ELET4223 Homework 4
Design of Tow-Thomas Biquad Filters:
1.
(a) Design a Tow-Thomas Lowpass filter with 𝜔0 = 10,000, 𝑄 = 5, and a DC gain of 1. All
capacitors must be 0.01μF. On your circuit, clearly indicate Vin and Vout.
(b) What change would you make to the circuit for a DC gain of 15?
2.
(a) Design a Tow-Thomas Bandpass filter with 𝜔0 = 5,000, 𝑄 = 8, and a midband gain of 1. All
capacitors must be 0.01μF. On your circuit, clearly indicate Vin and Vout.
(b) What change would you make to the circuit for a midband gain of 10?
3.
(a) Design a Tow-Thomas Band-eliminate filter with 𝜔0 = 7,500, 𝑄 = 9, and a DC gain of 1. All
capacitors must be 0.1μF. On your circuit, clearly indicate Vin and Vout.
(b) What change would you make to the circuit for a DC gain of 6?
4.
(a) Design a Tow-Thomas Allpass filter with 𝜔0 = 2000, 𝑄 = 7, and a gain of 1. All capacitors
must be 0.2 μF. On your circuit, clearly indicate Vin and Vout.
(b) What change would you make to the circuit for a gain of 5?
5.
(a) Design a Tow-Thomas Highpass filter with 𝜔0 = 4,000, 𝑄 = 5, and a high-frequency gain of
1. All capacitors must be 0.01 μF. On your circuit, clearly indicate Vin and Vout.
(b) What change would you make to the circuit for a high-frequency gain of 0.2?
Node Voltage Analysis of a Second-Order Circuit
6.
Do problem 5.1 on page 148-149 of textbook.
Hints for problem 5.1:

For part (a), start by using Node Voltage analysis to get
𝑉2
𝑉1
=
2
𝑠
𝑅1 𝐶
1
1
𝑠2 + 𝑅 𝐶 𝑠 + 2 2
𝑅 𝐶
1
. This
takes about a page and a half of algebra.

For part (b), start by normalizing the circuit by choosing R, C and R1 to give 𝜔0 = 1 and any
desired Q value. Then magnitude and frequency scale.

Parts (a) and (b) are two separate problems. You don’t have to do part (a) first!