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

Time Constant for an AM Diode Detector

Given AM signal:

v(t) = 10 [1 + 0.6 cos(2π × 10³ t)] cos(2π × 10⁶ t)

Compare this with the standard AM equation:

Ac [1 + m cos(2πfm t)] cos(2πfc t)

Parameters

• Carrier frequency

fc = 10⁶ Hz = 1 MHz

• Modulating frequency

fm = 10³ Hz = 1 kHz

• Modulation index

m = 0.6

Condition for Envelope Detector

For proper diode detection:

1/fc << RC << 1/fm

Carrier Period

1/fc = 1 / 10⁶ = 1 μs

Modulating Signal Period

1/fm = 1 / 10³ = 1 ms

Therefore:

1 μs << RC << 1 ms

Practical Value of RC

A common practical choice is:

RC ≈ 1 / (10 fm)

Substituting:

RC ≈ 1 / (10 × 10³)

RC ≈ 100 μs

Conclusion

A suitable detector time constant is approximately:

RC ≈ 100 μs

This value:

• is much larger than the carrier period → filters RF ripple
• is much smaller than modulation period → follows envelope properly

Correct answer is 0.17 msec