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AMPLITUDE MODULATION AND DEMODULATION AIM :
(i) To study amplitude modulation and to calculate the modulation index (ii) To study amplitude demodulation
APPARATUS : 1. 2. 3. 4. 5.
6. 7.
8. 9. 10.
CRO ------------------------------------------------------------------------------------- 1 Function Generators ------------------------------------------------ 2 DC Regulated Regulated Power Supply ----------------------------- 1 Transistor 2N3904 ---------------------------------------------------- 1 Capaci Capacitor torss : Modulation 0.1 µF ----- 4 100 µF ----- 1 0.01 µF ----- 1 Inductor --------------------------------------------------------------------------- 1 Resis Resistor torss : Modulation 20 k Ω ----- 1 1 k Ω ----- 2 10 k Ω ----- 1 Connecting Connecting probes probes and connecti connecting ng wires wires Bread board ------------------------------------------------------------------ 1 Diode (for Demodulation) Demodulation) OA79 ------------------- 1
Demodulation 0.01 µF ----- 1
Demodulation 10 kΩ ----- 1
THEORY : An Amplitude Modulated signal is composed of both low frequency and high frequency components. The amplitude of the high frequency (carrier) of the signal is controlled by the low frequency (modulating) signal. The envelope of the signal is created by the low frequency signal. If the modulating signal is sinusoidal, then the envelope of the modulated Radio Frequency (RF) signal will also be sinusoidal. This would be the case in a common AM radio. The low frequency signal would be an audio signal and the high frequency would be the transmitting frequency of the AM radio station. The mathematical representation for this AM waveform is as follows: SAM(t) = c(t) + k a m(t) c(t) = Ac cos(2π f ct) + k a Am cos(2π f mt) Ac cos(2π f ct) = Ac [1 + k a µ cos(2π f mt)] cos(2π f ct) where, m(t) = Am cos(2π f mt) is modulating signal c(t) = Ac cos(2π f ct) is carrier signal Am and Ac are the amplitudes of modulating signal and carrier signal respectively f m and f c are the frequencies of modulating signal and carrier signal respectively k a is amplitude sensitivity
µ = k a Am / Ac is the modulation index The circuit for generating an AM modulated waveform must produce the product of the carrier and the modulating signal (along with the carrier). This can be achieved in many ways, but often is done by biasing a transistor for nonlinear operation (creating the product term) and filtering the output with a tank circuit to remove the higher harmonics introduced. This type of modulator is shown in Figure 1.
For class B operation, the transistor is biased such that when both the carrier and modulating signals are zero, the DC voltage at the transistor base will be 0.7 V (i.e., the knee voltage of the base emitter junction). If a carrier is added via the coupling capacitor C1 while the modulating signal remains zero the transistor will be turned off for the negative half cycle of the carrier, producing only positive current pulses in the collector. The tank circuit will have large impedance at the carrier frequency (which is also the fundamental frequency of the current pulses) and low impedance at the higher harmonics of the current pulses. Thus, the voltage produced at the output will be a sinusoid of the carrier frequency. When the modulating signal is added via the coupling capacitor C5 the emitter voltage of the transistor will follow the modulating signal, causing the cutoff voltage of the transistor and also the collector current pulse amplitude to vary with the modulating signal. The collector current waveform has the shape of the positive half of the AM waveform shown in Figure 2. The tank circuit attenuates the higher harmonics to produce an output voltage as the AM waveform shown in Figure 2. After receiving an AM signal, it can be demodulated to recover the low frequency signal. One of the simplest types of AM demodulating circuits is the envelope detector shown in Figure 3.
The demodulation circuit is composed of a resistor, capacitor, and diode. In order to accurately recover the low frequency signal the envelope detector must satisfy an important condition; the time constant of the envelope detector network must be much longer than the period of the carrier signal (high frequency signal ) but much shorter than the period of the modulating signal(low frequency signal). Once the signal is demodulated, the high frequency signal is eliminated and what remains is the low frequency component. The envelope detector detects the lower envelope which has same frequency as that of the modulating signal. It can be noted that if the diode’s direction is reversed, the upper envelope is detected. The time constant set by the values of the resistor and capacitor needs to be much less than the period of the audio signal but much greater than the period of the RF (high frequency) signal. The relationship between the RC time constant, modulation frequency, and carrier frequency is shown in the in equation below: 1
f c
<
1
f m
PROCEDURE: PART 1 : AMPLITUDE
MODULATION
1. Connect the circuit as shown in the Figure 1. 2. Adjust the power supply to ensure a DC voltage of +18V. 3. Adjust the function generator (carrier signal) for a sine wave of frequency 500 k Hz and an amplitude between 0.5 V and 1 V. 4. Adjust another function generator (modulating signal) for a sine wave of frequency 500 Hz and an amplitude between 0 and 10V. 5. Turn on the circuit with the modulating signal connected to the Channel 1 of the CRO and the modulated output signal connected to the Channel 2 of the CRO. 6. With the modulating voltage adjusted to zero amplitude (i.e., switch off the second function generator), increase the carrier amplitude until the modulated output has a value of 2V peak to peak .This is the unmodulated output signal. 7. Increase the amplitude of the modulating signal until an AM waveform appears. 8. Observe the AM waveform at the output and record the values of A and B indicated in the Figure 2. 9. Calculate the modulation index µ using the following equation µ=
A −B A +B
10. Repeat the steps 7, 8 & 9 to get various values of µ ranging from 0 to 1 and also observe the over modulated AM waveform. 11. Observe the changes in the AM waveforms by varying the frequency and amplitude of the modulating signal individually and comment on it.
PART 2: DEMODULATION
1. Connect the circuit as shown in the Figure3. 2. Connect the AM output to the input of the demodulation circuit (diode detector). 3. Connect the modulating signal of modulation circuit to the Channel 1 of CRO and the demodulated output to the Channel 2 of CRO. 4. Turn on the power, observe the waveforms and compare their frequencies. 5. Repeat the procedure for various values of modulation index and observe the changes. NOTE: Make sure that the values of R & C in demodulator circuit satisfy the following inequation 1
f c
<
1
f m
OBSERVATIONS: Amplitude Modulation Ac = ______,
S.No Modulating voltage
f c = _______, f m = _______
A
B
(volts)
(volts)
----
----
%µ=
A −B A +B
x 100
Am (volts) 1 2 3
---
4 5 6
Demodulation Amplitude of the modulating signal = ____________ Frequency of the modulating signal = ____________ Modulation index of the AM wave = ____________
