Experiment 1 Design of Conventional Amplitude Modulator

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Virgil Bridges
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1 Name and ID: Preliminary Work Group Number: Date: Experiment 1 Design of Conventional Amplitude Modulator 1. Using the information given in this assignment, design your switching modulator that modulates a low frequency sinusoidal wave (tone modulation). You are free to choose the frequency of the message and carrier signals. Be careful to choose the frequencies at which the devices in our laboratory can produce and measure. You must calculate the values of your circuit elements according to your design. Be careful to choose these circuit element values that you may find in the market and buy 2. Simulate your circuit with PSpice. Your report should contain the circuit schematic and the amplitude modulated signal output (both in time and frequency domains) generated by PSpice. ATTENTION You will bring your own circuit elements to the laboratory! Since you may not get your expected results you obtained in your preliminary work and rather hard to find a wide range of circuit elements at our laboratory, please obtain a wide range of elements before attending the laboratory. Each group will submit ONLY ONE preliminary report. This means, you will prepare the report as a team. You will be asked questions about your design during laboratory hours. 1 THEORY Consider a sinusoidal carrier wave c(t) defined by, c(t) = A c cos(2πf c t) (1) where A c is the carrier amplitude and f c is the carrier frequency. Let m(t) denote the baseband message signal. Amplitude modulation is defined as a process in which the amplitude of the carrier wave c(t) is varied about a mean value, linearly with the baseband message signal m(t) An amplitude modulated (AM) wave may thus be described as a function of time as follows: s(t) = A c (1+k a m(t))cos(2πf c t) (2) 1

2 where k a is a constant called the amplitude sensitivity of the modulator. If k a m(t) < 1, then we can state that (1+k a m(t)) is always positive and the envelope of the AM waves s(t) equals to A c (1+k a m(t)). This type of AM modulation is called conventional or large carrier AM modulation and demodulation can be done via envelope detection. 1.1 Implementation of Conventional AM Modulator There are several methods for generating AM signals. Switching modulator will be described in this manual. You are supposed to implement switching modulator as your amplitude modulator Switching Modulator Details of this modulator is shown in Fig.1, where it is assumed that the carrier wave c(t) applied to the diode is large in amplitude, so that it swings right across the characteristic curve of the diode. We also assume that the diode acts as an ideal switch, that is, it presents zero impedance when it is forward biased (corresponding to c(t) > 0). We may thus approximate the transfer characteristic of the diode-load resistor combination by a piecewise-linear characteristic, as shown in Fig.2. Accordingly, for an input voltage v 1 (t) consisting of the sum of the carrier and the message signal: v 1 (t) = A c cos(2πf c t)+m(t) (3) where m(t) << A c the resulting load voltage v 2 (t) is v 2 (t) v 1 (t) if c(t) > 0 = 0 c(t) < 0 (4) That is, the load voltage v 2 (t) varies periodically between the values of v 1 (t) and zero at a rate equal tothecarrierfrequencyf c. Inthisway, by assuming a modulating wave that is weak compared with the carrier wave, we have effectively replaced the non-linear behaviour of the diode by an approximately equivalent piecewise-linear, time-varying operation. We may express Eq.4 mathematically as c t = A c cos(2πf c t) + + v t v 1 (t) v 2 (t) Rl Figure 1: Switching modulator v 2 (t) = [A c cos(2πf c t)+m(t)]g T0 (t) (5) 2

3 v 2 slope=1 0 v 1 Figure 2: Transfer characteristic where g T0 (t) is a periodic pulse train of duty cycle equal to one-half, and period T 0 = 1/f c. Representing this g T0 (t) by its Fourier series, we have g T0 (t) = π n=1 ( 1) n 1 2n 1 cos[2πf ct(2n 1)] (6) Therefore, substituting Eq.6 in 5, we find that the load voltage v 2 (t) consists of the sum of two components: The component A c 2 [ 1+ 4 ] m(t) cos(2πf c t) (7) πa c which is the desired AM wave with amplitude sensitivity k = 4/πA c. The switching modulator is therefore made more sensitive by reducing the carrier amplitude A c ; however, it must be maintained large enough to make the diode act like an ideal switch. Unwanted components: The spectrum of which contains delta functions at 0,±2f c,±4f c, and so on, and which occupy frequency intervals of width 2W centered at 0,±3f c,±5f c, and so on, where W is the message bandwidth. The desired AM signal is obtained by passing v 2 (t) through a bandpass filter with center frequency f = f c and bandwidth 2W. 2 PROCEDURE a. Construct the circuit you designed in your preliminary work. Note the frequency of the message signal f m and carrier signal f c below. f m = f c = b. Calculate theoretical center frequency and bandwidth of the bandpass filter you have designed in your preliminary work. Show necessary calculation steps 3

4 c. Check your result and determine if your modulator should work. f center (calculated)= BW(calculated)= d. Connect the signal generator outputs to the oscilloscope. Measure the exact frequency of message and carrier signals. Draw both waveforms below. Indicate peak voltages. f m (measured)= f c (measured)= Figure 3: Message signal waveform Volt/div= time/div= 4

5 Figure 4: Carrier signal waveform Volt/div= time/div= 5

6 e. As shown in Fig. 1, two signal generators must be connected in series. In order to prevent the short circuiting of two sources, the signal generator which generates carrier must be plugged to the outlet without ground connection. f. Now apply both signals to your circuit. Observe both the message signal and v 2 (t) in both channels of the oscilloscope. Indicate peak voltages. Volt/div(CH1)= Volt/div(CH2)= time/div= Figure 5: Message and AM signal g. Calculate the modulation index µ. µ= 6

7 3 Conclusion 3.1 Student Name and ID: 7

8 3.2 Student Name and ID: 8

9 3.3 Student Name and ID: 9

UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE Department of Electrical and Computer Engineering

UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE Department of Electrical and Computer Engineering EXPERIMENT 8 AMPLITUDE MODULATION AND DEMODULATION OBJECTIVES The focus of this lab is to familiarize the student