Modules 3 and 4 have each built a complete modulation scheme, taken it apart, and totalled up its bill. This lesson puts them side by side. It is deliberately the last lesson of the analogue half of the course, because a comparison is only worth making once both sides can be quantified — and now they can. Every number below comes from a lesson you have already read.
There are five axes worth comparing, and the useful discovery is that AM and FM do not split them three-to-two or four-to-one. They split cleanly: AM wins two, FM wins three, and none of the five is close. That is unusual and it is the reason both survived. A scheme that lost on every axis would have disappeared.
AM's transmission bandwidth is exactly twice the highest message frequency, from M3-L2. FM's comes from Carson's rule in M4-L2, and depends on the deviation as well as the message:
Put broadcast numbers in. Broadcast FM uses Δf = 75 kHz and fm = 15 kHz, so Carson gives 2(75 + 15) = 180 kHz, and the channel allocation is 200 kHz. Broadcast AM carries audio to about 5 kHz in a 10 kHz channel. FM therefore occupies 20 times the spectrum per station.
That comparison is a little unfair, because it compares hi-fi FM against restricted-audio AM. Take voice instead and compare like with like. Narrowband FM for two-way radio uses Δf = 5 kHz with fm = 3 kHz, so Carson gives 2(5 + 3) = 16 kHz, against 2 × 3.4 = 6.8 kHz for AM voice. Still a factor of about 2.4 in AM's favour — narrower, but no longer dramatic.
| Service | Scheme | Δf | fm | Bandwidth |
|---|---|---|---|---|
| Broadcast AM | DSB-FC | — | 5 kHz | 10 kHz channel |
| HF voice | SSB | — | 3 kHz | 3 kHz |
| Two-way radio | NBFM | 5 kHz | 3 kHz | 16 kHz |
| Broadcast FM | WBFM | 75 kHz | 15 kHz | 180 kHz (200 kHz channel) |
So the honest statement of this axis is that AM is narrower at every message bandwidth, by a factor that grows with the deviation you choose for FM. And note what the table shows about the narrowest entry of all: SSB at 3 kHz beats even AM, because — as M3-L4 explained — DSB spends half its bandwidth on a duplicate sideband.
This is the axis the whole comparison turns on, and it is the one that can be stated as a single number. M4-L2 gives FM's output signal-to-noise improvement over AM as a power ratio of 3β², where β = Δf/fm is the FM modulation index. That ratio comes with a comparison basis, and the basis is half the result: both systems receive the same power, both carry the same message bandwidth, and the noise is referred to that message band rather than to either system's RF channel — see the callout in M4-L2 for why the same physics reads as 3β²(1 + β) when the noise is referred to FM's own Carson bandwidth instead. For broadcast FM, β = 75/15 = 5, so the improvement is 3 × 25 = 75.
A power ratio of 75 in decibels is 10 log₁₀ 75 = 18.75 dB. M2-L4 shows the route without a calculator: ×100 is 20 dB exactly, and 75 is three quarters of 100, which costs 10 log₁₀ 0.75 = −1.25 dB. So 20 − 1.25 = 18.75 dB, agreeing with the printed figure to the last digit.
Read that exponent carefully, because it is the whole reason FM exists. The advantage goes as β² while the bandwidth goes as roughly β. Doubling the deviation roughly doubles the occupied spectrum and multiplies the noise advantage by four — 6 dB for one doubling of bandwidth. Spectrum converts into quality at a favourable exchange rate, which is precisely the knob M3-L4 listed as the thing AM lacks. It is also why Carson's 1922 objection was wrong in the end: he analysed narrowband FM, where β is small, and there the trade is not available.
Two further mechanisms belong on this axis, both from M4-L1. The limiter clips the incoming signal to constant height before demodulation, discarding amplitude noise wholesale, which is the circuit M3-L4 showed has no AM equivalent. And the capture effect means the stronger of two co-channel FM signals suppresses the weaker almost completely once it is a few decibels up — where two AM signals simply add and you hear both.
The honest caveat: the FM threshold. FM's advantage is not free at the bottom of the range. Below a carrier-to-noise ratio of roughly 10 dB at the demodulator, individual noise spikes start winning control of the instantaneous frequency, and the output degrades far faster than AM's would — a cliff rather than a slope. AM at the same point is noisy but still intelligible. So on a link that is genuinely marginal, AM degrades more gracefully, and that is a real argument, not a footnote. FM wins this axis decisively above threshold and loses it below.
M3-L4 established AM's figure: modulation efficiency m²/(2+m²), which peaks at 1/3 at m = 1 and falls to about 4.3% at a realistic average depth. Two thirds or more of an AM transmitter's output is a carrier that conveys nothing.
FM has no such term. Its amplitude is constant by construction, so there is no idle carrier sitting beside the information — the whole waveform is the information. As M4-L1 noted, at certain deviations the carrier component vanishes entirely and every watt is in the sidebands. FM's modulation efficiency is 100% in the sense that matters here.
Then FM wins the same axis a second time, for a completely different reason. Because an FM signal's envelope never changes, its power amplifier does not have to preserve amplitude — so it can be run hard in class C, non-linearly, at roughly 70% DC-to-RF efficiency. An AM transmitter must keep its amplifier linear enough to carry the envelope faithfully, which forces a less efficient class of operation. FM therefore wastes less power in the antenna and less power in the amplifier that feeds it. This second win is the one that matters most for a battery-powered radio, and it is why constant-envelope modulation dominates handheld two-way radio.
M3-L3 built the AM demodulator: a diode, a capacitor, a resistor, and one time constant. No oscillator, no phase reference, no power supply. M4-L3 built the FM demodulator: a limiter, then a slope detector, a Foster-Seeley discriminator, or a phase-locked loop — a frequency-to-amplitude converter of some kind, plus the circuitry that makes it linear over the deviation range.
In 1935 that difference decided markets. A crystal set cost nothing; an FM receiver needed a limiter and a discriminator built from tuned transformers that had to be aligned by hand at the factory, and it needed vacuum tubes, which meant a mains supply. AM's simplicity is a large part of why AM broadcasting had a fifteen-year head start it never entirely lost.
Be careful about carrying that judgement into the present, though, because this axis has largely inverted. A phase-locked loop is a few hundred transistors — a fraction of a cent of silicon — and it needs no alignment at all, while a hand-aligned tuned transformer is now the expensive component. In a modern receiver the demodulator is a few lines of arithmetic performed on samples, and computing an instantaneous frequency is no harder than computing an envelope. AM keeps this axis on a strict count of parts, and loses it entirely on cost, which is worth saying plainly: if you were choosing today with no legacy to support, demodulator complexity would not be the deciding factor.
Broadcast FM carries audio to 15 kHz; broadcast AM carries about 5 kHz. That alone settles the axis, and it follows from Axis 1: because the FM channel is 200 kHz wide, there is room for the full audio band, whereas AM's 10 kHz channel divided between two sidebands leaves 5 kHz. AM's dull sound is a direct consequence of the redundancy M3-L4 described.
The second reason is Axis 2: the 18.75 dB noise advantage is what makes a high dynamic range usable. There is no point transmitting 15 kHz of audio if the top octave is buried in hiss.
The third reason is the pre-emphasis and de-emphasis network M4-L2 describes. The transmitter deliberately boosts high audio frequencies before modulating, and the receiver cuts them by the same amount afterwards — which attenuates the noise the receiver's own demodulator adds at high frequencies, since FM noise rises with frequency. AM has no equivalent, because its noise is flat and there is nothing to shape against. And it is FM's constant envelope that makes the boost affordable: pre-emphasising an AM signal would push its peaks into over-modulation.
One thing AM does keep here: it has no threshold cliff, so a distant AM station fades gracefully into noise while a distant FM station goes from clean to unusable over a few decibels. Listeners who drive out of a city notice this immediately, and it is the same threshold effect from Axis 2 wearing a different hat.
| Axis | AM | FM | Winner |
|---|---|---|---|
| Bandwidth | 2fm — 10 kHz broadcast, 6.8 kHz voice | 2(Δf + fm) — 180 kHz broadcast, 16 kHz NBFM | AM, by 20× for broadcast |
| Noise immunity | No limiter possible; noise is amplitude and so is the message | 3β² = 75 at β = 5, i.e. 18.75 dB; plus limiter and capture effect | FM, above threshold |
| Power efficiency | m²/(2+m²) — 1/3 at best, ~4.3% typical; linear PA required | 100% of power in the signal; class-C PA at ~70% | FM, twice over |
| Demodulator complexity | Diode + RC; no oscillator, no power supply | Limiter + discriminator or PLL | AM by parts count, a draw by cost |
| Fidelity | ~5 kHz audio; graceful degradation | 15 kHz audio, high SNR, pre-emphasis; threshold cliff | FM |
A table of winners is not an engineering decision. The decision is made by asking which single constraint dominates your problem, because in practice one always does. Here are the four that decide real systems.
There is a fifth question that overrides all four, and it is the one that settled aviation: what does failure look like? M3-L4 made the case — civil aviation voice is AM precisely because AM lacks the capture effect, so two simultaneous transmissions are both audible instead of one silently disappearing. On that channel, the winner of Axis 2 is the wrong choice.
A worked decision. You are designing a voice link for a mountain rescue team: handheld radios, battery life critical, hills everywhere, and a licensed 25 kHz channel. Bandwidth is not scarce — you have 25 kHz for a 3 kHz message. Power is scarce. Fidelity is irrelevant; intelligibility is everything. Receiver cost is minor against the cost of the rest of the kit. So: NBFM at Δf = 5 kHz, giving 16 kHz inside a 25 kHz channel, with β = 1.67 and a noise advantage of 3 × 2.78 = 8.3, which is 9.2 dB. You have spent the spare bandwidth on battery life and noise immunity, which is exactly what the trade is for. That is also the specification of essentially every professional handheld radio ever sold.
One last thing, because a comparison lesson can leave the impression that these are the only two options. Every axis above has been re-argued from scratch by digital modulation, and Module 5 opens that argument.
Amplitude is not disqualified after all. QAM encodes information in amplitude and phase at once, and it is what carries essentially all modern data. What changed is not the physics but the machinery around it: with error-correcting codes, channel equalisers and digital synchronisation, a receiver can measure what the channel did to the amplitude and correct for it. AM's fatal defect was never that amplitude is a bad place to put information — it was that an analogue receiver had no way to find out what had happened to it.
And FM's central insight survives completely intact. The idea that you can spend bandwidth to buy noise immunity is the same idea Shannon formalised, and it is the reason spread-spectrum systems deliberately occupy hundreds of times the bandwidth their data rate requires. Armstrong's 1933 demonstration was the first working proof of the most important trade in communications, and Module 6 will state it as a law.