TRF and Superheterodyne Receivers

Every radio you will ever own is a superheterodyne, and the examiner knows it. This lesson is worth learning properly rather than memorising, because the two facts the paper leans on hardest — that the intermediate frequency is fixed, and that a superhet therefore has an image — are consequences of one another. Understand the mixer and both fall out; memorise them separately and you will mix them up under time pressure.

What a receiver has to do

Three jobs, and they pull in different directions.

• Select one signal out of the thousands arriving at the aerial at the same instant, and reject everything else — including stations only two or three kilohertz away.
• Amplify it enormously. A usable HF signal might be a fraction of a microvolt at the aerial; a loudspeaker wants volts. That is a voltage gain of a million or more, spread over several stages.
• Recover the information. A 7 MHz wave means nothing to an ear; the detector has to strip the speech or the Morse back off the carrier.

The crystal set and the TRF

The oldest receiver is the crystal set: an aerial, a tuned circuit, a diode detector and a high-impedance earpiece. No amplification at all — it runs on the power picked up by the aerial. It selects badly and it is deaf, but it demonstrates the whole chain in four components, and it is why the detector is still sometimes called the crystal.

The obvious improvement is to add gain before the detector, at radio frequency, with a tuned circuit at each stage to sharpen the selectivity as you go. That is the tuned radio frequency receiver, the TRF. Every stage is tuned to the incoming signal itself. It works, and it was the standard set of the 1920s, but it was abandoned for three connected reasons:

1. Selectivity changes across the band. The bandwidth of a tuned circuit is its resonant frequency divided by its Q, and Q does not improve as you tune upwards. A circuit that is 10 kHz wide at 500 kHz is 140 kHz wide at 7 MHz. The same receiver is therefore sharp at the bottom of its range and hopelessly broad at the top.
2. Tracking several tuned circuits is a mechanical nightmare. Four RF stages means four tuned circuits that must all peak on exactly the same frequency at every point of the dial, and stay there as the components age.
3. High gain at one frequency is unstable. Put a great deal of gain into several stages all tuned to the same frequency and the stray coupling between input and output turns the receiver into an oscillator.

Armstrong's answer: change the frequency

Edwin Armstrong's insight, in 1918, was that none of those problems is really about selectivity — they are all about doing the difficult work at a frequency that keeps moving. So do not move it. Convert every incoming signal, whatever it is, to one fixed frequency, and do the sharp filtering and most of the gain there. That is the superheterodyne: super (above audio) hetero (different) dyne (power) — a beat between two frequencies, one of them generated inside the receiver.

What the mixer does

A mixer is not an adder. It is a deliberately non-linear stage, and when two frequencies are applied to a non-linear device the output contains not only the two originals but also their sum and their difference.

Both appear. A tuned circuit immediately after the mixer keeps one and throws the other away, and the superhet always keeps the difference, for a plain reason: the difference is a low frequency where sharp filters and high-gain amplifiers are cheap and stable, while the sum is higher than the signal was to start with, which helps nobody.

Why "fixed" is the whole trick

The difference frequency is called the intermediate frequency, the IF. It never changes. When you tune the receiver, the RF input circuit and the local oscillator move together, always staying exactly one IF apart, so the mixer keeps delivering the same IF whatever you are listening to.

That single fact answers every one of the TRF's three complaints:

• The IF filter is built once, for one frequency, and can be made as sharp as you like — a crystal or mechanical filter, not a stagger-tuned coil. Its selectivity is identical at the top of the band and the bottom.
• Only two circuits have to move as you tune: the RF tuning and the local oscillator. That is why their variable capacitors sit on a common shaft. One control, two circuits — ganged tuning — and keeping them exactly one IF apart across the whole band is called tracking.
• The huge gain is now spread across two different frequencies, RF and IF, so stray feedback at one of them cannot go round the loop.

Which IF, and why

Two values appear in the exam and in almost every receiver ever made:

That is the trade-off in one line: a low IF gives better selectivity, a high IF gives better image rejection. You cannot have both from a single conversion, which is exactly why double-conversion sets exist.

The image frequency — the price of mixing

The mixer does not know or care which side of the local oscillator a signal arrived from. It subtracts. So there are always two input frequencies that produce the same IF: the one you want, and one sitting the same distance on the other side of the oscillator. That second one is the image. Once it has been converted to the IF, nothing downstream can tell it from the wanted signal — no IF filter, however sharp, will help, because the image is now on the IF.

The image is always 2 × IF away from the wanted signal, on the far side of the oscillator:

Worked example 1 — 40 m with a 455 kHz IF

You are tuned to 7.050 MHz. The IF is 455 kHz and the local oscillator is above the signal, so it runs at 7.050 + 0.455 = 7.505 MHz.

The image is 7.050 + (2 × 0.455) = 7.050 + 0.910 = 7.960 MHz.

Check it the long way: 7.960 − 7.505 = 0.455 MHz — the same IF the wanted signal produces. Both get through. Note that 7.505 MHz is the oscillator frequency and is offered as a wrong answer in every paper that asks this.

Worked example 2 — a 9 MHz IF, oscillator below

You are tuned to 21.200 MHz with a 9.000 MHz IF and the oscillator below the signal, at 21.200 − 9.000 = 12.200 MHz.

The image is 21.200 − (2 × 9.000) = 21.200 − 18.000 = 3.200 MHz.

Check: 12.200 − 3.200 = 9.000 MHz. Notice how far away the image has been thrown — 18 MHz, right out of the range the input tuned circuit passes at all. With a 455 kHz IF on that band the image would have been only 910 kHz away, comfortably inside the front end's passband. That is the argument for a high first IF, made with numbers.

The three cures

1. RF selectivity ahead of the mixer. The tuned circuit in the RF amplifier is the only thing in the receiver that can distinguish the image from the signal, because it is the only stage that sees them before conversion. This is the first line of defence and the reason a preselector exists.
2. A higher first IF. Raising the IF moves the image further from the signal — by twice as much as you raise the IF — where a modest front-end tuned circuit can reject it easily.
3. Double conversion. Convert first to a high IF for image rejection, then a second time down to a low IF for selectivity, and get both.

Single and double conversion

A single-conversion receiver has one mixer, one local oscillator and one IF. Simple, cheap, and forced to compromise between selectivity and image rejection.

A double-conversion receiver mixes twice: to a high first IF — 45 MHz and 9 MHz are common — and then down to a low second IF such as 455 kHz. The first conversion places the image far outside anything the front end will pass; the second delivers a frequency at which a sharp filter is easy. The cost is a second oscillator, and a second oscillator means more chances for spurious birdies inside the set.

Move the numbers yourself

Change the received frequency, the IF and the side the oscillator sits on in the panel below, and watch the image move. Do worked example 1 by hand first, then set the panel to 7.050 MHz with a 455 kHz IF and confirm you get 7.960 MHz. Then raise the IF to 10.7 MHz without changing anything else and see how far the image runs away.