Course Objectives: To learn design methods for practical passive, RC active and switched capacitor filters

1.0 Introduction (4 hours)

1.1 The filter design problem
1.2 Kinds of filters in terms of frequency response
1.3 History of filter design and available filter technologies

2.0 Approximation Methods (5 hours)

2.1 Ideal lowpass, highpass, bandpass and bandstop functions
2.2 Lowpass approximations including Butterworth, Chebyshev, inverse Chebyshev and elliptic LPF
2.3 Frequency transformations: lowpass to highpass, lowpass to bandpass and lowpass to bandstop
2.4 Bessel-Thomson approximation of constant delay

3.0 One-Port Passive Circuits (5 hours)

3.1 Properties of passive circuits, positive real functions
3.2 Properties of lossless circuits
3.3 Synthesis of LC one-port circuits, Foster and Cauer circuits
3.4 Properties and synthesis of RC one-port circuits

4.0 Two-port Passive Circuits (4 hours)

4.1 Properties of passive two-port circuits, residue condition, transmission zeroes
4.2 Synthesis of two-port LC and RC ladder circuits based on zero-shifting by partial pole removal
4.3 Properties of resistively-terminated lossless ladder circuits, transmission and reflection coefficient

5.0 Design of Resistively-Terminated Lossless Filters (5 hours)

5.1 Synthesis of LC ladder circuits to realize all-pole lowpass functions
5.2 Synthesis of LC ladder circuits to realize functions with finite transmission zeroes (the Darlington insertion loss method)
5.3 Impedance scaling and frequency scaling
5.4 Passband transformations to obtain a highpass, bandpass or bandstop filter from a lowpass prototype

6.0 Fundamentals of Active Circuits (5 hours)

6.1 Ideal and real operational amplifiers, gain-bandwidth product
6.2 Active building blocks: amplifiers, summers, integrators
6.3 First order active sections
6.4 Second order active sections (biquads)

7.0 Sensitivity (5 hours)

7.1 Definition of single parameter sensitivity
7.2 Centre frequency and Q-factor sensitivity
7.3 Sensitivity properties of biquads
7.4 Sensitivity of resistively-terminated lossless circuits

8.0 Design of High-Order Active Filters (6 hours)

8.1 Cascade of biquads
8.2 Ladder design with simulated inductors
8.3 Ladder design with frequency-dependent negative resistors (FDNR)
8.4 Leapfrog simulation of ladders

9.0 Switched-Capacitor Filters (6 hours)

9.1 The MOS switch and the switched capacitor
9.2 Switched-capacitor circuits for analog operations: addition, subtraction, multiplication and integration
9.3 First-order and second-order switched-capacitor circuits
9.4 Leapfrog switched-capacitor filters

Laboratory: The laboratory experiements will consists mainly of computer simulation, analysis and design of pasive and active filters. Commercially available programs for approximation, design of passive filters, analysis of active circuits and analysis of switched-capacitor circuits will be employed. Hardware implementations of some active filters will be contructed and tested.


1.0 M E Van Valkenberg, “Analog Filter Design“, Holt, Rinehar and Winston, Inc, New York, 1982.

2.0 W K Chen, “Passive and Active Filters: Theory and Implementations“, John Wiley and Sons, 1986. (A slightly more advanced treatment of approximation and properties of passive ciruits)

3.0 R Schaumann, M S Ghausi and K R Laker, “Design of Analog Filters: Passive, Active RC and Switched-Capacitor“, Prentice Hall, Englewood Cliffs, New Jersey, 1990

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