Sidebands and Bandwidth

Before describing the Superheterodyne receiver, you should first understand the need for it.

Edwin Armstrong originally conceived the Superheterodyne receiver as a way to locate aircraft by detecting the radio waves emitted by the ignition systems of their engines. The problem was that the faint radio waves emitted by the engines needed to be amplified. However, the RF amplifiers of the day could not work at the high frequencies produced by the engines. Armstrong realized that he could use heterodyning to shift the high-frequency radio emissions to a lower frequency that could be amplified.

Armstrong's goal was the amplification of frequencies too high to amplify. However, the Superheterodyne receiver also solved other fundamental problems with tunable radio receivers.

Amplitude Modulation seems straight-forward. The power output of the transmitter is varied according to the variations of the information to be conveyed (like Bell's voice-shaped currents AM is voice-shaped power). However, the AM signal becomes much more complicated.

Time domain and frequency domain

When we talk about "voice-shaped current" or the power output of an AM transmitter being "voice-shaped," we are talking about the time domain. That is, we have been examining the transmitter output as it varies over time. For an AM broadcast transmitter operating at 1MHz, that is modulated with a 1kHz tone, we see a 1MHz sine wave that is varying in power. Those variations happen 1,000 times per second (1kHz).

If we look at the frequency domain, that is, examine the frequencies that are produced in the process, we see that there is more to it. A close look at the transmitter output shows a 1 MHz sine wave that does not vary in amplitude at all. In addition, we see another sine wave at 1.001MHz (1,001kHz) and yet another at 0.999000MHz (999kHz). These two frequencies are 1kHz higher than the main frequency and 1kHz lower than the main frequency. These new frequencies, on the upper side and the lower side of the main frequency are called side frequencies (the main frequency is called the carrier). If the transmitter is modulated with a 2kHz tone, these side frequencies are 2kHz above and 2kHz below the carrier. When the transmitter is modulated with a complex signal, like voice or music, each frequency in the original signal has a corresponding frequency above and below the carrier. These bands of frequencies are called sidebands.

Sidebands

The upper sideband is a copy of the original modulating information (the baseband). For example, a square wave contains the fundamental frequency of the wave and all of the odd harmonics. Therefore a 100Hz square wave contains sine waves at 100Hz, 300Hz, 500Hz, 700Hz, 900Hz, etc., at decreasing powers as the frequency increases. If a 1MHz carrier is modulated with a 100Hz square wave, the upper sideband will contain sine waves at 1.0001MHz (1,000,100Hz), 1.0003MHz (1,000,300Hz), 1.0005MHz (1,000,500Hz), etc. This is 1MHz plus 100Hz, 1 MHz plus 300Hz, 1MHz plus 500Hz, etc. For every frequency in the baseband, there is a copy in the upper sideband. The lower sideband is a mirror image of the upper sideband. In other words, the lower sideband has frequencies 100Hz, below the carrier, 300Hz below the carrier, 500Hz below the carrier, etc.

To the left, the components of a 100 Hz square wave are shown in the time domain and the frequency domain. In the frequency domain, the horizontal position of each line represents the frequency and the vertical length of each line represents the relative magnitude of each frequency component. In the AM signal, the upper sideband is a copy of the baseband and the lower sideband is a mirror image of the upper sideband. The curved lines represent the removed distance between the baseband and the radio signals.

It may seem impossible that the carrier of the AM signal doesn't vary. After all, by definition, amplitude modulation means to vary the amplitude of the carrier. Nevertheless, careful examination of the AM signal, frequency-by-frequency, shows that when the amplitude of the carrier is varied, it doesn't actually change at all, but the sidebands seem to appear out of nowhere. Even closer examination of the signal shows that the carrier and sidebands interact with each other in such a way that they produce a single frequency—the carrier—that varies according to the modulating signal. In other words, the exact nature of the AM signal depends on whether you are examining it in the time domain (where it appears as a single frequency that varies in power) or the frequency domain (where it appears as an unchanging carrier frequency with sidebands).

This illustrates a significant design problem for radio receivers. The receiver must be able to receive the carrier plus the sidebands. If the receiver's filtering is so sharp and narrow (high Q) that only the carrier is picked-up—and the sidebands are rejected—the result is that no more than an unmodulated carrier is received. The modulating information is lost. All of the modulating information is contained in the sidebands.

A radio receiver must be able to receive the desired carrier and its sidebands without receiving any of the signals of the transmitters on adjacent frequencies. The following illustration shows how radio stations are spaced. On the AM broadcast band, the carriers are 10 kHz apart. Each sideband is allowed to extend up to 4 kHz from the carrier. This leaves a "guard band" of 2 kHz between adjacent channels. More on vector analysis-

Three adjacent AM radio stations centered on the AM broadcast band. The vertical lines represent the carriers and the three-sided boxes represent the sidebands that extend 4 kHz above and below the carriers.

The ideal filter for an AM broadcast receiver would pick up the carrier and its sidebands without picking up any of the sidebands of the adjacent channel. A simple tank circuit won't work. This is because a tank circuit can be designed to have a wide response or a sharp response but not both.

The curved line above shows the response of a low-Q tuned circuit used as a filter. The high point shows that the filter responds most to the resonant frequency, but the response doesn't drop off sharp enough to block the sidebands of adjacent channels.

A high-Q or narrow-band filter that has a sharp enough response to reject the adjacent channels also rejects the sidebands of the desired channel. Without the sidebands to interact with the carrier all that the receiver gets is an unmodulated carrier.

An ideal filter would have the sharp sides of the high Q filter but with the wide response of the broadband filter. Such filters can be made, but it is difficult to make them tunable. It is suitable for a specialized receiver that only has to tune to a single channel but is not practical for a receiver that needs to be able to tune to multiple channels.

The need for a tunable receiver that can pick up the carrier and all of the sidebands, without picking up frequencies from adjacent channels, led to the development of the Superheterodyne receiver.