Filter Prototype g-Values
Every filter design begins with the lowpass prototype: a normalised ladder of element values g₀…g_{N+1} that set the shape (Butterworth or Chebyshev) and order. Impedance and frequency scaling then turn them into real inductors and capacitors, and the same g-values feed distributed designs (stubs, coupled lines, stepped-impedance). This tool computes the g-values and the denormalised L/C for a chosen cutoff and impedance.
Equations & Parameters ▸
Butterworth: \(g_k=2\sin\dfrac{(2k-1)\pi}{2N}\)
Chebyshev: \(\beta=\ln\!\big[\coth\tfrac{L_{Ar}}{17.37}\big],\ \gamma=\sinh\tfrac{\beta}{2N}\)
\(g_1=\dfrac{2a_1}{\gamma},\ g_k=\dfrac{4a_{k-1}a_k}{b_{k-1}g_{k-1}},\ a_k=\sin\tfrac{(2k-1)\pi}{2N},\ b_k=\gamma^2+\sin^2\tfrac{k\pi}{N}\)
scaled: series \(L=\dfrac{g Z_0}{\omega_c}\), shunt \(C=\dfrac{g}{Z_0\omega_c}\)
Chebyshev: \(\beta=\ln\!\big[\coth\tfrac{L_{Ar}}{17.37}\big],\ \gamma=\sinh\tfrac{\beta}{2N}\)
\(g_1=\dfrac{2a_1}{\gamma},\ g_k=\dfrac{4a_{k-1}a_k}{b_{k-1}g_{k-1}},\ a_k=\sin\tfrac{(2k-1)\pi}{2N},\ b_k=\gamma^2+\sin^2\tfrac{k\pi}{N}\)
scaled: series \(L=\dfrac{g Z_0}{\omega_c}\), shunt \(C=\dfrac{g}{Z_0\omega_c}\)
| N | Filter order (1–10). |
| Response | Butterworth (maximally flat) or Chebyshev (equal-ripple). |
| LAr | Chebyshev passband ripple (dB). |
| Z0, fc | Impedance and cutoff frequency for the denormalised L/C. |
Reference: D. M. Pozar, Microwave Engineering, 4th ed., §8.3 (Tables 8.3, 8.4).
Inputs
1 – 10
Shape
dB
ChebyshevΩ
For L/CGHz
For L/CPrototype g-values & denormalised elements
Ladder