Signals & Wireless (RF)
How an envelope detector works, and how to pick R and C
An envelope detector recovers the sound from an AM radio signal with three parts: a diode, a capacitor and a resistor, often just the earpiece. The diode passes the tops of the carrier's cycles; the capacitor charges to each peak and holds it; the resistor lets it drain slowly between peaks. The output follows the outline of the peaks, the envelope, which is the sound that was sent.
Three parts, three jobs
A radio station's carrier is a sine far too fast to hear, with its strength shaped by the sound. The detector keeps the strength and throws away the carrier:
- The diode conducts only on the positive half of each cycle. A silicon diode takes about 0.6 V, so a 3 V carrier charges the capacitor to about 2.4 V.
- The capacitor, across the output, holds that level between peaks, when the diode is off.
- The resistor drains it, so the level can fall when the sound gets quieter.
The R × C window
The time constant has to be long next to one cycle of the carrier, so the level holds between peaks, but short next to one cycle of the sound, so it can follow it down:
For a 100 kHz carrier, one cycle is 10 µs. For a 2 kHz voice, one cycle is 500 µs. A 10 kΩ earpiece with 10 nF gives R × C = 100 µs: ten carrier cycles, a fifth of a voice cycle.
Live experiment
Hold the peaks, follow the voice
A 3 V, 100 kHz carrier goes through a silicon diode to a 10 kΩ earpiece with a capacitor across it. 10 pF empties every cycle into pulses; 1 nF buzzes; 10 nF holds a level a diode drop under the peak. Give the carrier a 2 kHz voice and 10 nF follows it, while 1 µF can't follow it back down.
“Hear the carrier” is lesson 6 of 6 in Carrier Cove, Signals & Wireless (RF) World 1. Free with an account. Lessons unlock in order, so you’ll do the 5 before it first.
Too small, 10 pF and 0.1 µs, and the capacitor empties every cycle: the output is a string of half-wave pulses. Too big, 1 µF and 10 ms, and it can't let go fast enough to follow the voice's troughs, so the sound is muffled and clipped.
A tighter check: for a sound at frequency fm and modulation depth m, the level can follow the troughs if R × C ≤ √(1 − m²) ÷ (2π fm m). At 50 % depth and 2 kHz that's about 140 µs, so 100 µs passes.
The diode's price
Anything smaller than the diode's drop never gets through. That doesn't matter for a strong signal, but a crystal radio, powered only by the antenna, hears more with a germanium or Schottky diode that drops a few tenths of a volt.
Free lesson
Now build it yourself
Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.
“Hear the carrier” is lesson 6 of 6 in Carrier Cove, Signals & Wireless (RF) World 1. Free with an account. Lessons unlock in order, so you’ll do the 5 before it first.
Or start from the very first lesson, no account neededPractice questions
Three quick questions from the lessons. Pick an answer to check it.
Show the answer
Answer: 2.4 V: the peak minus the diode's 0.6 V. The diode only conducts once the carrier is 0.6 V above the capacitor, so the capacitor stops 0.6 V short of the peak.
- Why not “0.6 V”? 0.6 V is the drop the diode takes, not what's left for the capacitor.
- Why not “3 V”? The diode only conducts while the carrier is 0.6 V above the capacitor, so the capacitor stops short of the peak.
- Why not “1.5 V”? The capacitor charges to the peak, not to half of it. Only the diode's drop is lost.
Show the answer
Answer: Empties completely: the output is pulses, not a level. The capacitor drains in a hundredth of a cycle. To hold between peaks, R × C must be many cycles: 10 nF with 10 kΩ gives 100 µs, ten of them.
- Why not “Holds the level”? To hold between peaks, R × C must be many cycles long. 0.1 µs is a hundredth of one.
- Why not “Charges further”? Between peaks the diode is off, so nothing charges the capacitor. It can only drain.
- Why not “Doesn't matter”? It decides everything: an output of pulses carries no steady level to hear.
Show the answer
Answer: Can't follow the sound: it barely moves at all. R × C must be long next to the carrier's cycle but short next to the sound. A second is far too long for a voice that changes hundreds of times a second.
- Why not “Is cleaner”? A huge R × C does flatten the carrier's ripple, but it flattens the sound away with it.
- Why not “Gets louder”? It holds the peaks, but a level that barely moves makes almost no sound.
- Why not “Turns into pulses”? Pulses come from an R × C that's too short. A whole second holds the level almost still.
“Hear the carrier” is lesson 6 of 6 in Carrier Cove, Signals & Wireless (RF) World 1. Free with an account. Lessons unlock in order, so you’ll do the 5 before it first.
Questions people ask
Why does my envelope detector's output sound distorted?
Usually R × C is wrong. Too long and the capacitor can't drain fast enough to follow the troughs of the sound, which clips them, a fault called diagonal clipping. Too short and the carrier leaks through as a buzz. Overmodulation at the transmitter distorts it too.
Why do crystal radios use germanium diodes?
Because a germanium diode starts conducting at about 0.2 to 0.3 V instead of a silicon diode's 0.6 V. A crystal radio has no battery and the signal from the antenna is tiny, so every tenth of a volt the diode doesn't take is signal you can hear. Schottky diodes do the same job today.
Can an envelope detector demodulate FM?
Not directly. An FM signal keeps a constant amplitude and carries its sound in small changes of frequency, so its envelope is flat and there's nothing to detect. FM receivers turn frequency changes into voltage with a discriminator or a phase-locked loop.
Related topics
- Amplitude modulation (AM) explainedTurn a carrier's height up and down with a voice: modulation depth, sidebands, and why past 100% it tears.
- RC time constant explainedτ = R × C: how long a capacitor takes to charge through a resistor, and the 63% rule.
- How does a diode work?A one-way valve for current: anode, cathode, the 0.7 V forward drop and Schottky diodes.
- How an LC band-pass filter picks one stationA coil and a capacitor in the signal's path cancel at one frequency, and fight every other.