S5-1.1 Amplitude Modulation

What this is and why it exists

Speech and music sit at low frequencies. An antenna able to radiate them directly would be kilometres long. Every station would also land on top of every other one. Modulation solves both problems with one move. It lifts a message up to a carrier frequency you choose.

Amplitude modulation is the oldest way to do that. It is also where this subject's method is set. Describe the signal in time. Describe it again in frequency. Then read the bandwidth straight off the spectrum.

The vocabulary

• Carrier — a steady high-frequency sine wave. It carries no information of its own.
• Message — the low-frequency signal you want to send. It is also called the baseband signal.
• Modulation index — how far the message swings the carrier amplitude, as a fraction of the carrier. Above one, the envelope folds over and the signal is over-modulated.
• Sideband — a copy of the message spectrum sitting beside the carrier. Full AM produces two, one above and one below.
• DSB-SC — double sideband, suppressed carrier. Both sidebands are sent and the carrier is removed.
• SSB — single sideband. Only one sideband is sent.
• VSB — vestigial sideband. One full sideband plus a trace of the other.
• Envelope detector — a diode, a capacitor and a resistor that follow the outline of the wave.
• Coherent detection — recovering a message using a locally made carrier at the right frequency and phase.
• Superheterodyne receiver — a receiver that mixes every station down to one fixed intermediate frequency.
• Image frequency — an unwanted input that mixes down to that same intermediate frequency.

The mental model

Hold two pictures of one signal at all times.

In the time picture, the carrier amplitude rises and falls with the message. Join the peaks and you draw the envelope. In the frequency picture, the message spectrum appears twice. One copy sits above the carrier and one below it. So full AM occupies twice the highest message frequency.

Now count the power. With a single tone at a modulation index of one, the carrier holds two thirds of the transmitted power. The two sidebands share the rest. Lower the index and the carrier's share only grows. The carrier conveys nothing, so at least two thirds of the power is wasted.

That number is the reason the other schemes exist. DSB-SC removes the carrier and keeps both sidebands. The saving is real and so is the cost. An envelope detector no longer works, because the envelope no longer follows the message. The receiver must rebuild the carrier itself, at the right frequency and the right phase. The Costas loop does this with two arms fed by carriers a quarter cycle apart. One arm carries the message and the other reports the phase error.

SSB goes further. One sideband already holds the whole message, so the second is redundant. You get the same message in half the bandwidth. The price is a filter with a very sharp edge, which is why SSB is used where spectrum is expensive. VSB is the compromise between the two. Leaving a vestige of the second sideband makes the filter buildable and keeps most of the saving. Analog television used it for exactly that reason.

Generation and detection are the practical half. A switching modulator makes the product with a nonlinearity and a filter rather than with algebra. A balanced modulator cancels the carrier instead of filtering it out. An envelope detector needs a well chosen time constant. Too long and the output cannot follow a falling envelope, which is diagonal clipping. Too short and the ripple of the carrier shows through.

The superheterodyne receiver is the block diagram radio has used for a century. Mixing every station down to one fixed intermediate frequency lets one set of sharp filters serve all of them. Its flaw is built in. Mixing responds to the difference in frequency, so two inputs sit at the same distance from the local oscillator, one above and one below. Both arrive at the same intermediate frequency. The unwanted one is the image, and it sits twice the intermediate frequency away from the wanted station. The image rejection ratio measures how well the front end suppresses it.

The figure of merit closes the topic. It states how much the modulation scheme itself helps or hurts the signal-to-noise ratio. It is what lets you compare AM against frequency modulation fairly.

What you should now be able to explain or do

Sketch full AM in time and in frequency, and read its bandwidth off the spectrum. Work out the power split for a given modulation index, and say why the carrier is waste. Explain why suppressing the carrier forces coherent detection, and follow the two arms of the Costas loop. Rank AM, DSB-SC, SSB and VSB by bandwidth and by receiver cost. Locate the image frequency of a superheterodyne receiver and say why it lies where it does.

Check yourself