Modulation and superhet

How wide is a signal?

Every signal has skirts that never quite stop. How wide it is therefore depends on where you cut. The occupied bandwidth is the range holding 99 % of the power, with half a percent left outside on each side. For interference on the adjacent channel the width at −40 or −60 dB tells you more: that is where it is decided whether someone 1 kHz away still hears your signal.

AM and SSB

AM puts the audio frequency left and right of the carrier, so the signal is twice as wide as the highest audio frequency, 5.4 kHz for 2.7 kHz. At 100 % modulation with one tone, 2/3 of the power sits in the carrier, which carries no information. Above 100 % the envelope breaks off: the transmitter goes quiet for a moment, and every break creates skirts far beside the channel. SSB drops the carrier and one sideband and gets by with the plain audio bandwidth.

FM

With FM the frequency is shifted and the envelope stays constant. The spectrum has lines spaced at the audio frequency, their heights follow the Bessel functions of the modulation index β = deviation / audio frequency. At β = 2.405 the carrier disappears completely, which is how you set the deviation by ear. Carson's rule of thumb for the bandwidth: 2 · (deviation + highest audio frequency). With 2.5 kHz deviation and a 3 kHz tone that is 11 kHz, which fits the 12.5 kHz channel spacing.

CW and key clicks

CW switches the carrier on and off. At 25 WpM a dot lasts 48 ms, and around 104 Hz of bandwidth would be needed. If the transmitter switches hard, in less than a microsecond, the spectrum at −60 dB reaches about 6.6 kHz: those are the key clicks that crackle on the adjacent channel. A cosine edge with 5 ms rise time brings the width at −60 dB down to about 440 Hz, with 1 ms it is 1.3 kHz, with 10 ms 250 Hz. Gaussian and cosine edges are close together, a straight ramp has kinks and reaches further.

When the PA limits

The nicest edge is no help if the PA is overdriven afterwards. It cuts off the top, and the round edge turns back into a corner. With 6 dB too much drive into a hard-limiting stage, the width at −60 dB goes from about 440 Hz to about 890 Hz. With SSB it is the same: two tones through a softly saturating PA give mixing products 25 dB below the tones at full drive, 3 dB back −35 dB, 6 dB back −46 dB, 10 dB back −62 dB. That is the splatter your neighbour hears. To measure what a PA puts out on the harmonics, use Measure harmonics.

FSK

RTTY at 45.45 Bd and 170 Hz shift needs about 250 Hz according to the ITU formula B + 2.4 · deviation. If the phase jumps at every change, the signal gets much wider: at −40 dB about 1600 Hz instead of 650 Hz with continuous phase. That is why good transmitters generate FSK with continuous phase.

Intermodulation

No amplifier is perfectly linear. When two strong signals f1 and f2 come in, mixing products appear. The most annoying are the third-order ones at 2·f1 − f2 and 2·f2 − f1: they sit exactly as far beside the two signals as these are apart, so right in the band, where no filter helps.

IP3

Every 1 dB louder per tone raises the third-order products by 3 dB. Extend both lines and they cross at the third-order intercept point, referred to the input IIP3. It is never reached, the amplifier saturates long before (with a cubic characteristic, 1 dB compression at IIP3 − 9.6 dB). But it tells you how loud the products are: IM3 = 3 · P − 2 · IIP3. Measuring works the other way round: margin Δ between tone and product, then IIP3 = P + Δ/2.

Numbers

A receiver with IIP3 +20 dBm, 12 dB noise figure and 2.4 kHz bandwidth has −128.2 dBm of noise. Two signals at −30 dBm each (S9+43) create products at −130 dBm, just below the noise. A simple receiver with IIP3 −10 dBm turns that into −70 dBm, which is S9+3 on a frequency where nobody is transmitting. The range between the noise and the level at which the products rise out of the noise is the dynamic range: 2/3 · (IIP3 − noise), 98.8 dB in the first case.

Preamp

A preamp with 20 dB gain and IIP3 +5 dBm in front of the same receiver lowers the noise figure from 12 to 1.5 dB. But the IIP3 of the chain drops to −1.2 dBm, because the receiver now sees 20 dB more. The products rise to −87.6 dBm, the dynamic range drops to 91.7 dB. On HF, where the band is noisier than the receiver anyway, that is a bad trade. What else the receive chain costs is worked out by the receive chain.

The superhet

The superheterodyne receiver mixes the signal with an oscillator (LO) to a fixed intermediate frequency (IF), where the sharp filters sit. The mixer forms sum and difference, so a second frequency on the other side of the oscillator gives the same IF: the image frequency, two IFs away from the wanted signal. At 14.2 MHz and 9 MHz IF the oscillator sits at 23.2 MHz, the image frequency at 32.2 MHz.

Preselection

Only what sits in front of the mixer helps against the image frequency. A tracking tuned circuit with Q 50 attenuates it by 39.2 dB at 9 MHz IF; for 60 dB it would need a Q of around 550. With 455 kHz IF the image frequency is only 910 kHz away, at 15.11 MHz in the 19 m broadcast band, and the same circuit manages 16 dB. 60 dB would need a Q of around 8000, which is why old shortwave receivers use two mixers in a row: first up, then down to 455 kHz.

High IF

Modern receivers mix to 45 MHz or higher. At 7.1 MHz the oscillator then sits at 52.1 MHz, the image frequency at 97.1 MHz in the FM broadcast band. A 5th-order low-pass with 30 MHz cut-off attenuates it by 51 dB. In exchange other responses move forward: the half IF at 29.6 MHz is still in the passband, and only a balanced mixer helps against it.