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TELE3013 TELECOMMUNICATION SYSTEMS 1 Lab 1: AMPLITUDE MODULATION 1. INTRODUCTION A sinusoidal carrier (Ac cos ωc t) which is amplitude modulated by a message signal, m(t), is represented by s(t) = [A [A c + m(t)] cos ω c t , ω c = 2π 2π f c (1) where Ac is the carrier amplitude, fc is the carrier frequency. When the modulating message is also a sinusoidal signal, ie. m(t) = Am sin ωm t, ωm = 2π fm , the corresponding AM signal may be expressed in simple form s(t) = A c [1 + m sin ω m t] cos ω c t, (2) where m is the modulation index. 2. PREPARATION P1. Using trigonometry write down a Fourier series representation for the AM signal with a message as given in equation (2) P2. From the result in question P1 give an expression for the AM signal s(t) as the real part of complex exponentials. Sketch a rotating phasor diagram for s(t) using the carrier frequency as a reference. P3. Write down the Fourier transform of s(t) in question P1. Sketch the amplitude of the AM signal frequency spectrum. P4. Determine the average power (i.e. find its mean–square value) of the AM signal assuming it is a voltage across a 1 ohm resistor. What is the power of each frequency components? Determine an expression for the fraction of power in the sidebands. 3013S2L1 TELE3013: Lab 1 1 3. EXPERIMENTS EQUIPMENT MODULES Audio Oscillator Adder Multiplier Utilities Modules Tuneable Low Pass Filter QTY 1 1 2 1 1 TRUNK SIGNALS Signal #1 16.6 kHz sine wave Signal #2 10 kHz sine wave Signal #3 Speech 3.1 Generation and Characteristics of AM Signals The signal of equation (2) can be conveniently modelled by the TIMS system using the block diagram below. Audio Osc. m cos ωmt (Message) Adder Multiplier 1 volt dc A c cos ωct (Carrier) AM Signal s(t) Using a 2 kHz sinusoidal (tone) signal and the 100 kHz sinusoidal signal both from the Master Signals panel as the carrier, generate an AM signal and investigate the following characteristics. Record the results in your laboratory notebook. 3.1.1 Time Domain Waveform Investigate the time domain waveform of the AM signal for m = 0.7 and 1.5. Sketch the waveforms observed and compare their envelopes with the message waveform. Replace the 100 kHz carrier with the 16.6 kHz carrier available from the trunks panel. What is the effect of decreasing the carrier frequency? Now use the Audio Oscillator for the message signal and note the effect of increasing the message frequency. 3.1.2 Frequency Domain Keep the 16.6 kHz carrier source from the trunks panel to assure that your frequency spectra are within the range of the Spectrum Analyser. Investigate the frequency spectrum of the AM signal for m = 0.7 and 1.5. Sketch the spectra observed. What is the effect of increasing the message frequency? Replace the 16.6 kHz with the 100 kHz carrier available from the trunks. 3013S2L1 TELE3013: Lab 1 2 3.1.3 Power in the Sidebands Determine the fraction of the total signal power that is in the sidebands for the cases m = 0.7 and 1.5. Calculate your answer from the relative heights of the spectral components in the frequency spectrum and compare your answers to the predictions from the formula that, for sinusoidal signals, the fraction of power in the sidebands is given by the expression: Q = m2 2 + m2 Draw up a suitable table for your results. 3.2 Demodulation by Envelope Detection The envelope of the AM signal can be recovered using an envelope detector. Implement a simple envelope detector using the half–wave rectifier in the Utilities module followed by the Tuneable Lowpass Filter. Note that to obtain the envelope the bandwidth of the Lowpass Filter must be wide enough to pass all significant frequency components of the envelope, but less that the carrier frequency (strictly, less than the carrier frequency minus the higher message frequency). Recovered message ~ m(t) Tuneable Lowpass Filter AM Signal (100 kHz carrier) Demodulate the AM signal for the cases m = 0.7 and 1.5. In each case sketch the envelope detector input and output waveforms and note the Lowpass Filter bandwidth. Does the AM signal envelope waveform correspond to the message in both cases? To help explain your results sketch a half–wave rectified cosine wave and write down the first three terms of its Fourier series representation. 3.3 Demodulation by Coherent Detection The AM signal can also be recovered using a coherent (synchronous) detector. LPF AM signal (100 kHz carrier) ~ m (t) Recovered message (100 kHz LO) Also demodulate the AM signal for the cases m = 0.7 and 1.5. In each case sketch the envelope detector input and output waveforms and note the Lowpass Filter bandwidth. Does the AM signal envelope waveform correspond to the message in both cases? Compare the results with those from envelope detection. 3013S2L1 TELE3013: Lab 1 3 3.4 AM Modulation and Demodulation of Speech Signals Generate an AM signal using the speech signal available from the Trunks Panel as your message. Observe the time domain waveform. The frequency spectrum will extend for about 3 kHz either side of the carrier. Since this is a stochastic (random) signal, the spectrum analyser may not give you much response apart from the carrier. Demodulate the signal by both envelope detection and coherent detection, and use the headphone amplifier to listen to the recovered speech. Observe and record the effect of increasing the modulation index in both cases. 3.5 Demodulation of Unknown Signals There are two unknown AM signals at the coaxial cable sockets on the coloured panel. Observe their time domain waveforms and spectra. Sketch the spectra and demodulate the signals to determine the message signals and their frequency components. 3013S2L1 TELE3013: Lab 1 4