# Branchline Coupler Calculator

This CalcTown calculator calculates the various parameters related to a Branchline Coupler circuit.

The branchline the simplest type of quadrature coupler, since the circuitry is entirely planar. Each transmission line is a quarter wavelength. Although, 3/4, 5/4 or 7/4 wavelengths, etc. could also be used on each arm if the circuit layout requires it,  in decreasing bandwidth. A signal entering the top left port is split into two quadrature signals on the right (ports 2 and 3), with the remaining port 4 fully isolated from the input port at the center frequency. We note that the lower output port (port 3) has the most negative transmission phase since it has the farthest path to travel.

#### Result

Ω
Ω

Where,

Where,

PA = Power output of Port 2

PB = Power output of Port 3

Z0 = Characteristic Impedance of the overall system

Z0A, Z0B = Branch output impedances

Generally branch-line couplers are 3dB, four ports directional couplers having a 90° phase difference between its two output ports named through and coupled arms. Branch-line couplers (also named as Quadrature Hybrid) are often made in microstrip or stripline form. It has a high degree of symmetry since any port can be used as the input port, with output ports always being on the opposite side of the junction from the input port, and the isolated port remaining on the same side as the input port. The 900 phase difference alters over ±50 for a 10% change in frequency around the center frequency .