Question

The circuit shown is driven by a sinusoidal input voltage, \( V_{\text{in}} \), resulting in the output voltage, \( V_{\text{out}} \). The frequency (in kilohertz) at which the voltage gain is 0 dB is _________ (round off to two decimal places)

Hint:

The cutoff frequency for a simple RC low-pass filter is determined by the formula \( f_c = \frac{1}{2 \pi R C} \), where \( R \) is the resistance and \( C \) is the capacitance.

Answer 1

Correct Answer: 15.8

The circuit is a simple low-pass filter, and the frequency at which the voltage gain is 0 dB corresponds to the cutoff frequency, \( f_c \). For a low-pass filter with a resistor and capacitor in series, the cutoff frequency is given by: \[ f_c = \frac{1}{2 \pi R C} \] where:
- \( R = 100 \, \text{k}\Omega \),
- \( C = 1 \, \text{nF} = 10^{-9} \, \text{F} \).
Substituting the values: \[ f_c = \frac{1}{2 \pi (100 \times 10^3) (1 \times 10^{-9})} = \frac{1}{2 \pi \times 100 \times 10^{-6}} = \frac{1}{6.28 \times 10^{-4}} \approx 1591 \, \text{Hz} = 1.59 \, \text{kHz}. \] Thus, the frequency at which the voltage gain is 0 dB is approximately \( 1.59 \, \text{kHz} \).