# Amplitude and Frequency Modulation

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1 University of Saskatchewan 1-1 Amplitude and Frequency Modulation Safety The voltages used in this experiment are less than 15 V and normally do not present a risk of shock. However, you should always follow safe procedures when working on any electronic circuit. Assemble or modify a circuit with the power off or disconnected. Don t touch different nodes of a live circuit simultaneously, and don t touch the circuit if any part of you is grounded. Don t touch a circuit if you have a cut or sore that might come in contact with a live wire. Check the orientation of polarized capacitors before powering a circuit, and remember that capacitors can store charge after the power is turned off. Never remove a wire from an inductor while current is flowing through it. Components can become hot if a fault develops or even during normal operation so use appropriate caution when touching components. Objectives: To observe the time domain waveforms and frequency spectra of amplitude modulated (AM) waveforms both before and after demodulation and to design an experiment utilizing an FM signal. Equipment: You will require a spectrum analyzer (either an HP 3580A, an SR770, or an oscilloscope that can calculate a DFT), two signal generators, a ±15 V power supply and an oscilloscope. For the first part of the lab, you will require an amplitude modulator module (EE18.xx) containing the Analog Devices AD532 analog multiplier. The module is available from the technicians in 2C94. Procedure: Amplitude Modulation 1. Prior to the laboratory period, review the theory of amplitude modulation summarized in Appendix A. Determine an expression for µ and write an expression for the product in terms of µ, A 0, A m, and A c. For the carrier and modulation voltages specified in part 2, determine an expression for the output voltage s(t) and sketch the expected time waveform and single-sided spectrum. You should verify these during the laboratory period. See also 2. DSB TC: Set up the analog multiplier board shown in Figure 1 and apply a 10 khz sinusoidal carrier with A c = 2 V to the X input. To the Y input, apply a message signal composed of 2 khz sinusoid with A m = 2 V and a DC offset of +4 V. Use the spectrum analyzer (linear scale is recommended) to confirm the expected frequencies and amplitudes of the components at the output. Remember that the AD532 multiplier output divides the product of the inputs by 10 V.

2 University of Saskatchewan 1-2 Message Signal Generator A 0 + A m cos " m t A c cos " c t Y X Carrier Signal Generator AD 532 Analog Multiplier Board EE18.xx Z Figure 1. Scope Spectrum Analyzer Fig. 1 Amplitude modulation of a sine wave message signal 3. Increase the carrier frequency to 30 khz while maintaining the message signal frequency at 2 khz. Observe the time waveform and the spectrum of the modulated signal. 4. Vary the modulation signal voltage A m over the range 0 V to 6 V and observe the time waveform and the spectrum of the modulated signal. The DC offset should remain at +4 V. 5. Change the message signal to a square wave (at 2 khz and with A m = 2 V). Adjust the message signal s DC offset voltage so that the carrier is gated on and off by the square wave. What new frequencies are present in the output? What are the peak heights? Compare the predictions of Fourier theory with your measurements. 6. DSB SC: Restore the message signal to a sinusoid (still 2 khz and A m = 2 V). While observing the spectrum analyzer, slowly decrease the message signal DC offset voltage so that the carrier component at 30 khz is eliminated. Observe the time waveform and the humps in the envelope that occur at twice the modulation frequency. Adjacent humps will have equal amplitude when the carrier is suppressed. When finished with this part, restore the dc offset to 4 V. 7. Diode Demodulator: AM DSB TC signals may be demodulated by using a rectifier and a low-pass filter (LPF). This part is facilitated by increasing the modulated output voltage which can be done by increasing the carrier amplitude A c to 6 V or even to 8 V. Be careful not to saturate the multiplier s output which will clip the signal. Assemble the semi-ideal, half-wave rectifier shown in Figure 2 using 1N914 silicon diodes. The first diode is used to offset the modulated signal voltage by +0.7 V so as to compensate for the 0.7 V drop in the rectifying diode. Observe the input and output voltages to confirm half-wave rectification. Observe and justify the rectified output spectrum. Identify the desired component in the spectrum? 8. Apply a 3 khz LPF to the diode detector output and observe the filtered output. Note that the filter will introduce some delay (phase shift) in the demodulated message signal. As in Part 6, slowly reduce the DC component and observe the rectifier output spectrum and also the filtered output signal.

3 University of Saskatchewan 1-3 Procedure: Frequency Modulation Fig. 2 Semi-ideal, half-wave rectifier Design your own experiment to verify the principles of frequency modulation. This is an open-ended design of a practical laboratory experiment. Your record keeping should include the objective, procedure, and outcomes of your experiment. Some topic suggestions are: a) Observation of FM spectrum with sinusoidal modulation. Refer to the virtual laboratory on FM, found at (See the first image below) b) Observation of FM spectrum with music or voice modulation. c) Demodulation of an FM signal using the CD4046 CMOS phase locked loop. (not so easy) d) Observation of demodulated signal spectrum in commercial FM broadcast. (see image below) e) Observation of demodulated noise when a FM receiver is off station. f) Observation of commercial broadcast FM spectra in the range MHz and the relation to the associated audio signals. FM spectrum with sinusoidal modulation demodulated spectrum in commercial FM

4 University of Saskatchewan 1-4 Appendix A Mathematics of amplitude modulation DSB SC (double sideband suppressed carrier) modulation can be produced by the product of A c cos" c t and A m cos" m t which equals 0.5A m A c [cos(" c + " m )t + cos(" c # " m )t] (using the trigonometric identity cos A cosb = 1 (cos(a + B) + cos(a " B)). Note that for this sinusoidal 2 modulation, the product contains sum and difference frequency components and no component at the carrier frequency. DSB TC (double sideband transmitted carrier) modulation is customarily described by the product of A c cos" c t and 1+ µ cos" m t. In this experiment, we instead use A 0 + A m cos" m t for the message signal, and the product is A 0 A c cos" c t + 0.5A m A c [cos(" c + " m )t + cos(" c # " m )t]. For this sinusoidal modulation, the output contains sum and difference frequency components (upper and lower side-tones) plus a component at the carrier frequency. Appendix B AD532 Multiplier The functional block diagram for the AD532 is shown in Figure 4, and the simplified schematic is shown in Figure 5. In the multiplying mode, Z is connected to the OUTPUT to close the feedback around the output op-amp. The X and Y are inputs to high-impedance, low-distortion differential amplifiers featuring good common-mode rejection. Amplifier voltage offsets are laser trimmed to zero during production. The product of the inputs is formed in the multiplier cell using Gilbert s linearized transconductance technique. The built-in op-amp is used to obtain low output impedance and make possible self-contained operation. The cell is laser trimmed to obtain V OUT = (X 1 " X 2 )(Y 1 " Y 2 )/10 V. Residual output voltage offset can be zeroed at V OS in critical applications; otherwise the V OS pin should be grounded. Fig. 4 Functional block diagram of AD532

5 University of Saskatchewan 1-5 Fig. 5 Schematic diagram of the AD532 multiplier Appendix C AM Modulator Board (EE18.xx) The AM modulator board has been constructed to facilitate connection to power supplies, signal generators, and monitoring instruments (Figs. 6 and 7). To enable modulation by a typical audio source (with typical amplitude 1 Vrms), an optional factor of 10 gain has been provided. The modulator board is also capable of adding a DC offset to the message signal via the DC offset control knob and the +/- switch. In this experiment, you will not be using these features. The x1/x10 switch on the modulator board should be set to the x1 position to avoid saturating the output. The DC offset should be switched off by rotating the knob completely counter-clockwise.

6 University of Saskatchewan 1-6 Fig. 6 Schematic of the AM module Appendix D Audio Filter (EE 32.xx) Fig. 7 AM Board EE18.xx The 3 khz / 15 khz low-pass filter is constructed as a cascade of two 8-pole, switchedcapacitor filter sections (Fig. 8). The switched-capacitor filters have a maximum signal range of ±4 V. The filter module includes a divide by 3 amplifier at the input and 3 amplifier at the output; thus, the filter module can operate with ±12 V signals. Switched capacitor circuits operate with sampled (i.e. PAM) signals and thus anti-alias and reconstruction low-pass filters are required at the input and output. The cutoff frequency of these filters is less than half the lowest sampling clock frequency. The analog signal cutoff

7 University of Saskatchewan 1-7 frequency of the switched capacitor filter itself is 1/100 of the clock frequency and can be varied. Fig. 8 Switched capacitor low-pass filter (LPF) with cutoff at 15 khz or 3 khz.

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