EE/CME 392 Laboratory 1-1

Revised Mar.4, 2013

Part I - Amplitude Modulation

Safety: In this lab, voltages are less than 15 volts and this is not normally dangerous to humans. However, you should assemble or modify a circuit when power is disconnected and don’t touch a live circuit if you have a cut or break in the skin. Objective: To observe the time domain waveforms and frequency spectra of amplitude modulated (AM) waveforms both before and after demodulation. It is possible to complete this procedure in about half the allotted time so don’t rush! Take time to ask questions and understand. We expect “real-time notekeeping” with little “fix-up” after the experiment. Equipment: You will require a spectrum analyzer (a HP 3580A, a SR770, or an oscilloscope that can calculate DFT), two signal generators (see Fig. 1), a ±15 V power supply and an oscilloscope. Obtain an amplitude modulator module (EE18.xx) containing the Analog Devices AD532 analog multiplier. (see technicians in 2C78 or 2C94). 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, A0, Am, and Ac. 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 http://www.engr.usask.ca/classes/EE/352/expindex2/VirtualLab-2f/am_fm_pm/sinmod.htm.

UProcedure: Circuit Assembly: Set up the analog multiplier board shown in Figure 1. Review the circuit

board schematic shown in Appendix B and the multiplier IC block diagram and schematic in Appendix C. Set the modulation gain to x1 and do not use dc offset from the multiplier board (turn offset knob fully ccw).

Fig. 1 Amplitude modulation with a sine wave message signal

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1. Verify DSB–TC: Apply a 10 kHz sinusoidal carrier with Ac = 2V (i.e. 4 Vp-p) to the X input. To the Y input, apply a message signal composed of 2 kHz sinusoid with Am = 2V 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. For the message signal, it is recommended that you NOT use the EE1634 generator since it does not provide a full range of dc offset. Set digital frequency generators to high impedance for correct readout of amplitude. Remember that the AD532 multiplier output divides the product of the inputs by 10 V.

2. Carrier - Increase the carrier frequency to 30 kHz while maintaining the message signal frequency at 2 kHz. Observe changes in the modulated signal spectrum.

3. Sinusoidal Modulation – Slowly increase the modulation signal voltage Am over the range 0 V to 4 V (i.e. increase up to 8 Vp-p) and observe the time waveform and the spectrum of the modulated signal. DC offset should remain at +4 V.

4. On-Off Modulation - Change the message signal to a square wave (2 kHz and with Vp-p = 4V). Adjust the message signal’s dc offset voltage so that the carrier is gated on and off by the square wave. Observe the range of frequencies present in the output and observe the ratios of component amplitudes. Compare your observations with Fourier Series theory.

5. Diode Demodulator – AM–DSB–TC signals may be demodulated by using a rectifier. Restore the message signal to a sinusoid (still 2 kHz). To help provide larger multiplier output voltages for the diode detector, we increase the amplitude of the modulation – try Am = 3V i.e 6 Vp-p and dc offset at + 5V. Assemble the semi-ideal, half-wave rectifier shown in Figure 2 using silicon diodes. The first diode is used to offset the modulated signal voltage by +0.7 V so as to compensate the 0.7 V drop in the rectifying diode. Observe the input and output voltages to confirm half-wave rectification. Note: To further increase the multiplier output voltage we can increase the carrier amplitude Ac

to 6 V or even to 8 V (i.e. 16 Vp-p). Be careful not to saturate the multiplier’s output - which would clip the signal.

Fig. 2 Semi-ideal, half-wave rectifier

6. Demodulated Spectrum – Observe the rectified output spectrum and identify the remaining carrier and sideband componennts and the desired baseband (2 kHz) component of the baseband spectrum. Apply a 15 kHz lowpass filter to recover the baseband information signal. Observe

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the filter output using spectrum analyzer and oscilloscope. Note that the filter will introduce some delay (phase shift) in the demodulated message signal.

7. DSB–SC: – While observing multiplier output spectrum, slowly decrease the message signal dc offset from 5 V (DSB-TC) to zero (DSB-SC) so that the carrier component at 30 kHz is eliminated. Observe the time waveform and “humps” in the envelope that occur at twice the modulation frequency. Also observe the rectifier output spectrum as the message dc offset is reduced - see that DSB-SC signals are NOT be properly demodulated using a rectifier detector.

Appendix A Mathematics of Amplitude Modulation DSB–SC (double sideband suppressed carrier) modulation is produced by the product of the message

!

Am cos"mt and carrier

!

Ac cos"ct equaling

!

0.5AmAc[cos("c +"m )t + cos("c #"m )t] (i.e trigonometric identity

!

cosA cosB = 12(cos(A + B) + cos(A " B)). Note that for sinusoidal

modulation, the product contains sum and difference frequency components and no component at the carrier frequency.

DSB–TC (double sideband transmitted carrier) modulation. We now use the message

!

A0 + Am cos"mt and the product is

!

A0Ac cos"ct + 0.5AmAc[cos("c +"m )t + cos("c #"m )t].

The output contains sum and difference frequency components (upper and lower side-tones) plus a component at the carrier frequency.

In textbooks, the message signal is customarily normalized to

!

1+ µ cos"mt and the carrier respectively scaled as

!

Ac2 cos"ct to yield

!

Ac2 cos"ct + 0.5Ac2[cos("c +"m )t + cos("c #"m )t].

Appendix B AM Modulator Board (EE18.xx) The AM modulator board has been constructed to facilitate connection to power supplies, signal generators, and monitoring instruments. To enable modulation by a typical audio source (with typical amplitude less than 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.

Fig. 3 Schematic of the AM module

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Fig. 6 AM Board EE18.xx

Appendix C AD532 Multiplier

A functional block diagram for the AD532 is shown in Figure 3, and a simplified schematic is shown in Figure 4. 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 gives low output impedance and allows self-contained operation. The cell is laser trimmed to obtain

!

VOUT = (X1 " X2 )(Y1 " Y2 )/10V . Residual output voltage offset can be zeroed at

!

VOS in critical applications; otherwise the

!

VOS pin should be grounded.

Fig. 3 Functional block diagram of AD532

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Fig. 4 Schematic diagram of the AD532 multiplier

Appendix D Audio Filter (EE 32.xx)

The 3 kHz / 15 kHz low-pass filter is constructed as a cascade of two 8-pole, switched-capacitor filter sections (Fig. 7). 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 frequency of the switched capacitor filter itself is 1/100 of the clock frequency and it can be varied.

Fig. 7 Switched capacitor low-pass filter (LPF) with cutoff at 15 kHz or 3 kHz.