Time Constant of Linear Diode Detector

The time constant of a linear diode detector (envelope detector) is the RC time constant of its filter network.

It determines how fast the capacitor:

• charges to the carrier peaks
• discharges between peaks

Time Constant Formula

τ = R × C

Where:

• R = load resistor
• C = filter capacitor
• τ = time constant in seconds

Diode Detector Circuit

Diode RF ----|>|----+---- Audio Out | C | R | GND

The capacitor charges quickly through the diode when the RF envelope rises.

When the envelope falls:

• diode becomes reverse biased
• capacitor discharges through R

That discharge speed is controlled by the RC time constant.

Choosing the Correct Time Constant

1/fc << RC << 1/fm

Where:

• fc = carrier frequency
• fm = modulation (audio) frequency

Meaning of the Condition

• RC should be much larger than the carrier period → removes RF ripple
• RC should be much smaller than the modulation period → follows the audio envelope correctly

Example

• Carrier frequency = 1 MHz
• Maximum audio frequency = 5 kHz

Carrier period:

1/fc = 1 μs

Audio period:

1/fm = 200 μs

A practical detector may use:

RC ≈ 20 μs

This:

• smooths the RF carrier
• still tracks the audio envelope

If RC is Too Small

• capacitor discharges too fast
• output contains RF ripple
• noisy/distorted output

If RC is Too Large

• capacitor discharges too slowly
• envelope cannot follow modulation
• causes diagonal clipping distortion

Conclusion

The RC time constant controls the tradeoff between:

• ripple filtering
• envelope tracking accuracy