ELEC 320
Prof. Rich Kozick
Fall, 1998

Homework 2

Date Assigned: Friday, August 28, 1998
Date Due: Monday, August 31, 1998

Reading: We will discuss Chapter 1 in the Kamen/Heck text next week. Please start reading Chapter 1 as follows: section 1.1, browse sections 1.2-1.4, and read section 1.5.

Problems: Please work on the following problems for Monday. Do your best to solve the problems, and come to class with questions. We will review the solutions in class on Monday.

1.

Consider the low-pass RC circuit filter that we discussed in class, which is shown below.

[CIRCUIT DIAGRAM OMITTED IN HTML VERSION]

(a)

What is the formula for the ``complex frequency response'' $H(\omega)$?

(b)

What are the formulas for the magnitude $\vert H(\omega)\vert$and the phase $\angle H(\omega)$ of the frequency response?

(c)

For the values R=1.1 $k \Omega$ and C=0.22 $\mu F$considered in class, produce rough sketches of $\vert H(\omega)\vert$ and $\angle H(\omega)$ versus $\omega$.What is the ``amplitude gain'' of the circuit at low frequencies?

(d)

Use your formula for $\vert H(\omega)\vert$ and the definition of cutoff frequency $\omega_c$ to derive an expression for $\omega_c$ as a function of R and C. This is the expression that is required in order to design a filter (i.e., choose R and C) to achieve a specified cutoff frequency. Hint: The cutoff frequency $\omega_c$ is defined as the value of frequency that produces amplitude gain $1/\sqrt{2}$, i.e., $\vert H(\omega_c)\vert = 1 / \sqrt{2}$.

2.

Please answer the same questions for the RC circuit shown below. What type of filter is this circuit (low pass, high pass, or band pass)?

[CIRCUIT DIAGRAM OMITTED IN HTML VERSION]