Principles of modulation

To transmit information using a wave, a property of the wave can be made to change in a pattern that represents the information. This process is called modulation.

The information signal contains the changes to be communicated, such as changes representing sound. The carrier wave is an oscillation, generally of higher frequency, that conveys those changes. Modulation varies a property of the carrier, such as its amplitude or frequency, in accordance with the information signal.

For example, if the carrier’s amplitude is varied, the way that amplitude rises and falls represents the changes in the information signal. The carrier itself continues to oscillate, but its changing amplitude carries the information.

At the receiving end, the imposed variation is detected and used to recover the information signal. This recovery is called demodulation.

Amplitude modulation

A carrier wave is a rapidly oscillating wave used to carry information. In amplitude modulation (AM), the information signal changes the amplitude of the carrier: as the information signal varies, the carrier’s oscillations become larger or smaller. The carrier frequency remains constant.

The AM envelope

On a graph of signal voltage against time, the envelope is the smooth outline joining the tops of the carrier oscillations. Its shape follows the variation of the information signal: where the information signal increases, the carrier amplitude increases; where it decreases, the carrier amplitude decreases. The outline joining the bottoms of the oscillations is a mirror image of the upper envelope about the centre line.

Frequencies from an AM graph

The graph shows two different timescales. The carrier period is the time for one of the rapid carrier oscillations. For a periodically varying information signal, the information-signal period is the time over which the envelope repeats.

For either signal, frequency is the reciprocal of its period:

Here $$T$$ is the period in seconds and $$f$$ is the frequency in hertz. Use the period of the rapid oscillations to find the carrier frequency, or the envelope’s repeating period to find the information-signal frequency.

Frequency modulation

In frequency modulation (FM), an information signal controls the frequency of a carrier wave. As the instantaneous value of the information signal changes, the carrier’s instantaneous frequency changes with it. The carrier’s amplitude remains constant.

The carrier frequency is the frequency of the unmodulated carrier. It is also called the centre frequency: modulation makes the instantaneous frequency vary above and below it as the information signal varies.

Reading an FM signal–time graph

On a signal-voltage–time graph, the horizontal spacing of the carrier oscillations shows their frequency. Where the oscillations are closer together, more cycles occur per unit time, so the instantaneous frequency is higher. Where they are farther apart, the instantaneous frequency is lower. The height of the oscillations remains constant because the carrier amplitude does not change.

If the information signal is periodic, the pattern of changing spacing repeats. The time taken for one complete repetition is the information signal’s period, $$T$$. Its frequency is:

Here, $$f$$ is the information frequency in hertz and $$T$$ is the period in seconds. The repetition period is measured across the whole pattern of changing carrier spacing, not across one carrier oscillation.

Estimating the carrier frequency

For a complete modulation cycle in which the information signal averages to zero, the carrier frequency can be estimated by counting the carrier cycles over that interval and dividing by the elapsed time:

This gives the average carrier frequency over the interval. It estimates the centre frequency because, over the complete cycle, the frequency deviations above and below the centre balance.

Bandwidth of AM and FM signals

A modulated signal occupies a range of frequencies around a carrier frequency. Its bandwidth is the width of that range: the highest occupied frequency minus the lowest. Bandwidth is measured in hertz ($$\text{Hz}$$).

AM bandwidth

In simple amplitude modulation (AM), the information signal produces frequencies on both sides of the carrier. If the highest frequency in the information signal is $$f_{\mathrm{M}}$$, the range extends by $$f_{\mathrm{M}}$$ on each side. The required bandwidth is therefore:

A higher maximum information frequency gives a wider AM bandwidth.

FM bandwidth

In frequency modulation (FM), the carrier frequency varies above and below its centre frequency. The largest departure from the centre frequency is the maximum frequency deviation, $$\Delta f$$.

The practical bandwidth requirement for simple FM is estimated by:

Here, $$f_{\mathrm{M}}$$ is again the highest frequency in the information signal. Both a larger maximum deviation and a higher maximum information frequency increase the estimated FM bandwidth. The expression is a practical estimate rather than a strict limit on every frequency component.

Channel data capacity

A communication channel carries information from a transmitter to a receiver. Its data capacity is the maximum rate at which information can be transmitted through it reliably. It is commonly expressed in bits per second ($$\text{bit/s}$$).

Reliability matters because the receiver must distinguish the signals used to represent different bits. If signals are sent at too high a rate for the channel, the receiver may make errors when interpreting them.

Bandwidth and data capacity

A channel’s bandwidth is the range of signal frequencies it can carry. A greater available bandwidth generally permits a greater data rate: the channel can support a wider range of frequencies, allowing signals to change more rapidly while remaining distinguishable at the receiver.

Noise and signal quality

Bandwidth alone does not determine capacity. Noise is unwanted variation that interferes with the received signal. If noise makes the signal patterns difficult to distinguish, the receiver is more likely to interpret bits incorrectly.

A better-quality received signal, relative to the noise, makes those patterns easier to distinguish and can allow reliable transmission at a higher rate. A noisy channel may therefore have a lower capacity than a channel with the same bandwidth but a clearer received signal.

Bandwidth availability in transmission media

A communication channel can use only a range of frequencies that can be transmitted and received effectively. The bandwidth of the channel is the width of that usable frequency range, not the frequency at which it operates.

The transmission medium affects which frequencies can be used. Frequencies that suffer too much signal loss or distortion over a particular link may not be usable, even if they could travel through the medium over a shorter distance.

Bandwidth in different media

Optical fibre can provide very large bandwidth because it can carry a wide range of optical frequencies. The bandwidth available on a particular fibre link also depends on the equipment used to send and receive the signals.

Copper conductors carry electrical signals over a more limited usable frequency range. The range depends on the link: for example, higher-frequency signals may be weakened more over a longer conductor, reducing the frequencies that can be used effectively.

Radio communication uses portions of the electromagnetic spectrum allocated to different services. An individual radio channel is limited to the bandwidth available within its allocation. Because the spectrum must be shared, a channel cannot simply use all frequencies that its equipment could transmit.

In every medium, the usable bandwidth of a particular link depends not only on the medium or allocation but also on its equipment and operating conditions. Transmitters and receivers must be able to handle the frequencies used, and conditions such as signal loss and interference can limit which frequencies remain usable.