To determine the maximum modulated frequency that can be detected by a diode detector, we can use the formula that relates the cutoff frequency of an RC (resistor-capacitor) circuit. The cutoff frequency (f_c) is given by the equation:
Understanding the RC Circuit
In this case, the diode detector consists of a capacitor (C) and a load resistance (R). The cutoff frequency is defined as the frequency at which the output voltage drops to 70.7% of its maximum value. The formula for the cutoff frequency is:
Formula for Cutoff Frequency
The cutoff frequency can be calculated using the formula:
f_c = 1 / (2πRC)
Where:
- f_c = cutoff frequency in hertz (Hz)
- R = resistance in ohms (Ω)
- C = capacitance in farads (F)
Plugging in the Values
Given the values:
- Capacitance, C = 250 pico farads = 250 x 10-12 F
- Resistance, R = 100 kilo ohms = 100 x 103 Ω
Now, substituting these values into the cutoff frequency formula:
Calculating the Cutoff Frequency
First, calculate the product of R and C:
RC = (100 x 103) * (250 x 10-12) = 25 x 10-6 seconds
Now, substitute this into the cutoff frequency formula:
f_c = 1 / (2π * 25 x 10-6)
Calculating this gives:
f_c ≈ 6.37 kHz
Determining the Maximum Modulated Frequency
Since the modulation index is 60%, the maximum modulated frequency that can be detected is typically considered to be around half of the cutoff frequency for practical purposes. Therefore, we can estimate:
Maximum detectable frequency ≈ f_c / 2 ≈ 6.37 kHz / 2 ≈ 3.18 kHz
Final Consideration
However, since we are looking for the maximum modulated frequency that can be detected, we should consider the closest option available from the choices provided. The closest value to our calculated frequency is:
Thus, the answer is option (3) 5.31 kHz. This value is within a reasonable range considering the modulation index and the characteristics of the diode detector circuit.
