Explain what a mixer outputs, work out FM bandwidth and deviation, and know why odd-order intermodulation products land closest.
Syllabus: Frequency changing; bandwidths of various modes; deviation; intermodulation
Compendium articles on the ideas in this lesson, beyond what the exam asks.
Practise the 13 pool questions for this group. Answers are shuffled, and every one comes with a one-line "why".
Mixing two RF signals is heterodyning. Out come the sum and difference of the two inputs, not their average, product or ratio. A receiver keeps the difference as a fixed IF (intermediate frequency). To receive a different signal, tune the local oscillator (LO), so a different input lands on the IF.
A second signal on the other side of the LO is also one IF away, so it lands on the IF too. This image response sits twice the IF from the desired signal.
RememberMixer output = sum and difference. LO tunes. Image = 2 × IF from the wanted signal.
A VHF FM transmitter often starts at a low frequency and uses a multiplier stage, which generates a harmonic of it, to reach the operating frequency. The frequency swing is multiplied too, so the oscillator swings by the final deviation divided by the multiplication factor.
factor = 146.52 ÷ 12.21 = 12, so deviation = 5 kHz ÷ 12 = 416.7 HzRememberFinal deviation ÷ multiplication factor = oscillator deviation.
As a rule of thumb (Carson's rule), the signal reaches the deviation plus the modulating frequency on each side of the carrier. Count one side, then double it.
2 × (deviation + modulating frequency) = 2 × (5 + 3) = 16 kHzRememberDouble the sum. Do not stop at 5 + 3 = 8.
Faster symbol rate means a wider signal. A receiver filter matched to the mode passes the whole signal and little else, so it gives the best signal-to-noise ratio. It is not an FCC rule, and it has nothing to do with impedance or power draw.
RememberHigher symbol rate = wider. Matched filter = best signal-to-noise.
A mode that transmits nearly continuously has a high duty cycle, so the average power is close to the key-down power. That can exceed the transmitter's average power rating even when the peak is fine.
RememberKnow the duty cycle so a high-duty mode doesn't overheat your transmitter.
A mixer mixes on purpose. Intermodulation is the same mixing in a non-linear circuit that produces unwanted spurious outputs. The order is the sum of the multipliers: 2F1−F2 is 2 + 1 = 3, an odd order.
| Product | Order | Odd or even |
|---|---|---|
| 2F1−F2 | 3 | odd |
| 3F1−F2 | 4 | even |
| 5F1−3F2 | 8 | even |
RememberOdd-order products (3rd, 5th) are the ones closest to your signals.