Create a System Block Diagram for the AM Radio Design

Visualize the big picture of the AM radio transmitter, receiver, and interfering signals with a system block diagram. Each block in the diagram has an underlying mathematical model.

Start with the AM signal model

The signal model for an AM signal is

where A_c is the carrier amplitude, f_c is the carrier frequency, m(t) is the message signal, and the modulation index is

The modulation index controls how much of the signal is made up of the message and how much is pure carrier.

The AM scheme also requires that min[m(t)] ≥ –1. A simple decomposition of x_c(t) shows that a pure carrier term and a double sideband modulation term are involved. The term double sideband comes from viewing x_c(t) in the frequency domain.

The second term follows from the modulation theorem for Fourier transforms (FT). For m(t) real, the magnitude spectrum |M(f)| is symmetrical about f = 0. Multiplying by cos(2πf_ct) shifts M(f) up and down in frequency by the carrier frequency f_c.

The spectrum of M(f – f_c) just above f_c is known as the upper sideband (USB), and the one just below f_c is known as the lower sideband (LSB). The same relation holds for the M(f + f_c) term. The USB and LSB contain the same information — hence the term double sideband.

The figure shows the frequency domain details of the AM signal.

Credit: Illustration by Mark Wickert, PhD

Look at the waveform

The AM waveform, shownhere for a particular m(t), motivates a simple receiver design.

Credit: Illustration by Mark Wickert, PhD

The envelope of x_c(t) is the dashed line, given by R(t) = A_c(1 + am(t)). As long as min[am(t)] > –1, retaining just the positive half cycles of x_c(t) allows R(t) to accurately contain m(t). In electronic circuit form, the recovery of m(t) from x_c(t) is accomplished with an envelope detector as shown.

Credit: Illustration by Mark Wickert, PhD

You need a direct current (DC) block or level shift to finally get a term proportional to m(t). Circuit theory tells you that a DC block can be as simple as placing a coupling capacitor in a series with the detector output and the next stage of signal processing, which may be an amplifier used to drive headphones or a speaker, for example.

Complete the diagram

The system block diagram for the transmitter and receiver (transceiver) is shown here.

Credit: Illustration by Mark Wickert, PhD

There's an additional component, namely a band-pass filter (BPF), in front of the envelope detector. The filter is expected to combat the adjacent channel interference to the receiver model. A tunable BPF filter centered at f_c can become a BPF with center frequency fixed at f_IF if you place a mixer (multiplier) in front of it.

Now you need a local oscillator (LO) to shift the frequency of the received signal from f_c to f_IF. The local oscillator signal is actually a cosine signal at frequency f_c +/– f_IF. The math behind the frequency shifting is based on the FT modulation theorem. The inclusion of the frequency shifting front-end is known as a superheterodyne receiver.