Coupled-Line Bandpass Filter
A parallel coupled-line bandpass filter is a cascade of N+1 quarter-wave coupled sections. Each section acts as an admittance (J) inverter, and the design reduces to picking, for each section, an even-mode impedance Z0e and odd-mode impedance Z0o that realise the required J-inverter. This tool turns a lowpass prototype (order, response, ripple) plus a centre frequency and fractional bandwidth into the J/Y₀ ratios and the Z0e, Z0o pair for every section.
Equations & Parameters ▸
\(\dfrac{J_1}{Y_0}=\sqrt{\dfrac{\pi\Delta}{2g_1}},\quad \dfrac{J_n}{Y_0}=\dfrac{\pi\Delta}{2\sqrt{g_{n-1}g_n}}\ (2\le n\le N),\quad \dfrac{J_{N+1}}{Y_0}=\sqrt{\dfrac{\pi\Delta}{2g_N g_{N+1}}}\)
\(Z_{0e}=Z_0\!\left[1+\dfrac{J}{Y_0}+\Big(\dfrac{J}{Y_0}\Big)^{2}\right],\quad Z_{0o}=Z_0\!\left[1-\dfrac{J}{Y_0}+\Big(\dfrac{J}{Y_0}\Big)^{2}\right]\)
\(\Delta=\dfrac{\omega_2-\omega_1}{\omega_0}\) is the fractional bandwidth; each section is \(\lambda/4\) long at \(f_0\).
\(Z_{0e}=Z_0\!\left[1+\dfrac{J}{Y_0}+\Big(\dfrac{J}{Y_0}\Big)^{2}\right],\quad Z_{0o}=Z_0\!\left[1-\dfrac{J}{Y_0}+\Big(\dfrac{J}{Y_0}\Big)^{2}\right]\)
\(\Delta=\dfrac{\omega_2-\omega_1}{\omega_0}\) is the fractional bandwidth; each section is \(\lambda/4\) long at \(f_0\).
| N | Filter order (1–9); gives N+1 coupled sections. |
| Response | Butterworth or Chebyshev prototype g-values. |
| LAr | Chebyshev passband ripple (dB). |
| f0, Δ | Centre frequency and fractional bandwidth (%). |
| Z0 | System impedance. |
Reference: D. M. Pozar, Microwave Engineering, 4th ed., §8.7.
Inputs
1 – 9
Shape
dB
ChebyshevGHz
Passband centre%
FractionalΩ
SystemCoupled-section impedances
Coupled-line cascade