Chebyshev Type I Filter Calculator
Calculate minimum order, ripple factor, achieved stopband attenuation, and pole locations from your passband/stopband specs.
What this chebyshev filter calculator does
This page is a practical Chebyshev Type I filter calculator for quick design sizing. You enter your electrical requirements (passband edge, stopband edge, ripple, and attenuation), and it computes:
- Ripple factor ε
- Exact order required (non-integer)
- Minimum realizable integer order n
- Expected stopband attenuation at that integer order
- Pole locations for implementation and simulation workflows
Engineers commonly use this workflow before moving into active filter design (Sallen-Key, MFB), LC ladder synthesis, or digital IIR conversion.
Input definitions
1) Filter type
Choose low-pass if you want low frequencies to pass and high frequencies to be attenuated. Choose high-pass for the reverse.
2) Passband edge, fp
Frequency at which the passband ripple specification is enforced. For Type I Chebyshev filters, the passband is intentionally rippled up to this edge.
3) Stopband edge, fs
Frequency where you require at least As dB attenuation. For low-pass: fs must be greater than fp. For high-pass: fs must be less than fp.
4) Ripple and attenuation in dB
Ap controls allowed passband ripple. As sets how deep the rejection must be. Tighter specs usually force higher order filters.
Equations used
The calculator uses standard Chebyshev Type I analog design equations:
n ≥ acosh( sqrt((10^(As/10)-1)/(10^(Ap/10)-1)) ) / acosh(Ωs)
where Ωs = fs/fp (low-pass) or fp/fs (high-pass)
After that, the exact order is rounded up to the next integer to guarantee the stopband requirement.
Design interpretation tips
- Lower ripple (smaller Ap) gives flatter passband but often increases order.
- Larger frequency separation between passband and stopband edges usually reduces required order.
- High order gives steep roll-off but can increase sensitivity to component tolerances and op-amp bandwidth limits.
- For very tight specs, compare Chebyshev, Butterworth, and elliptic responses before finalizing architecture.
Worked example
Suppose you need a low-pass response with fp = 1 kHz, fs = 2 kHz, Ap = 1 dB, and As = 40 dB. The calculator typically returns an order around 5 to 6 (depending on exact parameters), plus pole locations for stage-by-stage design.
You can then group poles into second-order sections and map them into active RC circuits or digital biquads.
Practical implementation checklist
- Verify pole/Q values against op-amp gain-bandwidth and slew rate.
- Include realistic component tolerances in simulation (e.g., Monte Carlo).
- If phase linearity matters, evaluate group delay behavior.
- For digital realization, use bilinear transform with pre-warping around critical frequencies.
In short: this calculator gives you a fast, reliable starting point for Chebyshev filter synthesis and helps connect requirement-level specs directly to realizable filter order and poles.