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Wilkinson power splitters

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 loss-less 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: if you put power into port 2 or port 3, all of it goes up in heat in the ideal case. The resistor adds no resistive loss to the power split from port 1, so an ideal Wilkinson splitter is 100% efficient.
A veteran of WWII, Mr. Wilkinson died on March 10, 2012.

Wilkinson power splittersIdeal two-port Wilkinson splitter

E.J. Wilkinson, "An N-way Power Divider", IRE Trans. on Microwave Theory and Techniques, vol. 8, p. 116-118, Jan. 1960
D.M. Pozar, Microwave Engineering, 4th Edition, John Wiley & Sons: New York, 1998, pp. 328-333

Click here to go to our main page on couplers and splitters

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

Two-port single-stage equal-split Wilkinsons (this page)

Designing Wilkinsons using Excel

Wilkinson isolation Rules of Thumb

Lumped-element Wilkinson

Multistage Wilkinsons (separate page, multiple examples!)

How many sections do you need in a Multi-stage Wilkinson?

Unequal-split Wilkinsons (separate page)

Compact Wilkinsons (separate page, multiple examples!)

N-way Wilkinsons (separate page)

N-way Wilkinsons with unequal split (separate page)

Here's a video by Sebastian that explains the basics of Wilkinson design. Check out Jaunty Electronics for more videos by Sebastian on designing electronics.

 

Sebastian explains Wilkinson splitters

 

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).

Wilkinson

Ideal two-port Wilkinson splitter

Wilkinson power splitters

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.

Wilkinson power splitters

Example of Wilkinson with input transformer

 

Wilkinson power splitters

S-parameters for above Wilkinson with input transformer

 

 
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