Chapter 21: Modulation Methods

Varying a radio wave’s amplitude, frequency or phase to carry information

Modulation puts information, such as speech, onto the radio wave (the carrier) by varying one of its properties. Recovering that information at the receiver is the reverse process, demodulation.

Demodulation

Getting the original signal back from the carrier is demodulation, also called detection. Modulation is the opposite job, done at the transmitter: putting the information onto the carrier.

Detection

The manual calls recovering the information demodulation or detection. An AM detector does contain a rectifier, but rectification only means changing AC into DC, not the whole recovery process.

The radio wave on which the information is imprinted

The carrier is the radio-frequency wave itself, the part that travels far; the information is imprinted on it. In AM the sidebands hold the information, but they are products of modulation, not the carrier.

Its frequencies are far too low to travel well as radio waves

Voice frequencies, roughly 50 Hz to 20 kHz, are far too low to propagate usefully as radio waves, so speech is imprinted on a radio-frequency carrier. How fast they change is not the problem; how low they are is.

Each is a way of modulating a carrier

All four put information on a carrier: by keying it on and off, varying its amplitude, sending one sideband, or varying its frequency. SSB suppresses its carrier, so they do not all transmit one.

About 50 Hz to 20 kHz

The manual gives the voice as roughly 50 Hz to 20 kHz, a generous figure. The narrower 300 Hz to 3 kHz is what speech needs to stay intelligible, so communications transmitters pass only that band.

Medium-wave broadcasting and VHF aviation radio

AM survives in medium-wave broadcasting and VHF aviation radio. Amateurs rarely use it now: on HF most phone contacts are SSB, which saves the power and spectrum that AM wastes.

100%

At 100% the carrier swings from twice its average down to zero, touching zero only at each trough of the tone. Overmodulation would hold it at zero for part of every cycle, leaving a flat gap.

Distortion and interference on nearby channels, as the carrier cuts off

Beyond 100% the carrier is driven down to zero and held there for part of each cycle, which distorts the audio and spreads the signal into nearby channels. The extra drive never buys a cleaner, louder signal.

60%

Depth = (64 − 40) ÷ 40 = 60%: the change from the 40 V average, over the average; the dip to 16 V matches. Upside down, 40 ÷ 24 = 167%, which would mean overmodulation.

65%

Average = (45 + 10) ÷ 2 = 27,5 V, so depth = (45 − 27,5) ÷ 27,5 = 63,6%, nearest 65%. Dividing the 35 V swing by the 45 V peak gives 78% (80%): the wrong reference.

A half-wave rectifier feeding a lowpass filter

Rectifying the AM signal and then removing what is left of the carrier with a lowpass filter leaves the envelope, which is the audio. A highpass filter would remove the audio and keep the RF.

The DC offset is 0 Hz, so its mixing products fall on the carrier frequency

Mixing gives the sum and difference of the frequencies multiplied. The DC offset is 0 Hz, so both its products equal the carrier frequency; every audio frequency, however low, gives products offset from it.

3 648,5 kHz and 3 651,5 kHz

Each sideband lies one tone frequency from the carrier: 3 650 − 1,5 = 3 648,5 kHz and 3 650 + 1,5 = 3 651,5 kHz. Moving 3 kHz each way doubles the tone.

The carrier itself

The carrier sits at the centre, with the upper sideband above it and the lower sideband below, each as wide as the audio. The lower sideband is on the low-frequency side, not in the middle.

A blocking capacitor in series with the output

The detector’s output is the audio riding on a DC offset; a series blocking capacitor passes the audio and stops the DC. A capacitor straight to earth cannot stop DC; it only bypasses AC to earth.

The relative amplitude of that component

Each line stands for one component: its place along the X axis gives its frequency, and its height that component’s relative amplitude. A plot against time is a waveform instead, like the manual’s envelope drawings.

The modulating signal, at low frequencies near 0 Hz

The modulating signal sits near 0 Hz (DC) in the spectrum, so it is called the baseband signal; modulation copies it up around the carrier. The lower sideband is one of those copies, not the baseband itself.

9 kHz

Each sideband reaches 4,5 kHz from the carrier, one above it and one below, so the signal is 2 × 4,5 = 9 kHz wide. Taking just the audio frequency, 4,5 kHz, counts only one sideband.

The audio frequencies in the modulating signal

Each sideband reaches out from the carrier as far as the highest audio frequency, so the audio frequencies set its width. Louder audio, deeper modulation, makes the sidebands stronger, not wider, unless it overmodulates.

About 6 kHz

Speech needs about 300 Hz to 3 kHz, and AM sends that band on both sides of the carrier: from 3 kHz below to 3 kHz above, 6 kHz in all. 3 kHz is the width of one sideband only.

About 300 Hz to 3 kHz

Intelligible speech needs only about 300 Hz to 3 kHz, so communications transmitters cut the rest. The wider 50 Hz to 20 kHz is the full range of the voice, not what is needed to understand it.

170 W

At 100% modulation the carrier is two thirds of the total: 250 × 2 ÷ 3 = 166,7 W, nearest 170 W. Half, 125 W, wrongly splits it equally; the two sidebands together get only the remaining third.

100 W

At 100% the two sidebands together carry half the carrier power, 200 W, shared equally: 100 W each, a quarter of the carrier. Giving 200 W to each sideband forgets that the half is shared.

One third

The carrier takes two thirds and the two sidebands share the remaining third, a sixth each. Two thirds is the carrier’s share: power that carries no information at all.

It sends the same information twice, once in each sideband

Each sideband carries a complete copy of the information, so AM uses twice the spectrum one sideband would need. The carrier is a single frequency: it wastes power, at least two thirds of it, not spectrum.

Double-sideband suppressed-carrier (DSBSC)

Removing only the carrier leaves both sidebands: a double-sideband suppressed-carrier (DSBSC) signal. Single sideband needs one of the two sidebands removed as well.

A balanced modulator

A balanced modulator multiplies the carrier by the modulating signal and cancels the carrier, leaving only the sum and difference products, the two sidebands. A frequency multiplier produces harmonics of its input instead.

No power is spent on the carrier, so it is more efficient

DSBSC drops the carrier, which carries no information yet takes most of an AM signal’s power, so the transmitter is more efficient. It still sends both sidebands, so it is just as wide as AM.

Multiplying the carrier by the audio alone, with no DC offset added

With no DC offset the product holds only the sum and difference frequencies, so no carrier appears. Adding an offset first gives AM: the offset mixes with the carrier and puts it back.

Zero

DSBSC is the carrier multiplied by the modulating signal with no DC offset, so when the modulating signal is zero the output is zero. Sitting at the carrier level is AM, whose offset keeps the carrier there.

Its phase is turned over (inverted)

Multiplying by a signal that changes sign turns the RF waveform upside down, a phase inversion, which marks the crossing. The sidebands themselves stay where they are; nothing jumps across.

Its envelope no longer has the shape of the audio waveform

Without a carrier the envelope rises on both halves of every audio cycle, the sign being carried only by phase flips that any rectifier ignores. A full-wave rectifier folds the envelope just the same.

Both sidebands carry the same information, so it is as wide as AM

Dropping the carrier saves power, but both sidebands still carry the same information, so DSBSC is as wide as AM and half its power goes on a duplicate. Generating it is easy: one balanced modulator does it.

Single sideband (SSB)

With the carrier and one sideband removed, a single sideband is left: SSB. Double-sideband suppressed-carrier removes only the carrier and keeps both sidebands.

It is reversed: low audio frequencies end up highest

In LSB each audio frequency is subtracted from the carrier frequency, so higher audio lands lower: the spectrum is inverted. A straight copy moved up in frequency is the upper sideband.

Lower sideband

Below 10 MHz the convention is lower sideband, above 10 MHz upper sideband, so 80 m uses LSB. USB on these bands is the usual mistake; the 5 MHz band is the one exception below 10 MHz.

The 5 MHz band

By convention LSB is used below 10 MHz and USB above it; the experimental 5 MHz band is the exception, using USB. The 7 MHz band follows the rule and uses LSB.

453,8 kHz

LSB keeps only the difference product: 455 − 1,2 = 453,8 kHz, a single steady RF signal. 456,2 kHz is the sum, the upper sideband, which this exciter removes.

14 250,2 to 14 252,8 kHz

USB adds each audio frequency to the carrier frequency: 14 250 + 0,2 = 14 250,2 kHz up to 14 250 + 2,8 = 14 252,8 kHz. The range below the carrier is the lower sideband, which USB removes.

2,4 kHz

An SSB signal is one sideband, as wide as the band of audio it carries: 2,6 − 0,2 = 2,4 kHz. Doubling it to 4,8 kHz counts two sidebands, as in AM or DSBSC.

Clear enough, but pitched too high or too low

With no carrier to lock to, any mistuning shifts every audio frequency by the same amount, so voices sound too high or too low. The strength is unchanged; a little retuning brings the pitch right.

850 Hz

The tone goes out on 14 201,00 kHz, which is 14 201,00 − 14 200,15 = 0,85 kHz above the receiver’s setting: 850 Hz. Tuning above the signal lowers the pitch; 1 150 Hz has the shift the wrong way.

Its distortion mixes the signal’s many frequencies into unwanted products

A multiplier works by distorting its input, and the many frequencies in an SSB signal then mix into products too close to filter out (pp153 and 173). The missing carrier is not the reason.

Keying

Switching the carrier on and off in the pattern of dots and dashes is keying, done with a Morse key. Squelching mutes a receiver while no signal is present; it never switches a transmitter.

Tube sets sent steady waves, unlike the damped waves of spark sets

Early spark transmitters produced damped waves, bursts that died away quickly; the tube transmitters that replaced them could send a steady, continuous wave. It was the spark sets, not the tube sets, whose waves were damped.

Switching the carrier on and off is a form of amplitude modulation

Switching the carrier on and off is amplitude modulation by the keying waveform, and that creates sidebands. A frequency shift on each element is chirp, a separate fault, not the reason sidebands exist.

Morse is slow, so its sidebands stay close to the carrier

Morse keying is slow, well under 50 Hz, so its sidebands lie close to the carrier and the signal stays narrow. Sidebands do exist, since keying is a form of amplitude modulation.

Keying with sharp, square edges, whose harmonics spread the signal

A carrier switched fully on and off at once has a square keying envelope, rich in harmonics, which spread sidebands far from the carrier and are heard as clicks. A frequency change on each element is chirp instead.

Let the carrier rise and fall gradually, not switch instantly

Softening the keying edges, with a rise and decay of a few milliseconds, removes the high harmonics that cause clicks. Switching faster makes the edges harder still and the clicks worse.

About 5 ms

The manual gives about 5 ms for the ramp up and the decay. At 50 ms the slopes would fill most of each dot at normal speeds and smear the Morse; microseconds would leave hard clicks.

A resistor and capacitor forming a lowpass filter

A capacitor charging and discharging through a resistor slows the rise and fall of the keying: a simple lowpass filter that removes the harmonics causing clicks. A tuned circuit at the carrier frequency would not soften the keying.

18 W

13 dB is 10 dB (×10) plus 3 dB (×2), a power ratio of about 20, so 350 ÷ 20 = 17,5 W, nearest 18 W. Dividing by 13, as if decibels were the ratio, gives 27 W.

It can be understood at far lower signal levels than voice

CW stays readable at signal levels far below what voice needs: about 13 dB less power than SSB. It does need a beat-frequency oscillator (or product detector) in the receiver to be heard as a tone.

Its amplitude

FM varies the carrier’s frequency and leaves its amplitude constant, as the manual’s figure shows. Frequency is the very thing being modulated, so it cannot be the constant.

The amplitude (loudness) of the audio

FM moves the carrier’s frequency in step with the audio’s amplitude: louder audio, larger deviation. The audio’s pitch sets how many times a second the frequency swings, not how far.

10 697 to 10 703 kHz

Deviation is how far the frequency moves each way from the centre: 10 700 ± 3 kHz gives 10 697 to 10 703 kHz, a 6 kHz swing in all. Taking 3 kHz as the whole swing halves it.

2

m = ΔF ÷ fmod = 4 kHz ÷ 2 kHz = 2. Dividing the audio frequency by the deviation, 2 ÷ 4 = 0,5, works the ratio upside down.

1,2

m = 3,5 ÷ 3 = 1,17, nearest 1,2. Dividing the other way, 3 ÷ 3,5 = 0,86, near 0,85, turns the ratio upside down: the deviation goes on top.

About 2,5 kHz

Amateur NBFM keeps the deviation to about 2,5 kHz, so the frequency swings 2,5 kHz either side of the centre. 75 kHz is the deviation of FM broadcast stations, which take far more bandwidth.

75 kHz

Broadcast FM uses 75 kHz deviation, trading a wide channel for high audio quality. About 2,5 kHz is the amateur narrowband figure, used for speech.

14 kHz

2 × (4 + 3) = 14 kHz; twice the deviation, 8 kHz, is only the carrier’s swing, and the sidebands spread further. The manual’s 5 to 6 kHz for narrowband FM is likewise little more than the swing.

When the received signal is well above the noise

Well above the noise, an FM receiver ignores amplitude disturbances and the audio is clean; but quality falls away quickly as the signal sinks towards the noise. Weak signals are where SSB does better.

Local contacts on VHF and UHF, such as 2 m and 70 cm

Local VHF and UHF paths usually give strong signals with little atmospheric noise, which suits FM. On HF, with signals often weak and noise strong, SSB is the choice for long-range contacts.

More bandwidth in return for better audio quality

A high deviation ratio spreads the signal over much more spectrum and in return gives clearer audio, as broadcast FM does. Quality is bought with bandwidth, not saved by narrowing it.

Frequency-shift keying (FSK)

Moving between two frequencies, called mark and space, is frequency-shift keying. PSK keeps one frequency and changes the carrier’s phase instead.

Phase-shift keying (PSK)

Switching between 0° and 180° shifts the carrier’s phase, so this is phase-shift keying, in its binary form BPSK. FSK would move the carrier between two frequencies instead.

A logic 1

The two RTTY frequencies are called mark and space: mark is logic 1 and space is logic 0. Neither is set aside for marking the start of lines or the end of a message.

RTTY and Packet Radio

The manual names RTTY (radio teletype) and Packet Radio as FSK modes. FM broadcasting varies the carrier’s frequency smoothly with the audio; it does not shift between two set frequencies.

About 45 Bd

RTTY runs slowly, at about 45 Bd (45,45 Bd in practice), each symbol one bit. 450 Bd is ten times too fast for the old teletype standard that sound-card RTTY still follows.

20 ms

At one bit per symbol, 50 Bd is 50 bits per second, so each bit lasts 1 ÷ 50 = 0,02 s = 20 ms. Reading 50 Bd as 50 ms per bit inverts the rate.

It uses bandwidth more efficiently

The manual’s reason is bandwidth: PSK fits the same data into less spectrum than FSK. No mode is immune to noise; that is why digital modes add error detection and correction.

2 bits

QPSK has four phases, and four different states are exactly what two bits give (00, 01, 10 and 11). Four is the number of phases, not of bits; BPSK’s two phases carry one bit.

0°, 90°, 180° and 270°

QPSK uses four phases a quarter-turn apart: 0°, 90°, 180° and 270°. Just 0° and 180° is binary PSK (BPSK), which has two states and so carries one bit at a time.

Real-time keyboard chat, each operator’s typing on the other’s screen

PSK-31 is a real-time keyboard mode: whatever one operator types appears at once on the other’s screen. E-mail and file transfers are what the manual gives Packet Radio, an FSK mode.

Two carriers 90° apart in phase, each amplitude modulated

QAM amplitude modulates two carriers a quarter-cycle (90°) apart, which the receiver can separate, so two signals share one channel; Wi-Fi uses it. Carriers 180° apart would just add or cancel, not separate.

PSK and FSK variants with heavy redundancy and very slow symbol rates

WSJT modes use variations of PSK and FSK, repeat the information many times over and run at very slow baud rates, so a computer can decode signals too weak to hear. Speed and power are not the trick.

Earth-moon-earth (EME) contacts on 144 MHz

JT65B is optimised for earth-moon-earth (moonbounce) contacts on 144 MHz, where it became the usual mode. Other WSJT modes are used for EME on the microwave bands.

They carry little more than callsigns and signal reports

Critics say WSJT gains its weak-signal reach by sending very little: callsigns and signal reports, not conversation. It needs less power, not more, and the software is a free download.

An extra number sent with the data, so the receiver can check it arrived intact

A CRC is a number worked out from all the bytes of a message and sent with it, so the receiver can tell whether anything was corrupted. Correcting errors without a repeat is the job of FEC.

Detect and often correct errors without contacting the transmitter

FEC sends redundant information with the data, so the receiver can find and often fix errors on its own, even over a one-way link. Asking for damaged packets again is a retransmission protocol (ARQ).

A request to repeat it (ARQ)

A damaged packet brings a request to repeat (ARQ, often called a NAK); a good one brings an acknowledgement (ACK), and a packet with no ACK in time is sent again. An ACK confirms success, so it is wrong here.

A two-way link, so that the receiver can ask for repeats

Retransmission works only if the receiver can reply, with an ACK or a request to repeat, so it needs a two-way link and adds overhead. Redundant bits inside each character are how FEC corrects errors one way.