The Heterodyne Receiver: Frequency Mixing and the Intermediate Frequency

The challenge faced by a radio receiver after snagging a desired radio frequency (RF) signal is to extract the audio signal that rides on the RF so that a speaker can be driven to reproduce the voice of the transmitting operator. This process is called demodulation, largely because the process of injecting the audio signal into the radio waves in the first place is called modulation.

Let’s consider a typical single-sideband (SSB) radio frequency signal with an audio envelope modulating the RF amplitude… In other words, thanks to the modulation process, the relatively tiny radio wavelengths vary in amplitude as determined by the amplitude of the very long audio wavelengths, like the figure below:

The audio waveform produced by a microphone (or other device) modulates the amplitude of an AM or SSB signal, creating an "envelope" that is imposed on the RF transmitted signal.

See how the RF signals are sort of enveloped top and bottom by the mirrored shape of the audio signal? And note how the long waveform of the audio signal is still present in the modulated signal, only it has been encoded into a much higher frequency RF signal. So, the trick the receiver has to perform is recreating that much lower frequency audio signal from the envelope shape of the much higher frequency RF signal.

A heterodyne receiver is a type of analog signal processing receiver that uses the principle of heterodyning, or signal mixing, to change a detected radio frequency to a much lower frequency, while preserving the modulating (audio) signal envelope. If the receiver uses this heterodyning trick, perhaps more than once, it can shift the received signal from those very high radio frequencies down to a frequency that is low enough for some audio signal filtering to be applied. After filtering all that remains is the original modulating audio signal form, ready to drive a speaker and make voice sounds.

So… how’s this heterodyning thing work? It works by mixing two different frequency signals together. When two signals of different frequency are combined or mixed, four product frequencies result: 1) the original higher frequency, 2) the original lower frequency, 3) a signal with a frequency that is the sum of the two original frequencies, and 4) a signal with a frequency that is the difference of the two original frequencies. The receiver does not use the two original frequencies further, and it does not use the sum frequency signal, and these are filtered out of the receiver's processing stream. But the difference frequency signal is preserved for further demodulation processing. Let’s consider how this lower frequency difference product is obtained.

The amplitudes (power) of the two mixed signals add together to produce a product signal containing beats, and the beats occur at a lower frequency than the mixed frequencies – the beats are in fact at a frequency that is the mathematical difference of the two mixing frequencies. Take a look at the graphic below to get a sense of how this works.

Two signals of differing frequency combine to produce beat frequencies that are lower in frequency than the original signals -- the beat is the difference product of the two frequencies.

Notice that where the two mixing frequency signals align the amplitude values add up to double the magnitudes, either positive or negative. But where the mixing frequencies are out of phase with one another the amplitudes cancel out to a value of zero. And there are all sorts of results in between those two extremes as the two signals ebb and flow with one other. The resulting signal forms are the beats, and they contain a frequency component much lower than the original RF signals, as depicted here.

Interestingly, if one of the mixed signals contains a modulating envelope, that envelope shape will be preserved in the lower frequency beat component, and ultimately it will be the filtered product signal that drives the speaker.

Now, pulling this all together: The heterodyne receiver has an electronic component called the mixer that accepts both the received RF signal and another unmodulated RF signal from an oscillator circuit. Of course, the mixer circuit mixes the two signals together to produce a lower frequency signal called the intermediate frequency (IF) – intermediate between the RF received frequency and the lower audio frequency that is ultimately desired.

Two combined frequency signals produce a beat frequency product of lower frequency at the receiver's intermediate frequency (IF). Importantly, the amplitude modulation is preserved in the intermediate frequency signal.

The IF retains the audio signal modulation envelope form that is processed further by the receiver into the audio frequency signal. A heterodyne receiver may use another mixing stage to lower the IF further, or other types of electronic filters may be implemented that allow the audio frequency enveloping waveform to be passed on for sound reproduction.

The audio waveform envelope processing effectively discards one of the mirror image audio waveforms and adjusts the voltage scale for the remaining waveform, as depicted in the last set of graphics.

After additional mixing down and/or filtering of the IF, the audio envelope waveform remains. It is adjusted in amplitude to produce an AC signal to drive a speaker that reproduces its sound.

In this way, the original audio waveforms of the transmitting station are extracted from the modulated RF signals sent from that station. The voice of the transmitting station’s operator is reproduced by the heterodyne receiver accurately recreating the audio waveforms for a speaker.

-- Stu WØSTU