Communication Systems and the AM Radio Example

1. message
2. transmitter
3. channel
4. receiver
5. AM radio

The first four terms are the general chain. The fifth is one concrete system in which you can point at every one of them.

Part 1

The communication chain

Sections 01–02 — the responsibility of each block, and the vocabulary for the three signals that pass between them.

No single block “does communication.” Each stage prepares, transports, selects, or reconstructs information.

In conventional AM, the message controls the carrier amplitude.

Modulation relocates the information into a frequency region appropriate for transmission and frequency-selective sharing.

Part 2

Channels and service patterns

Section 03 — medium and service pattern are two independent classifications, and they answer different questions.

Medium and service pattern answer different questions: a microwave link and a radio broadcast are both unguided.

Part 3

AM radio, end to end

Sections 04–05 — the same general chain, drawn as a concrete MW broadcast system, and the AM signal it transmits.

Every block of the general chain appears here as a physical piece of equipment.

The audio source is the message source. The AM modulator and RF power amplifier form the central transmitter functions.

The antennas couple the electrical signal to and from the wireless channel. RF amplification and filtering select the desired station before demodulation recovers audio for the loudspeaker.

\(f_m\)

message frequency

\(f_c\)

carrier frequency

\(A_m\)

message amplitude

\(A_c\)

carrier amplitude

\(\mu\)

modulation index

The carrier oscillates rapidly; its slowly changing amplitude traces an envelope related to the message.

In the spectrum we observe a carrier at \(f_c\), a lower sideband at \(f_c-f_m\), and an upper sideband at \(f_c+f_m\).

Week 3 will explain why.

Part 4

MATLAB, and checking yourself

Sections 06–08 — see the carrier and sidebands in a computed spectrum, then connect the chain and the spectrum.

Download the Week 2 MATLAB script ↓

%% Week 2: conventional AM (DSB-TC)
Fs = 100e3; T = 0.02; t = 0:1/Fs:T-1/Fs;
Am = 1; fm = 1e3; Ac = 1; fc = 10e3; mu = 0.6;
m = Am*cos(2*pi*fm*t);
c = Ac*cos(2*pi*fc*t);
s = Ac*(1 + mu*cos(2*pi*fm*t)).*cos(2*pi*fc*t);

figure;
subplot(3,1,1); plot(t*1e3,m); xlim([0 4]); grid on; title('Message'); xlabel('Time (ms)');
subplot(3,1,2); plot(t*1e3,c); xlim([0 1]); grid on; title('Carrier'); xlabel('Time (ms)');
subplot(3,1,3); plot(t*1e3,s); xlim([0 4]); grid on; title('AM-DSB-TC'); xlabel('Time (ms)');

N = length(s); S = fft(s)/N;
f2 = (-N/2:N/2-1)*(Fs/N);
figure; plot(f2/1e3,abs(fftshift(S))); grid on; xlim([-15 15]);
xlabel('Frequency (kHz)'); ylabel('Magnitude'); title('Centered double-sided spectrum');

P2 = abs(S); P1 = P2(1:floor(N/2)+1); P1(2:end-1)=2*P1(2:end-1);
f1 = (0:floor(N/2))*(Fs/N);
figure; plot(f1/1e3,P1); grid on; xlim([0 15]);
xlabel('Frequency (kHz)'); ylabel('Magnitude'); title('Single-sided spectrum');

fft returns DC first, followed by positive-frequency bins and then negative-frequency bins. fftshift rearranges those bins around zero for a centered double-sided view.

A real signal has conjugate-symmetric positive and negative frequency components; a single-sided magnitude plot keeps the nonnegative half and doubles interior magnitudes.

EE 351 · Week 2

Where do the carrier and sidebands come from?

In Week 2 we observed amplitude modulation in the time domain and through the FFT. In Week 3 we develop the mathematical explanation of frequency translation and show exactly why the carrier and sidebands appear.

Continue to Week 3 — Baseband to Sidebands →