ECE 241L
Lab 5 - AM Radio Receiver
This last lab is more of a project. You have three weeks to complete the three parts, so plan your time accordingly. The last part will take longer, so try to move pretty quickly through the first two parts.
Besides some resistors, a capacitor and an inductor, you will need a few components for this lab not in the tool box: (i) a basic diode such as a 1N4001, (ii) a basic op amp such as an LM741 and (iii) a variable capacitor. The IEEE store should have these items in stock, with a couple of options for the variable capacitor. You will also need a small speaker for this lab. You can use any old stereo or computer speaker you have, or you can buy one. You often find quite good ones at thrift stores.
Be warned that this is not a “recipe” lab. You will be learning about some circuit elements like diodes and op amps that we are not covering in class, and there is a certain amount of research and design expected of you!
Part 1. Half-wave rectifier with RC filter.
Anything that plugs into the wall uses ac (sinusoidal) power. However, for many applications it is convenient to take this convenient ac power source and convert it to dc. For example, anything with transistors generally needs dc power. The simplest circuit to convert ac to dc is the half-wave rectifier shown in Figure 1(a) below.
(a) (b)
Figure 1. Half-wave rectifier (a) unfiltered and (b) filtered.
You may not have learned about diodes yet, but for now we can simply think of them as a one-directional switch. For an ideal diode, if VD > 0, the “switch” is closed and the diode conducts like a short circuit. For VD < 0, the switch is open and the diode does not conduct, just like an open circuit. In a more practical model of the diode, we say that the diode is a short circuit for VD > VON and the diode is an open circuit for VD < VON. Typically, VON @ .7 V.
The addition of a capacitor in Figure 1(b) has a smoothing effect on the output. Say Vin = Vmcos(wt). Assuming an ideal diode, initially Vout charges up to Vm. When Vin falls below Vm, the diode is open, the RC network is isolated, and Vout = Vme-t/RC (as seen in section 4.1 in Hambley.) The exponential decay continues until Vout < Vin, at which time the diode will start conducting again.
How much Vout decays depends on the time constant RC compared to the period (T) of Vin. If we assume that the diode is open for almost the entire period, we can approximate the minimum Vout as Vout_min @ Vme-T/RC. The “ripple voltage” is defined as Vr = Vm – Vout_min. If RC > T, expanding the exponential gives Vr @ VmT/RC. Note that if we use the practical diode model, we can simply replace Vm with Vm – VON.
1. If Vin = 10cos(wt) in Figure 1(a), sketch on the same graph Vin(t), Vout(t) for an ideal diode and Vout(t) for a practical diode. The horizontal axis is time in arbitrary units.
2. If Vin = 10cos(wt) in Figure 1 (b), sketch on the same graph Vin(t) and Vout(t) for (i) RC @ T and (ii) RC > T.
3. Design, simulate in LTSpice and build in the lab a half-wave rectifier with Vm = 10 V, f = 60 Hz (remember w = 2pf = 2p/T), R = 1 kW and Vr £ 2% of Vm.
4. In both LTSpice and in the lab, adjust the RC time constant to be approximately 10x larger and then approximately 10x smaller. Comment on the effect on the ripple voltage that you observe.
Your report should include (i) the sketches for questions 1 and 2, (ii) a discussion of your designs and any relevant calculations, (iii) your LTSpice schematics and output plots, (iv) screen shots of your circuit outputs and (v) a discussion of the comparison between your design calculations, simulations and test results. Make sure your simulation and test outputs are scaled to clearly show the ripple voltage.
Part 2. An LC tank circuit.
If we didn’t get to second-order circuits in class, the TA will provide some background here. Refer to section 4.5 (page 193 especially.)
Consider an underdamped RLC circuit if R ® 0. The natural response will be an oscillation at w0 = with no damping - an undamped natural response. The circuit in Figure 2(a) consisting of an inductor and a capacitor only is called an LC tank. It has a very strong response around the resonant frequency w0. Practical circuits will never have zero resistance, so we see a sharp but not single frequency peak, as in Figure 2(b). The bandwidth BW is defined as w2 – w1, where w2 and w1 are the frequencies where the signal amplitude is 1/Ö 2 of the maximum amplitude. The quality factor Q of the circuit is defined as w0/BW. Tank circuits have very narrow bandwidth and very high Q. A common application of tank circuits is in radio tuners.
(a) (b)
Figure 2. (a) An LC tank circuit. (b) Output voltage versus frequency.
1. Verify that the statement “the natural response will be an oscillation at w0 = with no damping” is true for the circuit above.
2. Calculate the resonant frequency of the LC tank in Figure 2(a) with L = 600 mH and C = 100 pF. Verify your calculation with LTSpice simulations. You should do an ac sweep around f0, and also a transient run to observe the natural response. Suggestion: use the fft to verify the frequency of the oscillations. Calculate the Q of the circuit from the ac simulation. Note that the resonant frequency and the bandwidth can both be in Hz or both be in rad/s, as long as they are in the same units.
3. Build the tank circuit in the lab using the variable capacitor. Use a large resistor in series with the function generator to mimic a current source. Observe the resonant frequency and the Q of the circuit. There is more detail on testing the LC tank in Appendix A. Note that it is the total current you need to observe, using the voltage across the resistor as the output.
4. Find the maximum and minimum resonant frequencies achievable with this LC tank. The AM radio band is 530 – 1700 kHz. Can you tune your circuit over this entire range? (Don’t worry if not – it depends on the L and C you have available - as long as you can tune over a good part of it.) Note that when you attempt to make measurements around 1 MHz or higher, it becomes important to keep the wires in the circuit as short as possible to avoid picking up noise.
In your report, include calculations, simulations, test results and discussion as before. In particular, discuss the issues and limitations in building and measuring the tank circuit and any problems you encountered.
Part 3. Putting it together – an AM radio receiver.
Figure 3 shows a basic AM radio receiver. As you can see, you already have almost everything! The tunable tank circuit selects the frequency of the desired station. The diode and RC filter (your half-wave rectifier) perform demodulation: removing the high-frequency radio wave and leaving the low-frequency audio signal. See the appendix for more on modulation and demodulation.
Figure 3. An AM radio receiver.
Build the complete receiver by adding the simple non-inverting amplifier and connect it to a speaker. We will not be covering op amp circuits in class, but you can read about them in chapter 14, specifically 14.3. The TA will provide and explain the pinout of the chip. You will probably need a pretty substantial gain, maybe 50 or so. Remove the function generator and resistor and add an unshielded wire (maybe a few meters long) as an antenna. You should be able to pick up an AM radio station, though you will probably have more success outside of the lab.
You can also use the function generator to produce an AM signal as follows:
1. Connect the Channel 2 output to the AM input on the back of the FG.
2. Set Channel 2 to produce, for example, a 1 kHz sine wave at 1 volt peak to peak.
3. Set Channel 1 to produce say a 2 V peak-to-peak sine wave at, for example, 1 MHz.
4. Press the MODUL button and use the up/down arrows to scroll to AM.
You can use another unshielded wire connected to Channel 1 to serve as your transmitting antenna while you test your receiver. You should be able to see the demodulated signal on the scope as well as hear it out of the speaker.
Demonstrate the complete receiver to the TA. In your report, discuss how you built and tested the complete receiver circuit and how well it worked.
Appendix A - Testing the tank circuit
Figure A1: Tank Test Circuit
Change the function on the AFG (function generator) to NOIS and the amplitude to 1 V. At this setting, the AFG will produce white noise that you will feed through your tank circuit. Perform an FFT analysis on the voltage across the 1 MW resistor. Set Channel 1 to 100 ms per division and set the FFT to 500 kHz per division. For best results, you will need to have your probe set on 1X and the Channel 1 impedance on the Scope set to 1 MW. You should see something like Figure when you have everything set correctly.
Figure A2: FFT of Noise through Tank Circuit
FigureA2 shows an oscilloscope with Channel 1 activated, and the math plot set to FFT. The bump on the FFT plot corresponds to the resonate frequency of the tank circuit. If you were using this circuit to tune in a radio station, the station you would be hearing would be the one transmitting on frequency corresponding to the maximum in your FFT plot. As you adjust your capacitor, you will see the bump on your FFT move left and right. If you do not see this, you are looking at the wrong bump on the FFT. The correct bump will probably be between 100 kHz and 5 MHz.
Appendix B: some background on amplitude modulation.
Radio stations transmit electromagnetic waves at different frequencies. When you turn the tuning dial on your car radio, you change the frequency that your radio receives. For example, when your radio receives a AM station at 930 kHz, it is tuned to receive only signals with frequency content that is close to 930 kHz.
Radio transmitters “mix” the sound waves into the 930 kHz signal and convert it to an electromagnetic wave. This process of mixing two signals at different frequencies is called modulation. Your car radio receives the electromagnetic waves, converts them to electrical signals, separates the audio and radio signals and sends the audio signal to your speakers.
Radio stations use one of two methods to “mix” audio frequency sounds into a radio signal. They are frequency modulation (FM) and amplitude modulation (AM). AM modulation changes the amplitude of a high frequency, sinusoidal electromagnetic wave by an amount proportional to the amplitude of the sound wave. Figure B1(a) shows a radio signal with no modulation. Figure B1(b) shows a radio signal with amplitude modulation. The amplitude of the radio wave follows the amplitude of the sound wave.
Figure B1. Radio wave with (a) no modulation and (b) amplitude modulation.
The process of converting the received signal into an audio signal is called AM demodulation. One technique illustrated in this lab uses a simple diode half-wave rectifier circuit. As seen in Figure B2 below, the diode removes the negative portion of the incoming signal. The remaining signal is low-pass filtered to remove the radio frequency, leaving only the low-frequency audio signal.
Figure B2. Demodulated AM signal.