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1. A 1 m cosut wT For the case m lt 1 the absolute sign has no effect and so there is a linear relationship between the message and envelope as desired for AM This is clearly shown in Figure 1 which is for 100 AM m 1 Both a t and its modulus is shown They are the same Example 2 150 AM For the case of 150 AM the envelope is still given by e t of eqn 7 but this time m 1 5 and the absolute sign does have an effect Figure 2 shows the case for m 1 5 As well as the message upper trace the absolute value of the message is also plotted centre trace Notice how it matches the envelope of the modulated signal lower trace Example 3 DSBSC For a final example look at the DSBSC where a t cosut There is no DC component here at all Figure 3 shows the relevant waveforms ETES z T Figure 1 AM with m 1 n ce etn Figure 2 150 AM Figure 3 DSBSC Envelope detector Although the envelope is imaginary in the sense described above it is possible to generate from y t a signal e t having the same shape as this imaginary line The circuit which does this is commonly called an envelope detector A better word for envelope detector would be envelope generator since that is what these circuits do In this experiment you will model circuits which will generate these envelope signals Diode detector The ubiquitous diode detector is the prime example of an envel
2. contributions should be identical with respect to amplitude and frequency since they came from a matching pair of sidebands Now you can see what the phase adjustment will do The relative phase of these two contributions can be adjusted until they reinforce to give a maximum amplitude A further 180 degrees shift would result in complete cancellation Demodulation of SSB With SSB as the input to a synchronous demodulator there will be a message at the output of the 3 kHz LPF visible on the oscilloscope Whilst watching the message on the oscilloscope make a phase adjustment with the front panel control of the PHASE SHIFTER and note that a the message amplitude does NOT change b the phase of the message will change but how can this be observed If you have generated your own SSB then you have a copy of the message and have synchronized the oscilloscope to it Using the graphical interpretation as was done for the case of the DSBSC you can see why the phase adjustment will have no effect upon the output amplitude Two identical contributions are needed for a phase cancellation but there is only one available EXPERIMENT 1 ENVELOPE RECOVERY Ideal model The TIMS model of the ideal envelope detector is shown in block diagram form in Figure 7 PRECISION RECTIFIER within UTILITIES module Figure 7 Modeling the ideal envelope detector with TIMS The ideal rectifier is easy
3. which it is multiplied If the left movement causes the graphic to cross the zero frequency axis into the negative region then locate this negative frequency say fx and place the graphic there Since negative frequencies are not recognized in this context the graphic is then reflected into the positive frequency region at fx Note that this places components in the triangle which were previously above others now below them That is it reverses their relative positions with respect to frequency Special case fo fc In this case the down translated components straddle the origin Those which fall in the negative frequency region are then reflected into the positive region as explained above They will overlap components already there The resultant amplitude will depend upon relative phase both reinforcement and cancellation are possible If the original signal was a DSBSC then it is the components from the LSB which are reflected back onto those from the USB Their relative phases are determined by the phase between the original DSBSC on fc and the local carrier fo Remember that the contributions to the output by the USB and LSB are combined linearly They will both be erect and each would be perfectly intelligible if present alone Added in phase or coherently they reinforce each other to give twice the amplitude of one alone and so four times the power In this experiment the product demodulator is examined
4. which is based on the arrangement illustrated in Figure 6 This demodulator is capable of demodulating SSB DSBSC and AM It can be used in two modes namely synchronous and asynchronous Synchronous demodulator ai For successful demodulation of DSBSC and AM the synchronous demodulator requires a local carrier of exactly the same frequency as the carrier from which the modulated signal was derived and of fixed relative phase which can then be adjusted as required by the phase changer shown OUTPUT the message Figure 6 Synchronous demodulator l a0 Carrier acquisition In practice this local carrier must be derived from the modulated signal itself There are different means of doing this depending upon which of the modulated signals is being received So as not to complicate the study of the synchronous demodulator it will be assumed that the carrier has already been acquired It will be stolen from the same source as was used at the generator namely the TIMS 100 kHz clock available from the MASTER SIGNALS module This is known as the stolen carrier technique Asynchronous demodulator a l For asynchronous operation acceptable for SSB a local carrier is still required but it need not be synchronized to the same frequency as was used at the transmitter Thus there is no need for carrier acquisition circuitry A local signal can be generated and held as close to the desired frequency
5. DULATION All of the modulated signals you have seen so far may be defined as narrow band They carry message information Since they have the capability of being based on a radio frequency carrier suppressed or otherwise they are suitable for radiation to a remote location Upon receipt the object is to recover demodulate the message from which they were derived In the discussion to follow the explanations will be based on narrow band signals But the findings are in no way restricted to narrow band signals they happen to be more convenient for purposes of illustration Frequency translation When a narrow band signal y t is multiplied with a sine wave two new signals are created on the sum and difference frequencies Figure 5 illustrates the action for a signal y t based on a carrier fc and a sinusoidal oscillator on frequency fo A f v u 4 y t i hti Figure 5 Sum and difference frequencies Each of the components of y t was moved up an amount fo in frequency and down by the same amount and appear at the output of the multiplier Remember neither y t nor the oscillator signal appears at the multiplier output This is not necessarily the case with a modulator A filter can be used to select the new components at either the sum frequency BPF preferred or an HPF or difference frequency LPF preferred or a BPF the combination of MULTIPLIER OSCILLATOR and FIL
6. EE 400L Communications Laboratory Exercise 2 Analog Linear Modulation Department of Electrical and Computer Engineering University of Nevada at Las Vegas PREPARATION 1 Envelope Recovery Envelope definition When we talk of the envelopes of signals we are concerned with the appearance of signals in the time domain Text books are full of drawings of modulated signals and you already have an idea of what the term envelope means It will now be given a more formal definition Qualitatively the envelope of a signal y t is that boundary within which the signal is contained when viewed in the time domain It is an imaginary line This boundary has an upper and lower part You will see these are mirror images of each other In practice when speaking of the envelope it is customary to consider only one of them as the envelope typically the upper boundary Although the envelope is imaginary in the sense described above it is possible to generate from y t a signal e t having the same shape as this imaginary line The circuit which does this is commonly called an envelope detector For the purposes of this discussion a narrowband signal will be defined as one which has a bandwidth very much less than an octave That is if it lies within the frequency range f1 to f2 where f 1 lt f2 then log2 f 1 f2 lt lt 1 Another way of expressing this is to say that f 1 f2 so that f2 f1 f 2
7. TER is called a frequency translator When the frequency translation is down to baseband the frequency translator becomes a demodulator Interpretation The method used for illustrating the process of frequency translation is just that illustrative You should check out using simple trigonometry the truth of the special cases discussed below Note that this is an amplitude versus frequency diagram phase information is generally not shown although annotations or a separate diagram can be added if this is important Individual spectral components are shown by directed lines phasors or groups of these sidebands as triangles The magnitude of the slope of the triangle generally carries no meaning but the direction does the slope is down towards the carrier to which these are related When the trigonometrical analysis gives rise to negative frequency components these are re written as positive and a polarity adjustment made if necessary Thus V sin ot V sin ot usl3 Amplitudes are usually shown as positive although if important to emphasize a phase reversal phasors can point down or triangles can be drawn under the horizontal axis To interpret a translation result graphically first draw the signal to be translated on the frequency amplitude diagram in its position before translation Then slide it the graphic which represents the signal both to the left and right by an amount fo the frequency of the signal with
8. arrier phase locked to but not necessarily in phase with the transmitter carrier It will need adjustment with a PHASE SHIFTER module For the lowpass filter use the HEADPHONE AMPLIFIER This has an in built 3 kHz LPF which may be switched in or out If this module is new to you read about it in the TIMS User Manual A suitable TIMS model of the block diagram of Figure 6 is shown below in Figure 11 Figure 11 TIMS model of Figure 6 T13 patch up the model of Figure 11 above This shows Wo Wi Before plugging in the PHASE SHIFTER set the on board switch to HI T14 create an Am signal with m 0 5 and connect it to input of the synchronous demodulator Examine the output of demodulator Record your observation TIS increase depth of modulation to 100 and 150 Did this demodulator work for these signals Remember that Envelope detector cannot use in these cases TI5 create a DSB and connect it to input of the synchronous demodulator Examine the output of demodulator Record your observation Asynchronous demodulation We now examine what happens if the local carrier is off set from the desired frequency by an adjustable amount df where df fc fo l 14 The process can be considered using the graphical approach illustrated earlier By monitoring the VCO frequency the source of the local carrier with the FREQUENCY COUNTER you will know the magnitude and direction of this offset by subtracting it from the
9. as circumstances require and costs permit Just how close is close enough will be determined during this experiment Local asynchronous carrier For the carrier source you will use a VCO module in place of the stolen carrier from the MASTER SIGNALS module There will be no need for the PHASE SHIFTER It can be left in circuit if found convenient its influence will go unnoticed Demodulation of DSBSC With DSBSC as the input to a synchronous demodulator there will be a message at the output of the 3 kHz LPF visible on the oscilloscope The magnitude of the message will be dependent upon the adjustment of the PHASE SHIFTER Whilst watching the message on the oscilloscope make a phase adjustment with the front panel control of the PHASE SHIFTER and note that a the message amplitude changes It may be both maximized AND minimized b the phase of the message will not change but how can this be observed If you have generated your own DSBSC then you have a copy of the message and have synchronized the oscilloscope to it The process of DSBSC demodulation can be examined graphically using the technique described earlier The upper sideband is shifted down in frequency to just above the zero frequency origin The lower sideband is shifted down in frequency to just below the zero frequency origin It is then reflected about the origin and it will lie coincident with the contribution from the upper sideband These
10. desired 100 kHz VCO fine tuning Refer to the TIMS User Manual for details on fine tuning of the VCO It is quite easy to make small frequency adjustments fractions of a Hertz by connecting a small negative DC voltage into the VCO V in input and tuning with the GAIN control SSB reception Consider first the demodulation of an SSB signal You can show either trigonometrically or graphically that the output of the demodulator filter will be the desired message components but each displaced in frequency by an amount df from the ideal If df is small say 10 Hz then you might guess that the speech will be quite intelligible For larger offsets the frequency shift will eventually be objectionable The effect upon intelligibility will be dependant upon the direction of the frequency shift except perhaps when df is less than say 10 Hz T17 replace the 100 kHz stolen carrier with the analog output of a VCO set to operate in the 100 kHz range Monitor its frequency with the FREQUENCY COUNTER T18 as an optional task you may consider setting up a system of modules to display the magnitude of df directly on the FREQUENCY COUNTER module But you will find it not as convenient as it might at first appear can you anticipate what problem might arise before trying it hint 1 second is a long time A recommended method of showing the small frequency difference between the VCO and the 100 kHz reference is to display each on separate oscil
11. e detector modeled as Figure7 For the lowpass filter use the TUNEABLE LPF module Your whole system might look like that shown modeled in Figure 9 below T3 set the frequency of the AUDIO OSCILLATOR to about 1 kHz This is your message T4 adjust the triggering and sweep speed of the oscilloscope to display two periods of the message CH2 A T5 adjust the generator to produce an AM signal with a depth of modulation less than 100 Don t forget to so adjust the ADDER gains that its output DC AC will not overload the MULTIPLIER that is keep the MULTIPLIER input within the bounds of the TIMS ANALOG REFERENCE LEVEL 4 volt peak to peak This signal is not symmetrical about zero volts neither excursion should exceed the 2 volts peak level T6 for the case m lt I observe that the output from the filter the ideal envelope detector output is the same shape as the envelope of the AM signal a sine wave Ioh cone 10ckHe TTL argh no ENVELOPE mazaga an 8 GENERATOR RECOVERY Figure 9 Modulated signal generator and envelope recovery DSBSC envelope Now let us test the ideal envelope detector on a more complex envelope that of a DSBSC signal T7 remove the carrier from the AM signal by turning g fully anti clockwise thus generating DSBSC Alternatively and to save the DC level just used pull out the patch cord from the g input of the ADDER or switch the MULTIPLIER to AC Were you expecting t
12. e is a fullwave rectifier Note carefully that the operation of rectification is non linear The so called ideal rectifier is a precision realization of a rectifier using an operational amplifier and a diode in a negative feedback arrangement It is described in text books dealing with the applications of operational amplifiers to analog circuits An extension of the principle produces an ideal fullwave rectifier You will find a halfwave rectifier is generally adequate for use in an envelope recovery circuit Envelope bandwidth You know what a lowpass filter is but what should be its cut off frequency in this application The answer the cut off frequency of the lowpass filter should be high enough to pass all the wanted frequencies in the envelope but no more So you need to know the envelope bandwidth In a particular case you can determine the expression for the envelope from the definition given before and the bandwidth by Fourier series analysis Alternatively you can estimate the bandwidth by inspecting its shape on an oscilloscope and then applying rules of thumb which give quick approximations An envelope will always include a constant or DC term This is inevitable from the definition of an envelope which includes the operation of taking the absolute value It is inevitable also in the output of a practical circuit by the very nature of rectification The presence of this DC term is often forgotten For the ca
13. f1 lt lt 1 A wideband signal will be defined as one which is very much wider than a narrowband signal Every signal has an envelope although with wideband signals it is not always conceptually easy to visualize To avoid such visualization difficulties the discussion below will assume we are dealing with narrow band signals But in fact there need be no such restriction on the definition as will be seen later Suppose the spectrum of the signal y t is located near fo Hz where o 2 pi fo saad We state here without explanation that if y t can be written in the form y t a t cos o t p t up where a t and j t contain only frequency components much lower than fo 1 e at message or related frequencies then we define the envelope e t of y t as the absolute value of a t That is envelope e t a t a3 Remember that an AM signal has been defined as y t A 1 m cospt cosat wd It is common practice to think of the message as being m cosut Strictly the message should include the DC component that is 1 m cosut But the presence of the DC component is often forgotten or ignored Example 1 100 AM Consider first the case when y t is an AM signal From the definitions above we see a t A 1 m cosut eS pt 0 1 6 The requirement that both a t and j t contain only components at or near the message frequency are met and so it follows that the envelope must be e t where e t
14. loscope traces the speed of drift between the two gives an immediate and easily recognized indication of the frequency difference T19 connect an SSB signal to the demodulator input Tune the VCO slowly around the 100 kHz region Record output Report results TUTORIAL QUESTIONS Q1 use phasors to construct the envelope of a an AM signal and b a DSBSC signal 19 Q2 use phasors to construct the envelope of the sum of a DSBSC and a large carrier when the phase difference between these two is not zero as it is for AM The technique should quickly convince you that the envelope is no longer a sine wave although it may be tedious to obtain an exact shape Q3 explain the major differences in performance between envelope detectors with half and fullwave rectifiers Q4 would you define the synchronous demodulator as an SSB demodulator Explain Q5 if a DSBSC signal had a small amount of carrier present what effect would this have as observed at the output of a synchronous demodulator Q6 suppose while you were successfully demodulating a DSBSC based on 100 kHz carrier a second DSBSC based on a 90 kHz carrier was added to it Suppose the amplitude of this unwanted DSBSC was much smaller than that of the wanted DSBSC a would this new signal at the demodulator INPUT have any effect upon the message from the wanted signal as observed at the demodulator OUTPUT b what if the unwanted DSBSC
15. o see the waveforms of Figure 10 What did you see You may not have seen the expected waveform Why not Figure 10 DSBSC signal T8 a lower the frequency of the AUDIO OSCILLATOR and watch the shape of the recovered envelope When you think it is a better approximation to expectations note the message frequency and the filter bandwidth and compare with predictions of the bandwidth of a fullwave rectified sinewave b if you want to work with a 2 kHz message then replace the TUNEABLE LPF with a 60 kHz LOWPASS FILTER Now the detector output should be a good copy of the envelope Record the highest frequency that gives good envelope with this filter Diode detector It is assumed you will have referred to a text book on the subject of the diode detector This is an approximation to the ideal rectifier and lowpass filter There is a DIODE DETECTOR in the UTILITIES MODULE The diode has not been linearized by an active feedback circuit and the lowpass filter is approximated by an RC network Your textbook should tell you that this is a good engineering compromise in practice provided a the depth of modulation does not approach 100 b the ratio of carrier to message frequency is large You can test these conditions with TIMS The patching arrangement is simple T9 connect an Am signal with m lt 1 directly to the ANALOG INPUT of the DIODE LPF in the UTILITIES MODULE and the envelope or its app
16. ope generator It is well documented in most textbooks on analog modulation It is synonymous with the term envelope demodulator in this context But remember the diode detector is an approximation to the ideal We will first examine the ideal circuit Ideal envelope detector The ideal envelope detector is a circuit which takes the absolute value of its input and then passes the result through a lowpass filter The output from this lowpass filter is the required envelope signal See Figure 4 Absolute envelope value out operator Figure 4 Ideal envelope recovery arrangement The truth of the above statement will be tested for some extreme cases in the work to follow you can then make your own conclusions as to its veracity The absolute value operation being non linear must generate some new frequency components Among them are those of the wanted envelope Presumably since the arrangement actually works the unwanted components lie above those wanted components of the envelope It is the purpose of the lowpass filter to separate the wanted from the unwanted components generated by the absolute value operation The analysis of the ideal envelope recovery circuit for the case of a general input signal is not a trivial mathematical exercise the operation being non linear So it is not easy to define beforehand where the unwanted components lie Ideal rectifier A circuit which takes an absolute valu
17. roximation can be examined at the ANALOG OUTPUT You should not add any additional lowpass filtering as the true diode detector uses only a single RC network for this purpose which is already included The extreme cases you could try would include a an AM signal with depth of modulation say 50 and a message of 500 Hz What happens when the message frequency is raised Is gt gt u b aDSBSC Here the inequality gt gt u is meaningless This inequality applies to the case of AM with m lt 1 It would be better expressed in the present instance as the carrier frequency must be very much higher than the highest frequency component expected in the envelope This is certainly NOT so here T10 repeat the previous Task but with the RECTIFIER followed by a simple RC filter This compromise arrangement will show up the shortcomings of the RC filter There is an independent RC LPF in the UTILITIES MODULE TII you can examine various combinations of diode ideal rectifier RC and other lowpass filters and lower carrier frequencies use the VCO The 60 kHz LPF is a very useful filter for envelope work T12 check by observation is the RECTIFIER in the UTILITIES MODULE a halfwave or fullwave rectifier 2 Product Demodulator Synchronous demodulation The demodulator of Figure 6 is easily modeled with TIMS The carrier source will be the 100 kHz from the MASTER SIGNALS module This will be a stolen c
18. se of an AM signal modulated with music the DC term is of little interest to the listener But it is a direct measure of the strength of the carrier term and so is used as an automatic gain control signal in receivers It is important to note that it is possible for the bandwidth of the envelope to be much wider than that of the signal of which it is the envelope In fact except for the special case of the envelope modulated signal this is generally so An obvious example is that of the DSBSC signal derived from a single tone message DSBSC Envelope Bandwidth So The bandwidth of a DSBSC signal is twice that of the highest modulating frequency So for a single tone message of 1 kHz the DSBSC bandwidth is 2 kHz But the bandwidth of the envelope is many times this DSBSC cosut cosat 8 a t cos ot p t id because u lt lt then a t cosut 10 pt 0 Pe and envelope e t a t by definition 12 e from the mathematical definition the envelope shape is that of the absolute value of cosut This has the shape of a fullwave rectified version of cosut e by looking at it and from considerations of Fourier series analysis the envelope must have a wide bandwidth due to the sharp discontinuities in its shape So the lowpass filter will need to have a bandwidth wide enough to pass at least the first few odd harmonics of the 1 kHz message say a passband extending to at least 10 kHz 2 PRODUCT DEMO
19. to build does in fact approach the ideal for our purposes and one is available as the RECTIFIER in the TIMS UTILITIES module For purposes of comparison a diode detector in the form of DIODE LPF is also available in the same module this will be examined later The desirable characteristics of the lowpass filter will depend upon the frequency components in the envelope of the signal as already discussed We can easily check the performance of the ideal envelope detector in the laboratory by testing it on a variety of signals The actual envelope shape of each signal can be displayed by observing the modulated signal itself with the oscilloscope suitably triggered The output of the envelope detector can be displayed for comparison on the other channel AM envelope For this part of the experiment we will use the generator of Figure 8 and connect its output to the envelope detector of Figure 7 T1 plug in the TUNEABLE LPF module Set it to its widest bandwidth which is about 12 kHz front panel toggle switch to WIDE and TUNE control fully clockwise Adjust its passband gain to about unity To do this you can use a test signal from the AUDIO OSCILLATOR or perhaps the 2 kHz message from the MASTER SIGNALS module message C m t G a t UH te g st signal c t DC voltage 100kHz Figure 8 Generator for AM and DSBSC T2 model the generator of Figures and connect its output to an ideal envelop
20. was of the same amplitude as the wanted DSBSC Would it then have any effect c what if the unwanted DSBSC was ten times the amplitude of the wanted DSBSC Would it then have any effect Explain Q7 what are the differences and similarities between a multiplier and a modulator 20

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