Sideband

carrier frequency

, fm is the maximum modulation frequency

In

of the modulated signal except the carrier. The signal components above the carrier frequency constitute the upper sideband (USB), and those below the carrier frequency constitute the lower sideband (LSB). All forms of modulation produce sidebands.

Sideband creation

We can illustrate the creation of sidebands with one trigonometric identity:

${\displaystyle \cos(A)\cdot \cos(B)\equiv {\tfrac {1}{2}}\cos(A+B)+{\tfrac {1}{2}}\cos(A-B)}$

Adding ${\displaystyle \cos(A)}$ to both sides:

${\displaystyle \cos(A)\cdot [1+\cos(B)]={\tfrac {1}{2}}\cos(A+B)+\cos(A)+{\tfrac {1}{2}}\cos(A-B)}$

Substituting (for instance)  ${\displaystyle A\triangleq 1000\cdot t}$  and  ${\displaystyle B\triangleq 100\cdot t,}$  where ${\displaystyle t}$ represents time:

${\displaystyle \underbrace {\cos(1000\ t)} _{\text{carrier wave}}\cdot \underbrace {[1+\cos(100\ t)]} _{\text{amplitude modulation}}=\underbrace {{\tfrac {1}{2}}\cos(1100\ t)} _{\text{upper sideband}}+\underbrace {\cos(1000\ t)} _{\text{carrier wave}}+\underbrace {{\tfrac {1}{2}}\cos(900\ t)} _{\text{lower sideband}}.}$

Adding more complexity and time-variation to the amplitude modulation also adds it to the sidebands, causing them to widen in bandwidth and change with time. In effect, the sidebands "carry" the information content of the signal.^[1]

Sideband Characterization

In the example above, a cross-correlation of the modulated signal with a pure sinusoid, ${\displaystyle \cos(\omega t),}$ is zero at all values of ${\displaystyle \omega }$ except 1100, 1000, and 900. And the non-zero values reflect the relative strengths of the three components. A graph of that concept, called a Fourier transform (or spectrum), is the customary way of visualizing sidebands and defining their parameters.

Amplitude modulation

because the carrier and both sidebands are present. This is sometimes called double sideband amplitude modulation (DSB-AM), but not all variants of DSB are compatible with envelope detectors.

In some forms of AM, the carrier may be reduced, to save power. The term

BPSK

where the signal is continually present.

If part of one sideband and all of the other remain, it is called

. Since the sidebands are mirror images, which sideband is used is a matter of convention.

In SSB, the

: in USB mode, the dial frequency is subtracted from each radio frequency component to produce a corresponding audio component, while in LSB mode each incoming radio frequency component is subtracted from the dial frequency.

Frequency modulation

Carson's rule

is a useful approximation of bandwidth in several applications.

Effects

Sidebands can

and public service FM transmitters generally utilize ±5 kHz deviation.

To accurately reproduce the modulating waveform, the entire signal processing path of the system of transmitter, propagation path, and receiver must have enough bandwidth so that enough of the sidebands can be used to recreate the modulated signal to the desired degree of accuracy.

In a non-linear system such as an amplifier, sidebands of the original signal frequency components may be generated due to distortion. This is generally minimized but may be intentionally done for the

fuzzbox

musical effect.

See also

• Independent sideband
• Out-of-band communications involve a channel other than the main communication channel.
• Side lobe
• Sideband computing is a distributed computing method using a channel separate from the main communication channel.
• TV transmitter

References