Explanation:

An envelope detector is a simple circuit that is used to recover the low-frequency signal from the amplitude modulated high-frequency carrier wave. The envelope detector circuit consists of a diode, capacitor, and resistor. The capacitor and resistor are connected in parallel to form an RC circuit.

The choice of the product RC in a simple envelope detector using a diode and an RC circuit is governed by both the lowest and the highest modulation frequencies. The product of the resistance and capacitance (RC) determines the time constant of the RC circuit. The time constant of the circuit should be large enough to provide a smooth output but not too large that it affects the modulation frequency.

Factors affecting the choice of product RC:

Lowest modulation frequency:
The product RC should be large enough to allow the lowest modulation frequency to pass through the circuit. If the product RC is too small, the capacitor will discharge quickly and the output will not follow the envelope of the modulated signal.

Highest modulation frequency:
The product RC should be small enough to allow the highest modulation frequency to pass through the circuit. If the product RC is too large, the capacitor will take a long time to discharge and will not follow the envelope of the modulated signal.

Depth of modulation:
The depth of modulation also affects the choice of product RC. If the depth of modulation is high, the product RC should be large to allow the capacitor to discharge fully during each cycle. If the depth of modulation is low, the product RC can be small.

Carrier frequency:
The carrier frequency does not affect the choice of product RC in a simple envelope detector. The envelope detector circuit is designed to recover the low-frequency signal from the carrier wave.

Conclusion:

In summary, the choice of the product RC in a simple envelope detector using a diode and an RC circuit is governed by both the lowest and the highest modulation frequencies. The product RC should be large enough to allow the lowest modulation frequency to pass through the circuit and small enough to allow the highest modulation frequency to pass through the circuit. The depth of modulation also affects the choice of product RC. The carrier frequency does not affect the choice of product RC in a simple envelope detector.