 200 kHz the spurious lines in the spectrum are In Item 4 of the In Lab portion you will simulate a doubly balanced modulator You should have time to do that part in lab but you may do it as a prelab if you wish IN LAB 1 Build the AM modulator of Figure 1 Note The 2 2mH inductors are available but you cannot get exactly the 287 pF capacitors But you can get close by using series or parallel combinations of capacitors that are available The resonant frequency of the bandpass filter
7. filter H s Phase detector vo VCO Figure 2 The basic phase locked loop The locally generated reference is the VCO output volt Ao cos 2m fet O9 t 7 2 The output of the multiplier and LPF is the error signal _ Ao Aj _ Ao Aj e m EE valt Km sin 6 t 00 6 Km sin 62 1 The combination of multiplier and LPF is a product phase detector and Km is its gain Phase detectors with non sinusoidal characteristics are also available but all are odd functions of e see Figure 4 20 in Couch Define i L so that we may write valt Kasin 6 t 0o t The loop filter is a linear system with transfer function H s and impulse response h t we shall come back to it later The output of the PLL v2 t is fed back into the VCO As we have said the VCO produces the reference volt Ao 2 fet O9 t 7 2 whose instantaneous frequency varies according to vo t 149 _ 14 dt ciae gp where K is a constant representing the VCO gain in units of Hz V Phase Locked Loop 5 3 An Equivalent Model In the analysis of PLL we are not interested in the signals v t vo t and v2 t as much as in the phases 6 t and 09 t and the phase error 6 t 0 t 09 t Therefore we shall replace the block diagram of the basic loop Figure 2 by a mathematically equivalent one which operates on the phases We do this as follows First valt
8. is an even function we can not tell from cos 0 t whether 0 t is larger than 69 t or the other way round We need an error function which is an odd function of 0 t This is easily obtained by advancing the locally generated signal by 90 That is the locally generated signal should be volt Ao cos 2m fet O9 t 7 2 Ao sin 2m fet 00 4 we have vi t uo t 244 sin 0 6 0 4 244 sin 4n fet 6 t 00 0 Again the second term is eliminated by a low pass filter and we are left with our desired error signal Ai Ao A Ao sin e t 7 sin 6 t 6o t If 6 t 006 A 0 then an error signal with the same sign as the phase error is produced Suppose that this error signal is filtered and applied to a device that produces a sinusoidal output whose instantaneous frequency varies according to the voltage applied to it Such a device is called a voltage controlled oscillator VCO When the control voltage is 0 the VCO runs at its quiescent frequency fe A positive negative control voltage causes the VCO to increase decrease its instantaneous frequncy thus forcing the control voltage to decrease increase The block diagram of the system we have described is in Figure 2 This is the basic PLL The input is vit Ai cos 2r fet 0 t Phase Locked Loop 4 v t Low pass va t Loop filter va t M9
9. xlabel Frequency Hz subplot 212 plot f 20 log 1 O0 abs P grid title Signal Spectrum in dB xlabel Frequency Hz figure subplot 211 plot f abs X grid title Signal Spectrum of X xlabel Frequency Hz subplot 212 plot f 20 log 10 abs X grid title Signal Spectrum in dB xlabel Frequency Hz Using Matlab generate a random binary bit pattern with length 15 Use the function generator to create and store this signal Because we can not create a truly random signal the idea is that we will create a pseudo random signal By using 15 random bit values repeated at the proper frequency we will be able to control the symbol rate Instructions on how to create an arbitrary function can be found in the instruction manual Design and build an RC filter with the same bandwidth as the raised cosine filter of the prelab 6kHz Record the values of your Resistor and Capacitor Thesymbol frequency is still 9kHz Set the output of the function generator accordingly and attach the signal to the filter Display the eye pattern on the oscilloscope What effect does changing the symbol rate have on ISI Demonstrate your results with experimentation and commentary APPENDIX BASICS OF THE DIGITAL STORAGE OSCILLOSCOPE 1 Introduction This appendix contains basic information about digital storage oscilloscopes in general and some specific information about the Agilent 54622D oscillo scope
10. 1kHz This is the Message Signal input in Figure 6 Connect the RC lowpass filter from the second week prelab to pin 2 as indicated in Figure 6 e Display the demodulated signal output of the LPF on the DSO Hint Use the SYNC output of the function generator for your trigger e Investigate the effect of varying the frequency of the message signal and explain your observations Lab 7 8 LPF Figure 6 FM Demodulator Circuit References Carlson A Bruce Carlson Paul B Crilly and Janet C Rutledge Com munication Systems An Introduction to Signals amp Noise in Electrical Communication 4 ed McGraw Hill 2002 Couch Leon Couch Digital and Analog Communication Sys tems 6 ed Prentice Hall 2001 LABORATORY 8 MORE FREQUENCY MODULATION DEMODULATION OBJECTIVES investigate direct FM using a VCO and slope detection of FM PRELAB 1 Read Sections 4 13 and 5 6 in Couch or Section 5 3 in Carlson on direct generation of FM and slope detection of FM 2 There are many ways of generating and detecting FM we saw one in Laboratory 7 using PLL In this lab we shall consider one method of direct FM using a voltage controlled oscillator VCO A VCO is also an integral part of the PLL We shall use the popular 555 timer as the VCO in this lab 555 is basically a multivibrator it can be operated in monostable mode i e as a one shot or in astable mode
11. Repeat items 1 2 and 3 with an FM signal having modulation index 8 3 25 Keeping the carrier frequency and the message frequency fixed investi gate the effect on the FM spectrum of changing the modulation index Determine the smallest frequency deviation for which the carrier power is zero and compare to your prelab Lab 7 a COMP 2 z T Figure 1 Block Diagram of the CD4046 PLL 6 We shall now study the characteristics of a particular phase locked loop CD4046 is a digital PLL chip implemented with CMOS technology the block diagram of the chip is shown in Figure 1 Any PLL consists of three blocks a phase detector or phase compara tor a low pass filter and a voltage controlled oscillator VCO See Figure 4 19 in Couch or Figure 7 3 2 in Carlson and Figure 2 in Appendix E of this manual The CD4046 provides two different phase detectors and the VCO the lowpass filter must be connected exter Specification data for the CD4046 PLL National Semiconductor Corp Document no RRD B30M115 1995 Lab 7 4 Figure 2 PLL Circuit nally by the user That is the user can design the filter to obtain the desired PLL behavior Phase detector I is an exclusive OR gate phase detector which provides a triangle characteristic and phase detector II is an edge controlled memory network essentially it is a flip flop phase detector which provides a sawtooth ch
12. cos 27 fet lowpass AM at fe 1 a2 2 0 cos Am fet line at 2f The spectrum Z f of z t given by Eq 1 consists of three parts as indi cated e The first term has spectrum 2 2 a X x X f ca X f 75 f which is a lowpass signal with bandwidth 2W e The second term Aoa 1 a t cos 27 fet is an AM signal at carrier frequency fe with modulation index u 2a2 Q1 e The third term is a line at frequency 2 fc Hence if z t is passed through centered at f and having bandwidth 2W the output will be the AM signal given by the second term in Eq 1 Figure 3 is the basic AM modulator circuit It is called an unbalanced modulator or mixer or a single ended modulator In Section 4 we shall see what kind of electronic devices can be used for the square law device but first let us continue investigating frequency conversion systems Mixers amp Frequency Conversion 5 2 01 4 aiwita2uy w1 t gt Ao cos 27 fet RC w t 02 Figure 4 Balanced modulator for DSB 2 2 Double sideband suppressed carrier AM To suppress the carrier line and thereby generate DSB modulation we can use two identical square law devices in a balanced configuration we gener ate two AM signals subtract them and the carrier line is suppressed The block diagr
13. 7T You can run a more accurate simulation as follows 1 From your simulation estimate how long the transient lasts In my simulation it lasts about 150 200 us Run the simulation for much longer so that the output is mostly steady state Now look at the 2 Better still in the simulation setup enter a no print delay large enough so that the the initial transient data is not collected Display the output voltage and its FFT You should find that the carrier line is suppressed 8 The moral of this little exercise is that you have to pay attention to transients in simulations Sometimes you want to see the tran sient But sometimes it is unimportant and if you don t set up your simulation appropriately you may be misled when you go to make steady state measurements on the circuit 9 One final point Why did you not build this circuit It seems to be simple enough Answer look at how the carrier must be connected Can you connect the function generator this way The answer is no The function generator produces a single ended output meaning that it must be connected between a node and ground The carrier gen erator called for in Figure 2 must have a differential output It s the same sort of reason that you cannot use the oscilloscope probe to measure the voltage across two nodes you must always measure from a node to ground measure across nodes you need a differen tial probe they are available but expensive A 20
14. Remember that the spectrum analyzer input impedance is 500 Lab 5 2 Signal Output HE Figure 1 Simple Envelope Detector e Determine the ratio of the power in the sidebands to the power in the carrier 3 Obtain numerical values in Item 2 if fm 15 kHz u 1 2 and the carrier amplitude and frequency are A 1 and fe 300 kHz Also use Mathcad or Matlab to plot the AM signal ze t 4 Repeat Item 2 for a message x t which is a square wave of amplitude 1 zero dc level 50 duty cycle and fundamental frequency fj 5 Obtain numerical values in Item 4 if fm 15 kHz 1 2 and the carrier amplitude and frequency are A 1 and f 300 kHz Also use Mathcad or Matlab to plot the AM signal ze t 6 In lab you will display the AM signal on the oscilloscope Devise a way to measure the modulation index from the plot of the AM signal Hint consider the maximum and minimum peak to peak swings of the AM signal look at Figure 5 1 b in Couch or Figure 4 2 1 b in Carlson 7 As explained in Section 4 13 of Couch or Section 4 5 of Carlson an AM signal with less than 100 modulation i e with lt 1 be easily demodulated using an envelope detector shown in Figure 1 In fact this is the reason for AM we transmit a large amount of wasted power in the carrier but we can use a non synchronous detector In practice the situation is more complicated the envelope detector has very
15. Using the R and C values from Item 3 simulate the Sallen Key filter in PSpice and obtain a Bode plot of the amplitude gain in dB over the frequency range 1 Hz to 100 kHz Determine the slope in dB per decade of the high frequency asymptote Be sure to choose Ve and the input ampltitude so that the op amp does not saturate i e make sure the circuit is operating as a linear system In lab you will use Vee 5 so choose the input amplitude appropriately Hint Recall that to get a frequency response plot in PSpice use the VAC source for the input and in the simulation setup set the paramters under AC Sweep It is convenient to use a voltage dB marker or phase marker at the ouput depending on which part of the frequency response you want Compare your theoretical Bode plot from Item 4 with the circuit sim ulation result from Item 5 They should of course be close Your theoretical anlaysis was based on an ideal op amp and your simulation Lab 3 3 uses the Spice model of the op amp so supposedly the simulation is more accurate to some degree This should always be your procedure You do some analysis and design based on a simplified mathematical model Now you have some idea of how the system should behave Next you verify your analysis by doing as accurate a simulation as you can Now you are pretty sure how the system should behave and you are ready to build the prototype in the lab and make some measurements Here is whe
16. When you are testing a circuit especially one that you have built if the output signal is not what you expect do not go in and randomly replace chips and other components The Introduction 3 key is to be logical and systematic don t just try things at random hoping to get lucky First look for obvious errors that are easy to fix Is your measuring device correctly set and connected Is the power supply set for the correct voltage and is it connected correctly Is the signal generator correctly set and connected Next check for obvious misconnections or broken connections at least in simple circuits If the problem is not one of these trivial ones then you need to get to work As you work through your circuit use your notebook to record tests that you make and changes that you make as you go along don t rely on your memory for what you have tried Identify some test points in the circuit at which you know what the signal should be and work your way backwards from the output through the test points until you find a good signal Now you have a section of the circuit to focus your efforts on Here is where a little thought about laying out your board before connecting it up will pay off if your board looks like a bird s nest it is going to be very hard to troubleshoot but if it is well organized and if the wires are short it is going to make your job a lot easier Final remark if you do discover a bad component or wire do not just thr
17. and so Oels _ 8 Oi Po 8 Now we should like to have O s Oo s which implies G s 1 But this implies that 21K K4H s s 2n K 3 and this in turn implies that s 0 That is it would appear that the PLL performs as we want it to only for zero frequency and then H s can be anything This is of course unacceptable It is true however that for many types of loop filter H s we can show that 8 is approximately O s We shall analyze the linear model for the two cases of H s most commonly encountered in practice Phase Locked Loop 8 4 1 First order loop The first order loop refers to the case H s 1 which results in the closed loop G s being of first order Oo s u Vo s 21 K is O s 4 SFK Ka Or in terms of frequency f where s j2r f ae LL EL 4 O f jf 1 35f fo where fj Ky Kg Note that G f is just the transfer function of an RC low pass filter with bandwidth fy That is the first order loop produces output 00 2 which is essentially 6 t passed through an RC low pass filter Hence if fj is large enough compared to the bandwidth of 0 2 we will have 0o t 0 t The parameter fj is called the loop gain of the first order loop Example 1 Suppose that 0 t 2 Ku t That is consider the step response of the first order linear model if you have taken the controls cour
18. rate X k will be a good approximation to the Fourier transform X f Regardless of the number of points in the waveform record the Agilent DSO uses 2048 points for the FFT Three windows are available Hanning rectangular and flat top See the User s Guide for advice on using windows Note that the vertical units for the FFT display are dBV It would be to your benefit to read FFT Measurement Hints on pages 5 20 5 30 in the User s Guide especially the discussion of frequency resolution Always remember Every time you make a measurement with an oscilloscope you must know how the input is coupled how the waveform is acquired how the oscilloscope is triggered and the sampling rate being used APPENDIX B BASICS OF THE SPECTRUM ANALYZER 1 Introduction This appendix contains some general information about spectrum analyzers and some specfic information about the Agilent E4411B spectrum analyzer that you will use in the communication laboratory Remember that the spectrum analyzer User s Guide is included in the Equipment Manuals folder on the PC desktop at your lab station Like an oscilloscope a spectrum analyzer produces a visible display on a screen the Agilent spectrum analyzer has a VGA screen rather than a CRT screen Unlike an oscilloscope however the spectrum analyzer has only one function to produce a display of the frequency content of an input signal But it is possible to display the waveform on
19. Gl BPF fc fo fo f Figure 2 Up converter bandpass to bandpass conversion Mixers 4 Frequency Conversion 3 x t w t z t v t 0 RA ania d BPF NES AM Ao cos 27 fet Figure 3 Square law AM modulator Note that in this communications application we do not multiply two arbitrary signals we multiply a signal by a sinusoid That is the multiplier blocks in Figures 1 and 2 are not general multipliers In communications a device that multiplies by a sinusoid is called a mirer and the whole system consisting of mixer and filter if the filter is needed is the up down converter 2 Amplitude Modulators 2 1 Double sideband AM with carrier Let us begin with the simpler case of amplitude modulation or up conversion of a baseband signal There are several ways to realize the mixer multiplier electronically but the most common is with a nonlinear device that has a square law characteristic Consider the system shown in Figure 3 The signal z t is a baseband message signal having absolute bandwidth W as in Figure 1 The local oscillator produces the carrier Then the sum of Mixers 4 Frequency Conversion 4 the message and carrier is the input to the nonlinear device The output is 2 z t a Ao cos 27 fet xe Ag cos 2n fot t Ag cos 27 fot Ce t 2ar t Ag cos 2n fet A2 cos 2n fot 2 2 t az t 5 Ao 2azz t
20. Mixers amp Frequency Conversion 11 Smith Jack R Smith Modern Communication Cir cuits 274 ed McGraw Hill 1998 APPENDIX E THE PHASE LOCKED LOOP 1 Introduction A phase locked loop PLL is a feedback control system used to automati cally adjust the phase of a locally generated signal to the phase of an incom ing signal The PLL is widely used for carrier synchronization in coherent demodulation of AM and PM signals both digital and analog The PLL is also widely used in FM demodulation we can use it to recover the phase 0 t in an angle modulated signal It is probably accurate to say that almost all synchronous receivers built today analog or digital AM or FM use the phase lock principle It turns out that the PLL has one other important feature The feedback structure of the loop results in improved performance in noise over slope detection of FM Unfortunately we shall be unable to pursue this We shall concentrate on how the PLL recovers 6 t Historical note a large part of PLL theory was worked out during the 1960 s and 1970 s and it is still an active topic of research but it was only recently that easy and inexpensive implementations became available 2 The Basic Loop Suppose that the incoming signal v is a narrowband signal with constant envelope i e an angle modulated wave u t A cos 2n fet 0 t where 0 is slowly varying with respect to
21. Sedra Smith Adel S Sedra and Kenneth C Smith Microelectronic Cir cuits 4 ed Oxford University Press 1998 LABORATORY 4 SINUSOIDAL OSCILLATORS OBJECTIVES become familiar with two kinds of feedback oscillators used to produce sinusoidal signals the Wien bridge oscillator and a phase shift oscillator PRELAB 1 2 Read Appendix of this manual and Sections 12 1 12 3 of Sedra Smith Design a Wien bridge circuit having an oscillation frequency of 10 kHz with amplitude stabilization use the circuit in Figure 12 6 in Sedra Smith as your template What value of resistance from the tap to point b of the potentiometer P will just sustain oscillations Verify your design in PSpice look at the output at both points a and b Use a 741 op amp You may use the generic breakout diode Dbreak There is a POT part in the Spice library Make sure to run your simulation for a long enough time that you can verify that oscillation is sustained and that the amplitude is stabilized Verify the purity of the ouput waveform by looking at its Cal culate the THD if there are measureable harmonics present For the basic Wien bridge oscillator without the amplitude stabiliza tion circuit 1 Figure 8 in Appendix C calculate the frequency stability factor Sp Comment IN LAB 1 Build the Wien bridge with amplitude stabilization that you designed in Prelab 4 2 e Record the oscillo
22. Sedra and Kenneth C Smith Microelectronic Cir cuits 4 ed Oxford 1998 4 2 m wu o a oO Oo aie z 74 f xx I leo un 1 1 3 La e ow gt 5S p ow 3 R1 L py O N 4 2 C C C LE IER c CN Te C LL p Figure 1 Phase Shift Oscillator With Amplitude Stabilization LABORATORY 5 AMPLITUDE MODULATED SIGNALS AND ENVELOPE DETECTION OBJECTIVES To take measurements of AM signals in the time and frequency domains and to investigate envelope detection of AM signals PRELAB 1 Read Section 5 1 Amplitude Modulation and Section 4 13 Detector Circuits read Envelope Detector subsection in Couch or Sec tion 4 2 Double Sideband Amplitude Modulation and Section 4 5 especially the subsection on Envelope Detection in Carlson 2 An AM signal is written as Telt A 1 ux t cos 27 fet where f is the carrier frequency is the carrier amplitude u is the modulation index and x t is the baseband message signal We assume that x t has absolute bandwidth W lt fe and that its amplitude has been normalized so that z t lt 1 If x t is a cosine of amplitude 1 and frequency fm amp fe e Obtain an expression for the amplitude spectrum of the AM signal ze t e Determine the power in the carrier and in the sidebands Express the powers in units of dBm into 500 load
23. The Wien Bridge Oscillator A Wien bridge oscillator uses a balanced bridge as the feedback network The circuit is shown in Figure 8 at the top below it the feedback network is redrawn to show explicitly that it is indeed a bridge Again the limiter used for amplitude stabilization is omitted see Figures 12 5 and 12 6 in Sedra Smith Note that there are two feedback paths a positive feed back through 21 and 22 which determines the frequency of oscillation and negative feedback through and R which determines the amplitude of oscillation We have Z2 R mco ndi Ae 21 22 E TOR and therefore RCs L s A s B s 1 z RC s 3RCs 1 Hence Ry 1 He 1 m 3 j ROw gl By the Barkhausen criterion the frequency of oscillation is HE 2n RC and the oscillations will be sustained if Ry c Ro fo Appendix 12 Rz R m ya R1 zi Tol Rz Figure 8 The Wien Bridge Oscillator Appendix 13 4 Crystal Controlled Oscillators We have already alluded to the major concern with electronic oscillator circuits frequency stability As component characteristics change with age temperature signal level etc the oscillation frequency drifts A crystal oscillator is often used in those cases in which the frequency drift must be kept small The crystals used in oscillators are usually quartz although other ma terials can be used in specialized applications The pro
24. Y axis For example in the X cut crystal shown in Figure 9 a mechanical stress along the Y axis causes charges to accumulate on the flat sides of the crystal positive charges on one face and negative on the other and so a voltage is developed across the faces If the direction of the mechanical stress is reversed from tension to compression or vice versa the polarity of the charges and hence the polarity of the voltage on the faces reverses Conversely a voltage applied across the faces causes a mechanical stress along the Y axis When an alternating voltage is applied across the crystal in the direction of an electrical axis alternating mechanical stresses will be produced in the 3Piezo comes from the Greek it means press Appendix 14 2 y y X cut T Figure 9 Quartz crystal showing X and Y cuts Figure 10 Crystal circuit symbol direction of the perpendicular mechanical axis The crystal will therefore vibrate and if the frequency of the applied voltage is close to a frequency at which mechanical resonance can exist in the crystal the amplitude of the vibrations will be large Many other cuts at different angles are also used to obtain different resonant frequencies in fact X and Y cuts are rarely used in crystals today Physically a crystal oscillator consists of a flat section cut from a quartz crystal sandwiched between two
25. about flat top sampled PAM and naturally sampled PAM Section 6 2 in Carlson discusses only flat top PAM but naturally sampled PAM was discussed in lecture 3 Consider a sinusoidal message signal x t Ao cos 2m fot Suppose we create a naturally sampled PAM waveform z t using a sampling waveform having sampling frequency fs and duty cycle d See Figure 3 1 in Couch Assume that f exceeds the Nyquist rate for x t If fo 500 Hz fs 5kHz 40 us and Ao 1 V e Calculate and plot the PAM signal z t e Calculate and plot the magnitude spectrum X f Lab 9 2 You may of course make the plots carefully and to scale by hand on graph paper but it will be much easier and more efficient to use Math cad or Matlab You should use the FFT function in these programs to obtain the plot of X f 4 In lab you will implement naturally sampled PAM using an electronic switch Specifically you will use the CD4016 CMOS quad bilat eral switch Simulate the circuit of Figure 1 in PSpice The part CD4016BD is available in the EVAL library of Microsim PSpice the message is applied to pin 1 the sampling waveform is applied to pin 13 Vcc is applied to pin 14 Vec is applied to pin 7 and the PAM output is on pin 2 Use a sinusoidal message and a sampling waveform as in Item 3 Set the amplitude of the sampling waveform for a V swing Plot the PAM output signal and its spectrum using the FFT in Probe
26. acquisitions This mode helps reduce random noise e Real Time Mode oscilloscope produces the waveform from samples collected during one trigger It should only be necessary at sweep speeds of 200 ns div or faster You also control signal acquisition with the RUN STOP and SINGLE buttons 3 Triggering Another important function that you need to learn how to control is trig gering basically triggers determine when the DSO will start acquiring and displaying a waveform That is the trigger determines the time zero point Once a trigger occurs the DSO acquires samples to construct the post trigger to the right or after in time part of the waveform The DSO automatically acquires enough samples to fill in the pre trigger part of the waveform oscilloscope will not recognize another trigger until the acquisition is complete 3 1 Trigger Source You can obtain your trigger from one of the input channels from the AC power line useful for testing signals related to the power line frequency such as when you are testing a power supply or from an externally supplied source for example you can use the SYNC signal produced by the function generator as the trigger source Appendix 4 3 2 Trigger Types The DSO has several types of triggers that you can use The default type and the only type you will need in this course is the Edge type An edge trigger occurs when the trigger source passes through a specifie
27. all AM and FM radios used to work when you turned the tuning knob you were actually turning the adjustment on a variable capacitor and thereby adjusting the frequency of the local oscillator Appendix 20 At microwave frequencies the mechanically tunable elements are YIG elements dielectric resonators and waveguide cavities In many applications such as direct FM or in phase locked loops we need the tuning of the oscillator to be automatic One way to achieve this is with a voltage controlled oscillator VCO A device that can be used in a VCO is the varactor diode Any diode is a PN junction and so has a junction capacitance varactor diode is designed so that the junction capacitance can be controlled by the reverse bias voltage across the junction C V por d where V is the reverse bias is a constant and V4 is the diffusion barrier voltage of the junction Another technique that is becoming more and more common is direct digital synthesis basic idea is to store samples of the desired waveform such as a sinusoid in a microprocessor memory produce the PCM data for these samples and use a D A converter to produce the analog waveform Most of your radio and TV sets now use this technique and the tuning is done by pushing a button Many arbitrary function generators used in labs use this technique to produce a variety of waveforms as well as allowing the user to enter his own data samples and lettin
28. any network can be used as the feedback as long as the Barkhausen criterion is satisfied In the following subsections we discuss some commonly used configurations 3 1 The Phase Shift Oscillator A simple example of the ideas we have discussed is the phase shift oscillator shown in Figure 5 in both FET and op amp versions For simplicity the amplitude limiting circuit is not shown The phase shift oscillator consists of an inverting amplifier with a three section RC ladder network as feedback The amplifier causes a 180 phase shift it has negative gain so in order to satisfy the Barkhausen criterion the feedback must provide another 180 shift three RC sections is the minimum number that will work at a finite frequency Consider the FET version shown in Figure 5 The transfer function of the RC network from Vg the voltage from drain to ground to V which is the negative of the feedback factor is 8 ROS PS vi ROPS 6 SROs F1 j RCPu3 B 1 _ j RC u3 6 RC 2w jbRCw 1 1 592 99 64 B w where y 1 RCw The phase shift of V Vq is 180 when 5 6 or when 1 2x RCA 6 At this frequency of oscillation 8 1 29 Hence in order to satisfy the amplitude half of the Barkhausen criterion A must be 29 A must be a little larger than 29 in practice In the op amp version the virtual ground between the 4 and terminals means that the phase shift network is the sa
29. impedance of the series RLC branch The zeros are 4 or defining the natural frequency and damping ratio of the series circuit in the usual way L WIV 2 S Likewise the second degree polynomial in the denominator of Z s has zeros which along with s 0 are the poles of Z s de 2L E 2L 1 LC 51 52 1 VLC the zeros of the numerator of Z s are R 6 3 81 82 Cu d ET m NOEL EAC um or if we define TENES EE WEM E then the denominator zeros are R 2 7 51 52 Appendix 17 209 Figure 12 Impedance magnitude near the two resonant frequencies We have two resonant frequencies namely the series resonance and the parallel resonance At the series LCR circuit is in resonance and its impedance is R which is small compared to the impedance of Look at Table 1 At w2 we have parallel resonance both branches have high impedance and so Z jw2 is high A typical plot of the magnitude of the equivalent impedance for a quartz crystal is shown in Figure 12 See also Figure 12 15 in Sedra Smith Note from the equations defining the two resonant frequencies that w2 gt w1 but usually gt gt and so the parallel resonant frequency is only slightly greater than the series resonant frequency look at Table 1 again Note that the damping ratio is very small or in other words t
30. just because it looks like sine wave does not make it a sine wave You have to look at its spectrum Make a Probe plot of the output waveform then use the FFT tool in Probe to get the spectrum of the output Measure the amplitudes of any harmonics and calculate the total harmonic distortion THD 8 You should have found from your simulation in Item 7 that provided you do not saturate the op amp the system is indeed linear there is zero THD Lab 3 4 you know it is possible to operate the system non linearly by plying large enough input signal to cause the op amp to saturate An input amplitude of 6 V should do Since the gain at 500 Hz is ap proximately 1 an input amplitude of slightly more than Vee will cause saturation and the larger the input is the further into saturation the op amp will go i e the more nonlinear the circuit becomes You will now find the output to be distorted Use the FFT in Probe to display the output spectrum and calculate the THD IN LAB 1 Build the Sallen Key filter using the values of R and C that you used for the prelab calculations and simulations R 8 2kQ and 0 01 uF Set Vie 5 V By applying test input sinusoids at properly chosen frequencies verify the prelab calculations and simulations for the frequency response amplitude and phase of the filter Hint The frequency response of a linear filter can be expressed as H f HP where H f is the
31. low input impedance so we need a large resistor at the input then voltage division between the input resistor and the envelope detector causes the output signal level to be unacceptably small and so we need to amplify it envelope detector circuit you will use in lab is shown in Figure 2 The resistor H4 raises the input impedance to nzpon Y 5 Lab 5 Figure 2 Envelope Detector Be Used In Lab Lab 5 4 I 1 Message i 0 Carrier 4 Figure 3 Using the MULT Part to Generate an AM Signal in PSpice at least The envelope detector consists of D1 Ra and The amplifier is required to overcome voltage division between and the envelope detector The Ra C circuit is a high pass filter to block any dc in the signal coming from the envelope detector Suppose that the AM input signal to the demodulator of Figure 2 is the signal from Items 2 and 3 in which the message is a cosine wave e Show that the bandwidth of the Ro C lowpass filter is appropri ate for this AM signal e Show that the bandwidth of the R3 C highpass filter is appro priate e Calculate the gain of the op amp stage e Simulate the demodulator circuit in PSpice Hint You can generate an AM signal by using the MULT part in the evaluation library See Figure 3 IN LAB 1 Set the HP Agilent function generator to produce the AM signal of Items 2 and 3 in the Pr
32. mixer has the advantage that the output eliminates all of the output spectral components except the input feedthrough and the desired up and down conversion terms Consider the singly balanced mixer of Figure 4 but again with the modifications that the input is a bandpass signal at fe and the local oscillator produces The input z t to the is z t vi t vo t 2aiv t Aa2v t cos 27 fot 3 Compare this with Eq 2 now the only undesired term is the input feedthrough term Remarks 1 The balanced mixer in principle eliminates the other spectral components There is of course no such thing as perfectly matched square law devices That is one device will have coefficients and ag and the other will have a5 the coefficients will be close but not identically equal The result is that there will be small unwanted components in the output 2 There is also such a thing as a doubly balanced mixer This mixer eliminates the input feedthrough term as well as the local oscillator and its harmonics You will simulate but not build one kind of doubly balanced mixer in lab as a DSB modulator 4 Square Law Devices We now come to the question of how to realize a square law nonlinearity Several devices can be used but the most common ones are diodes and FETs Mixers 4 Frequency Conversion 9 4 1 Diode mixers junction diode is modeled by the 4 0 equation ilv Isle 1 where J
33. so the spectrum need not be symmetric about fe see Figure 5 3 1 Conversion with an unbalanced mixer Consider the unbalanced square law mixer of Figure 3 with the following modifications the input is the bandpass v t at f Figure 5 rather than The conversion of a bandpass spectrum to 0 frequency is rarely encountered that is after all the function of the demodulator in the receiver Therefore we shall not discuss bandpass to lowpass conversion Mixers 4 Frequency Conversion T a lowpass signal and the local oscillator produces Ao cos27 fot where we shall assume that fo f for now The output of the square law device is 2 z t ay gt Ao 2r fot gt Ag cos 2n fot aiv t cos 2m fot azv t 2a5 Agv t cos 2m fot I II IV 2 aA cos 2m fot V If you sketch a picture of the spectrum of the signal in Eq 2 you will find the following frequency components Term I This is just the input bandpass signal at fe Term II This is of course a line at fo Term III We need to do a little work to see what the spectrum of v t is Since v t is a bandpass signal it has a quadrature carrier description u t vi t cos 2n fet vg t sin 27 fet where v t and v4 t are lowpass signals Then v t v t cos 2n fet 20 9 6 cos 2n fet sin 2r fet v2 t sin 2r fet 1 1 1 1 50 t 2 20700 cos 4m fet 2440 cos 4n fet vi t uq t sin 4
34. that you will use in the communication laboratory The function of any oscilloscope of course is to provide a visual display of a time varying signal i e voltage In an analog oscilloscope the signal is directly displayed on a cathode ray tube an internally generated ramp causes the electron beam to scan horizontally across the CRT and the signal being measured is applied across the vertical deflection plates In a digital storage oscilloscope DSO the signal is acquired in an entirely different way In order to understand the advantages and limitations of a DSO we must begin with an understanding of the way in which the oscilloscope acquires the signal 2 Signal Acquisition in a DSO In broad terms a DSO first samples the input signal and then displays the waveform that is reconstructed from the samples This analog to digital conversion performed by the DSO results in several advantages over an ana log oscilloscope The major advantage is that we can perform signal pro cessing operations on the sampled signal such as differentiation integration addition of signals calculation of Fourier transforms as well as storage of the waveform in memory At the same time the digital to analog conversion has its limitations and you must be aware of these as you make measure ments if you are not careful the signal you display i e the reconstructed signal may not bear any resemblance to the true signal Appendix 2 21 Sampling
35. the spectrum analyzer screen with the proper settings And also like an oscilloscope the spectrum analyzer will always produce a picture on the screen but if you do not know how to properly use the spectrum analyzer that picture may be complete gibberish CAUTION The input of the spectrum analyzer cannot tolerate large signals before you connect a signal to the input be sure you know that the signal will not exceed the maximum allowable input rating of the spectrum analyzer The maximum signal input is printed right on the front panel near the input connector 2 Signal Acquisition in a Spectrum Analyzer Most spectrum analyzers including the Agilent models in the communica tion lab are heterodyne spectrum analyzers also called scanning spec Heterodyne is derived from the Greek meaning mixing different frequencies Appendix B 2 x t Fixed Narrowband Filter cos 27 fot Figure 1 Frequency Mixing or Heterodyning trum analyzers A heterodyne analyzer is essentially a radio receiver a very sensitive and selective reciever Radio receivers including those based on the heterodyne principle are covered in some detail in the lecture course see Section 4 16 in Couch or Section 7 1 in Carlson for now we shall content ourselves with a simple description of the basic ideas Given a voltage signal x t how do we resolve it into its frequency com ponents for display on a screen As we know one so
36. use the reduced VF bandwidth with care it will reduce the indicated amplitudes of wideband signals such as video modulation and short duration pulses When you have finished this item put the spectrum analyzer back in its default configuration with the PRESET button Use the function generator to produce a 100 kHz square wave of am plitude 200 mV y with 50 duty cycle and zero dc offset Get good display of the fundamental and the first several at least out to the 5 harmonics Which harmonics do you expect to see and what do you observe Explain Measure how far below the fundamental the harmonics are in dBm Comment on the difference in amplitude between the even and odd harmonics Compare with the theoretical values Get the display of the square wave spectrum the way you want it print it and include it in your notebook Explore the File control menus Lab 2 4 13 Note that as with the oscilloscope you can save the screen or the instrument configuration internally or on a floppy you can organize the file structure create directories rename files etc Build an RC lowpass filter having 3dB bandwidth 120 kHz Use the square wave from Item 11 as the input to the RC filter and observe the spectrum of the output on the analyzer Measure the fundamental and at least out to the 58 harmonic of the output Compare with theory Also print out the filter output and include in your notebook Note depending on how you c
37. will be slightly off You may adjust the carrier frequency to match the resonant frequency of your filter if you like Display the output voltage signal on the oscilloscope and display its FFT on the oscilloscope Display the output spectrum on the spectrum analyzer Compare the frequencies of the lines you observe with your prelab simulation and compare the differences in dB of the line amplitudes from the carrier with your prelab simulation In this part you will simulate but not build one type of doubly balanced mixer for generation of DSB Layout the circuit of Figure 2 in Schematics This type of doubly balanced mixer is discussed Section 4 11 of Couch The message and the carrier are the same as in the preceding parts Run the simulation for what you think would be good time to get an accurate FFT Display the FFT You should see a prominent carrier line But isn t this circuit sup posed to produce DSB This simulation demonstrates a phenomenon apparent only in the simulation PSpice starts the simulation at t 0 Lab 6 SELEH LU Figure 2 DSB Modulator Lab 6 5 and so the circuit experiences a transient In this circuit the BPF res onates at f 200 kHz and it is seeing sin 27z f t u t at the start of the simulation As a result the filter rings for a short time and so a significant line at 200 kHz is seen
38. your measurements to your Prelab calculations 7 Build the envelope detector of Figure 2 Apply the AM signal of Item 1 sinusoidal message and display the demodulated output on the DSO Compare the demodulated signal to the message signal and comment on any discrepancies Investigate the effect of varying the message frequency and the modulation index 8 Repeat for the AM signal of Item 5 square wave message 5 6 References Carlson A Bruce Carlson Paul B Crilly and Janet C Rutledge Com munication Systems An Introduction to Signals amp Noise in Electrical Communication 4 ed McGraw Hill 2002 Couch Leon W Couch II Digital and Analog Communication Sys tems 6 ed Prentice Hall 2001 LABORATORY 6 MODULATORS OBJECTIVES To simulate build and test an unbalanced AM modulator and to simulate one kind of doubly balanced modulator PRELAB 1 Read Section 4 3 in Carlson especially Square Law and Balanced Modulators Section 4 11 in Couch and Appendix D of this lab manual You are going to build and test the very simple unbalanced diode AM modulator shown in Figure 1 In this circuit the message is a 30 kHz sinusoid and the carrier is 200 kHz sinusoid The R R2 R3 network adds the carrier and the modulating signal the square law device is the 134148 diode and the L4 Ci1 R4 network is the bandpass filter The output is the voltage across L4 R4 to ground as indicated
39. 2 2 21 52 sg 2Cwys wA Suppose as before that 0 t 25 Kt u t so that O s 27 K s Then 2n K 9 els 52 2Cwns w2 If lt 1 then we have 2n K belt 1 Ct e Uu beta Tt G and lim 6 t 0 too Hence 0 0 for the second order loop 5 The PLL as an FM Demodulator Suppose that the input v f A 2n fet 94 is signal We shall show that the PLL can be used to demodulate this FM signal When using the PLL as an FM demodulator we want v2 t m t so we need to know the transfer function Vo s M s For FM t 80 mie and so on f n f 2208 7M o M s But 8 Oo s 5 Vo s VAS o s Therefore 14 Hence if the VCO gain K is equal to the frequency deviation constant fA of the FM signal 2n Ky Ka4H s s 2nK K4H s G s 6 All of our preceding analysis shows us that in both the first and second order loops a large loop gain results in 0 4 0 t which implies that va t m t when the input is an FM signal 6 Concluding Remarks e Using the PLL as an FM detector requires a large loop gain which implies a large loop bandwidth This is especially true for the first order loop Too large a bandwidth is undesirable because it increases the output noise power which results in a decreased s
40. EEL 45141 COMMUNICATION LABORATORY LABORATORY MANUAL G K HEITMAN ELECTRICAL AND COMPUTER ENGINEERING UNIVERSITY OF FLORIDA SPRING 2007 TABLE CONTENTS Laboratory Title 00 1 Appendix Introduction To the Communication Laboratory Digital Storage Oscilloscope the Function Generator and Measurements The Spectrum Analyzer and Measurements Frequency Response of Systems and Distortion Sinusoidal Oscillators Amplitude Modulated Signals and Envelope Detection AM Modulators The Phase Locked Loop and Frequency Modulation and Demodulation More Frequency Modulation Demodulation Sampling and Pulse Amplitude Modulation ISI and Eye Diagrams Title Basics of the Digital Storage Oscilloscope Basics of the Spectrum Analyzer Some Background on Oscillators Amplitude Modulators Mixers and Frequency Conversion The Phase Locked Loop INTRODUCTION TO THE COMMUNICATION LABORATORY 1 Purpose of the Laboratory Course The goals of the communication laboratory are 1 to allow you to perform experiments that demonstrate the theory of signals and communication systems that will be discussed in the lecture course 2 to introduce you to some of the electronic components that make up communication systems which are not discussed in the lecture course because of time limitations and 3 to familiarize you with proper laboratory procedure this includes pre cise record keeping
41. M signal and record the ratios or differences in dB between adjacent peaks Compare with your prelab item 3 PAM spectrum 7 Now connect the PAM output signal to the input of the Sallen Key filter with cutoff fe 530 Hz Display the demodulated signal on the oscilloscope and include a printout in your notebook Is it what you expect Motorola Semiconductor Technical Data MC54 74HC4016 Motorola Inc 1995 Lab 9 5 8 10 Display the spectrum of the demodulated signal on the oscilloscope and include a printout in your notebook Measure the magnitudes and differences in magnitudes of any spectral peaks and compare with your calculations from item 5 of the prelab Calculate the THD of the demodulated signal and compare with your prelab Investigate systematically the effect of sampling pulse duration 7 or duty cycle d and sampling rate fs on the PAM signal and on the demodulated signal Record your observations systematically and quantitatively Compare your observations to what you should expect the effects to be in theory Be sure to decrease f below the Nyquist rate so that you can observe aliasing References Carlson A Bruce Carlson Paul B Crilly and Janet C Rutledge Com munication Systems An Introduction to Signals amp Noise in Electrical Communication 4 ed McGraw Hill 2002 Couch Leon W Couch II Digital and Analog Communication Sys tems 6 ed Prentice Hall 2001 Ov
42. MHz differential probe for our oscilloscopes costs around 500 References Carlson A Bruce Carlson Paul B Crilly and Janet C Rutledge Com munication Systems An Introduction to Signals amp Noise in Electrical Communication 4 ed McGraw Hill 2002 Couch Leon W Couch II Digital and Analog Communication Sys tems 6 ed Prentice Hall 2001 LABORATORY 7 THE PHASE LOCKED AND FREQUENCY MODULATION AND DEMODULATION OBJECTIVES investigate signals in the time and frequency domains to measure the characteristics of a phase locked loop PLL to use a PLL for frequency modulation and demodulation PRELAB Prelab 1 Read Section 5 6 Phase Modulation and Frequency Modulation and Section 4 14 Phase Locked Loops and Frequency Synthesizers in Couch or Sections 5 1 Phase and Frequency Modulation and 5 2 Transmission Bandwidth and Distortion and Section 7 3 Phase Lock Loops in Carlson and Appendix E Phase Locked Loop in this manual 2 Obtain an expression for the spectrum of an FM signal with single tone modulation where the carrier amplitude is the carrier frequency is fe the message frequency is fm and the modulation index is 8 e For such an FM signal what is the smallest value of for which the carrier spectral component is zero e Plot the FM spectrum for the following values A 100 mV fc 100 kHz fm 10kHz and 8 1 Express the amplitudes of the l
43. Msamples sec for two channels and maximum memory of 4Mbytes When you set the horizontal time base the oscillo scope chooses the sampling rate and the record length hence the memory depth There are some complications in the relationship under some cir cumstances the sampling rate can be faster than the rate at which samples are stored This is handled internally by smoothing operation The signal frequencies used in this lab should not cause any difficulties But you should always be aware of the sampling rate that the instrument is using Press the Main Delayed button to see it 2 22 Acquisition Modes Now you have the basic idea of the operation of a DSO take a finite record length of samples of a signal and display the time signal reconstructed from the samples There are many aspects of the signal acquisition that you can control the main being the choice of acquisition mode See the manual for more The sampling theorem is discussed in detail in the lecture course EEL 4514 Appendix 3 information e Normal Mode This is the default The oscilloscope creates a record by saving the first sample of perhaps several during each acquisition interval e Peak Detect Mode Any signal wider than 5ns will be displayed regardless of sweep speed e Average Mode The DSO acquires data after each trigger using Normal mode and then averages the record point from the current acquisition with those stored from previous
44. Sequence Generate a raised cosine filter impulse response The bandwidth is 6kHz What condition must we impose on the sampling frequency and why We will use a sampling frequency of 27kHz Assume that we use symbol rate of 9000symbols s What is the rolloff factor Consider the raised cosine from 5 to 5T where T is the symbol period Plot the raised cosine filter Note the rolloff factor is a parameter between 0 and 1 Carlson et al Sec 11 3 use parameters p and r to define the raised cosine filter the relationship is a 2 T and 1 is the rate Couch Sec 3 6 uses a parameter f in the raised cosine definition his f4 is the same as Carlson s p or 2 Matlab code Fs 27000 Zo Sampling frequency is 27kHz T 1 9000 Zo Symbol period t 5 T 1 Fs 5 T Set time scale t t le 10 So that t 0 is not included alpha 0 5 Set roll off factor p sin pi t T pi t T cos alpha pi t T 1 2 alpha t T 2 is the raised cosine pulse clf plot t p plot the filter hold on stem t p xlabel Time s ylabel Amplitude hold off Run the PAM sequence through the raised cosine filter Remember that to use the filter function in Matlab the two vectors must have the same sampling frequency so it will be necessary to upsample the PAM vector al a2 a3 becomes a1 0 0 a2 0 0 a3 0 0 N length PAM r Fs T pams zeros size 1 r N pams 1 r r N PAM upsa
45. aim of this appendix is to outline these for you The References list contains some titles that will help you pursue your own research into this area 2 The Negative Resistance Oscillator As you know from your basic circuits course the voltage across a parallel resonant LC circuit with no resistance will oscillate sinusoidally when an initial condition is applied To review quickly consider the LC circuit in Figure 1 without the load resistor connected Suppose that the initial volt age across the capacitor is Vo and the initial current through the inductor is 0 Then the initial value problem describing this circuit is v t w2v t 0 with initial conditions v 0 Vo and 0 0 and where 1 V LC The solution for the voltage is u t Vocos wnt gt 0 Appendix 3 Voil A sinusoidal oscillator But there is problem this circuit cannot deliver power to an external circuit which an oscillator must do of course Suppose that the external circuit has equivalent resistance Rz i e consider the circuit in Figure 1 with the load resistor connected and with the same initial conditions Now we have the differential equation t 2600 2 w t 0 with v 0 Vo and 2 0 Vo RLC and where 1 L 3m Vc is the damping ratio The differential equation is also written in terms of the Q factor of the circuit t olt w2w t 0 Q where Q 1 26 If gt 1 the voltage response is critica
46. al will be distorted This distortion is not nonlinear distortion Lab 9 3 Sampling Input VWoc 6 Message Input F4 MCC 100k PAM Output P4 i Figure 1 Generation of naturally sampled PAM but is present simply because the filter is not an ideal LPF it passes some unwanted frequency components As we have seen in Lab 3 one fairly quick way to quantify the distortion is to calculate the total harmonic distortion Calculate the THD of the demodulated signal at the output of the filter 6 Simulate the demodulation of the PAM signal in PSpice connect the output of the PAM circuit to the input of the Sallen Key circuit Plot the demodulated output of the filter in Probe and its spectrum Also calculate the THD of the demodulated signal in this simulation IN LAB 1 Build the circuit shown in Figure 1 This circuit implements the natu rally sampled PAM system shown in Figure 3 2 of Couch the signal to be sampled is the input to a switch the opening and closing of which is controlled by the sampling signal consisting of a sequence of rectangular pulses The CD4016 is a quad analog CMOS bilateral Lab 9 4 switch That is there are four switches on the chip and on each switch the signal flow can be in either direction Pins 1 2 and 13 constitute one switch pins 1 and 2 are the input and output and pin 13 is the on off control signal The other pins that are tied low pin 7 is ground are the in
47. am for the balanced modulator also called a singly balanced modulator is shown in Figure 4 We have vi x t Ao cos 2m fet a2 x t Ao cos 2n fet 5 a x t Ao cos 2 fet t cos 47 fet Ao x t cos 27 fet and v2 t a1 2x t Ao cos 2m fet ag 2x t Ao cos Qn fot a2 A A2 a x t cos2m fet azz t 4 5 EM cos 47 fet Ao x t cos 27 fet input to the BPF then is vi va t 2ai1x t Ao x t cos 27 fet Mixers amp Frequency Conversion 6 fe 0 fe f Figure 5 A bandpass spectrum at fe to be shifted to fy Therefore with a BPF centered at fe and having bandwidth 2W the output v t is DSB supressed carrier signal v t 4a2 Ao x t cos 27 fet 3 Frequency Conversion same basic systems that we considered in Section 2 the unbalanced mixer and the singly balanced mixer can be used to move a bandpass spec trum from one carrier frequency to another but we have to be careful about the details of the analysis Suppose that we have a bandpass signal u t at some carrier frequency fe and we wish to move this spectrum to a new carrier f fo up conversion or f fo down conversion We assume that v t is a real signal so that V f is an even function of f and arg V f is an odd function but v t can be any type of modulated signal and
48. aracterisitic see Figure 4 20 in Couch or Figure 7 3 1 in Carlson In this lab we shall use phase detector I e Build the PLL circuit shown in Figure 2 e Note that Signal In pin 14 VCO Out pin 4 and Out pin 2 are digital signals i e they are square waves with LOW 0 V and HIGH 10 V 7 Set Signal In equal to zero Connect pin 14 to ground Set the free running frequency of the VCO to fo 100 kHz by adjusting the 20 potentiometer until you see a 100 kHz square wave at the VCO Out pin 4 and a symmetric error voltage i e equal LOW and HIGH durations at the Phase Comparator I output pin 2 Display both signals on the DSO 8 Use the function generator to generate a 100 kHz square wave that switches between 0 V and 10 V Disconnect pin 14 from ground and use the function generator as Signal In Note Pin 14 of the CD4046 Lab 7 SIGNAL IN COMPARATOR PHASE CIE 2 VOD iw PHASE COMPARATOR I Vou VoL VOL eur ue t aq ng Typical Waveform Employing Phase Comparator I in Locked Condition UUW PASS FILTER OUTPUTS Figure 3 Typical PLL Waveforms in Locked Condition is a high impedance input Display and print the signals at PC1 Out pin 2 Comparator In pin 3 VCO In pin 9 and Signal In pin 14 Typical waveforms that you should see are shown in Figure 3 Be sure to record the voltage levels and frequencies of the signals Note You may use the Sig
49. arkhausen criterion also requires that 0 2 0 be exactly 1 If A8 lt 1 then oscillations will be damped out if AG gt 1 then the amplitude of the oscillations will continue to increase Of course such an increase can continue only until it is limited by the onset of nonlinearity in the active devices constituting the amplifier In fact this onset of nonlinear ity is an essential feature of practical oscillators Suppose that we initially have A fo 8 fo 1 As the circuit characteristics drift we soon have A fo B fo either smaller or bigger than 1 in the former case the oscilla tion stops in the latter it increases until limited by the onset of nonlinearity Hence in order to make sure that oscillations are sustained we always de sign a practical oscillator to have 0 2 0 slightly greater than 1 say by 596 and let nonlinearity limit the amplitude of the oscillations In fact most practical oscillators are designed with a limiting circuit of some kind on the output see Section 12 1 in Sedra Smith especially Figure 12 3 As a result we have to accept small amount of distortion in the output sinusoid In practical feedback oscillator circuits the amplifier A s is an active device such as an op amp or an FET with high input impedance some Appendix times at least at low frequencies BJT amplifier is used feedback system G s is usually a passive resonant network In principle
50. as an oscillator When used as an oscillator it of course provides a square wave output The FM modulator is shown in Figure 1 The message is the sinusoidal source labeled VMod it has an amplitude of 1 V and a frequency of 5 kHz The DC offset Voff must be present because the 555 control input must always be positive You may of course set the offset in the sinusoidal source Simulate the modulator and display the output and its spectrum Remember that you are looking at tone modulation of a square carrier Is the spectrum what you expect See the 555 data sheet for further details LM555 Timer Specifications National Semiconductor Corp February 2000 Lab 8 Rload 1 k 330p Figure 1 FM Modulator Lab 8 3 R5 200k Input Figure 2 FM Slope Detector 3 The demodulator is the simple slope detector of Figure 2 This is an FM to AM converter it differentiates the FM signal and passes the resulting mixed FM AM signal through an envelope detector The front end is a tuned bandpass filter its resonant frequency is slightly higher than the carrier frequency so that the incoming FM signal lies on the left side of the filter frequency response so that it acts as differentiator The diode and circuit is of course the envelope detector and the C4 Rs circuit is the highpass filter DC block e Calculate the resonant frequency of the bandpass filter e Calculate the time constant of the lowapss
51. as to operate on the negative resistance part of its characteristic It should be pointed out that at microwave frequencies the resonator is not simple lumped parallel LC circuit The resonator may consist of waveguide cavities microstrip transmission lines and dielectric resonators We shall not be using these oscillators in lab and so we shall not pursue the analysis of them further 3 Feedback Oscillators basic idea in generating sinusoidal oscillations electronically is that itive feedback around a linear amplifier when chosen with appropriate gain will cause the amplifier output to oscillate sinusoidally Remember that if the input to a linear circuit is a sinusoid then the output is also a sinu soid hence if a linear feedback amplifier without input signal excitation oscillates the output waveform must be sinusoidal Consider Figure 4 The output of the amplifier is Xo s A s X s and the output of the feedback network is X p s B s Xo s A s B s Xi s Hence the open loop gain is In amplifier design we usually try to avoid oscillation There is an old saw in electronic design that says an oscillator is just a badly designed feedback amplifier Appendix 5 Negative resistance region A Figure 3 i v characteristic of a negative resistance device 1 2 Amplifier 20 A s 2 Tf Feedback B s Figure 4 amplifier and feedback network not y
52. aying on the screen a waveform that in no way represents the signal you are trying to measure Reset the function generator to produce the 2 5 kHz sine wave from Step 2 a Find out how to save the trace and the oscilloscope settings to one of the three internal memories and do so Disconnect the signal gen erator Recall the saved trace from the internal memory location and display it This is useful when you want to compare a measurement to a known good measurement that has been stored b Clear the recalled trace from the screen Reconnect the signal generator and redisplay the live sine wave Now save the trace and oscilloscope settings to a floppy disk and recall the saved trace from the floppy Saving the trace and settings on a disk allows you to transfer them to another oscilloscope the same or compatible model Lab 1 of course Note that you can also save the screen other formats such as Windows bitmap bmp Display the amplitude spectrum of the sine wave on the oscilloscope Remember that the oscilloscope does this by calculating the FFT of the samples of the signal it has acquired You will need to adjust the sampling rate through the horizontal sweep control the center fre quency and the frequency span to get good display Compare with your prelab calculations Why is the spectrum as shown by the oscil loscope not a pure line spectrum as in your prelab plot In particular address these
53. d voltage level in a specified direction i e slope The other trigger types available are pulse pattern CAN duration sequence SPI TV and USB You can find details in the DSO user manual 3 3 Trigger Modes The mode determines what the DSO will do in the absence of a trigger There are three modes e Normal In this mode the DSO will acquire a waveform only when the trigger conditions are met e Auto This mode will allow the DSO to acquire a waveform even if a trigger does not occur In auto mode a timer starts after a trigger occurs if another trigger is not detected before the timer runs out the oscilloscope forces a trigger The duration of the timer depends on the time base setting Note that if triggers are being forced successive acquisitions will not be triggered at the same point on the waveform and so the waveform will not be synchronized on the screen it will roll across e Auto Level Works only when edge triggering on analog channels or external trigger The oscilloscope first tries to Normal trigger If no trigger is found it searches for a signal at least 10 of full scale on the trigger source and sets the trigger level to the 50 amplitude point If there is still no signal present the oscilloscope auto triggers This mode is useful when moving a probe from point to point on a circuit board 3 4 Other Aspects of Triggering Holdoff When the DSO sees a trigger it disables the trigger system until t
54. e THD Caution Your input in the simulation was a pure sine wave and that should be your test signal in this Item If your function generator contains spurious frequencies record its FFT you will need to account for them 3 You have now verified that the Sallen Key circuit does in fact behave as the linear model predicts But as you know from the lecture class and from your reading in Item 1 of the Prelab a linear system can distort a signal it causes linear distortion if H f is not constant or if 0 f is not linear Does the Sallen Key circuit satisfy the conditions for distortionless transmission Does it satisfy the conditions over a small range of f Perform the following two tests e Apply 100 Hz square wave without causing saturation and observe the input and output on the oscilloscope e Apply a 1000 Hz square wave and observe the input and the out put Explain the differences in the two outputs in reference to linear dis tortion caused by the circuit 4 Now drive the circuit with a large enough sine wave 6 V amplitude at 500 Hz so that it operates non linearly Verify your THD calculation from Prelab References Carlson A Bruce Carlson Paul B Crilly and Janet C Rutledge Communication Systems An Introduction to Signals amp Noise in Electrical Communication 4 ed McGraw Hill 2002 Lab 3 Couch Leon W Couch II Digital and Analog Communication Systems 6 ed Prentice Hall 2001
55. e measured rise time The Delayed Sweep feature of the oscilloscope will be helpful here you Lab 1 5 can use it to zoom in on the rising edge of the output waveform and get a more accurate measurement of the rise time LABORATORY 2 THE SPECTRUM ANALYZER AND MEASUREMENTS OBJECTIVES 1 To become familiar with the features and basic operation of the Agilent E4411B spectrum analyzer 2 To investigate signals in the frequency domain PRELAB 1 Review Appendix B on the basic operation of the spectrum analyzer 2 You will need your Prelab calculations from Laboratory 1 Fourier series for sine and square waves transfer function for an RC lowpass filter and the outputs of an RC filter for sine and square inputs 3 Design an RC lowpass filter with a 3dB break frequency of 120 kHz or as near as you can get with the available resistors and capacitors 4 Review Section 2 1 in Couch about normalized signal power signal power into a load and signal power in units of dBm IN LAB 1 As discussed in Appendix B you need to let the spectrum analyzer warm up for 5 minutes and go through its internal alignment proce dure 2 Record the answers to the following questions in your lab notebook Lab 2 2 e What is the frequency range that this spectrum analyzer will measure e What is the maximum DC level that can be applied to the RF input e What is the input impedance of the RF input e What is the maximum
56. each student will maintain a standard laboratory notebook into which all calculations measurements prelabs answers to questions etc are entered Your note book will be checked each week for adequate progress during the course The laboratory notebook is a record of your lab activity not a series of for mal lab reports You should try to keep the notebook neat and organized but perfection is not expected Occasionally you will make an entry that is simply wrong do not erase or tear out the page but merely cross out the entry In industry you will be required to keep a patent notebook in ink no erasures at all are allowed We shall be more relaxed small errors may be erased but do not waste time erasing a half page just cross it out Most of the lab experiments have prelabs involving PSpice Mathcad or Matlab as well as derivations or calculations to do by hand All of the prelabs must be entered into your notebook any printouts they include should be securely pasted or taped into your notebook The same is true of any printouts you make of the oscilloscope and spectrum analyzer dis plays You may also paste the experiments from this lab manual into your notebook but that is not required nor is it recommended Each student is expected to participate in the lab and to maintain a notebook remember your notebook will be checked each week and there will be a final practical exam if you have not kept up with the labs you will
57. edance as function of frequency is en olw arg Z jw 2 arctan Boe The derivative of the phase is 2 Qun wz w i GeO At the resonant frequency this becomes _ 20 di Wn Hence the frequency stability is d un 2Q The negative sign merely means that lt 0 for Aw gt 0 This result should not be surprising it simply says that the higher the Q of the resonant circuit the higher the frequency stability of the oscillator Although the details differ for each oscillator the general conclusion is the same This is why we want the resonators in oscillator circuits to have a high Q Another reason is that a high Q circuit will do a better job of filtering out harmonics and noise 6 Variable Frequency Oscillators As you know from the lecture course it is often necessary to have a variable frequency oscillator For example in the superheterodyne receiver the local oscillator must tune over an appropriate range so that the mixer will shift the incoming RF signal down to the intermediate frequency In this section we shall only comment on some of the ways of obtaining a VFO you are left to pursue the references for details There are several ways of varying the frequency of an oscillator which to use depends on the application One obvious way is to simply use a variable capacitor or inductor in the resonant circuit and to manually adjust it This is in fact how
58. elab Display the AM signal on the oscilloscope watch your impedances Lab 5 5 Notes 1 In AM mode the carrier amplitude is reduced to half the set value so you will need to set the carrier amplitude to 4 Vy y 2 You may find it useful to use the SYNC output of the function generator as a trigger source The SYNC output is high pulse look at it on the oscilloscope produced at each zero crossing of the modulating signal See the 33120A User s Guide for more information about the SYNC output 2 Measure the modulation index Item 6 in the Prelab and check against the set value on the function generator 3 Display the spectrum of the AM signal on the spectrum analyzer in units of dBm into 502 Measure the power level of the carrier and of the sideband line How many dB below the carrier is the sideband line Compare your measurements to your Prelab calculations 4 Investigate the effect on the AM spectrum of varying the modulat ing frequency i e message frequency and the modulation index In particular investigate the effect on the sideband power of varying the modulation index 5 Set the function generator so that the message is the square wave of Items 4 and 5 from the Prelab Display the AM signal on the DSO and measure the modulation index 6 Display the AM signal on the spectrum analyzer Measure the carrier and at least five sideband pairs How many dB below the carrier are the sideband lines Compare
59. electrodes with leads for connection to an external circuit The circuit symbol shown in Figure 10 is a representation of this construction The crystal can be modeled with the electrical equivalent shown in Fig ure 11 Here C1 models the electrostatic capacitance between the electrodes Appendix 15 C1 L Figure 11 Equivalent circuit model of a crystal when the crystal is not vibrating and the series LCR circuit represents the electrical equivalent of the vibrational characteristics inductance L models the crystal mass C models the mechanical compliance and R mod els the mechanical friction Typical values for a quartz crystal are listed in Table 1 4 It is a simple matter to calculate the impedance of the crystal modeled by the equivalent circuit of Figure 11 s A E A Z s a 1 Cis Pee RU L LCC or uw zu mci Z jw LE L LCC Note that Z s has a pole at w 0 at dc the crystal is just a piece of rock From Terman Appendix 16 Mechanical characteristics Electrical characteristics Length 2 75cm L 2 8 8H Width 3 33 0 042 pF Thickness 0 636 cm 5 8 pF Resonant frequencies R 45180 Series 427 50 kHz Parallel 429 05 kHz Table 1 Characteristics of a typical quartz crystal and its impedance is infinite We shall not concern ourselves further with the pole In Equation 1 the numerator of Z s is just the
60. eoretical value 1 44 fe Ry 2R3 Ci See the 555 data sheet Now connect the message with DC offset as in Figure 1 Display the output and its spectrum compare with your prelab simulation Build the slope detector of Figure 2 Test the slope detector by using the function generator to provide an FM signal of the same carrier frequency and tone modulating frequency as your 555 FM modulator Choose the frequency deviation to give you approximately the same FM bandwidth as your 555 modulator You can test with sinusoidal and square carriers Display the demodulated output and its spectrum Now connect the output of the 555 modulator to the input of the slope detector Remove the load resistor in Figure 1 Display the demodulated output and its spectrum Explain sources of distortion in the detector References Carlson A Bruce Carlson Paul B Crilly and Janet C Rutledge Com munication Systems An Introduction to Signals amp Noise in Electrical Communication 4 ed McGraw Hill 2002 Couch Leon W Couch II Digital and Analog Communication Sys tems 6 ed Prentice Hall 2001 LABORATORY 9 SAMPLING AND PULSE AMPLITUDE MODULATION OBJECTIVES To investigate the time and frequency domain properties of PAM signals with natural sampling PRELAB 1 Review the discussion of the sampling theorem in Section 2 7 of Couch and Section 6 1 of Carlson 2 Read Section 3 2 in Couch
61. erview Prelab Prelab LABORATORY 10 ISI and Eye Patterns e The goal of the prelab will be to use simulation to generate an eye pattern for a binary or 4 ary PAM signal The eye pattern will be observed for several different roll off factor values This will be a multi step problem 1 In Lab Generate a random PAM signal Generate a Raised Cosine filter pulse Run the PAM signal through the Raised Cosine filter Plot the Eye Pattern Display the Fourier transform of the output e The goal of the in lab portion of the experiment is to observe an eye pattern on the oscilloscope that is formed by running a PAM signal through a low pass filter This is also a multi step problem 1 Generate pseudo random PAM signal using the arbitrary function generator Build an RC filter Run the PAM signal through the RC filter Plot the output eye pattern onto the oscilloscope Display the PSD of the output Read the section in the book pertaining to ISI and eye pattern diagrams Carlson Crilly Rutledge Secs 11 1 and 11 3 Couch Sec 3 6 Generate a random 4 ary PAM signal at least 100 symbols Display the random PAM sequence on a stemplot The following Matlab code will do this or you can write your own to achieve the same result a 3 1 13 Zo Create the 4 ary constellation ind floor 4 rand 100 1 1 Create a Random bit Sequence PAME a ind Random 4 PAM sequence stem PAM Plot
62. es not exceed it All good measurement equip ment has overload protection but it is still possible to do damage do not rely on the equipment to protect you from your own mistakes In general the signals in this laboratory course will not cause damage to the oscilloscope You can find the maximum voltage ratings on the front panel next to the connectors The same is not true of the spectrum analyzer you must be very careful what signal you apply to it Again the maximum signal that can be applied is printed on the front panel A big part of this laboratory course is learning how to use measurement equipment you learn how to make good measurements by actually using the instruments to measure things The lab experiments in this manual will not be a step by step procedural list you will not be told which button to push which menu to bring up in order to make the instrument do something Rather you will be told things such as display the output signal on the oscilloscope and determine its frequency components You will have to learn how to accomplish this To help you the complete User s Guide for each instrument is on the PC at each station On the PC desktop you will find a shortcut to a folder called Equipment Manuals all of the User s Guide are there in PDF format Double click the one you want to open in the Acrobat Reader Troubleshooting Things will not always go as expected that is the nature of the learning process
63. et connected to form a closed loop Appendix 6 Suppose that we could have z t ie the instantaneous values are equal for all t Since the amplifier cannot distinguish the source of the input signal applied to it it would appear that if we connect points 1 and 2 the amplifier would continue to provide the same output signal xo t Since z t 4 is equivalent to A s G s 1 we come to the following conclusion The Barkhausen Criterion A feedback amplifier with no external input signal will oscillate at frequency fo if the loop gain at fo is unity A fo B fo 1 Note that the Barkhausen criterion really implies two conditions for oscil lation 1 the magnitude of the loop gain must be 1 and 2 the phase of the loop gain must be 0 or an integral multiple of 27 Remarks 1 The Barkhausen criterion requires that the closed loop phase shift be zero at the frequency of oscillation fg Hence the frequency stability of the oscillator is determined by the slope of the phase of L f near fo Component characteristics especially those of the transistors making up amplifiers drift with temperature age voltage level etc A large slope in the phase of L f at fo implies a more stable frequency of oscillation because any change in phase from 0 due to drift in amplifier parameters results in a small change in frequency see Figure 12 2 in Sedra Smith We shall consider frequency stability in Section 5 2 The B
64. filter in the envelope detector and show that it is appropriate for the message and carrier frequencies e Calculate the time constant of the highpass filter and show that it is appropriate 4 Connect the FM modulator of Figure 1 to the slope detector of Fig ure 2 and simulate the whole system Remove the load resistor in Figure 1 connect the output directly to the FM Input in Figure 2 Display the output and its FFT Note As always you will want to run the simulation for a long enough time to get good FFT you will also see that the output has a transient before it settles into a steady state that you will probably not want to include in the FFT But if you try to run the simulation for too long you will encounter a limitation of the evaluation version of PSpice the 555 is mixed analog digital part and if you try to run the simuation for too many periods of the square wave output you will find a limitation on the Lab 8 4 number of transitions allowed in the digital circuit You will have to find good compromise for the simulation time IN LAB 1 Build the circuit of Figure 1 without the modulating signal and its DC offset replace them with a small capacitor This is the free running astable circuit the output across the load resistor will be square wave Display the output and its spectrum and measure its fundamental frequency This square wave is the carrier Compare the measured frequency against the th
65. g the instrument produce the analog waveform References Clarke Hess Kenneth K Clarke and Donald T Hess Com munication Circuits Analysis and Design Addison Wesley 1971 Reprinted by Krieger Publishing Co 1994 Collin Robert E Collin Foundations for Microwave Engineering 204 ed McGraw Hill 1992 Couch Leon W Couch I Digital and Analog Com munication Systems 6 ed Prentice Hall 2001 5YIG stands for yttrium iron garnet a magnetic crystal material with frequency of oscillation proportional to an applied bias magnetic field Appendix Millman Rohde Whitaker Bucher Sedra Smith Smith Terman 21 Jacob Millman Microelectronics Digital and Analog Circuits and Systems McGraw Hill 1979 Ulrich L Rohde Jerry C Whitaker amp T T N Bucher Communications Receivers Prici ples and Design 274 ed McGraw Hill 1997 Adel S Sedra and Kenneth C Smith Micro electronic Circuits 4 ed Oxford 1998 Jack R Smith Modern Communication Cir cuits 274 ed McGraw Hill 1998 Frederick Emmons Terman Electronic and Ra dio Engineering McGraw Hill 1955 APPENDIX D AMPLITUDE MODULATORS MIXERS AND FREQUENCY CONVERSION 1 Introduction As we know from the communications course amplitude modulation consists essentially of frequency translation a lowpass message spectrum is shifted up to a high carrier frequency The frequency translation is accomplished by
66. he Q factor of the parallel resonance is very high this is reflected in the very narrow peak at f in Figure 12 The high Q of the parallel resonance peak means that the parallel res onant frequency of the crystal is very stable We take advantage of this by using the crystal in the feedback section of an oscillator circuit For example a crystal can replace the inductor in a Colpitts oscillator an example of this kind of crystal oscillator is shown in Figure 12 16 in Sedra Smith As an other example consider our general oscillator configuration Figure 6 with the op amp replaced by a FET which also has a high input impedance We can use a crystal for 21 a tuned LC tank for Z2 and the capacitance Cag between drain and gate for 23 We conclude with two remarks 1 The oscillation frequency of a crys tal is very stable but remember that it is also fized you have to change the crystal to change the frequency 2 The oscillation in a crystal is due Appendix 18 to mechanical vibrations which can be longitudinal flexural shear with all mechanical vibrations there is a fundamental frequency and its harmonics the word overtones is preferred instead of harmonics because the overtone frequencies are usually not exact integer multiples of the fun damental Hence we can have oscillations at overtone frequencies The Q at the overtones can be as high as it is at the fundamental but the magnitude of the piezoelect
67. he acquisition is complete Some repetitive signals especially digital pulses contain many valid trigger points a simple trigger might result in a series of waveforms on the screen You can set the holdoff time to be longer than the acquisition interval to get a stable display Appendix 5 Coupling Coupling determines what part of the trigger signal is passed to the trigger circuit Your choices are DC all of the signal AC the dc part is blocked low frequency rejection frequencies below 50 kHz are blocked TV high frequency rejection frequencies above 50 kHz are blocked and noise rejection makes the trigger circuit less sensitive to noise but may require a higher amplitude signal to trigger 4 Signal Spectra on the DSO As we have said one very useful feature of the DSO is its ability to display the results of mathematical operations on the signals Your Agilent 54622D can display the product of the two channels the difference between the channels the derivative of a signal the integral of a signal and the amplitude spectrum of a signal Here we shall discuss the display of the spectrum DSO calculates the spectrum by calculating the discrete Fourier transform DFT of the signal be precise the oscilloscope calculates the fast Fourier transform FFT which is just an efficient algorithm for the DFT It is important that you have a basic understanding of how the DSO calculates the FFT because it is possible
68. his spectrum analyzer has the ca pability of storing screen captures and instrument states internally or on an external floppy disk You access this through the file menus References Carlson A Bruce Carlson Paul B Crilly and Janet C Rutledge Com munication Systems An Introduction to Signals amp Noise in Electrical Communication 4 ed McGraw Hill 2002 Couch Leon W Couch II Digital and Analog Communication Sys tems 6 ed Prentice Hall 2001 APPENDIX SOME BACKGROUND OSCILLATORS 1 Introduction In this appendix we present a brief background on sinusoidal oscillator cir cuits which you will investigate in Laboratory 4 Oscillators are ubiquitous in communications we need to generate carrier signals normally sinusoids in both the transmitter and receiver We shall discuss only sinusoidal os cillators One way to obtain a sinusoid is to produce some easily generated periodic waveshape such as square wave by means of a multivibrator circuit and then to filter out all of the frequency components except the fundamental Another way is to generate a triangle wave again with a mul tivibrator and to use a waveshaping circuit to produce a sine wave This is the way in which many function generators work since they are designed to produce several types of waveforms But in communications circuits we need just a sine wave not a function generator There are many factors that need to be taken into acc
69. ignal to noise ratio Hence we always have to design with this trade off in mind e Another drawback of the first order loop is the non zero 6 this is eliminated in the second order loop For FM demodulation 0 however of little concern is ss e When using the PLL for carrier recovery a small 0 a second order loop would be preferred is required Hence ss e The PLL can be used to demodulate PM by integrating the VCO output e The PLL can also be used for frequency generation see Figure 4 25 in Couch e See Section 5 4 in Couch or Section 7 3 in Carlson for a special PLL called a Costas loop for coherent demodulation of DSB References Carlson A Bruce Carlson Paul B Crilly and Janet C Rutledge Com munication Systems An Introduction to Signals amp Noise in Electrical Communication 4 ed McGraw Hill 2002 Couch Leon W Couch II Digital and Analog Communication Sys tems 6 ed Prentice Hall 2001
70. in the time and frequency domains PRELAB 1 Review Appendix of this manual it contains basic information on how a digital storage oscilloscope works in general with some specific information on the Agilent 54622D DSO Calculate and plot the exponential Fourier series coefficients for a sinusoidal voltage of amplitude A frequency fo phase angle 0 and dc value i e average value of K Calculate and plot the exponential Fourier series coefficients of a square wave of amplitude A frequency fo duty cycle 5096 and dc value K Use an odd square wave Calculate and plot the transfer function of an RC lowpass filter for a given time constant T RC Indicate the 3 dB bandwidth on your plot For your RC lowpass filter calculate and plot the output spectrum and the output time signal for a sinusoidal input and for a square input Be sure to heed the advice in the Introduction about plots and graphs Lab 1 2 6 Design an RC lowpass filter having time constant 10 us What is the 3 dB break frequency IN LAB 1 On the desktop of the computer at your station you will find a short cut to a folder called Equipment Manuals This folder contains in PDF format the complete User s Guides to the oscilloscope function generator multimeter DC power supply and spectrum analyzer In addition there is a Quick Reference Guide and a Front Panel Guide for the function generator Locate these manua
71. ines in units of dBm into 500 e For these values use Carson s rule to estimate the FM bandwidth Lab 7 2 e Determine the 99 power bandwidth of the signal That is the frequency band containing 99 of the total power e Finally plot the FM signal in the time domain Hint In Math cad use the following to calculate the Bessel functions JO x returns Jo x J1 x returns Ji x and Jn m x returns Jj x for 0 m lt 100 In Matlab use BESSELJ e Repeat for 8 3 25 3 Design an RC lowpass filter having half power bandwidth between 1 5 kHz and 2 5 kHz the lower the cutoff frequency the better and having R gt 10kQ You will use this filter in the PLL demodulator part of the lab IN LAB 1 Use the function generator to produce tone modulated FM signal with a sine wave carrier having the following parameters carrier fre quency f 100kHz carrier amplitude A 100mV message fre quency fm 10kHz and modulation index 8 1 You set 8 by setting the peak frequency deviation on the function generator Display the FM signal on the DSO Display the FM signal on the spectrum analyzer e Measure the frequencies and power levels in dBm of the carrier and the first five lines above the carrier Compare with your prelab e Use the spectrum analyzer to measure the 9996 power bandwidth of the FM signal Compare with your prelab bandwidth calcula tions and with the Carson s rule bandwidth
72. ion and Section 4 9 on nonlinear distortion or in Carlson Section 3 2 2 A popular type of Butterworth second order lowpass filter is the Sallen Key circuit shown in Figure 1 Assuming an ideal op amp show that the transfer function of this linear system is Vout 8 1 V s n Ri RoC C282 Ry 8 1 H s 1 A useful assumption for design is Ry Rg under this assumption obtain an expression terms of R and C for the 6dB break frequency The 6dB frequency is simply more convenient to deal with than the usual 3dB frequency lYou will learn about Butterworth filters in Electronics 2 Sallen Key circuit was invented around 1955 by Sallen and Key surprisingly and it is popular because it requires only one op amp hence it is inexpensive and does not consume much power Its Q factor is however more sensitive to component tolerances than other configurations especially for large Q But in lowpass filters Q is not large and the sensitivity problem is not a concern See Sec 11 8 in Sedra Smith Lab 3 2 Input 3 Figure 1 Sallen Key Lowpass Filter Find the 6dB break frequency for the values R 8 2kQ and C 0 01 Using Mathcad or Matlab obtain a plot of the amplitude gain and phase shift of the Sallen Key filter using Equation 1 It is best to make Bode plots frequency on a logarithmic scale and amplitude gain in dB
73. is the pinch off voltage and 1 V4 is the vas 0 channel length modulation and V4 is the Early voltage Assuming that V4 gt gt 1 the Spice default is oo so that e 0 we see that in saturation the FET is a square law device ip vas B vas Vi 802 5 20 Vivas Ipss 6 In real devices we usually cannot say 0 we must modify Eq 6 slightly to account for the term 1 and this correction term depends on the bias point remember that we are operating in saturation But the FET still is a square law device FET mixer is popular in balanced configuration because very closely matched JFET s are commercially available The JFET s are built on a single substrate References Clarke Hess Kenneth K Clarke and Donald T Hess Com munication Circuits Analysis and Design Addison Wesley 1971 Reprinted by Krieger Publishing Co 1994 Collin Robert E Collin Foundations for Microwave Engineering 2 ed McGraw Hill 1992 Couch Leon W Couch II Digital and Analog Com munication Systems 6 ed Prentice Hall 2001 Rohde Whitaker Bucher Ulrich L Rohde Jerry C Whitaker amp T T N Bucher Communications Receivers Prici ples Design 274 ed McGraw Hill 1997 Sedra Smith Adel S Sedra and Kenneth C Smith Micro electronic Circuits 4 ed Oxford 1998 3I am using the standard Spice notation and terminology for these quantitites
74. is the saturation current Vr kT q is the thermal voltage at room temperature 25 2mV and 1 lt n lt 2 depending on the physical construction of the diode For example the PSpice model of the familiar 1N4148 signal diode uses n 2 and J 2 682nA If we expand the function i v in a Taylor series about any v vo we have i v vo v 90 Ld vo v v i vo v wg 2 3 22 eto nVr 1 gt 1 v vo 1 v vo 7 nVr 2 nVr 1 3 1 3I nVr 3 v 1 Thus for v near vo v vo amp 1 we have e I5e o nVr 1 emm v vo 4 v v9 i 2 nVr 2 4 In fact since 2 nVr il P e 5 lt 3 n Vr we can say that Eq 4 holds for v vo lt 7 In particular near vo 0 we have 1 1 VT is cu 5 is the diode acts as square law device 4 2 FET mixers JFET junction FET has the following ip vgg characteristic 0 if vag lt V ip 4 8 2 vas Vi ups 958 1 Avps if vas gt V and vps vas Vi B vas 1 Avps if vas gt V and ups gt vas V Mixers amp Frequency Conversion 10 first case is the cutoff region the second is the triode region and the third is the pinch off or saturation region See Sedra Smith for more details In these equations 8 Ipss V7 is the transconduction coefficient Ipss in 2 2 V
75. lly damped overdamped and there is no oscillation If 0 lt lt 1 the voltage response is underdamped it tries to oscillate but the power consumption of the resistor causes the oscillations to be exponentially damped 1 u t Voe cos wt 2 sinet c and 1 2 c and w are just the real and imaginary parts of the characteristic roots of the differential equation idea of the negative resistance oscillator is very simple design the resonant circuit with a negative resistance of value Rneg Rr so that when the load is connected to the oscillator the LC circuit sees an equiv alent resistance of infinity and so the output voltage will be sinusoidal See Figure 2 The question arises where do we get a negative resistance Certain semiconductor devices such as tunnel diodes Gunn diodes and IMPATT diodes have i v characteristics that have negative slope hence negative resistance over part of the curve see Figure 3 These devices can where 116 is probably better to say that we design the circuit with a negative conductance Gnee so that the conductance seen by the LC circuit is zero and to call it a negative conductance oscillator Appendix 4 Rneg RL Figure 2 Negative Resistance Oscillator provide oscillation frequencies in the range from 1 GHz up to 100 GHz Note that a DC voltage must be supplied the semiconductor device must be bi ased so
76. logical troubleshooting safety and learning the capabilities as well as the limitations of your measurement equipment 2 General Laboratory Procedure The most important rule to follow in any laboratory is think before you do anything If you follow this one rule you will avoid injury to yourself damage to the system you are testing damage to your measurement equipment and you will not waste time going down dead end streets Safety In general you will not be using voltage levels high enough to cause injury nevertheless you should always pay attention to what you are doing Circuit Damage Your voltage levels can cause damage to the circuit un der test if you are not careful Make sure that your circuit diagram is correct and be careful to build the circuit correctly on the proto board If you need to make changes to the circuit disconnect the power supply and the input signal Introduction 2 Equipment Each lab station has the following permanent equipment that you will use for most labs Spectrum Analyzer Agilent E4411B Spectrum Analyzer Oscilloscope Agilent 54622D Mixed Signal Oscilloscope Signal Generator Agilent 33120A Arbitrary Function Generator 2 per station Multimeter Agilent 34401A Digital Multimeter Power Supply Agilent E3631A Triple Output DC Power Supply Before you use any measurement equipment know the maximum in put signal level it can withstand and make sure that the signal you are trying to measure do
77. ls and be ready to open them as needed Double click on the name to open the manual with the Acrobat reader 2 Use the function generator to produce a sine wave of frequency 2 5 kHz and peak to peak amplitude 200 mV with zero dc offset Use a coax ial cable with BNC connectors on the ends to connect the output of the signal generator to one of the analog inputs on the oscilloscope Display the sine wave on the oscilloscope and measure the frequency and amplitude in two ways 1 By counting divisions on the screen to determine the amplitude and the period Use the cursors to help you make the measurements see the oscilloscope manual for informa tion on using cursors 2 By having the oscilloscope automatically make the measurements Manual again Always pay attention to the information on the status line above the waveform display and on the measurement line below the waveform display see p 2 11 in the manual Is there a discrepancy between your measured amplitude and the am plitude you entered into the function generator Explain Hint check the output impedance of the function generator and the input impedance of the oscilloscope Take a look at the Function Generator Front Panel guide in the Equipment Manuals folder 3 Take a few minutes to become familiar with the front panel controls of the two devices On the function generator learn how to select waveshapes ampli tudes and frequencies using the keypad and the co
78. lt 80 d y 40 d 40 di d 2 di fort gt 0 But also 400 E 2n Ky Kq4 sin 0 t and so assuming the ramp 6 t the phase error must satisfy the first order differential equation 40 21 27 0 2nK t0 5 10 dO dt 1 2n K K Ka ss Figure 5 The phase plane plot A plot of d0 dt vs 0 1 is called the phase plane plot as shown Fig ure 5 The phase error 0 4 and the frequency error 40 4 must satisfy the differential equation 5 i e they must both lie on the graph of Fig ure 5 Suppose that the initial condition in Eq 5 is 0 Then at t 0 the frequency error is d0 dt 27K So we start at the point labeled 1 in Figure 5 Now for dt gt 0 if dO dt gt 0 we have 40 gt 0 That is if dO dt gt 0 then the operating point moves to the right because 0 must increase Likewise if 402 41 lt 0 then the operating point moves to the left Therefore starting at point we have d0 dt 27K gt 0 so we move to the right to point 2 Point 2 is a stable operating point If e tries to decrease from 2 then d0 dt gt 0 and so d0 gt 0 forcing the operating point back to 2 Likewise if tries to increase this results 00 lt 0 again forcing the operating point back to 2 Therefore after a certain time interval the operating point is point 2 and it
79. lution is provided by the digital storage oscilloscope calculate the FFT of the signal from its internally stored samples Another solution would be to pass x t through a bank of very narrow bandpass filters having adjacent passbands and then plot the amplitudes of the filter outputs That is if filter 1 has passband f B 2 lt f fi B 2 and filter 2 has passband fo B 2 lt f fo B 2 where B 2 f B 2 and so on and if B is small enough then the filter outputs give us the frequency components X f1 X f2 This is of course not a practical solution A better solution is suggested by a simple property of Fourier transforms recall that if we multiply in the time do main a signal by a sinusoid the spectrum of the signal is shifted in frequency by an amount equal to the frequency of the sinusoid That is x t cos 27 fot PE ai fo 4 fo Now instead of a bank of narrow filters we shall have one narrow filter centered at a fixed frequency say fr and we shall scan the signal spec trum across this filter by multiplying x t by a sinusoid of varying frequency fo See Figure 1 The filter is a narrow bandpass filter at a fixed center frequency called the intermediate frequency in a spectrum analyzer its bandwidth is selected by the user The oscillator frequency fo is ad justable as indicated in Figure 1 In an ordinary AM or FM radio when Appendix B 3 you tune the recei
80. m fet The first two terms are lowpass signals and the last three terms are bandpass signals all at 2 2 Term IV This is our desired signal the bandpass v t shifted up to fe fo and down to f fo Term V This consists of a line at 0 and one at 2 fo Hence with the proper choice of f and fo the up and down conversion parts of the spectrum Term IV are isolated and we can select either one with a at that frequency That is if the in Figure is at fe fo the system is an up converter and with the filter at f fo it is a down converter Mixers 4 Frequency Conversion 8 Remark We assumed in this analysis that fo lt fe so that the down conversion frequency is positive It is left for you to show that if fo gt fe the down conversion part of the spectrum has the upper and lower sidebands reversed In normal applications for down conversion we want fo lt fe For up conversion the down conversion spectrum is irrelevant anyway 3 2 Conversion with a singly balanced mixer The unbalanced mixer will in principle work as a bandpass to bandpass fre quency converter but as we saw Eq 2 the spectrum is rather crowded In particular the unbalanced mixer has input feedthrough i e the input v t appears at the output and there are lines at fo this could be close to fe fo and at 2 0 this could be close to f fo and so heavy filtering may be required to block these lines A singly balanced
81. magnitude response and 6 f is the phase response If a sinusoid say x t 2 fot is the input then the output will be the sinusoid y t A H fo cos 2m fot 6 fo ALB fo I cos 24 s Hence by observing the input and output sinusoids simultaneously remember that your oscilloscope has two analog channels we can measure the amplitude gain H fo of the filter at frequency fo and the time shift between input and output at fo from which we can calculate the phase shift 0 fo Take a sufficient number of data points so that you can produce plots of the amplitude and phase responses You may produce the plots on graph paper or you may read the data into Mathcad or Matlab to make the plots If you make the plots by hand I suggest you make Bode plots since the amplitude Bode plot should consist except near the break points of straight line segments Be sure that the theoretical 6 dB frequency is one of your test signals Lab 3 5 Remark You will probably want to set the function generator to high impedance output termination but do not rely on the function gen erator readout for an accurate value of amplitude Instead measure the function generator amplitude with the oscilloscope 2 Verify your calculation of THD in the linear system from the Prelab Apply a sine wave of frequency 500 Hz and small amplitude Observe the output of the circuit on the oscilloscope and display its FF T Cal culate th
82. me as the one in the FET oscillator and so the frequency of oscillation is the same Since the op amp gain is R R we require R4 R to be slightly greater than 29 This oscillator is usually used in the range from several Hz to several hundred kHz and so includes the range of audio frequencies Appendix VOD Feedback Amplifier E R R r Figure 5 Phase Shift Oscillators Appendix 9 Figure 6 Oscillator With Network Feedback 3 2 Oscillators With Network Feedback Many oscillator circuits use impedances arranged in a network as the feedback the op amp version is shown in Figure 6 Assuming the standard op amp model shown in Figure 7 it is easy to calculate the loop gain Without feedback we have a load Zz on the output consisting of Z in parallel with the series combination of 21 and 23 7 22 21 Za 21 Za 23 The open loop gain 1 without feedback is A Zr Zr Ro The feedback factor is 21 2 2 42 B Appendix 10 vn Aviv p vn 9 Figure 7 The Standard Model Hence the loop gain is Av 2122 L p 22 21 23 Ro Z1 Zo Za Given a desired frequency of oscillation fo we need to choose the impedances so as to satisfy the Barkhausen criterion Suppose that the impedances are purely reactive either inductive or capacitive so that 2 7X Then we have Av X1 L
83. mpled version of PAM xn filter p 1 pams runs vector pams through filter p figure plot xn 1 200 a portion of the filter output clf hold on Generate the eye pattern Remember that eye patterns are typically shown over a time period of 2T Is there a delay to the signal If so why Now change a rolloff to various values between 0 and 1 Make eye diagrams for several different rolloff factors How does the rolloff factor affect the ISI as seen through the eye diagram How does the eye diagram show the effect of ISI on sensitivity to timing error and the noise margin What is the primary negative effect of high ISI d 5 T Fs 1 calculating delay for i d 6 300 6 start from point 16 delay In Lab plot xn i i 6 plot the first 7 samples 2T end the loop will plot on top of itself Experiment with the spectral characteristics of the system Using 2048 samples generate frequency spectrum plots for both the filter and the output signal Print out both the Signal spectrum of the output and the filter in amplitude and dB How does changing the roll off factor of the pulse shaping filter affect the signal spectrum of the output and the filter Make printouts to substantiate your assertions Nfft 2048 P fftshift fft p Nfft Displays the fft of p X fftshift fft xn Nfft Displays the fft of xn f Fs 2 Fs Nfft 1 Fs 2 Frequency axis scale figure subplot 211 plot f abs P grid title Signal Spectrum of
84. multiplying the message signal by a sinusoid at the carrier frequency This frequency conversion operation is not limited to AM there are many times when we wish to shift a bandpass spectrum regardless of its origin to another frequency For example in the superheterodyne receiver the incoming modulated signal at carrier fe is shifted to the intermediate carrier frequency f and then demodulated In principle the idea of frequency conversion is very simple It is based on the Fourier transform property x t cos 2m fot fo fo Hence if x t is a lowpass or baseband signal then v t x t cos 27 fet is a bandpass signal at fe see Figure 1 This is just double sideband supressed carrier modulation If x t is a bandpass signal at fe then w t x t cos 27 fot contains bandpass spectra at fe fo We then obtain the desired bandpass signal v t by passing w t through bandpass filter If the BPF is at fo we have up converter and if the filter is at fc fo we have down converter Figure 2 illustrates an up converter You will learn about the operation of the superheterodyne receiver in the communi cations class Mixers 4 Frequency Conversion x t gt v t 0 0 jaw Figure 1 Lowpass to bandpass conversion DSB modulation z t x vO BPF vi XO code tot vcl 0 fe f 0 fe fo f IW
85. n set the function gen erator output impedance to high or to 50 Q make sure you have it set 2 3 10 11 12 appropriately Get a good display of the spectrum on the analyzer Measure the input power in dBm don t forget that you are not mea suring normalized power of the lines and compare with theory Make sure that you look for lines other than the ones you expect to see and that you record their frequencies and amplitudes Change the vertical unit from dBm to mV and repeat item 5 Adjust the resolution bandwidth RBW up and down and observe the effect on the displayed spectrum Explain the appearance of the spectrum as you change the RBW especially when you set the RBW to 1 MHz and 3MHz Use the Sweep control to obtain a single sweep and a continuous sweep the default What is the purpose of single sweep With the sine wave spectrum displayed become familiar with using the FREQUENCY SPAN AMPLITUDE and Res BW controls Be come familiar with the Marker controls for frequency and amplitude measurements including the difference markers and the Peak Search control What is the function of the Signal Track control Investigate the effect of the Video BW video filter bandwidth button on the display of the calibration signal The video filter is post detection filter used to reduce noise in the displayed spectrum to its average value making low level signals easier to detect Note you should
86. nal In to trigger the DSO 9 We shall next measure the hold in and pull in ranges of the PLL Refer to Figure 4 23 and the accompanying discussion in Couch The hold in range is the range of frequencies about fo over which a locked loop will remain in lock the pull in range is the range of frequencies over which a loop will acquire lock The pull in range is never larger than the hold in range see Figure 4 e Verify that the VCO output pin 4 and the input signal pin 14 are both at fg 100 kHz e Set the input frequency to a value below such that the PLL is out of lock when the loop is out of lock the VCO output signal will be unstable e Slowly increase the input frequency until the VCO output be comes stable This is the lower frequency of the pull in range the PLL has just pulled in the input frequency e Slowly increase the input frequency until the VCO output be comes unstable The PLL has now lost lock this is the upper The hold in range is also called the lock range and the pull in range is sometimes called the acquisition range or capture range Lab 7 6 A fy Af fin fo Figure 4 Pull in and Hold in Ranges Pull in 2A fp Hold in 2A fr frequency of the hold in range e Slowly decrease the input frequency until the PLL again acquires lock this is the upper frequency of the pull in range e Continue decreasing the input frequency until the PLL lo
87. not do well on the final 4 Prelabs Most of the experiments have prelabs You will be expected to have the prelab completed before the lab period you will not be permitted to do the in lab part of the experiment without a complete prelab You are encouraged to use any computer tool that you consider appropriate to help you complete the prelab The tools available in the ECE computer lab NEB 288 that you will find most useful are PSpice Mathcad and Matlab The computers at each station in the lab also have Microsim PSpice and Mathcad installed If you use one of these tools to produce a circuit diagram a graph or a table then you must secure that page in your lab Introduction 5 notebook your graphs must have titles and axis labels and if you have more than one trace on a graph the traces must be labeled Circuit diagrams drawn by hand should be entered directly into your notebook as neatly as possible with all components clearly labeled If you choose to draw a graph by hand then you must do it on appropriate graph paper using a straightedge to draw axes You are an engineer you are expected to present data and calculations clearly and precisely LABORATORY 1 THE DIGITAL STORAGE OSCILLOSCOPE THE FUNCTION GENERATOR AND MEASUREMENTS OBJECTIVES 1 2 become familiar with the features and basic operation of the Agilent 54622D oscilloscope and the Agilent 33120A function generator investigate signals
88. ntrol knob What is the maximum frequency and maximum amplitude sine wave that the function generator can produce What is the minimum frequency Lab 1 and minimum amplitude that it can produce Make sure that the maximum amplitude does not exceed the maximum input rating of the oscilloscope On the oscilloscope learn how to select channels to display and how to get a good display without using the Autoscale button Autoscale does not do anything you cannot do with the controls and there is no guarantee that it will give the display settings you need Spend some minutes investigating the following features you do not need to record this in your notebook unless you want to for your own reference a What does the Delayed Sweep feature do b What are the three triggering modes that this oscilloscope pro vides c What are the trigger coupling modes d The signal must also be coupled to the input of the oscilloscope what is the difference bewtween AC and DC input coupling e What are the different acquisition modes that this oscilloscope has f What do the RUN STOP and SINGLE buttons do You must learn to become familiar with these features and to pay attention to them Every time you make a measurement with an oscil loscope you must know how the input is coupled how the waveform is acquired how the oscilloscope is triggered and the sampling rate being used If you do not pay attention you could end up displ
89. onnect the function generator to your circuit and how you connect the output of the circuit to the RF input of the analyzer you will probably use the cables that have a BNC connector on one end and alligator clips on the other your amplitude measurements may not be accurate due to impedance mis matches But your relative amplitude measurements will be accurate i e the amplitude values of the lines in dBm may not agree with theory but the differences between the lines in dB should Remarks In this lab we of course have not used the spectrum analyzer to its full advantage we did nothing here that could not have been done with the FFT feature of the oscilloscope The purpose of this lab was simply to introduce you to the spectrum analyzer and its basic operation In future you will be expected to be able to set the analyzer controls to get a good display of the spectrum of any signal and to be able to read the frequencies and amplitudes of the spectral components from the display and convert the amplitudes into voltage levels or normalized powers References Couch Leon W Couch II Digital and Analog Communication Sys tems 6 ed Prentice Hall 2001 LABORATORY 3 FREQUENCY RESPONSE OF SYSTEMS AND DISTORTION OBJECTIVE measure the frequency response of a linear filter and to investigate linear and nonlinear distortion PRELAB 1 Read the following in Couch Section 2 6 subsection on distor tionless transmiss
90. ount when design ing an oscillator such as its physical size power consumption fabrication cost and complexity and so on but every oscillator is meant to provide a sine wave at a fired frequency and with a fired amplitude That is whatever else the design engineer needs to worry about there are three fundamental measures of merit for any oscillator e The purity of the sine wave its spectrum should consist of one line Every circuit is going to produce some harmonics of course but the power contained in the harmonics should be small relative to the fun damental One way to quantify this is with the THD e The frequency stability of the oscillator should be good That is the frequency of the sine wave should not drift both in the short term and the long term Appendix 2 RL Figure 1 Parallel Resonant Circuit e The amplitude stability of the sine wave should also be good The subject of oscillators is quite large and no single reference covers everything The main reason is the huge range of operating frequencies oscillators find application in circuits operating over the whole of the elec tromagnetic spectrum from tens of Hz the low end of the audio range up to around 300 GHz the upper end of the microwave range The devices and circuit design techniques become quite different as we move into higher and higher frequencies Nevertheless some general classifications of oscilla tor types can be made and the
91. ow it back in the box Neatness When you have finished for the day return all components to their proper storage bins return all test leads and probes to their storage racks or pouches return all equipment to its correct location and clean up the lab station Computers On occasion you will find that measurements made in lab do not check with your prelab calculations or simulations the PC s at each station have Mathcad and Microsim PSpice on them so that you can check your prelabs PC s are not conncected to the campus network The PC s are also used to give you access to a printer so you can print out oscilloscope and spectrum analyzer displays Do not install other software on the computers change the system settings such as the display change the desktop install your own wallpaper or screen saver etc You may temporarily save your own files on the hard disk you will find a shortcut to the My Documents directory on the desktop You may create your own folders under My Documents to store files in Do not however expect those files to be there next time you use the computer the computers will be cleaned up periodically to provide disk space Always copy any files you need to save onto your own floppy before you leave the lab Introduction 4 Final note when you start the PC do not logon When the logon screen comes up just hit the Esc key 3 Record Keeping You will be working in groups of 2 at the lab stations but
92. perty that quartz possesses that we use is the piezoelectric effect electrical stresses i e voltages applied across the crystal in certain directions produce mechani cal stresses i e deflections in other directions and conversely mechanical stresses produce voltages We take advantage of the back and forth transfer of electrical and mechanical energy to produce very stable oscillations Piezoelectric quartz crystals are grown in the form of a rod having a hexagonal cross section See Figure 9 The longitudinal Z axis is called the optical axis electrical stresses applied in this direction produce no piezo electric effect Consider now a slice of the crystal perpendicular to the op tical axis Axes passing through the corners of the hexagon such as the X axis in Figure 9 are called the electrical axes and axes perpendicular to the faces of the hexagon such as the Y axis in Figure 9 are called the mechanical axes flat section cut from the crystal in such a way that the flat sides are perpendicular to an electrical X axis is called an X cut see Figure 9 Likewise a section cut with the flat sides perpendicular to a mechanical Y axis is called a Y cut A mechanical stress in the direction of a Y axis produces an electrical stress in the direction of the X axis that is perpendicular to that Y axis and conversely an electrical stress in the direction of an X axis produces a mechanical stress in the direction of the perpendicular
93. puts and controls of the other three switches the open pins are the outputs of the other three switches These pins must be connected as indicated to prevent crosstalk You should understand that the device is a switch but it is not an ideal switch In particular it has a non zero propagation delay from input to output approx imately 15ns non zero resistance approximately 215 and its frequency response is not flat it has a 3dB break frequency of about 150 MHz 2 Set one function generator to produce the rectangular sampling wave form with parameters f and from item 3 of the Prelab Set the amplitude of the sampling signal for V swing Pay attention to how you connect the function generator to the circuit what should you set the output impedance of the function generator to 3 Use the other function generator for the sinusoidal message signal to be sampled set f 500 Hz and 1 V 4 Display the PAM signal on the oscilloscope It may help to get your trigger off the message signal Is its amplitude what you expect Explain Remember the switch is not ideal To make measurements easier adjust the message signal amplitude so that the PAM signal has swing 2 Vp p Include a printout of the PAM signal in your notebook 5 Display the spectrum of the PAM signal on the oscilloscope Include a printout of the spectrum in your notebook 6 Record the magnitudes of the spectral components of the PA
94. quivalent model of the PLL 4 Equivalent Linear Model Let us assume that the phase error is small t lt lrad for all t Then sin 6 4 e t and we thus obtain an approximate linear model the nonlinear box K sin in Figure is replaced by a constant gain box Let us now do our analysis in the Laplace transform domain sop ss yate dt Vo s L ve s Oi s 210 3 2160 8 es 216 1 3 Then the integration box 27K n of Figure 3 is replaced by the transfer function 21 K s The PLL is therefore approximately modeled by the linear control system of Figure 4 We have Va s 8 0 5 Oo s eure H s Va s Let us first calculate the closed loop transfer function G s 8 8 2n Ky 2n K 2n MG H s Va s 7 B 8 7 O s O s Va s Loop filter 5 gee Oo s o 2n K Figure 4 The approximate linear model of the PLL Therefore 2n K 2n Kq K 8 2 KqH s H s 6i 5 O0 s t H s o s aH 5 6 5 Hence P Oo s 2xK K4H s G s O s s c2zK K4H s 2 We can also calculate the transfer function 8 8 from input phase to phase error Oe s Oi s Oo s Oi s G s Oi s
95. re you will discover effects that your mod eling did not accurately take into account and the loop returns to the beginning you try to model these effects then run a simulation and so forth 7 Our theoretical analysis of the filter assumes a linear model the sys tem from input to output is assumed to be a linear system But as you know there is really no such thing as a perfectly linear system As you know from the reading you did for Item 1 one way to mea sure how close a system is to being truly linear is to apply a sinusoid and look for harmonics in the output If the system is truly linear it cannot introduce any harmonics in the output signal But a nonlinear system does introduce harmonics of the input frequency in fact we could take this as the definition for nonlinear system If the added harmonic components are small in amplitude or in other words if the total harmonic distortion is small then to that extent the system is close to linear at least for that test frequency For the Sallen Key circuit use the R and C values from Item 3 and set 5 V Do a PSpice simulation to see if there is any harmonic distortion You need do this at only one test frequency try one well below the 6 dB break frequency say 500 Hz Apply a sinusoid of this frequency to the input keeping its amplitude small enough so that the op amp does not saturate and observe the output voltage Observing the output waveform is not good enough
96. ric effect gets progressively smaller at the overtones 5 Frequency Stability As we have said frequency stability is of prime importance in oscillator design We are not using stability in the control theory sense of location of poles of a transfer function Rather a better term would be frequency sensitivity to changes in circuit parameters The study of frequency stability can get quite complicated and each oscillator presents its own problems but we can say something useful by considering a very simple example The feedback oscillators that we con sidered involved an active amplifier with a passive resonant feedback net work the frequency of oscillation wo is determined by the feedback network Suppose that the phase changes by then the frequency of oscillation must change by a Aw to cause a phase shift of to maintain zero phase shift around the closed loop Remember that the phase of L s must be zero Thus the greater the magnitude of the phase change for a change from wo the greater the frequency stability Le a smaller Aw will be required to bring the loop back to zero phase Hence we define the frequency stability as ais Aw wo 040 For simple example consider a parallel RLC circuit The impedance i A EO 8 82 8 where wn 1 v LC and Q R4 C L as usual Then 2 w Z ju Appendix 19 phase angle of the imp
97. rough an internal alignment or calibration procedure You will hear clicking and see the alignment screens flash by This procedure only takes a couple of minutes analyzer then continuously runs its alignment check you will hear occasional noises as this goes on but it will not interrupt your measurements You can also manually run the alignment but this should never be necessary FREQUENCY control In normal operation the frequency control selects the range that the variable oscillator in Figure 1 sweeps through Pressing the FREQUENCY button causes the frequency menu to appear at the right side of the screen You can select the center frequency CF and the start and stop frequencies You select the numerical values by turning the control knob pressing the up down arrows the step size is controlled by the CF Step entry in the menu or by entering the value with the numerical keypad SPAN Control Pressing the SPAN button brings up the frequency span menu Here you select the frequency span displayed on the screen as opposed to selecting start and stop frequencies and you can select span zoom zero span and full span AMPLITUDE control Pressing this button displays the amplitude menu Here you select the reference level whether the amplitude units are power dBm or linear mV and the scale in dB division when using the logarithmic scale Here is where the spectrum analyzer seems strange compared to an oscilloscope you mea
98. scope display of the output point b Measure the oscillation frequency e Measure the potentiometer resistance required to sustain oscilla tion and compare with your Prelab calculation e Record the FFT of the output on the oscilloscope Compare with Prelab 2 Vary the potentiometer resistance up and down and record your ob servations What should happen to the output as you increase and decrease the resistance and what do you observe 3 Build the op amp phase shift oscillator shown in Figure 1 This is just the phase shift oscillator of Figure 5 in Appendix C with the same simple amplitude stabilization used in the Wien bridge The left hand resistance of the POT between the tap and C3 is R in Figure 5 of Appendix C and the right hand resistance plus R is the same as the feedback resistor R in Figure 5 of Appendix e Adjust the potentiometer until oscillation is sustained Record the oscilloscope display of the output Measure the oscillation frequency e Measure the potentiometer resistance required to sustain oscil lation Compare with the theoretical values calculated in Ap pendix C if R is the resistance between and the tap and Rpr is the resistance to the right of the tap then R should be 10 R3 should be greater than 29 and under these conditions the frequency of oscillation is fo 1 2x RC V6 e Record the FFT of the output on the oscilloscope References Sedra Smith Adel S
99. scope will display FFT of a signal The DSO s display of the FFT has the advantage of capturing one shot events as well as being able to store the in memory or on a floppy But the scanning spectrum analyzer usu ally holds the advantage over the in frequency range sensitivity and dynamic range If you find yourself working in communications especially in RF and microwave communications you will probably find that you will frequently be using a spectrum analyzer for spectral measurements 3 Spectrum Analyzer Controls In this section we shall describe some of the basic controls on the spectrum analyzer that you will frequently use More details on these and descriptions of the more obscure controls can be found in the user manual Mainly you will use the three large buttons labeled FREQUENCY SPAN and AMPLITUDE the various MARKER buttons for making measurements and the BW Avg button for selecting the resolution bandwidth In addition you will use the control knob the up and down buttons labelled with large arrows above the control knob and the numerical keypad for entering values that will control the display Appendix B 4 When you use the spectrum analyzer always pay attention to the in formation about the instrument state given in the top left and bottom margins of the screen Calibration The manufacturer recommends a 5 minute warm up for the analyzer When the spectrum analyzer is turned on it goes th
100. se you know that the step response is a standard measure of control system performance Then vi t Ai cos 2m fet 2n Ku t and Oj s 2n K s Then 2n K 2n Ky 8 s mK Ka Hence o t 2rK 1 e t u t where MOM i 21 K Kg i 2n fo is the time constant Draw a sketch of 09 t Note that as the loop gain f is increased we have T 0o t 2n Ku t 0 t as Phase Locked Loop 9 Example 2 Let 0 t 27Ktu t and so O s 27 52 That is con sider now the ramp response Therefore _ 2n K 21 K Ka Vote c er ei Hence Oo t K t re u t where 1 27 as before Again we have 0o t 27Ktu t 0 t as oo 4 2 digression validity of the linear model The preceding analysis depends on the validity of the linear approximation Kasin Before we analyze the second commonly encountered case of the PLL let us investigate the validity of the linear model We shall show that in the linear model the phase error does indeed tend to drive the loop into lock Consider the first order loop H s 1 but without the assumption of linearity That is v t sin 6 t 8o t frequency deviation of the VCO output is o InKyv2 t 2n 6 6 69 t Consider very simple example suppose that 0 t Kt u t Then i 2rKu t Now belt 6 t E bo
101. ses lock this is the lower end of the hold in range e The device manufacturer gives the following approximate rela tionship between the hold in and pull in ranges 2A fa I T Fa Compare your measured values to this formula 10 We shall now use the PLL as an FM modulator build the circuit of Figure 5 Set the free running frequency of the VCO pin 4 to 100 kHz see item 7 e Use one function generator to produce 100 kHz square wave that switches between 0 V and 10 V Use this for the Carrier In signal pin 14 e Use your second function generator to produce a 1 kHz 5 Vy sine wave Use this for the Message Signal e Display the FM signal the VCO output at pin 4 on the DSO e Systematically investigate the effect on the FM signal of varying the amplitude and frequency of the message signal Explain your observations 11 We shall now use the PLL as an FM demodulator build the circuit of Figure 6 Set the free running frequency of the VCO to 100 kHz 3Specification data for the CD4046 op cit p 11 Lab 7 Figure 5 Modulator Circuit e Use the function generator to produce the following FM signal Carrier sine wave at 100 kHz 10 Vp p with 5 V dc offset this is the Carrier In signal on pin 14 The dc offset must be present because the pin 14 signal must have LOW level 0 and HIGH level 10V Message sine wave at 1 kHz Peak frequency deviation
102. signal power in dBm and in Watts that can be applied to the RF input Before you connect any signal to the RF input be sure that its ampli tude or power does not exceed the maximum rated input If you are unsure measure the signal with the oscilloscope 3 Given your answers to the questions in Item 2 calculate e the maximum amplitude sine wave with zero DC offset that can be applied to the RF input e the maximum amplitude square wave with zero DC offset hav ing 5096 duty cycle that can be applied to the RF input When doing these calculations don t forget what the input impedance of the analyzer is e What is the center frequency and the frequency span on power up e What is the resolution bandwidth on power up e What is the reference level and the amplitude scale in dB division e What is the attenuation What is the purpose of the internal attenuator 4 With no signal applied and with the analyzer in its default config uration if you changed any of the settings you can get back to the default state by pressing the PRESET button you will see the display of the noise floor This noise is approximately white noise mean ing its power spectral density which is what you are looking at on the screen is approximately constant for all frequencies Measure the power level in dBm and in W of this noise 5 Use the 33120A function generator to produce a 1 MHz sine wave of amplitude 200 mV y Remember that you ca
103. stays there At point 2 we have a steady state frequency error of dt 0 but we have a non zero steady state phase error 0 It is easy ss 11 to see that 6 arcsin K K Ka Note that we get frequncy lock d0 dt 0 only if the phase plane plot crosses the d e dt 0 axis Hence to achieve frequency lock we must have 2z K lt 0 or gt For this reason in Hz is called the lock range or hold in range Note also that for large loop gain we get small 0 look at the loop transfer function see this ss Oo s 2n Ky Kg 1 O s s 2nK Ka s 2mK K4 1 As K K4 oo 90 s Oi s 1 so 60 06 t This also follows from 06 arcsin amp K K 0 as K K4 oo Keep in mind that the first order loop behaves as a low pass filter so large loop gain implies large bandwidth Thus we have now seen that the phase error tends to drive the loop into lock which justifies the linearity assumption Kasin 0 t zz K40 t But we have also seen that the first order loop requires a large loop gain to work properly which implies a large loop bandwidth Furthermore we have seen that the first order loop achieves frequency lock but it has a steady state phase error In some applications the steady state phase error does not present a problem while it other applications it does If we desire 6 0 another t
104. sure signal levels from the top of the screen or down from the reference level For example on power up the reference level is 0 dBm meaning that the top line on the screen is at 0dBm and you measure the amplitudes of lines in the spectrum down from that level Once again you are cautioned to be careful about applying signals to the spectrum analyzer it is easy to cause extensive and expensive damage Resolution Bandwidth control The resolution bandwidth is essen tially the bandwidth of the fixed narrowband filter in Figure 1 In reality there are several stages of filtering Pressing the BW Avg button displays the menu from which you can select the resolution bandwidth the video bandwidth and associated controls Note that you cannot select a continu ous range of RBW there is only a finite selection available Appendix B 5 The resolution bandwidth determines how close frequency components in the signal spectrum can be and still be displayed as distinct components on the screen Sweep control The sweep time determines how often the input signal is scanned through the analyzer Note that you can select continuous sweep and single shots just as you can with the oscilloscope Markers Just as the oscilloscope has markers the spectrum analyzer has four markers to help you make measurements You select markers difference markers or no markers with the MARKER control buttons and their menus File control Like the oscilloscope t
105. that it will display utter gibberish as any computer will if you do not understand its limitations The basic idea is this we wish to calculate the Fourier transform of a continuous time signal on a digital computer so we first truncate the signal to a finite time duration by multiplying it by a window function and then we sample the windowed time function at an appropriate rate to create a finite length record of samples Suppose that x t is the waveform and after windowing and sampling we have N samples say z9 21 2wN 1 The DFT of the samples is defined by the equation N 1 1 X k 5 M e BO n 0 and the inverse DFT is N 1 Oe k 0 The DFT is similar but not identical to the discrete time Fourier transform for discrete time signals that you learned about in EEL 3135 3See Section 2 8 of Couch s book Appendix 6 Note that the DFT X k is a discrete frequency function if we select the windowing function correctly and if we sample at the appropriate rate X k will be a good approximation to the Fourier transform X f We shall not go into details about the DFT here for now we shall merely state some of the limitations about using the DF T as an approximation to the continuous Fourier transform that you should keep in mind These lim itations are summarized in the conditional statement we made earlier if we select the windowing function correctly and if we sample at the appropriate
106. two points a Why is there more than one line Hint measure the amplitude level in dB of the higher order lines relative to the fundamental line How much power is contained in the higher order lines Is the signal generator producing a perfect sine wave b Why are the lines not truly lines That is they have non zero width Hint In order to calculate the FFT the oscilloscope can only use a finite number of samples i e the signal is windowed to have a finite time duration What is the Fourier transform of a sinusoidal pulse Save the display of the spectrum on a floppy as a bitmap print it out and include it in your notebook Use the HP function generator to produce a 10 kHz square wave with peak to peak value 200 mV 5096 duty cycle and zero dc offset Dis play it on the oscilloscope and display its FFT Include a printout of the square wave and its FFT in your lab notebook Compare its amplitude spectrum out to the first five peaks with your prelab cal culations Build the RC lowpass filter having time constant 10 us from your prelab Use the square wave from Step 7 as the input to the RC filter Display the output signal and its FFT insert a printout in your notebook Compare the output to your prelab calculations Measure the time constant 7 of the RC circuit and compare with the designed value Hint use a square wave test input and measure the rise time of the output Calculate from th
107. ver you are selecting this frequency so that the desired signal will pass through the filter in a spectrum analyzer this frequency is automatically scanned repeatedly over a range which must be selected so that the frequency component X f is shifted to and passed by the filter For example if we want to view the frequency content of x t from fi to fo then we must select fo to scan from f fr to fo fr Of course much more signal conditioning is going on inside the spectrum analyzer than is indicated in Figure 1 but the frequency mixing is the fundamental step In particular the signal first is passed through a lowpass filter whose bandwidth is chosen to eliminate image frequencies Once again see the section on the superhet in Couch or in Carlson Also most scanning spectrum analyzers are multiple conversion analyzers they have two to four intermediate frequency stages at successively lower frequencies reason is that we have two conflicting goals to achieve we would like to have the filter bandwidth as small as feasible and we would like to be able to scan over large frequency ranges It is hard to build sharp narrow filters at high frequencies but it is also hard to build multipliers that will work over large frequency ranges Therefore we achieve narrow filters at low intermediate frequencies by shifting the frequency down in several steps You may naturally ask why we have a spectrum analyzer if the oscillo
108. ype of loop filter must be used we shall now consider a commonly used filter ss 4 3 Second order loop In the second order loop the loop filter is s a H s x Then the overall loop transfer function is second order Gays 2nK KaH s 21 Ky Ka s a 8 2 5 s 2n K Kqs 2n Ky wns w2 82 2Cwns w2 See also Equation 4 104 in Couch The analysis we did was for the first order loop H s 1 and so the loop filter does not enter In general the lock range is K K4H 0 as shown in Couch s Equation 4 104 Phase Locked Loop 12 Magnitude of Loop Transfer Function Magnitude Gain dB Normalized Radian Frequency 0 2 777 mzeta 707 szeta l zetas Figure 6 Frequency Response of Second Order Loop 1 2 C 5 02 is the damping ratio and Wn 2n Ky is the natural frequency This transfer function is that of a second order lowpass filter see Figure 6 Again the loop acts as a low pass filter with bandwidth fn 22 1 262 1 D Also as with the first order loop a large loop gain implies a large bandwidth where 13 major advantage of the second order loop is that the steady state phase error is 0 see this consider the transfer function from input phase to phase error from Equation 3 Oels _ 8 82 8 8 2 4 5

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