AM Demodulation
Three components — a diode, a capacitor, a resistor — and no power supply. Getting the message back off an AM carrier is the cheapest trick in radio, and it rests entirely on one number.
The Envelope Is the Message
Not a code for it. Not a transform of it. A scaled, shifted copy of the original waveform. So any circuit that traces the outline of the received wave has already recovered the audio — without knowing the carrier’s frequency precisely, and without knowing its phase at all.
Diode, Capacitor, Resistor
- The diode rectifies — negative half-cycles gone
- The capacitor charges to each carrier peak
- Between peaks it discharges through R, following the envelope down
- Across R sits the envelope — the recovered message
A Radio With No Battery
A coil, a variable capacitor, a diode, an earpiece. That is a complete AM receiver, and it draws the few microwatts it needs to move the diaphragm straight out of the radio wave. Nothing else in this course will ever be this cheap again.
Squeezed From Both Sides
RC must be long compared with one carrier period, so the capacitor barely droops between peaks — and short compared with one message period, so it can still follow the envelope down.
Ripple One Way, Clipping the Other
Diagonal Clipping
Ripple is added at fc, far outside the message band, so a filter deletes it. Clipping replaces the envelope with the detector’s own discharge curve, inside the message band. One is recoverable. One is not.
A Window 200× Wide
Speech to 5 kHz at m = 0.8. Carrier period 1 µs, message period 200 µs, clipping ceiling 23.9 µs. Pick 20 µs and every condition holds at once.
The Diode Curves
A diode needs about 0.6 V to conduct properly — 0.2 V for germanium. Below that it does not switch, it curves, and its current follows the square of the voltage. So the distortion is worst at low signal and low modulation depth, which is the reverse of most people’s intuition.
Kill the Carrier, Break the Trick
DSB-SC recovers the two thirds of power the carrier was wasting. But now the envelope is |x(t)| — the magnitude of the message, not the message. Every zero crossing flips the phase 180°, and a detector that cannot see phase reports it as positive.
Stop Discarding Phase
Multiply by a local cosine at the same frequency and same phase, then low-pass. The sidebands translate back down onto baseband and up to 2fc, where the filter deletes them. Coherent detection is just modulation applied twice.
Output Scales as cos φ
Get the phase wrong by 60° and you lose half the amplitude — 6 dB, in the units of M2-L4. Get it wrong by 90° and you get silence, however strong the transmission. A frequency error is worse still: the output fades in and out for ever.
The Superheterodyne
- RF + mixer — shift any station to one fixed frequency
- IF amplifier — all the gain and all the selectivity, at 455 kHz
- Detector — the diode and RC of slide 3
- Audio + AGC — the DC the detector makes becomes the gain control
The by-product of demodulation turns out to be exactly the measurement the receiver needed.
Key Takeaways
- The envelope is the message, so a diode and RC recover it — no phase reference
- One design number: 1/fc ≪ RC ≪ 1/fm
- Too short → carrier ripple; too long → diagonal clipping
- The clipping bound collapses to zero at m = 1 — a second reason to stay below it
- Diode curvature makes distortion worst at low signal level
- Suppress the carrier and you need synchronous detection, which scales as cos φ
M3-L4: Limitations of AM
We can now build AM and take it apart again. So why did anyone invent anything else? The next lesson totals up the bill — the wasted power, the noise that lands straight on the signal, and the fading no receiver can undo.