massachusettsinstitut eoftechnology department of electrical
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1. 2 G G y Ox o Egn 3 3dB 2C Z o q But if is much greater than G 2C then 1 D O a ie a a eR The bandwidth is the distance between 3dB points so ay ee or ye Egn 4 2RC RC Lab No 1 12 2 4 2015 Although the approximation made in equation 3 obscures the fact that is not really quite exactly between the two sag frequencies the bandwidth is always 1 RC regardless of the approximation is While the expression p Q T is very useful for an intuitive understanding of what Q means there are other ways of expressing Q that we can use to predict the Q for the parallel tuned circuit If we substitute the right side of equation 2 into the numerator and the rightmost expression for bandwidth from equation 4 into the denominator we can derive the following useful expression C Op R 7 Eqn 5 Thus we have two major considerations in the design of this frequency selective resonant circuit given by equations 2 and 4 above Depending on which circuit elements are easily and practically varied you can see that resonance and bandwidth may be independently adjusted Note that L does not appear in the bandwidth equation but that C occurs in both the resonance equation and the bandwidth equation Directions Build the circuit shown in figure 2 STOP Before connecting the transformer to the 15 volt supply make sure you have removed the connection from the transformer t2. but it will vary with the value of the parasitic series resistance of the inductor caused by the resistance of the fine wire used to make the coil We shall ignore the existence of this parasitic resistance just now Bandwidth is defined as BW Af f y f RE LE Q of the circuit is defined as O BW Note that the resonant With very high resistance approaching infinity in parallel with the reactive elements the bandwidth approaches 0 Hz and the Q approaches infinity Questions Q1 2 Parallel resonant circuits are often presented with the R the L and the C all in parallel However we are driving our resonant circuit from a voltage source with a low source impedance and therefore the resistance must be in series with the two reactive elements Explain what would happen if we placed the resistance in parallel with the reactive elements in this case What is the value of the source resistance of your function generator Q1 3 What is the input impedance that the oscilloscope probe presents to the circuit Usually specified as a resistance in parallel with a capacitance Q1 4 How does it compare with the input impedance that the multimeter would present to the circuit Q1 5 Will it affect the primary circuit of the transformer in the same way as the multimeter would Explain Lab No 1 7 2 4 2015 Q1 6 Review your table of calculated and measured results What combinations of load and source resistances offer the
3. and this causes the inductance to change Thus you may have tuned the transformer to resonance at one frequency and voltage level but at the same frequency with a different voltage level the circuit may no longer be tuned to resonance Check it every time Lab No 1 2 2 4 2015 Experiment 1 O and bandwidth of Parallel tuned circuits NOTE THIS LAB REQUIRES A CHECKOFF FOR EXPERIMENT ONE on Tues Feb 10 Get checkoff during staffed lab hours See course website A FEW LINES ABOUT LAYOUT Layout on your protoboards is very important especially at high frequencies Leads should be kept as short as possible especially signal leads to prevent stray inductance and capacitance from affecting your readings You must follow these directions for building your circuit if your circuit does not meet these standards you will not be checked off until it does 1 Remove the protoboard assembly from your lab kit The four protoboards are screwed to an aluminum plate that is attached to the kit by Velcro GROUNDING THE SHIELD Look at the bottom of the plate Loosen one of the screws and fasten a small piece of black hookup wire under the screw and then cut the wire just long enough so that it will reach the top of the protoboard where it can be plugged into your ground bus Be sure that the anodizing on the aluminum plate is scratched away under the screw so that the wire makes good connection to the plate There is a special reamer tool locate
4. circuits tuned circuits and with RF transmission and demodulation of amplitude modulated AM signals You will also learn to use the Tektronix 2445 and TDS 30XXB series oscilloscopes and the Hewlett Packard 33120B Function Generator AM FM Modulator or the Agilent 33220B Function Generator AM FM Modulator Note that although we have attempted to be relatively thorough in this write up there will certainly be things that you may have to figure out for yourself If you don t know how to do something you would probably benefit from playing around a bit to see if you can figure it out There is very little that you can do with the equipment required for this laboratory that can damage it provided you use common sense However if you are having trouble don t hesitate to ask for help Please DO NOT USE INDIVIDUAL single conductor banana plug to alligator clip leads to connect from the function generator to your circuits These wires are unshielded and unpaired and will pick up stray signals and have uncontrolled stray capacitance and inductance DO USE the BNC bayonet nut connector to EZ Hook or BNC to alligator shielded cables that are available at the stockroom windows Insist on them they were purchased for 6 101 student use Be sure to retune your IF transformer coil slug every time you make a change to the circuit elements and or the signal level The large signal levels we are using tend to saturate the adjustable core in the IF transformer
5. observe that the full sine wave appears there The tank is responding to the stimulus of a half sine by returning its natural response a sine wave When you are making your measurements at 400 Hz please also measure the DC voltage present at the detector output Increase the modulation level to 80 and record the DC voltage again Reduce the level of RF input to the circuit and record any change in DC voltage Questions Q3 1 If the RF signal level at the input to the diode detector is less than 500 mV what will the output of the detector be Lab No 1 18 2 4 2015 Experiment 4 Transmitting AM signals Series Resonant Circuits NOTE PLEASE BRING A PORTABLE AM RADIO TO LAB FOR THIS EXPERIMENT A FEW AM RADIOS WILL BE AVAILABLE AT THE STOCKROOM WINDOW You have built and analyzed much of the circuitry required to amplify bandwidth limit and detect AM radio signals Now it s time to transmit some amplitude modulated RF radio frequency signals We will continue to use 455kHz in most of our work since we have designed our receiving circuits to be sensitive to this frequency This frequency is the same as the 455kHz used in all modern AM radios internally as the Intermediate Frequency IF Most current AM radio design uses the superheterodyne method of receiving where all the signals in the AM band 530kHz to 1 7MHz are converted in the receiver to the IF frequency This allows us to customize most of the amplifying stages in the re
6. parallel resonance where we showed that to achieve a high Q and thus a very narrow bandwidth we would have to use a large capacitor and therefore a small inductor L Since Q is still defined as Q L in this case Q 27f Therefore to achieve a Fortunately our Agilent Function Generators provide both AM and FM modulation and plenty of RF output to drive our antenna If more than one of you is operating at the same time in the lab at the same frequency you may find that you are interfering with one another Therefore you may wish to turn down the output of your function generator to a level that will allow you to receive your own signal but which will prevent your signal from reaching another s receiver It will also be best if those transmitting at the same time locate themselves to distant corners of the lab Obtain a 6 101 loop antenna This is a one foot square wooden form with ten turns of wire wound on it in a single layer flat coil You will also need a trimmer capacitor which is an adjustable capacitor with three legs on it These legs will NOT fit into the protoboards so don t even think of trying it Two of the legs of the capacitor are electrically connected together and to one Lab No 1 20 2 4 2015 plate the third leg is the other plate Please solder short pieces of hook up wire onto two legs and then insert the trimmer into the protoboard DO NOT USE YOUR KIT PROTOBOARD USE A FREESTANDING PROTOBO
7. primary at 455kHz Once again make up this value from a parallel combination of fixed capacitors and a trimmer capacitor Build the receiving antenna into your transistor amplifier as shown in figure 8 Be very careful with the fine wires of the antenna coil You will again need to solder some solid hookup wire to these leads in order to insert them into the protoboard Obtain a piece of double sticky foam tape about Ye square from the stockroom window and stick it down to your protoboard next to the point where the antenna coil connects into the circuit Slide the ferrite rod core into the antenna coil and stick one end of the rod onto the double sticky tape Note that the transformer coil is loose on the core Obtain a wooden toothpick and slide it CAREFULLY between the coil and the ferrite core to keep the coil from sliding down the core 15 V O Pri Sec turns ratio a Antenna Coil 0 1 uF White Red 10 kQ Green Black 12 100 pF trimmer Lab No 1 23 2 4 2015 Figure 8 Resonant antenna antenna coil connected to IF amplifier Return to your transmitting antenna and reconnect the function generator For this experiment we will again use the 455kHz carrier frequency Connect your scope across the secondary of the IF transformer just before the detector diode to monitor the carrier signal strength Adjust the function generator output and watch your scope for indication of a carrier Your transmitting antenna
8. should be about 3 feet away from your receiving antenna at this point With enough drive into your transmitting antenna to provide a visible signal on the scope adjust your trimmer capacitor for a peak If a clear peak in the carrier at the IF transformer primary is not obtainable adjust the value of any fixed capacitors you are using to resonate the antenna coil primary Once again you may find it easier to compare the phase of the function generator output with the phase of the transformer secondary signal in order to locate the maximum Once the capacitor is correctly adjusted remove the toothpick between the coil and the ferrite core and GENTLY slide the coil along the core until you see maximum output on the scope You should readjust the trimmer cap now as moving the coil will change the inductance slightly Interactive adjustments are a fact of life in RF design If you don t have a decent signal level at the primary of your IF transformer you can obtain more gain in the IF amplifier by adjusting the value of Rx The gain of circuits of this type is primarily dependent on the value of the transistor collector current If you replace Rx with a 10kQ potentiometer from your kit in series with a 5 1kQ fixed resistor you will be able to adjust the circuit gain by adjusting the pot This works because Rx is the sole current setting resistor for both transistors which split the current through Rx equally Once you have a large enough si
9. the generator set to 455kHz every time you make a circuit change The cores in these transformers can saturate easily depending on current and voltage levels and this will change the value of the inductance Best to recheck that the transformer primary is resonant at 455kHz every time you make a change in the value of R Then make the calculations required to fill out the Calculated Data section of the table Note that Rip is the value of the load resistor reflected to the primary Ay Vour Vin is the voltage gain This can be calculated from your measured input and output voltages r Rpara is the value of the transistor current generator source resistance ro in parallel with any parasitic resistance Rpara that exists in the transformer and is in parallel with Rip You know the parasitic resistance from Experiment 1 Together these three resistances comprise the conductance G that we used above Lab No 1 13 2 4 2015 to derive the resonance equations To calculate ry Rpara use the measured bandwidth that you get from the infinite load resistance case first line of table 2 and use the bandwidth equation Copy it into the chart for the other values of load resistance Then use r Rpara Rip to calculate the bandwidths for the other cases These calculated bandwidths will probably not be exactly the same as the measured bandwidths in the left hand section of the chart but they should be close Of course the calculated b
10. wave which is its natural response Therefore in previous sections of this lab you could have been overdriving the transistor stages with a large enough sine wave input signal to produce clipping a square wave in the transistor driving the tank However since the output load is a high Q resonant circuit the response to a square wave input will be a sine wave Almost like magic Now this is fine as long as we are talking about unmodulated signals but when we take an amplitude modulated sine wave send it at too high a level into a transistor amplifier and clip the signal well we have just removed the modulation the very thing we are trying to detect Therefore if you do not see any audio sine waves at the output of your detector first make sure you are modulating your carrier and then turn down the carrier amplitude signal generator output until you see the proper audio output from the demodulator A good way to observe this highly recommended is to put your scope probe between the emitters of the transistors and ground The emitter of the left hand transistor is the output of that transistor and the emitter of the right hand transistor is the input of that transistor It s a little easier to observe this on the scope with the modulation turned off Now crank up your input until you see evidence of clipping one half of the sine wave is missing Then move your scope probe to the collector of the right hand transistor and
11. ARD ON THE LAB BENCH OR GET ONE OUT FROM THE STOCKROOM 12 100 pF trimmer L Antenna T 100 Figure 7 Antenna tuning circuit for transmitting AM carrier from function generator Connect the circuit shown above in figure 7 Make sure that the modulation on your function generator is turned off Be sure to use shielded cable BNC to E Z hook or BNC to alligator clips between the function generator and the protoboard Look on the frame of the loop to find where the inductance of the loop is marked and calculate the required capacitance needed to achieve 1 resonance at 540kHz NOT 455kHz _ je 274 LC capacitors from your kit or from those available from the stockroom window and placing them in parallel with the trimmer cap Adjust the function generator to full output 20 volts peak to peak at 540 kHz not 455kHz Q4 1 Why does the function generator amplitude display show a voltage value that is incorrect Make up this capacitance by selecting fixed Connect one channel of your scope across the 10 Q series current measuring resistor making sure that the ground clip is connected to the side of the resistor that is connected to the signal generator ground The scope ground clip is permanently connected to electrical ground Adjust the scope amplitude control for the channel across the resistor as required to see a signal the signal level will be very low until resonance is achieved We are trying to obtain
12. Hz modulating frequency at 50 modulation consult the function generator manual a copy is available from your instructor Put your scope across the detector load resistor and observe the detected signal Record the output voltage and then increase the modulating frequency to 1kHz 3 kHz and 5kHz Record the level of audio output voltage for all four of these test frequencies If the output voltage at 5 kHz is not 3 dB down from the voltage recorded at 400 Hz then you will need to increase Cr until the 5kHz signal is 3dB down If you have a great deal of trouble getting the response at 5kHz to hold up you may need to choose a different R in order to get a wider bandwidth from the transformer especially if you find yourself using smaller and smaller capacitors and you are starting to see a lot of carrier ripple in your audio output Record the values of these two circuit elements If the output is more than 3dB down at 5kHz then you will have to start over with a smaller value of Cr and then add capacitance as necessary NOTE At this point you may not be able to see the modulating audio frequency at the output of the detector You may just see a distorted ghost of a waveform This is due toa very important characteristic of high lightly or under damped resonant circuits namely when you stimulate a high Q resonant circuit with a pulse a square wave a part of a sine wave most anything the resonant circuit will return a sine
13. MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE 6 101 Introductory Analog Electronics Laboratory Spring 2015 Laboratory No 1 READING ASSIGNMENT Review 6 002 notes on resonance and read the text in this lab You should read the documents The ABC s of Probes and The XYZ s of Oscilloscopes The links are on the course website under the tab Reference Many of you will be using our the Tektronix TDS30XXB Oscilloscopes The user manual are also on the course website Note that the TDS30XXB series are digital scopes with its inherent advantages and disadvantages For some applications a better scope for is the Agilent MSO X 3035A some of which are in the 6 101 lab These are state of the art 500Mhz scopes literally straight from the production line OVERVIEW This is the first of six labs that will occupy you for the first half of the term This one is probably the longest but it is also the most cookbook like of all the labs You will normally receive a new lab on Thursday at 2 30 pm in class because this lab is longer and you have an extra couple of days to complete it Each subsequent lab will deal with topics that will be presented in class and each lab will become more design oriented and less cookbooky as time passes In other words we want to take you from training wheels to bicycle racing In Experiment 1 we start out to examine the effects of resonance especially ba
14. acitance will be divided by the square of transformer turns ratio and reflected back to the primary where it will appear in parallel with the capacitor built into the transformer This will not significantly change the value of the Lab No 1 5 2 4 2015 190 pF primary capacitance since 100 pF a 16 is only 6 25 pF However the Agilent multimeter s freguency response is NOT specified above 300 kHz so we have no idea what the numbers on the readout mean at 455kHz Moral of this story always consider the effect of connecting test equipment or other external stuff into your circuit 4 Now slowly change the frequency of the function generator upwards and observe that the amplitude of the waveform on the scope is decreasing Continue to increase the frequency until the peak to peak value of the waveform has decreased to 0 707 of the value you recorded in step 3 This is fy or the high frequency 3dB point You can make this job easy by setting your adjustable scope cursors to 707 X 600 mV 425 mV and then just changing the signal generator frequency until the waveform just fits in between the two cursors 5 Now slowly change the frequency of the function generator downwards and observe that the amplitude of the waveform on the scope is increasing and then decreasing again as it passes through resonance Continue to decrease the frequency until the peak to peak value of the waveform has decreased to 0 707 of the value you recorded i
15. andwidth for the infinite load resistor case will be the same as the measured bandwidth in order to calculate the value of r Rpara Note Your DMM measures AC voltage in RMS volts your oscilloscope reads in peak to peak volts In order to get an accurate gain calculation you will need to convert one kind of voltage unit to match the other Your function generator can be set to read either peak to peak or RMS volts Questions Q2 2 What value of load resistance offers the widest bandwidth The narrowest bandwidth Q2 3 What is the value of load resistance that comes closest to giving the bandwidth discussed above as appropriate for AM reception in the USA Q2 4 What are the high and low 3dB frequencies you obtained with this value of R1 Q2 5 What would happen if we decided to vary C instead of L in order to tune this parallel tuned circuit to 455kHz Q2 6 Why do you think that the gain decreases as the value of load resistance decreases Lab No 1 14 2 4 2015 Vin P P Lab No 1 TABLE 2 RESONANCE DATA USING CASCODE AMPLIFIER AND CENTER TAP C 190 pF a 4 1 MEASURED DATA 455 kHz source Vout P P RL 2 0 V p p Open ckt 2 0 Vp p 10 000Q 2 0Vp p 5 1000 2 0Vp p 1 0000 fu kHz fi kHz BW kHz O t BW o Rpara Rtpri CALCULATED DATA Fo Reara Repri BW kHz H kHz 2 4 2015 f KHz Q f BW Av Experiment 3 Detector for Amplitude Modulated Signals Note This detector wil
16. carrier wave approximate the much lower audio frequency again the spacing here is exaggerated for clarity Note how there appears to be two complete audio waveforms in figure 6a we can dispense with one of them and that is exactly what the diode in the detector circuit of figure 6b does And the remainder of the circuit is simplicity itself a low pass filter Of course it s intuitive that to remove the carrier we need to filter out the high frequencies and save the low audio frequencies Lab No 1 16 2 4 2015 Y Cr A Figure 6a The carrier peaks outline the audio freguency Figure 6b AM detector circuit Use a 1N914 or 1N4148 for D Until now we have been substituting a simple load resistor R for the detector circuit and you should have learned that the value of R is reflected to the primary of the transformer and is the primary element in determining the circuit Q and therefore the bandwidth Bandwidth control is very important in AM to reject unwanted modulation from adjacent stations Now we must determine a method of finding the input resistance to the detector so that we can control the bandwidth of the modulated signal When an AC signal is rectified and then used to charge a capacitor we have produced a fairly constant DC voltage across the storage device the capacitor There will be some slight ripple on top of this DC voltage due to the tendency of the capacitor to discharge into the resistor but let s ignore that
17. ceiver to perform well at only this frequency as you have just done in Experiment 2 Normally one would not choose to broadcast using 455kHz as it could not be received on normal AM radios and is the same as the standard IF frequency and so would cause interference However our transmissions will be limited to 10 feet or so and also will be contained within this building due to the shielding built into the building for frequencies in the AM band Antennas for transmission or reception fall into two broad categories 1 physically resonant the antenna is 1 4 Vb 3 4 etc of a wavelength depending on whether the antenna is end fed or center fed and 2 physically small compared to one wavelength i e less than 0 14 Resonant antennae are useful at higher frequencies where the wavelengths are shorter than they are in the AM band An antenna resonant at 455kHz would have to be almost 200 feet long Therefore we are using a physically small antenna A physically resonant antenna looks very close to a pure resistance when it is driven as a transmitting antenna however a small antenna may look inductive or capacitive depending on the frequency Our antenna looks inductive at 455kHz therefore in order to drive a useful amount of current into the antenna we will have to series resonate the antenna with a series capacitor in order to cancel out the impedance due to the inductance Series Resonance Analysis Series resonant circuit analysis is ident
18. d as a differential amplifier and which we will study in more detail later in the course The cascode connection is a common collector emitter follower amplifier that drives a common base amplifier This circuit is very useful especially at high frequencies because it prevents the unwanted multiplication of the transistor collector base capacitance by the stage gain the dreaded Miller effect when the common emitter transistor amplifier is used This effect will be studied later in the term 15 V Pri Sec turns ratio a 4 1 4 Ri Your 500 Inside FG 0 1 uF O 15V Figure 2 Cascode amplifier circuit driving resonant IF transformer In this new circuit you should understand that the transistor collector terminal is a pretty good current source with a fairly high source resistance whose value is dependent on the transistor biasing conditions Let s simplify figure 2 so that we can derive properly some of the resonance equations that were listed in Expt 1 We will just concern ourselves with the second transistor and the resonant transformer circuit The first transistor serves as an emitter follower and provides a relatively high input impedance and a low output impedance to drive the low emitter input impedance of the common base transistor that drives the resonant tank You can tell that the first transistor is an emitter follower or common collector configuration because the collector is connected directl
19. d in the lab on a chain near the curve tracer on the metal topped bench that will quickly and cleanly remove the anodizing from the countersunk edges of the screw hole Please use it ALWAYS connect this wire to your ground bus In this way capacitive coupling will occur between the little metal protoboard receptacles under each group of five holes and the metal plate and the capacitive coupling between adjacent receptacles will be minimized This metal plate also provides some shielding from the many transmitting antennas on top of the Prudential building located within eyeshot of your lab space See the Joe Sousa RF interference demonstration mounted just to the left of the big bank of lockers in the 34 600 corridor If coupling between receptacles is still a problem try spacing out the connections so that an unused receptacle lies between two used ones Then the unused receptacle can be grounded to provide a shielding effect between the two receptacles that are in use When working on your protoboard turn the set of boards so that the SHORT side is towards you and so that the long deep grooves in the four protoboards are parallel to the front edge of the bench Start wiring using one of the four protoboards Put the ground bus on the 2 row from the bottom of the protoboard Reserve the 1 row for your negative supply bus Please note that these rows are not continuous they are disconnected in the center where the center screw co
20. el leads All these stray or parasitic circuit elements aren t on the schematic but they have a huge influence on circuit behavior especially at high frequencies above 100 kHz IC s and some transistors and JFETs should be mounted so that they straddle the deep groove in the protoboards 6 When you build larger more complex circuits you should start in the upper left corner of the top protoboard wire from left to right until you run out of space then continue your circuit from the left side of the next lower protoboard etc If you run into problems with circuits on the first protoboard interfering with circuits on the second protoboard you may need to leave an unused protoboard between the two boards in use 7 Run your power and ground leads from the lab kit binding posts to your protoboard Try to keep them as short as possible and twist all three of them together to form a cable Use red for positive black for ground and pick a nice color for the negative voltage Bypass the positive and negative leads to ground with 0 1uF 50 volt capacitors at the point where they enter the protoboard 8 Neatness counts Locate the 455kHz Radio Frequency RF transformer in the parts kit and also a short purple PLASTIC adjustment screwdriver to adjust the coil slug Build the circuit shown in figure one but please note that you will not need a capacitor it is built into the transformer and is wired across in parallel with the full prima
21. eted use some of the equations below to enter the data in the calculated data section of the table Please remember that the load resistor on the secondary is reflected to the primary according to the turns ratio That is to say the secondary resistance appears in parallel with the primary but multiplied by the turns ratio squared a This value is Rip in Table 1 on page 8 Rey is the parallel combination of the secondary load reflected to the primary in parallel with the source resistance The fact that the calculated and the measured bandwidths are different is explained by the parasitic resistances in the coil and the capacitor which we are modeling as a resistance in parallel with Re The primary losses in this circuit are due to the coil wire resistance The following equations will be useful in understanding the behavior of parallel resonant circuits and in calculating values for your table They will be derived in a later section of this lab Lab No 1 6 2 4 2015 1 Resonance occurs when C T the magnitudes of the impedances are equal Due to their Oo equal but opposite locations on the imaginary axis these impedances cancel each other for ideal circuit elements only leaving only the resistive elements in the circuit at resonance 1 1 Solving for the resonant frequency o or g le OE e o TEE frequency does not depend on the values of any resistances in parallel with both the L and the C
22. gnal at the primary of the IF transformer move the scope leads across R Vout With the modulation turned off at the function generator the only signal you should see across R will be the DC voltage due to the rectification of the carrier This value will vary depending on your signal strength If you now program your function generator to produce a 400 Hz modulating frequency at 80 modulation you should see the 400Hz audio signal riding on top of the DC voltage at your detector output While keeping the carrier frequency output level constant and also the distance between the transmitting and receiving antennae constant in other words don t move anything program in the following audio frequencies 400 Hz 1000 Hz 3000 Hz 5 000 Hz all at 50 modulation Record the output levels as observed on your oscilloscope If the output at 5000 Hz relative to the 400 Hz output is no longer down by 3dB you will have to adjust either the value of your capacitor Cr to correct this or if the bandwidth is not correct remember that R determines the bandwidth of the circuit you will need to change R and take all the measurements above again Be sure not to move your antenna or your receiver while you are making these measurements Questions Q5 1 In a previous experiment you carefully adjusted the value of the detector equivalent resistance to tailor the bandwidth of the IF transformer so that it would just accept 455kHz 5000 Hz Now you
23. have added a second tuned circuit to your receiver If this new tuned circuit were to have exactly the same Q and bandwidth as the first tuned circuit what would happen to the overall bandwidth of the receiver Lab No 1 24 2 4 2015 5 2 What can you say about the steepness of the bandwidth response curve with two tuned circuits A bandwidth response curve is just the inverse of the curve in figure 4 except that the Y axis represents the output voltage Q5 3 For the measurements you made of the audio output in the paragraph above record the output voltage vs audio output frequency in a table so that you can compare these values with the values from the single tuned circuit of Experiment 3 Q5 4 Record the value of Rx that you ended up using Q5 5 By now you should have noticed that the output signal level will vary greatly depending on the distance of the receiving antenna from that of the transmitting antenna and also with the power input to the transmitting antenna You have also noticed that there is a DC voltage produced across the detector load resistance that is proportional to the received carrier signal strength Given that you have also observed that the gain of the IF amplifier can be adjusted by varying Rx in order to vary the transistor collector currents can you think of a way that the carrier proportional DC voltage can be used to automatically adjust the gain of the IF amplifier Lab No 1 25 2 4 2015
24. he high frequency audio response of the complete transmit receive system Lab No 1 1 2 4 2015 Then we go on in Experiment 5 to substitute a receiving antenna for the function generator which also adds a second tuned circuit which if it is tuned to the same center frequency as the transformer is tuned will give us a two resonant circuit receiver and the combined bandwidth of the two resonant circuits will reduce the audio response around 5kHz even more the Q of the ferrite rod coil trimmer cap arrangement is not as high as the Q of the transformer therefore the two resonance curves are not the same shape The idea is to measure a few high audio frequencies in Experiment 3 say 400 1000 3000 5000 Hz and then repeat those measurements in Experiment 5 and compare them to see how the addition of the second tuned circuit affects the audio response AM broadcasting in the USA is limited to 5 kHz due to our 10 kHz station spacing in many other parts of the world the high frequency limit is 4 5 kHz and the station spacing on the dial is 9 kHz OBJECTIVE In this laboratory you will transmit an AM radio signal to a rudimentary AM receiver that you will build This is one of many ways to achieve wireless communication and this experience will help you make a decision on what kind of design project to undertake during the second half of the term The objective of this laboratory is to gain familiarity with practical series and parallel resonant
25. ical to that of parallel resonant circuit analysis except that we shall use impedance concepts rather than admittance notation The bandwidth curve admittance plot of figure 4 can be converted into the impedance curve for the series resonant circuit by replacing the Y s with Z s For a simple series R L C circuit driven by a perfectly resistanceless voltage source v 1 R jou or aC J I p i Eqn 5 R dar e WC 1 PRES The circuit is said to be resonant when wl and the resonant frequency is given by aC Lab No 1 19 2 4 2015 1 1 w or i Egn 6 VLC 27v LC The 3 dB points of equation 5 above will occur when real equals imaginary in the denominator 0 707 1 71 1 414 Solving for wsgg by setting the real part of the denominator equal to the imaginary part in Eqn 5 1 R 0 L Orage This is rewritten as Using the quadratic solution 2 R R Ozi m a o Egn 7 But if o is much greater than R 2L 2 then R Dag O 2L The bandwidth is the distance between 3dB points so e or ki gt Egn 8 2L L Although the approximation made in equation 7 obscures the fact that is not really quite exactly between the two sygp frequencies the bandwidth is always R L regardless of the approximation 2af R L high Q in a series resonant circuit we will have to use a large inductor and therefore a small capacitor Contrast this with the case of
26. l be connected to the IF transformer secondary in place of the load resistor that was used in the previous experiment Now we have a useful circuit that will both amplify and select a narrow band of desired frequencies Next we need to prepare a circuit that will demodulate or detect an AM signal The expression for an amplitude modulated signal is KA v COS t boso t cosa O x where c subscripts refer to the carrier frequency in this case it s 455kHz and m subscripts refer to the modulating frequency which is an audio frequency between 50Hz and 5kHz K is a scaling factor By inspecting this equation we can see that an AM modulated signal contains three frequencies the carrier frequency and both the sum and the difference of the carrier frequency and the audio signal When the audio is turned off the carrier is the only signal Figure 5a shows a sketch of an AM modulated signal with the carrier frequency exaggerated normally the carrier frequency would be so much larger than the audio frequency that the individual carrier waveforms would blend together Figure 5b shows the frequency spectrum of the amplitude modulated V We Wm W Wet wm signal Figure 5a Amplitude modulated carrier Figure 5b Frequencies in modulated carrier wave not to scale In order to demodulate and recapture the audio we need to remove the carrier If we examine figure 6a we can see more clearly how the peaks of the
27. l results for this experiment in Table 1 2 Starting with the 10kQ series resistor in the circuit and no load resistor on the secondary adjust your function generator to provide about 600 mV peak to peak at 455kHz measured across the transformer secondary While observing the voltage at the output with your oscilloscope slowly and carefully adjust your transformer coil slug with the plastic screwdriver NO METAL SCREWDRIVERS until the output peaks DO NOT FORCE THE SLUG IT WILL HIT BOTTOM AND THEN FRACTURE INTO PIECES You have just adjusted trimmed the value of the transformer primary inductance so that it resonates exactly with the built in capacitor at 455kHz NOTE it may be easier to monitor both the input and output voltages paying attention to the phase shift between the two voltages When they are both exactly in phase or exactly out of phase by 180 degrees depends on which secondary terminal is grounded then resonance is achieved since the capacitive reactance has cancelled the inductive reactance leaving only resistance 3 Set your oscilloscope to measure voltage using the built in cursors and adjust the function generator output slightly so that the waveform on the scope is exactly 600 mV peak to peak You may be tempted to hook up your Agilent 34401A multimeter to help you make the following measurements but please consider that the input impedance of the multimeter is 1 MQ 2 in parallel with 100 pF This shunt cap
28. maximum current into this series resonant circuit so your main task will be to monitor the voltage across the 10 Q resistor as you tune the circuit You may have to add or subtract some of the fixed capacitors that you have installed but when the combined value of the fixed capacitors plus the trimmer is correct you will be able to tune the trimmer and observe the voltage across the 10 Q resistor pass through a maximum Once again it may be easier to monitor the output voltage of the function generator on one scope channel and the voltage across the resistor on a second channel and make your adjustment until the phase angle between the two waveforms is either 0 or 180 degrees depending When the trimmer is tuned to produce this maximum you have achieved series resonance and are driving maximum current Lab No 1 21 2 4 2015 into the antenna Once resonance is achieved you may remove or short out the 10 resistor which will increase the current into the antenna somewhat and lower the bandwidth as well Now adjust your function generator so that your carrier is AM modulated with a 400Hz modulating frequency at 100 modulation Turn on your AM radio and tune it to 540kHz while holding it near your transmitting antenna You should clearly hear the modulating tone in your AM radio Change the tone to different frequencies and listen again You are now broadcasting AM radio Move your radio about the lab and see how far away from your anten
29. mes through You will need to jumper the left half of the bus to the right half if you need the whole width of the board Going upwards from the 2 row past the vertical columns of five holes each all connected together past the groove the next set of vertical columns we come to two more rows You should use the top or 4 row for your positive supply bus and the 3 row may be used for another ground bus or possibly a signal bus in certain cases HOWEVER using dual ground busses may Lab No 1 3 2 4 2015 cause ground loops and thus the second ground bus should be used sparingly and never connected to the first lower ground bus except at ONE point 5 You should strive to copy the schematics we give you as closely as possible in your physical layout on the protoboards Inputs at the left grounds at the bottom positive supply highest negative supply lowest We draw the circuits as clearly and logically as possible Inputs should always be kept away from outputs to avoid undesirable negative or positive feedback Leads should always be kept as short as possible Only when you are trying various values of capacitors or resistors etc should you use these parts with the long leads that they come with When you install such parts permanently be sure to clip the leads short before installing them on the board Long leads have extra inductance at high frequencies and long parallel leads have more capacitance between them than do short parall
30. much the same way an AM radio does You will be using what is known asa loopstick receiving antenna a ferrite rod with an antenna coil transformer wound around it In parallel with the large primary winding receiving antenna you will again place a capacitor to resonate with the inductor and therefore provide sensitivity to only one frequency ata time If this were a real radio instead of using a combination of fixed capacitor and trimmer for this purpose you would be using a varactor diode or a variable capacitor that would have a huge adjustable range so that you could tune the whole AM band The inductor you will be using has a primary inductance of about 723uH and a turns ratio of 40 1 primary to secondary This turns ratio allows the high impedance primary circuit to be coupled to the low impedance input of the transistor stage The step down transformer reduces the source impedance of the coil to nearly zero to avoid losses when driving a low impedance transistor input Another way of looking at this is that the transformer steps up the low value of input impedance of the transistor amplifier so that when it is reflected over to the primary it is large enough to prevent it from lowering the bandwidth of the resonant primary circuit This receiving antenna has nulls off the ends of the rod and is most sensitive in the direction perpendicular to the rod s long dimension Calculate the value of capacitance you will need to resonate the
31. n step 3 This is f or the low frequency 3dB point 6 Now repeat the above procedure first with the selection of load resistors indicated in Table 1 and then replace the series resistor with the larger values indicated in Table 1 again with the same selection of load resistors Notice that as the series resistor is increased and as the load resistor is also increased the sharpness of the tuning increases and the bandwidth decreases the 3dB points are much closer to the resonant frequency of 455kHz The measure of the sharpness of this resonant peak is called Q and its value is infinite for infinite series resistance Q1 1 Would infinite series resistance work Why but in the real world is limited by parasitic resistance and such nasty practicalities as load resistances You will have to recheck your output reference levels at 455kHz each time you change the value of either the Rsource or the value of Ri Be sure to set your function generator back to 455kHz each time you set your output reference levels When you get to the measurements using the 1 MQ series resistor and the smaller load resistors you will have to settle for a much lower reference voltage at 455kHz due to the large drop across the 1 MQ resistor and the loading effect of the load resistors You should be able to achieve about 80mV peak to peak at 455kHz measured across the secondary under the worst case conditions 7 When the measurements for Table 1 are compl
32. na you can pick up the signal You will achieve maximum range with the carrier amplitude set at maximum output and with the 10 resistor shorted out Rotating the loop antenna will affect its output The output is greater perpendicular to the edge of the loop and lower perpendicular to the plane of the loop When you are through listening to your test tones over 540kHz tune your function generator back to 455kHz Retune your antenna by adjusting the value of the trimmer and or the fixed capacitors so that the current in the antenna is once again a maximum Now disconnect your antenna while you build the circuit for experiment 5 Questions Q4 2 With the 10 resistor shorted out what is the resistance in the series resonant circuit Q4 3 Can this resistance be adjusted or reduced to zero Q4 4 Calculate the bandwidth of this series resonant circuit Q4 5 What would be the effect on the transmitted signal if the bandwidth of the transmitter were too small Q too high Q4 6 What would happen if we reversed the scope leads that are connected across the 10 Q resistor Q4 7 Calculate the length of one wavelength at 540kHz Experiment 5 Receiving the signal from your transmitting antenna In this last experiment we will make some changes to the transistor circuit you built in experiment 2 We will add another parallel tuned circuit as part of a receiving antenna so that you can pick up Lab No 1 22 2 4 2015 what you transmit
33. ndwidth using just a 455 kHz transformer with built in parallel capacitor the function generator and resistors One resistor will transform our function generator into a current source the other resistor will be used to control the bandwidth of the parallel tuned circuit Then we progress in Experiment 2 to driving the transformer using a more real world source a transistor which has its own unique value of source resistance and is a real current source rather than a converted voltage source We are still using a simple load resistor on the transformer secondary in order to control bandwidth the trick here is that the source resistance of the transistor is a new factor that also affects bandwidth along with the load resistor on the secondary Then in Experiment 3 we replace the load resistor with the diode detector RF filter load resistor combination and we study how the diode changes the effective value of the load resistor and we study how the capacitor can affect the high frequency audio response around 5 kHz as well as how the bandwidth adjustment can affect the high frequency audio response around 5 kHz due to changing the value of the load resistor which should be the main adjustor of the audio bandwidth In Experiment 4 we take a look at a simple method of transmitting AM modulation that also gives us a Chance to study series resonant circuit behavior The bandwidth of the series resonant circuit can also have an effect on t
34. o ground that ou used in Experiment 1 Otherwise you will apply the full power supply across the primary and melt the fine wires in the transformer and ruin it Please note that you are now going to drive the transformer from the center tap Connect your function generator as shown at the left of the schematic so that the output of the generator is connected to the input of the transistor through the coupling DC blocking capacitor The two 10Q resistors in parallel in combination with the 50Q source resistance of the signal generator form a voltage divider to reduce the output voltage enough to prevent overloading this high gain stage Due to the presence of this voltage divider you cannot rely on the function generator readout to measure Vip Use the oscilloscope to measure Vin The function generator is only accurate for 500 loads when set to the 500 setting and for loads larger than 1kO when set to the High Z setting Put your oscilloscope probe across the transformer secondary and adjust your input voltage to produce an output voltage of 2 0 volts peak to peak with R Retune the transformer for maximum output when your input frequency is exactly 455kHz Now take the measurements required to fill in the Measured Data section of Table 2 You will have to readjust your input voltage at 455kHz each time you change the load resistor in order to maintain the 2 0 V at the output Also be sure to retune your transformer with
35. re NOT equal and the load will have a net inductive or capacitive admittance in parallel that will increase the net value of admittance and thus decrease the output voltage Just how fast the total load admittance increases from the peak value determines the sharpness of the tuning often called the selectivity of the circuit This is a desirable quality of these circuits for selectivity allows us to tune to only the station we want and to exclude adjacent stations that would otherwise cause interference Amplitude Modulated AM stations in the USA have a maximum bandwidth of 5kHz around the carrier frequency so in this case we would only be interested in passing frequencies of 450kHz to 460kHz and excluding the rest 4 5 kHz in Europe and elsewhere Lab No 1 11 2 4 2015 The bandwidth of a circuit is defined as the difference between the frequencies at which the W3db Wo W3db i response is down 3 dB dB 20l0g1oV2 V A curve of Y G j wC 1 mL is shown in figure 4 Figure 4 Plot of Admittance vs angular frequency showing bandwidth The 3 dB points of equation 1 above will occur when real equals imaginary in the denominator a 0 707 1 jl 1 414 Solving for o3j We set the magnitude of the real part of the denominator in Eqn 1 equal to the magnitude of the imaginary part 1 G gC Ozap L G 2 2 34B To Osan o 0 o This is rewritten as Using the quadratic solution
36. ripple just now Our task is to determine an input resistance looking into the detector just before the diode let s call it Re for equivalent We ll calculate this resistance by assuming that the DC power dissipated in the load R is equal to the AC power delivered by the transformer carrier signal into Reg Assuming that Cr charges up to the peak value of the carrier voltage then V 2 Pye at R The ac power dissipated by the transformer source in the equivalent resistance of the detector is Vy lr R 2R eq eq If we equate the input power with the output power then it is easy to see that Reg R 2 Therefore we need to choose R first as it controls the bandwidth of the tuned circuit Choose a value for R that will give a bandwidth of 10kHz 5kHz around the 455kHz carrier frequency as measured across the IF transformer primary Next we could choose Cr from what we know about low pass filters However in this case we are not sure what kind of source resistance the Lab No 1 17 2 4 2015 transformer secondary and the diode provide If we could easily estimate or measure these values then we could quickly design the low pass filter Instead we will design the filter empirically by first trying a value for Cr equal to 0 01 uF and then modulating the carrier with 400 Hz at 50 modulation To do this keep your function generator carrier frequency at 455kHz and then turn on the AM modulation function and adjust for a 400
37. ry You should connect the ground terminal connected to the can which is also a shield from outside interference to the grounded side of the function generator and your scope ground clip should also be connected to the same ground You will make a series of 15 measurements using various load and series input resistances and will enter these measurements into Table 1 Then you will make some calculations for the rest of the table and then we ll ask you to draw conclusions about these circuits by answering some questions Keep your hands as far away from the transformer assembly as you can when making adjustments and measurements on this circuit The stray capacity from your hands will affect your readings Also please be aware that the long protoboard tracks along the top and bottom of the protoboards viewed with the short side of the kit facing you are not continuous They are divided into two sections at the screw in the middle of the long side Lab No 1 4 2 4 2015 Pri Sec turns ratio 4 1 PRI 3 pins Rseries Vg Function Generator Po Pe Board A pri sec Figure 1 Circuit for parallel resonance Experiment 1 1 You should connect your oscilloscope across the output secondary of the IF transformer Connect one side of the secondary to the same part of the circuit that the Function Generator FG ground is connected Connect your scope ground clip to the same ground point Record al
38. widest bandwidth The highest Q The lowest bandwidth The lowest Q Q1 7 Do all of your measured and calculated values of bandwidth and Q agree If not make a list of the differences and explain why they occur Why does the error get worse as the value of the resistor in series with the function generator gets larger for the case with infinite load resistance Q1 8 Calculate the value of the parasitic resistance associated with the transformer from the data you took using the 1 Megohm source resistance and the infinite R Lab No 1 8 2 4 2015 R SERIES 10 000 10 000 10 000 10 000 100 000 100 000 100 000 100 000 1 Meg Q 1 Meg Q 1 Meg Q 1 Meg Q Lab No 1 MEASURED DATA 455 kHz source R LOAD Open circuit 10 000 Q 5 1000 1 000 Q Open circuit 10 000 Q 5 100 Q 1 000 Q Open circuit 10 000 Q 5 100 Q 1 000 Q fu kHz fu kHz BW kHz Q f BW Rtpri CALCULATED DATA Rett BW kHz 2 4 2015 fu kHz TABLE 1 RESONANCE DATA USING FG AND SERIES RESISTOR C 190 pF a 4 1 f kHz Q f BW Experiment 2 O and bandwidth of Parallel tuned circuits driven by transistor stage Next we will repeat some of the previous measurements and calculations using a real world circuit The circuit in figure two below is a version of the long tailed pair known as the cascode connection The long tailed pair is a fundamental circuit that can also be use
39. y to the DC supply Vcc which is an AC ground You can tell that the second transistor is a common base configuration because the base is connected to ground through a capacitor Q 2 1 What is the reactance impedance of this capacitor at the 455kHz frequency we are using Lab No 1 10 2 4 2015 Figure 3a shows the tuned transformer driven by the transistor current source and figure 3b shows the same circuit with the secondary resistance multiplied by the primary secondary turns ratio squared and referred to the primary and labeled G for conductance to facilitate a simpler mathematical analysis Pri Sec turns ratio a 4 1 LOAD o L y Figure 3a Tuned Load on IF amplifier Figure 3b Secondary Load referred to Primary Now we will use admittance notation to solve for the resonance equations Please remember that we are adjusting the admittance of the inductor using the tuning slug so that it just cancels the admittance of the capacitor at 455kHz so that the load on the current generator looks like a pure conductance From figure 3b 1 vera iz si or JoL V Eqn 1 G fac 3 oL eee 1 ae Ai The circuit is said to be resonant when Oe and the resonant frequency is given by Oo A or p Eqn 2 274 LC So we see that L and C must have values that will make f 455kHz and that fo does not depend on the value of G 1 R However at frequencies higher or lower than f the values of 1 L and C a
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