AM Modulation and Demodulation

1. Objective

Students will build and test a different type of amplitude modulation (AM) transmitter. The modulation will be accomplished by exploiting the nonlinear characteristics of a diode. Students will design, build and test the bandpass filter subsystem and the radio frequency (RF) amplifier stage. Students will also design, build and test an envelope detector for AM demodulation.

2. Background

2.1 Modulation using diode nonlinearity

Amplitude modulation can be accomplished using a nonlinear element such as a forward biased diode near the turn-on voltage. The overall system to be implemented, shown in block diagram form in Figure 1, is composed of a summer (Figure 2), a nonlinear circuit (Figure 3), a radio frequency (RF) amplifier, and a bandpass filter. The heart of the system is the nonlinear circuit shown in Figure 3. This circuit has an input-output function like that shown in Figure 4. This curve is governed by the voltage-current characteristic curve of the diode. Note that when the input voltage is in the 0.3V-0.5V range, the curve appears quadratic. We will exploit this to create a double-sideband large-carrier (DSB-LC) AM signal.

The input to the nonlinear circuit is the sum of a message signal, the carrier, and a DC bias voltage. Specifically this is given by:

vl(t) = 1() ( c(t) + B. (1)

Limiting the model order of the nonlinear circuit to a second order polynomial, yields:

v2 (t) = cx (m(t) + c(t)+B) + c2 (m(t) + c(t) + B)2. (3)

This model seems reasonable, based on inspection of the input-output curve in Figure 4. Multiplying out the terms in (3) yields:

v2(t) = 2c2m(t)c(t) + (2c2B+cl)c(t) (DSB-LC) + c2B2+c1B (DC) (4) + (2c2B + c1)m{t) + c2m2(t) (baseband)

+ c2c2(t) (harmonic & DC)

obtaining some DC terms, baseband terms, a harmonic term and the desired DSB-LC signal. The DSB-LC signal can be extracted by putting the signal through a bandpass filter. Assuming that the carrier is at a much higher frequency than the baseband signal, a bandpass filter centered at the carrier frequency should be able to effectively eliminate the DC, baseband and harmonic terms.

Neglecting the gain constant from the RF amplifier, this leaves us with the following signal

v3(t) = 2c2m(t)c(t) + (2c2B +c1)c(t). (5)

which represents a DSB-LC signal for a sinusoidal carrier.

Figure 1: AM modulator using nonlinear element

The modulation index is given by

2

2 1

2 | min{ ( )} |2

c m tmc B c

=+

(6)

Note that the modulation index is controlled in large part by the DC bias voltage and the message amplitude. We generally have little control over the polynomial parameters q and c2.

Because of the nature of the diode circuit, the voltage out of the nonlinear circuit is relatively small (typically less than 0.7V). Thus, an RF amplifier stage can be used to boost the signal prior to sending the signal to an antenna. As in the previous lab, we use a simple end-loaded wire antenna.

2.2 Demodulation using envelope detection

The envelope detector circuit is shown in Figure 5. It comprised of a diode followed by an RC circuit. When the input voltage is positive, the capacitor charges (i.e., step response). When the input goes negative, the diode becomes an open circuit and voltage on the capacitor exponentially

decays (i.e., natural response) at a rate determined by the time constant (T = RC). By choosing an appropriate value for the time constant, the voltage will closely follow the envelope of the modulated signal. The capacitor gets recharged by every peak but does not fall to zero between peaks because the time constant limits the decay. Thus, choosing the time constant of the RC circuit depends on the carrier frequency and message frequency. A rule of thumb is to use

1 1c

RCf Bτ = (7)

2

where fc is the carrier frequency in Hz and B is the bandwidth of the message signal. A low-pass filter can be employed after the envelope detector to smooth out ripple in the received signal.

Figure 3: Nonlinear circuit used for modulation.

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Figure 2: Summing amplifier circuit.

Figure 4: Input/Output voltage relationship for nonlinear circuit (data from PSPICE with D1N4148 diode and 1.8k Ohm resistor with no additional load).

Figure 5: Envelope detector for simple demodulation of DSB-LC signals.

3. Prelab Assignment

• Design a simple RLC bandpass filter centered at 600kHz with a 40kHz bandwidth (i.e., attenuation < -3dB in a 40kHz passband) using available component values. The lab has 10uH, 47uH, and 100uH inductors. The available resistor values are shown in Table 1 and the available capacitor values are shown in Table 2. Make sure you convert your design frequencies to radians/sec before using standard filter formulas. Verify your design with a PSPICE frequency sweep analysis.

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