Question

In the bandpass filter circuit shown, \( R_0 = 50 \, \Omega \), \( L_0 = 1 \, \text{mH} \), \( C_0 = 10 \, \text{nF} \). The Q factor of the filter is _________ (round off to two decimal places).

Answer 1

Correct Answer: 6.22

The Q factor of a bandpass filter is given by the formula: \[ Q = \frac{1}{R_0} \sqrt{\frac{L_0}{C_0}} \] Given:
- \( R_0 = 50 \, \Omega \),
- \( L_0 = 1 \, \text{mH} = 1 \times 10^{-3} \, \text{H} \),
- \( C_0 = 10 \, \text{nF} = 10 \times 10^{-9} \, \text{F} \).
Substituting the values into the formula: \[ Q = \frac{1}{50} \sqrt{\frac{1 \times 10^{-3}}{10 \times 10^{-9}}} = \frac{1}{50} \sqrt{100 \times 10^6} = \frac{1}{50} \times 10000 = 200 \] Thus, the Q factor is \( \boxed{200} \).