Wilkinson Splitter / Combiner

[ab cd]

The Wilkinson Power Splitter splits an input signal into two equal phase output signals, or combines two equal-phase signal into one in the opposite direction. Wilkinson splitter relies on quarter-wave transformers to match the split ports to the common port.

Wilkinson Power Splitter is a specific class of power divider circuit that can achieve isolation between the output ports while maintaining a matched condition on all ports. The Wilkinson design can also be used as a power combiner because it is made up of passive components and hence reciprocal. This circuit finds wide use in radio frequency communication systems utilizing multiple channels since the high degree of isolation between the output ports prevents crosstalk between the individual channels.

Ideal two-port Wilkinson splitter​

Zo = the characteristic impedance of the system (such as 50Ω, 75Ω, etc)

Wilkinson Splitter - operation as splitter (source)​

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 Splitter - operation as combiner (source)​

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.

Wilkinson Splitter in microstrip technology​

Zo = the characteristic impedance of the system (such as 50Ω, 75Ω, etc)

The one below is a low cost commercial splitter based on Wilkinson principle​

Wilkinson divider / combiner advantages: (source)​

• 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:(source)​

• 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.

.

 

[Janos Konya]

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.

It’s a good summary, but of course this scope doesn’t allow us to look at this useful stuff in a really detailed (analytical) way.

"...and half is dissipated in the resistor"
Well, it is true if signal entering in port 2 is out of phase compared to the quarter wave lines.
- If input frequency is matched to the line WL, feeding P2 (0°) would mean the same signal on P3 but with 180° phase. (2x quarter wave line between P2 and P3) As a result, there will not be current on the resistor, thus no loss and no dissipation.
It works when P3 and all of used and unused ports are closed (or shorted) by the planned impedance.

- Bandwidth can be much wider if we use more than one step to reach the planned impedance. (so called: multi-stage impedance matching). We pay by having worse Isolation between ports. A narrow band combiner is not always a disadvantage. It means the possible best isolation and also less out of band signals on the output port(s). I would not point at either wide-band or narrow-band splitters/combiners as "disadvantage". It depends on the use only...
A narrow-band splitter can be disadvantage if you can not find the right one as an offer in a webshop.

 

[Janos Konya]

Added to abcd's great description - to the size section:

Manufacturers and designers have found a way to avoid having to use an overly large divider because of the lower frequencies. The possibility arises from the fact that the line can be described by electrical properties: the inductance of the conductor and the parallel capacitance between the conductor and the shield. Knowing these, a Hybrid or Lumped Element splitter / combiner can be created - even on a significantly smaller scale.

Made of SMD inductors and capacitances, my experimental version of the 4-way Wilkinson splitter designed for 1090 MHz was made in approximately a matchbox or bias panel size. (excluding connectors)

The putative simplicity is "lost" for the prise of getting a really precise combiner. On the other hand, creation of the other solution - tuned (microstrip) lines on a circuit board (diy) - is more about luck.