RF Toolbox

Directional Coupler & Hybrid Designer

Designs three fundamental coupler/hybrid topologies. Coupled-line: gives even/odd mode impedances for a target coupling level. Branchline (90° hybrid): gives all four arm impedances for equal or unequal power split. Rat-race (180° hybrid): gives ring impedance and dimensions for equal split sum/difference operation.

Equations & Parameters ▸
Coupled-line: \(Z_{oe}=Z_0\sqrt{\frac{1+C}{1-C}}\quad Z_{oo}=Z_0\sqrt{\frac{1-C}{1+C}}\quad C=10^{-C_{\rm dB}/20}\)
Branchline: \(Z_{\rm series}=Z_0\quad Z_{\rm shunt}=Z_0/\sqrt{2}\) (equal split); all arms = λ/4
Rat-race: \(Z_{\rm ring}=Z_0\sqrt{2}\quad \text{circumference}=3\lambda/2\)
ZoeEven-mode impedance (both lines driven in phase)
ZooOdd-mode impedance (lines driven out of phase)
CCoupling coefficient (linear). C=3 dB → C=0.707, Zoe≈120Ω, Zoo≈21Ω
λ/4All arms are one quarter-wavelength long at the centre frequency
Design Type
Inputs
dB
Results
Diagram