12.6 Mixing, Image Frequencies & Spurious Products

12.6 Mixing, Image Frequencies & Spurious Products

Quick Answer: Mixing is the combination of two signals to produce sum and difference frequencies. A mixer's output holds the original frequencies plus the sum and the difference. The image is rejected in the RF stage. Image = LO ∓ IF on the opposite side of the LO from the wanted signal: 151 MHz signal, 140 MHz LO, 11 MHz IF → image 129 MHz. Overdriving a mixer generates spurious mixer products.

Sub-topic 3-F-044 (Mixers) contains the single most calculation-heavy idea in the Receivers topic. Get the image-frequency geometry straight and four of its six items fall out.

What mixing does

What is the mixing process in a radio receiver? The combination of two signals to produce sum and difference frequencies.

A mixer is a non-linear device fed two signals — the incoming RF and the local oscillator. Non-linearity is essential: a perfectly linear stage would simply add the two waveforms and produce no new frequencies at all. The non-linear transfer characteristic multiplies them, and multiplication of two sinusoids produces their sum and difference.

What are the principal frequencies that appear at the output of a mixer circuit? The original frequencies and the sum and difference frequencies.

Four components, and the pool's answer names all four:

The pool asks this concretely — "RF input to a mixer is 200 MHz and the local oscillator frequency is 150 MHz. What output would you expect at the IF output prior to any filtering?" — and the keyed answer is 50, 150, 200 and 350 MHz. All four, because the question says prior to any filtering. The IF filter then selects the one you want, normally the difference.

The image frequency

This is the concept that separates candidates who memorised from candidates who understood.

A mixer produces the IF from any input that differs from the LO by the IF amount — and there are always two such inputs, one above the LO and one below it. One is your wanted signal; the other is the image.

Image = wanted signal − 2 × IF (when the LO is below the signal) Equivalently: image = LO − IF when the wanted signal is LO + IF

The pool's worked example

Normal channel 151.000 MHz, IF 11.000 MHz, LO 140.000 MHz. What is the image frequency? 129.000 MHz.

Lay it out on a line:

Both 151 and 129 differ from the 140 MHz LO by exactly 11 MHz, so both produce an 11 MHz IF. The mixer cannot tell them apart. Check by subtraction: 151 − 129 = 22 = 2 × IF, which is always the spacing between a signal and its image.

The second pool example

"If a receiver mixes a 13.8 MHz VFO with a 14.255 MHz receive signal to produce a 455 kHz IF, what type of interference will a 13.345 MHz signal produce?" → an image response.

Verify: 14.255 − 13.8 = 0.455 MHz ✓. And 13.8 − 13.345 = 0.455 MHz ✓. Both land on the 455 kHz IF, and 14.255 − 13.345 = 0.910 MHz = 2 × 455 kHz. Textbook image.

Where the image must be rejected

In what radio stage is the image frequency normally rejected? The RF stage.

This is forced by logic, not by convention. Once mixing has happened, the image and the wanted signal occupy exactly the same IF frequency. No IF filter, however sharp, can separate them — they are literally the same frequency by then. The only opportunity is before the mixer, in the tuned RF amplifier and preselector, which is 22 MHz away from the wanted signal in the first example and must roll off enough over that span.

Three consequences worth knowing:

1. A higher IF improves image rejection, because the image moves further from the wanted signal (2 × IF away) and the RF selectivity has an easier job.
2. A lower IF improves adjacent-channel selectivity, because sharp narrow filters are easier to build at low frequencies.
3. Those two pull in opposite directions, which is exactly why double-conversion receivers exist: a high first IF for image rejection, then a low second IF for selectivity (section 12.1).

Overdriving the mixer

What might occur in a receiver if excessive amounts of signal energy overdrive the mixer circuit? Spurious mixer products are generated.

A mixer is deliberately non-linear, but only in a controlled way. Drive it too hard — a strong local transmitter, a nearby broadcast station, too much RF gain — and higher-order products appear: 2RF ± LO, RF ± 2LO, 3RF ± 2LO and beyond. These land on frequencies unrelated to anything you intended, producing "phantom" signals that appear and disappear as the offending transmitter keys.

The practical fixes are the ones the pool implies elsewhere: back off the RF gain, insert attenuation ahead of the receiver, or add a preselector filter. This is also the reason a receiver's intermodulation and blocking specifications matter as much as its sensitivity (section 12.4) — on a ship's mast or an airport ramp, the noise floor is rarely the limiting factor; strong nearby transmitters are.