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# Wilkinson power splitters

Revised October 15, 2010

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Here's a clickable index to our treasure-trove of material on Wilkinson power splitters:

Designing Wilkinsons using Excel New for August 2008!

Wilkinson isolation Rules of Thumb

Lumped-element Wilkinson

Multistage Wilkinson (separate page, multiple examples!)

Unequal-split Wilkinson (separate page)

Compact Wilkinsons (separate page, multiple examples!)

N-way Wilkinsons (separate page)

N-way Wilkinsons with unequal split (separate page, new for September 2009!)

The Wilkinson power splitter was invented around 1960 by an engineer named Ernest Wilkinson. It splits an input signal into two equal phase output signals, or combines two equal-phase signal into one in the opposite direction. Wilkinson relied on quarter-wave transformers to match the split ports to the common port. Because a lossless reciprocal three-port network cannot have all ports simultaneously matched, Wilkinson knew he had to cheat so he added one resistor and the rest is history. The resistor does a lot more than allow all three ports to be matched, it fully isolates port 2 from port 3 at the center frequency. The resistor adds no resistive loss to the power split, so an ideal Wilkinson splitter is 100% efficient.

### Two-port Wilkinsons

In its simplest form, an equal-amplitude, two-way split, single-stage Wilkinson is shown the figure below. The arms are quarter-wave transformers of impedance 1.414xZ0 (thanks for the correction, Rod!) Here we show a three-port circuit (the most common in practice by far, but Wilkinson described an N-way divider).

 Ideal two-port Wilkinson splitter

 S-parameters of ideal 2-way Wilkinson power splitter

Here is how the Wilkinson splitter works as a power divider: when a signal enters port 1, it splits into equal-amplitude, equal-phase output signals at ports 2 and 3. Since each end of the isolation resistor between ports 2 and 3 is at the same potential, no current flows through it and therefore the resistor is decoupled from the input. The two output port terminations will add in parallel at the input, so they must be transformed to 2xZ0 each at the input port to combine to Z0. The quarter-wave transformers in each leg accomplish this; without the quarter-wave transformers, the combined impedance of the two outputs at port 1 would be Z0/2. The characteristic impedance of the quarter-wave lines must be equal to 1.414xZ0 so that the input is matched when ports 2 and 3 are terminated in Z0.

Okay, what about as a power combiner? Consider a signal input at port 2. In this case, it splits equally between port 1 and the resistor R with none appearing at port 3. The resistor thus serves the important function of decoupling ports 2 and 3. Note that for a signal input at either port 2 or 3, half the power is dissipated in the resistor and half is delivered to port 1. Why is port 2 isolated from port 3 and vice-versa? Consider that the signal splits when it enters port 2. Part of it goes clockwise through the resistor and part goes counterclockwise through the upper arm, then splits at the input port, then continues counterclockwise through the lower arm toward port 3. The recombining signals at port 3 end up equal in amplitude (half power or the CW signal is lost in resistor R1, while half of the CCW signal is output port 1. And they are 180 degrees out of phase due to the half-wavelength that the CCW signal travels that the CW signal doesn't. The two signal voltages subtract to zero at port 3 and the signal disappears, at least under ideal circumstances. In real couplers, there is a finite phase through the resistor that will limit the isolation of the output ports.

Below we show an example of extending the bandwidth of a Wilkinson splitter by placing a quarter-wave transformer on the common-node and optimizing its impedance along with the impedances of the quarter-wave legs.

 Example of Wilkinson with input transformer

 S-parameters for above Wilkinson with input transformer

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