Laboratory Exercise Amplitude Modulation and Demodulation In this lab you will study electronics for amplitude modulation, and two different techniques for demodulation. Introduction All analog and many digital communications systems that transmit data over cable or using electromagnetic waves use some form of signal modulation. In measurement systems, modulation techniques are useful for measuring very small signals with large amounts of noise. In this laboratory exercise, you will amplitude modulate an audio signal on a carrier frequency, and study two different methods for demodulating the signal. Consider a signal V(t) = A sin f. For a simple sine wave, A is constant and the phase f is a linear function of time, f = wt + f o. To use this signal to carry information, we can let either A, w or f o be a function of time. These three possibilities are referred to as amplitude modulation (AM), frequency modulation (FM) and phase modulation (PM). These various types of modulation are often combined; for instance, color television uses AM for brightness, FM for sound, and PM for the hue. In this lab you will study the first of these techniques, amplitude modulation. Consider a signal that you wish to transmit, that has the form S(t) = m cos w m t. To transmit this signal requires you to have a carrier signal with a higher frequency than w m, and an amplitude greater than m. Adding the signal and carrier gives an output of the form A(t) = A o cos w c t (1 + m cos w m t). If the signal is at a single frequency, the Fourier spectrum of the amplitude-modulated signal comprises the unmodified carrier w c and two side bands at w c ± w m. Figure 1: Frequency spectrum of a modulated single-frequency signal
The form of this frequency spectrum can be derived from the trigonometric function-product relations (cos a cos b): A(t) =A 0 cosw c t(1+ mcosw m t) = A 0 [cosw c t + m cosw c t cosw m t] [ ] = Acosw c t + m /2 cos(w c -w m )t + cos(w c + w m )t If the signal contains more than one frequency, where each modulation frequency w m has a different modulation factor m, we end up with the carrier and two side bands, as in Figure 2. Figure 2: Frequency spectrum of an amplitude modulated signal with many frequencies. Since the carrier carries no information, it is useful in applications such as AM radio transmitters to reduce the amplitude of the carrier with respect to the side bands. Because the side bands are symmetric, it is possible to reproduce the signal from only one of the two side bands, and some radio transmitters suppress one of the side bands to economize on power. Demodulation of such a signal is much more complicated, however, and we will not discuss it here. AM Modulation In this section of the lab, you will study a circuit that modulates a high frequency carrier signal T E with a lower frequency sine wave. The circuit modulates T E with T F using a CA3080 transconductance amplifier (Figure 3). The CA3080 produces an output current i o = g m (v + - v - ), where the transconductance g m is set by an Amplifer Bias Control current i ABC applied to pin 5 of the device. This has the effect of multiplying the values of g m and (v + - v - ), making the CA3080 very useful for amplitude modulation applications.
Figure 3: Equivalent schematic of the CA3080 transconductance amplifer Figure 4: Pin configuration of a 741 operational amplifier (op-amp) A number of 741 operational amplifiers (Figure 4) are also used. Study the pin configurations of both circuits to help you better understand the physical circuit. The board containing the modulation circuit has two BNC connectors for the carrier signal T E and the modulation signal T F. T F is a modulated voltage, so it must be converted to a current to send to the 3080 as i ABC. This is done by amplifying T F using a 741 op-amp, and feeding it to the i ABC pin of the 3080 through a resistor R M. The output i o of the 3080 must be converted to a voltage before transmission. This is done with an additional 741 op-amp connected as a current-to-voltage converter. Figure 5 shows an approximate schematic for the modulation circuit. Two additional 741 op-amps on the board produce matched copies of the modulated output with positive and negative polarities, and a third 741 produces a TTL-compatible square wave (clock) derived from the carrier signal.
Figure 5: Amplitude modulation circuit Connect the modulation board to the +/-15V power supply provided, and use two oscillators to provide a carrier frequency (~2-3 khz, ~1V) and modulation(~200-300 Hz, ~1V). Study the modulated output V 0 on the oscilloscope, and adjust the carrier and modulation frequencies and amplitudes until you obtain a good output signal with a high degree of modulation. Use the digital oscilloscope to measure TF, TE, and one of the modulated outputs from the board, and sketch them, labeling relevant frequencies and amplitudes. Experiment by changing the amplitude and frequency of the carrier and modulation signals, and note the effects. Use the Fourier transform function of the scope to analyze and sketch the frequency spectrum of the modulated output, including relevant frequency values and amplitudes. Adjust the modulation amplitude and verify that the side bands cannot have an amplitude more than half that of the carrier frequency band. What happens to the frequency spectrum if you try to raise the modulation amplitude above the point where the side bands are half the amplitude of the carrier frequency band? AM Demodulation using a Diode Rectifier The simplest way to demodulate an AM signal is rectification using a non-linear component (such as a diode). In this section, you will use a simple diode rectifer such as the one in Figure 6 to extract the modulated signal. Figure 6: Diode rectifier demodulation circuit and output
Choose one of the modulated signal outputs, and build a diode demodulation circuit such as the one shown in Figure 6. A Germanium diode is preferable for demodulation since it has a low turn-on voltage. Choose appropriate R and C values to allow the output to closely follow the peaks of the rectified output. Build an additional low-pass filter with cutoff frequency well below the carrier frequency in order to improve the quality of the output. Draw and label the demodulation circuit, and the output. Connect the output of the white noise generator to the noise input of the card, which will add the injected noise to Vo. Observe the effect of the noise on the modulated signal and the demodulated output. Describe quantitatively and qualitatively the effect of the white noise on the demodulated output. AM Demodulation using Frequency Lock-In In this section, you will use a frequency lock-in circuit to rectify the modulated signal. This is a far more powerful technique than the diode rectifier circuit, since it has a very narrow frequency response. It uses an analog switch driven by a square wave derived from the reference frequency T E to choose between an inverted and non-inverted version of your input signal (Figure 7). Figure 7: Lock-in demodulation using an analog switch The frequency lock-in technique can be a powerful tool to eliminate noise. While the capacitor in the simple diode rectifier integrates all frequencies, the lock-in circuit ensures that signals with the same frequency and phase as the square wave will always present a positive amplitude to the integrating capacitor. Signals with any other frequency will present equal parts positive and negative to the capacitor over time, giving a zero integral. Spend a few minutes demonstrating to yourself how this works. The analog switch used is the Maxim MAX333A, shown in Figure 8. The device has four identical switches, of which only one is used. To produce the frequency lock-in using switch 1, for example, connect the positive and negative modulated outputs to N01 and NC1. Connect the square wave (clock output) to IN1. The output of the switch is COM1. The relatively slow slew rate of the 741, coupled with different delays between devices, means that at higher frequencies the square wave is no longer synchronous with the carrier signal. Therefore for this part of the lab the carrier frequency should be lowered to around
1 khz. Figure 8: The MAX333A analog switch Measure and draw the square wave, the non-inverted and inverted inputs to the switch, including relevant time scales and amplitudes. Filter Measure the unfiltered and filtered output of the demodulator. Again, add the output of the white noise generator to the modulated signal as you did in the previous part of the lab, Observe and describe the effect on the demodulated output. An example of an application of frequency lock-in could be a thermocouple (resistance varies with temperature) placed inside a noisy environment (for example, a computer case). A current is driven through the thermocouple, and the voltage drop is measured. If the current is DC, the environment noise could be greater than the small signal variation being measured. So a better method is to drive an AC current (carrier) through the thermocouple and use a frequency lock-in circuit to isolate the carrier frequency and measure that amplitude. Write a short report on the lab, your observations and conclusions, and hand it in to the lab instructor.