Wilkinson Power Divider, Splitter & Combiner

From https://www.electronics-notes.com/

The Wilkinson configuration is a very effective and convenient form of power divider / splitter & combiner

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Power dividers or splitters and combiners can be realised using a topology known as the Wilkinson design.

The Wilkinson power divider / splitter / combiner utilises quarter wave transmission lines to effect the combination or split. This often means that the Wilkinson power divider or combiner tends to be used more at microwave frequencies where the transmission line lengths become manageable.

Whilst the Wilkinson power divider may make use of PCB transmission lines at microwave frequencies where the wavelengths are short, it is also possible to make a Wilkinson power divider or combiner using coaxial cable or other forms of transmission line. Even lumped circuit elements can be used.

Wilkinson power divider beginnings

The Wilkinson power divider or Wilkinson splitter as it is also known takes its name from Ernest Wilkinson, the electronics engineer who initially developed it in the 1960s.

Wilkinson published his idea in IRE Trans. on Microwave Theory and Techniques, in January 1960 under the title: “An N-way Power Divider”.

It can be seen from the title of the paper that the idea for what is now known as the Wilkinson power splitter is for a multiple port device, although the most common implementation seen in practice these days is for a two way divider.

Wilkinson power divider advantages & disadvantages

In order to determine whether to use a Wilkinson power divider splitter / Wilkinson combiner, it is necessary to weigh up the advantages and disadvantages of using them.

Wilkinson divider / combiner advantages:

Simplicity: The Wilkinson divider / splitter / combiner is particularly simple and can easily be realised using printed components on a printed circuit board. It is also possible to use lumped inductor and capacitor elements, but this complicates the overall design.
Loss: If perfect components were used, the Wilkinson splitter divider would not introduce any additional loss above that arising from the division of the power between the different ports. In addition to this, the real components used for the Wilkinson splitter can be very low loss, especially when PCB transmission lines are used along with low loss PCB substrate material.
Isolation: The Wilkinson divider / combiner provides a high degree of isolation between the “output” ports.
Cost: When the Wilkinson power divider is realised using printed circuit board elements, the cost is very low – possibly the only increase above that of the single resistor used results from an increase in the board area used as a result of the printed elements. However to reduce losses, a low loss PCB substrate may need to be used and this would increase the cost.

Wilkinson divider / combiner disadvantages:

Frequency response: As the Wilkinson splitter is based around the use of quarter wave transmission lines, it has a limited bandwidth, although there are some Wilkinson splitters available that offer reasonably wide bandwidths.
Size: At lower frequencies the size of the quarter wave transmission lines means that it can be too large for many applications, and therefore the Wilkinson power divider topology is most widely used at microwave frequencies.

2 way Wilkinson power divider basics

Although the Wilkinson power divider concept can be used for an N-way system, it is easiest to see how it operates as a two way system, and later expand it out to see how the Wilkinson power splitter can be used as an n-way device.

The Wilkinson power divider / Wilkinson combiner uses quarter wave transformers to split the input signal to provide two output signals that are in phase with each other.

Wilkinson splitter / divider / combiner showing quarter wavelength transformers — Wilkinson power divider, splitter / combiner circuit

The resistor between the two output ports enables the two outputs to matched while also providing isolation. The resistor does not dissipate any power, and as a result the Wilkinson power divider can theoretically be lossless. In practice there are some losses, but these are generally low.

The values within the two way Wilkinson divider / combiner can be calculated:

R = 2 Z_{0}

Z_{match} = \sqrt{2} Z_{0}

Z_{match} = 1.414 Z_{0}

Where:
R = the value of the terminating resistor connected between the two ports
Zo = the characteristic impedance of the overall system
Z_match = the impedance of the quarter wave transformers in the legs of the power divider combiner.

In order to see how the Wilkinson divider works, consider a signal entering the left hand port, port 1 in the diagram above. The signal reaches the physical split and passes to both outputs, ports two and three of the Wilkinson divider. As the two legs of splitter / divider are identical, the signals appearing at the outputs will have the same phase. This means that ports 2 and 3 will be at the same potential and no current will flow in the resistor.

As the power is being split, it is necessary to ensure that the impedances within the Wilkinson divider are maintained. To achieve this, the two output ports must each appear as an impedance of 2 x Zo – the two output ports of 2 Zo in parallel will present an overall impedance of Zo. The impedance transformation is achieved by placing a quarter wave transmission line between the star point and the output – the transmission line has an impedance of 1.414 x Zo. In this way, the impedance within the system is maintained.

Wilkinson combiner operation

The Wilkinson power divider operates in both directions and can also be used as a combiner. In this mode signals entering ports 2 and 3 will emerge at port 1, and none at port 3, i.e. it is isolated.

Consider power entering port 2. It will split equally between the resistor and port1. Thus half the power passes to port 1 and half is dissipated in the resistor – fact that should be considered for power applications.

As the signal enters port 2, half passes through the resistor and the other half passes through the first quarter wave transformer. It then appears at the star point. Any power passing through the other quarter wave transformer to port 3 will be out of phase with that appearing via the resistor as it will have passed through two quarter wave lines. As a result there is isolation between the two ports, half the power is dissipated within the resistor and half appears at port 1.

The Wilkinson power divider or combiner is for many RF applications. Some of its key advantages: low level of loss and its high level of isolation between the output ports means that the Wilkinson power divider is a particularly attractive proposition. A further advantage at microwave frequencies is that it can often be made very cheaply because the transmission line elements can be printed on the circuit board. This means that the only component required for the Wilkinson divider is a resistor, although it may mean that additional board space is required.

The Wilkinson power divider, splitter, combiner is widely used in many areas and is able to provide excellent performance.