Mixing, Multiplying, and Intermodulation

Mixing

What is another term for the mixing of two RF signals?

Heterodyning.

What combination of a mixer’s Local Oscillator (LO) and RF input frequencies is found in the output?

The sum and difference

Feed a mixer two frequencies and you get both their sum and their difference — plus, in a real mixer, the originals and a spray of higher-order products. A filter after the mixer selects the one you want.

Which mixer input is varied or tuned to convert signals of different frequencies to an intermediate frequency (IF)?

Local oscillator

This is the superheterodyne principle. Rather than building a filter that tunes, you tune the local oscillator so that whatever you want lands on a fixed intermediate frequency, where one very good filter does the work. It is why a receiver has a fixed IF and a tunable VFO.

Image response

What is the term for interference from a signal at twice the IF frequency from the desired signal?

Image response.

The mixer produces sum and difference, and it cannot tell which input produced which. So a signal on the other side of the local oscillator — spaced twice the IF away from the one you want — mixes down to exactly the same IF and appears as an unwanted station on frequency.

The defence is filtering ahead of the mixer, which is what a receiver’s front end is for and what cheap wideband receivers lack.

Multipliers and deviation

What is the stage in a VHF FM transmitter that generates a harmonic of a lower frequency signal to reach the desired operating frequency?

Multiplier.

Generating a stable, modulated signal is easier at low frequency, so a classic FM transmitter modulates something like 12 MHz and multiplies up to 146 MHz.

And a multiplier multiplies the deviation as well as the carrier, which gives the pool’s calculation:

$\Delta f_{osc} = \frac{\Delta f_{out}}{N}, \qquad N = \frac{f_{out}}{f_{osc}}$

Worked: a 12.21 MHz reactance-modulated oscillator, in a 5 kHz deviation transmitter operating on 146.52 MHz.

N = 146.52 / 12.21 = 12, so the oscillator deviation is 5000 / 12 = 416.7 Hz.

That small deviation at low frequency is precisely why the scheme works — a reactance modulator can manage 400 Hz far more linearly than 5 kHz.

FM bandwidth

$BW = 2\,(\Delta f + f_m)$

Carson’s rule: twice the sum of peak deviation and highest modulating frequency.

What is the total bandwidth of an FM phone transmission having 5 kHz deviation and 3 kHz maximum modulation frequency?

2 × (5 + 3) = 16 kHz. Which is where the “15 kHz” figure for an FM repeater channel comes from, and why deviation limits exist.

Intermodulation

What process combines two signals in a non-linear circuit to produce unwanted spurious outputs?

Intermodulation.

Two signals in something non-linear produce sums and differences of their harmonics. Unlike mixing, this is unwanted — it happens in an overloaded receiver front end, in a saturated amplifier, and sometimes in corroded metalwork near a transmitter.

Which intermodulation products are closest to the original signal frequencies?

Odd-order.

Which of the following is an odd-order intermodulation product of frequencies F1 and F2?

2F1-F2

Work it through with real numbers. F1 = 146.0 and F2 = 146.1 MHz:

• 2F1 − F2 = 292.0 − 146.1 = 145.9 MHz — third-order, 100 kHz below F1, right in the band.
• 2F1 + F2 = 438.1 MHz — far away, easily filtered.

That is the whole problem with odd-order products: they land near the signals that created them, where no filter can remove them without removing the wanted signal too. Even-order products land far away and are harmless.

It is why receiver third-order intermodulation performance is the specification that matters, and why adding a preamplifier to a crowded band often makes reception worse.

Bandwidth and symbol rate

What is the relationship between transmitted symbol rate and bandwidth?

Higher symbol rates require wider bandwidth.

A fundamental limit, not an implementation detail. Faster signalling needs more spectrum, which is why FT8 is slow and narrow while a fast data mode is wide.

Why is it good to match receiver bandwidth to the bandwidth of the operating mode?

It results in the best signal-to-noise ratio.

Noise power scales with bandwidth, so every hertz wider than the signal is noise for free.

Duty cycle and your transmitter

Why is it important to know the duty cycle of the mode you are using when transmitting?

Some modes have high duty cycles that could exceed the transmitter’s average power rating.

A transmitter rated 100 W on SSB may not survive 100 W of continuous FT8. SSB transmits only on syllables; digital modes hold a constant carrier. The rating is about heat, and heat is average power.

The practical rule: back off to 50% or less of rated output for high-duty-cycle digital modes, and watch the finals’ temperature the first time.

Check yourself

1. Your receiver’s IF is 455 kHz and you are tuned to 7.100 MHz. Where is the image?
2. A 2 metre transmitter multiplies a 12 MHz oscillator by 12. What deviation does the oscillator need for 5 kHz out?
3. Why are third-order intermodulation products worse than second-order?