BeginnerTopic 34 of 101Signals, Control & Comms
Butterworth, Chebyshev and elliptic filters
Classic analogue prototypes with different ripple and roll-off.
In depth
Butterworth: maximally flat passband. Chebyshev I: passband ripple, steeper roll-off; Chebyshev II: stopband ripple. Elliptic (Cauer): ripple in both bands, steepest transition for a given order. Bessel: best group delay. Choose by flatness vs sharpness vs phase.
Key points
- Order n from specs
- 3 dB cutoff
- Pole locations on circle or ellipse
ExampleAn elliptic filter needs about a third of the order of a Butterworth for the same selectivity.
Butterworth, Chebyshev and elliptic filters are classic designs with different trade-offs between flatness, roll-off and ripple.
What is Butterworth, Chebyshev and elliptic filters?
Classic analogue prototypes with different ripple and roll-off.
Why is it important to understand butterworth, Chebyshev and elliptic filters?
Butterworth, Chebyshev and elliptic filters are classic designs with different trade-offs between flatness, roll-off and ripple.
What is the main feature of a Butterworth filter?
It is maximally flat in the passband, with no ripple, but its roll-off is gentler than the others for the same order.
What does Chebyshev trade?
It allows ripple in the passband to gain a steeper roll-off than Butterworth for the same order.
How is Butterworth, Chebyshev and elliptic filters used in practice?
Typical applications include choosing a maximally flat filter for an instrument amplifier, selecting a Chebyshev filter for a steep roll-off in a communication channel and using an elliptic filter when the lowest order that meets a sharp specification is needed.
What should I learn before Butterworth, Chebyshev and elliptic filters?
Study "Filter design methods" first (topic 33 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Butterworth, Chebyshev and elliptic filters?
Order n from specs. 3 dB cutoff. Pole locations on circle or ellipse.
Can you give an example of Butterworth, Chebyshev and elliptic filters?
An elliptic filter needs about a third of the order of a Butterworth for the same selectivity.
What comes after Butterworth, Chebyshev and elliptic filters?
The next topic is "Multirate processing", which builds directly on this one.
How difficult is Butterworth, Chebyshev and elliptic filters?
It is classed as Beginner in Signals, Control & Comms (topic 34 of 101). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.