Wilkinson Power Divider Calculator

What is Wilkinson power divider?

Wilkinson Power Divider uses the quarter-wave transformers to split the input signal into two equal phase output signals. It also provides isolation between the output ports while maintaining a matched condition on all ports. It is used in the field of microwave engineering.

Wilkinson power divider has three ports (shown below Fig). The Wilkinson power divider splits an input signal from port 1 into two equal phase output signals (port 2 & port 3). It provides isolation between the output ports while maintaining a matched condition on all ports.

Also, it can operate in both directions, i.e., it can also be used as the power combiner to combine the signals that enter ports 2 and 3 into one (will emerge at port 1).  

Ideal two-port Wilkinson power divider

A two-way Wilkinson power divider construction features an input branch with characteristic impedance (Zo),  two quarter-wave transformers with the impedance of 1.414 x Zo and a resistor (R) across port 2 and port 3 to provide impedance matching as well as isolation between the output ports (2&3).

When a signal enters the input port 1, it will be divided into two signals, with equal amplitude & equal phase, and appear as the output at ports 2 & 3. Since the resistor (R) across ports 2 & 3 is at the same potential, there is no current flow through the resistor; hence the resistor is decoupled from the input.

By changing the value of resistor (R), the amount of power division between ports 2&3 can be varied. The relation between the R, Zo, and amount of power division is given by the following formula.

R = Zo (K + 1/K)

Where, K2 = P3 / P2; (P3 - power at port 3) (P2 - power at port 2). 

Where,

P_A = Power output of Port 2

P_B = Power output of Port 3

Z₀ = Characteristic Impedance of the overall system

R_w = Terminating resistance between two output ports.

Z₁, Z₂, Z₃, Z₄ = Branch impedances

Equal equal-splitting Wilkinson Divider is obtained when K=1.