, 2:15 (+ 1 hr optional) Lab 3-mod: Diode Circuits Reading: Problems: Finish Chapter 1, including P ower in reactive circuits (pp 33-35) Appendix E Problems in text. Additional Exercises 7,8. FEBRUARY 2002 45 min., total of 3 subparts 15 min. 3-1. LC Resonant Circuit Response to Sinusoid (10 mh inductor is a grey cylinder, faintly 3 labelled 103J : 10 X 10 microhenries.) Figure L3.1: LC parallel resonant circuit Construct the parallel resonant circuit shown above. Drive it with a sine wave, varying the frequency through a range that includes what you calculate to be the circuit s resonant frequency. Compare the resonant frequency that you observe with the one you calculated. (The circuit attenuates the signal considerably, even at its resonant frequency; the L is not perfectly efficient, but instead includes some series resistance.)
L3 2 Lab 3-mod: Diode Circuits L3 2 Estimate the circuit s Q ( quality factor, a term whose name apparently reflects the use of resonant circuits in radio tuners, where high selectivity is good): Q is defined as follows: Q f resonance/delta-f where delta-f represents the width of the resonance peak between its half-power or -3dB points: Figure L3.2: Y ou can measure Q, by getting precise δf measure, with DVM Y ou can make a very good measurement of Q if you use a frequency counter to reveal the small change in frequency between the points, below and above f resonance, where output amplitude is down 3dB. If you re energetic and curious, you can look at the effect on Q of substituting a 10k resistor for the 100k. Y ou ll notice that the amplitude out increases, with this reduced R (V OUT /V IN, theoretically 1 at resonance, never achieves that value); but Q degrades. As usual, you re obliged to trade away one desirable trait to get another. But good Q is likely to be much more important than large amplitude; an amplifier can solve the problem of low amplitude. A Pretty Sweep Use the function-generator s sweep feature to show you a scope display of amplitude-out versus frequency. (See Lab 2 notes, if you need some advice on how to do this trick.) When you succeed in getting such a display of frequency response, try to explain why the display grows funny wiggles on one side of resonance as you increase the sweep rate. Clue: the funny wiggles appear on the side after the circuit has already been driven into resonant oscillation; the function generator there is driving an oscillating circuit. 1 15 min. Finding F ourier Components of a Square W ave This resonant circuit can serve as a F ourier Analyzer: the circuit s response measures the amount of 16 khz (approx.) present in an input waveform. Try driving the circuit with a square wave at the resonant frequency; note the amplitude of the (sine wave) response. Now gradually lower the driving frequency until you get another peak response (it should occur at 1/3 the resonant frequency) and check the amplitude (it should be 1/3 the amplitude of the fundamental response). With some care you can verify the amplitude and frequency of the first five or six terms of the F ourier series. 1. The W avetek 27XT DVM, for example, includes such a frequency counter.
L3 3 Lab 3-mod: Diode Circuits L3 3 Here is a reminder of the F ourier series for a square wave: Figure L3.3: F ourier series for square wave Classier: Frequency Spectrum Display If you sweep the square wave input to your 16kHz-detector, you get a sort of inverse frequency spectrum: you should see a big bump at f resonance, a smaller bump at 1/3 f resonance, and so on. 15 min. Ringing Now try driving the circuit with a low-frequency square wave: try 20 Hz. Y ou should see a brief output in response to each edge of the input square wave. If you look closely at this output, you can see that it is a decaying sine wave. (If you find the display dim, increase the square wave frequency to around 100 Hz.) What is the frequency of this sine wave? (No surprise, here.) Why does it decay? Does it appear to decay exponentially? Y ou will see such a response of an LC circuit to a step input whenever you happen to look at a square wave with an improperly grounded scope probe: when you fail to ground the probe close to the point you are probing, you force a ground current to flow through a long (inductive) path. Stray inductance and capacitance form a resonant circuit that produces ugly ringing. Y ou might look for this effect now, if you are curious; or you might just wait for the day (almost sure to come) when you run into this effect inadvertently. 15 min. 3-2. Half-wave Rectifier Figure L3.4: Half-wave rectifier Construct a half-wave rectifier circuit with a 6.3V ac (rms) transformer and a 1N914 diode, as in the figure above. Connect a 2.2k load, and look at the output on the scope. Is it what you expect? P olarity? Why is V peak > 6.3V? (Don t be troubled if V peak is a bit more than
L3 4 Lab 3-mod: Diode Circuits L3 4 6.3V 2: the transformer designers want to make sure your power supply gets at least what s advertised, even under heavy load; you re loading it very lightly.) 20 min. 3-3. Full-wave Bridge Rectifier Figure L3.5: Full-wave bridge Now construct a full-wave bridge circuit, as above. Be careful about polarities the band on the diode indicates cathode, as in the figure. Look at the output waveform (but don t attempt to look at the input the signal across the transformer s secondary with the scope s other channel at the same time; this would require connecting the second ground lead of the scope to one side of the secondary. What disaster would that cause?). Does it make sense? Why is the peak amplitude less than in the last circuit? How much should it be? What would happen if you were to reverse any one of the four diodes? (Don t try it!). Don t be too gravely alarmed if you find yourself burning out diodes in this experiment. When a diode fails, does it usually fail open or closed? Do you see why diodes in this circuit usually fail in pairs in a touching sort of suicide pact? Look at the region of the output waveform that is near zero volts. Why are there flat regions? Measure their duration, and explain. 25 min., total 10 min. 3-4. Ripple 3-4 a) Observe ripple, given C and Load Now connect a 15µF filter capacitor across the output (Important observe polarity). Does the output make sense? Calculate what the ripple amplitude should be, then measure it. Does it agree? (If not, have you assumed the wrong discharge time, by a factor of 2?)
L3 5 Lab 3-mod: Diode Circuits L3 5 15 min. 3-4 b) D1: Design Exercise: Choose C for acceptable ripple Now suppose you want to let your power supply provide a current of up to 20 ma with ripple of about 1V. Y our design task is to do the following: choose R so as to draw about 20mA (peak) load choose C so as to allow ripple of about 1V Draw your design: Try your circuit. Is the ripple about right? (Explain, to your own satisfaction, any deviation from what you expected.) This circuit is now a respectable voltage source, for loads of low current. T o make a power supply of higher current capability, you d use heftier diodes (e.g., 1N4002) and a larger capacitor. (In practice you would always follow the power supply with an active regulator, a circuit you will meet in Lab 12.)
L3 6 Lab 3-mod: Diode Circuits L3 6 30 min. 3-5 D2: AM Radio Receiver (fun!) T o make this exercise fun, you ll need a strong source of radio signals: that requires a pretty good antenna (or a poor antenna whose signal has been amplified for you by someone who knows how to make a high-frequency amplifier). W e get a strong signal in our teaching lab by running about 30 feet of wire from the window of the lab to a fire escape on the next building. The antenna is nothing fancy: just an old piece of wire, insulated from the fire escape by a piece of string. It gives us almost a volt in amplitude. If you looked (with a scope) at the signal coming from the antenna, it would look something like the image below, left; after selection with a resonant circuit, the signal would look like the image below, right. The 60Hz noise is gone; that much is apparent. Y ou cannot see a second benefit: the carriers of other radio stations also have been eliminated from the muddle of frequencies that came in on the antenna. Figure L3.6: Raw radio signals: straight from antenna, and then after selection with a resonant LC In order to detect an AM ( amplitude modulated ) radio signal, you need to do two tasks and you already know how to do both; 1. select a particular radio station s carrier frequency, at approximately 1 to 1.5 MHz: 2. then detect the audio signal that rides this carrier. Y ou can do the detection as follows: a. rectify the signal (use a Schottky diode 1N5817 or similar: its low forward-voltage will let it rectify a signal of just a few tenths of a volt; b. then low-pass filter this rectified signal. The output of your circuit will be a small audio signal (much less than a volt). It may be audible on old-fashioned high-impedance earphones; it can be made audible on an ordinary 8-ohm speaker if someone provides you with an audio amplifier with a gain of 20 or so (an LM386 audio amplifier works fine). Y ou will have recognized that we have offered you only a strategy, not part values. We said select the carrier, but didn t say how. W e said rectify, but did not suggest a value for the R to ground. W e said low-pass filter, but did not suggest f 3dB. So, we have left to you some hard and interesting parts of the job. Here are some suggestions: to detect the carrier, use an LC circuit like the one you built at the start of this lab, but showing the following differences: the resonant frequency should be around 1 MHz; you need no upper resistor in the divider: the antenna can drive the LC directly.
L3 7 Lab 3-mod: Diode Circuits L3 7 The value of the resistor to ground is not critical; try 10k; the low-pass filter s job is to kill the carrier, keep the audio. F ortunately, these two frequencies are very far apart; so, you have a lot of freedom in placing f 3dB. The form of the low-pass you design may strike you as odd (though this depends on the way you chose to do the task: the odd configuration uses the rectifier s resistor to ground as the R in the RC low-pass). Just make sure to put this in time-domain terms that RC is very long relative to the 1MHz carrier period, but short relative to the signal or audio period. The reward we hope you will get is, of course, to hear the radio signal. (Y u will o probably need to experiment with your LC circuit by tacking in small additional caps in parallel, in order to select a particular station (or you can cheat by doing what everyone else who ever built a radio does: use a variable capacitor!) If you lack both high-impedance earphones and an audio amplifier, then at least look at the fruits of your labor on the scope.
L3 8 Lab 3-mod: Diode Circuits L3 8 Y ou should see something more or less like what s below: we recapitulate the raw unfiltered stuff coming off the antenna, then show the selected carrier, the rectified, and finally the filtered and rectified output. Figure L3.7: Stages of AM radio detection
L3 9 Lab 3-mod: Diode Circuits L3 9 1 hr., total Signal Diodes +30 min. 3-6. Rectified Differentiator (if time) Figure L3.8: Rectified differentiator Use a diode to make a rectified differentiator, as in the figure above. Drive it with a square wave at 10kHz or so, at the function generator s maximum output amplitude. Look at input and output, using both scope channels. Does it make sense? What does the 2.2k load resistor do? Try removing it. Hint: Y ou should see what appear to be RC discharge curves in both cases with and without the 2.2k to ground. The challenge here is to figure out what determines the R and C that you are watching and this problem is quite subtle! +30 min. 3-7 Diode Clamps Figure L3.9: Diode clamp Construct the simple diode clamp circuit shown just above. > Drive it with a sine wave from your function generator, at maximum output amplitude, and observe the output. If you can see that the clamped voltage is not quite flat, then you can see the effect of the diode s non-zero impedance. P erhaps you can estimate a value for this dynamic resistance (see T ext sec. 1. ); try a triangle waveform, if you attempt this estimate. Figure L3.10: Clamp with voltage divider reference
L3 10 Lab 3-mod: Diode Circuits L3 10 Now try using a voltage divider as the clamping voltage, as shown just above. Drive the circuit with a large sine wave, and examine the peak of the output waveform. Why is it rounded so much? (Hint: What is the impedance of the voltage source provided by the voltage divider? If you are puzzled, try drawing a Thevenin model for the whole circuit. Incidentally, this circuit is probably best analyzed in the time domain.) T o check your explanation, drive the circuit with a triangle wave; compare with figure 1.83 in the text. As a remedy, try adding a 15µF capacitor, as shown with dotted lines (note polarity). Try it out. Explain to your satisfaction why it works. (Here, you might use either a time- or frequency-domain argument.) This case illustrates well the concept of a bypass capacitor. What is it bypassing, and why? (Lb3FE02.mod ; 9/18/102 12:32pm)
Figures Figure 1: LC parallel resonant circuit.............................. 1 Figure 2: Y ou can measure Q, by getting precise δf measure, with DVM.. 2 Figure 3: F ourier series for square wave............................ 3 Figure 4: Half-wave rectifier..................................... 3 Figure 5: Full-wave bridge...................................... 4 Figure 6: Raw radio signals: straight from antenna, and then after selection with a resonant LC..................................... 5 Figure 7: Stages of AM radio detection............................ 8 Figure 8: Rectified differentiator.................................. 9 Figure 9: Diode clamp.......................................... 9 Figure 10: Clamp with voltage divider reference..................... 9