Practice Problems

Problem 1.

Calculate the cutoff frequency for a circuit with:

a. \(R = 1\ \text{k}\Omega\) and \(C = 3\ \text{nF}\)

b. \(R = 5\ \text{k}\Omega\) and \(C = 1.5\ \mu\text{F}\)

Problem 2.

What should the resistor value be for the following filters:

a. \(f_{cutoff} = 1.5\ \text{kHz}\) and \(C = 500\ \text{nF}\)

b. \(f_{cutoff} = 417\ \text{Hz}\) and \(C = 56\ \text{nF}\)

c. \(f_{cutoff} = 2\ \text{kHz}\) and \(C = 500\ \mu\text{F}\)

Problem 3.

Are the circuits below high or low pass filters? How do you know?

Problem 4.

Calculate the cutoff frequency of the following systems.

a. A transmission line modeled as an R-L circuit with \(R = 4\ \Omega\) and \(L = 5\ \mu\text{H}\).

b. An R-C low pass filter with \(R = 60\ \Omega\) and \(C = 5\ \text{nF}\).

c. A C-R high pass filter with \(R = 100\ \Omega\) and \(C = 8\ \mu\text{F}\).

Problem 5.

Your communications radio has a lower frequency bound of \(800\ \text{kHz}\). You know it has a capacitor value of \(100\ \text{nF}\), but what is the resistor value?

Problem 6.

Design a high pass filter to get rid of a DC bias (\(0\ \text{Hz}\)) using a \(100\ \Omega\) resistor you have available.

Problem 7.

For the circuit below, what is the magnitude of the gain, \(\left|\frac{v_{o}}{v_{in}}\right|\), at \(60\ \text{Hz}\)?