RF systems can’t always be designed in the same way as digital systems or low-frequency analog systems. Instead, some components have to be created as printed elements to provide the desired functions. This is understandable; some RF components are simply too expensive, are not board-mountable, or they simply don’t meet performance requirements.
One of the common printed interconnect elements used in RF systems is a Wilkinson power divider. The idea behind these printed elements is simple: an input signal is sent into the power divider, and the power is split equally along the outputs. While these printed elements are normally designed with two outputs, they can be scaled up to any number of outputs in a few creative ways. We’ll look at how to design these circuit elements in this article.
Starting a Wilkinson Power Divider Design
Wilkinson dividers are basically constructed as printed elements with controlled impedance transmission lines and termination resistors. These structures are intended to split power evenly between two or more output ports at a specific frequency.
If fabricated on standard PCB materials, these structures are normally placed on the surface layer due to manufacturing constraints, as we’ll see momentarily. Two example Wilkinson divider structures are shown below.
Two Wilkinson power divider structures operating at approximately 2 GHz. [Source: Cadence]
In this design, we have one input port (on the left) and two output ports (on the right). There is a resistor that bridges the two transmission lines that make up the output ports. The standard Wilkinson power divider structure is intended to have the following performance characteristics:
- The device should operate at only 1 frequency
- The input power should split evenly across all output ports
- Each transmission line in the structure must have specific impedance values
- The terminating resistor must have negligible parasitics at the operating frequency
- The phase difference between the output ports should be zero
- The circuit should be reciprocal, although it will not be operated in this way
The basic topology of a standard Wilkinson power divider is shown below. The divider can be designed to hit a specific characteristic impedance of the input transmission line at Port 1.
Standard Wilkinson power divider design.
Each of the narrow transmission line legs in this circuit after the division is a quarter-wave transformer at the operating frequency, but it is designed with slightly larger impedance than the characteristic impedance of the transmission line at Port 1. The terminating resistor sets the input impedance at Port 1 to be equal to the characteristic impedance Z0. This then ensures the phase shift is consistent across each port, and that reflections are suppressed at the input port.
N-port Power Dividers
The above 2-port topology can in principle be extended to N ports. Just as an example, consider the 3-port Wiklinson power divider topology shown below:
3-port Wilkinson power divider.
This pattern can be extended to any number of ports, but with a scaling factor of N (instead of 3) on the line impedance and resistor values. The challenge with this design in a PCB is that board space will eventually limit the number of possible ports. In addition, each port reduces the power by a factor (1/N), and eventually there may not be useful power left after enough divisions.
Dual-band Power Dividers
The standard Wilkinson power divider operates at one frequency, but there are variations designed to operate at two frequencies. These dual-band power dividers effectively operate as filters by taking advantage or reflection at a stub in the standard 2-port Wilkinson divider. The topology used in this type of design is shown below.
Dual-band 2-port Wilkinson power divider.
The above design is discussed in an IEEE paper:
- Zhang, Hualiang, and Hao Xin. "Designs of dual-band Wilkinson power dividers with flexible frequency ratios." In 2008 IEEE MTT-S International Microwave Symposium Digest, pp. 1223-1226. IEEE, 2008.
Cascaded Wilkinson Power Dividers
It is also possible to cascade Wilkinson power dividers. In other words, the output from one Wilkinson divider can be connected to the input of another divider. This allows one signal to be split into 3x signals, 4x signals, and so on. An example topology with 2-port Wilkinson dividers is shown below.
Cascaded Wilkinson power divider topology.
In this case, we just take each power divider and design it as if it were to operate in isolation. Because the 1st power divider is just a 2-port divider, we do not worry about the downstream power dividers thanks to impedance matching applied at the output port.
As long as there is very precise impedance matching between the input and output ports along the power divider chain, then the only losses will be due to insertion loss along each arm of the power divider. In the idea case, the power division (as a fraction or ratio) would be multiplicative as we would expect. In the case of N cascaded power dividers, we would also have to cascade the S-parameters to determine the total S-parameter matrix, but remember that S-parameters do not always multiply straight across.
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