How do RF and Microwave Power Splitters, Dividers, and Combiners Work?

RF and microwave power splitters and dividers create two copies of the same signal, while ideally preventing crosstalk between the outputs. Doing this with minimal loss while maintaining signal integrity is a challenge. In this article we explain how power splitters work and what the tradeoffs are to common types. 

Basic Concept of RF Splitters

An RF splitter is designed to take a single input signal and copy it to multiple outputs. Multiple outputs are identical if each one has the same signal level and if the signals arrive at the same time. This is called equal amplitude and phase, and it is quantified by the amplitude balance (ideally zero dB) and phase balance (ideally zero degrees). The easiest way to do this is simply take the transmission line the signal is traveling on, and split it in two (as is commonly done in low frequency circuits).

This will split the input signal into equal amplitude copies with identical phase, but with two highly undesirable side effects:

1. Reflections and Impedance Mismatch: While the voltage on each arm will be equal, the current must split in two. For a wave this can't be done instantaneously, so there will be a reflection. This can be mitigated by making the width of the output lines half as wide, but they will be at a different impedance as the input. 
2. Crosstalk between outputs: The insertion loss between the outputs (called isolation will be minimal. If used only as a splitter, and if the outputs have the exact same load, this might not be a problem. If there is any difference between the output loads this will cause degraded signal integrity in the system.

Now we'll look at two options to solve the first problem, then discuss how to solve the second.

Resistive Power Splitting

The easiest way to eliminate reflections is to add resistive matching to the lines. There are a variety of resistive circuits that can be used, with the most common being equal value resistors in series on all arms:

The benefits of this circuit are that it is very small and functions virtually the same at all frequencies (until the parasitic capacitance and inductance of the resistors comes into play). The downside is that there is intrinsic loss in the circuit. Any power splitter has a 50% (3 dB) reduction in power for a two way split, but this resistive power splitter has an additional 50% (3 dB) of loss for a total of 6 dB loss per side. The isolation is equal to the insertion loss. Isolation can be increased with other circuits at the expense of further loss. 

For applications where power loss and lack of isolation are acceptable, Marki offers a line of resistive power dividers in surface mount (to 70 GHz) and connectorized (to 110 GHz) form factors.

Reactive Impedance Transformation

A second solution to convert the split impedance to the required output impedance is to use an impedance transformer. At low RF frequencies this can be done with wirewound impedance transformers. At higher microwave frequencies a distributed solution is necessary. The most straightforward solution is a quarter wave transformer, which uses a short section (equal to 1/4 the wavelength of the required frequency when traveling in the transmission line) of transmission line with an impedance equal to the geometric mean of the input and output impedance. It could look like this:

At a the specific frequency of operation, where the wavelength matches, this will eliminate the impedance mismatch reflections. The insertion loss as a splitter and input return loss plotted against frequency will look like this:

Depending on the bandwidth of the application, the performance of this circuit may be sufficient to work as a splitter. If the bandwidth of the application exceeds the bandwidth of the return loss notch due to the quarter wavelength transformer a multi-section transformer can be applied to broaden the bandwidth of the match. 

There is s still a problem with this circuit, however, in that there is still no isolation between the two output ports. Is this a problem? It depends on the application. Lets consider two cases of reflections from the loads. In one case the reflections are completely identical, in the sense that they have the same magnitude and polarity. This is called the even mode. In the other case the magnitude of the reflections is the same, but the sign of the voltage is opposite (equivalent to a 180 degree phase shift). This is called the odd mode.

Even Mode Reflections

If the reflections from the output loads are identical, there will be no voltage drop between the two arms. In this case the waves will travel back through the output arms without creating any electric field between them, since there is no voltage drop between the arms. When they meet at the junction the currents will add constructively and the wave will continue through to the input port without interruption. In this case the insertion loss and return loss will be the same for the waves traveling backwards as they were for the waves traveling forwards.

Odd Mode

If the reflections from the loads are identical, but the polarity is opposite, then some interesting things happen. There will be an electric field between the two arms due to the voltage drop across them. At the center line there will be a 'virtual ground' where the voltage (to ground) is 0. When the two waves reach the split point this means that there will be a current wave but no voltage, leading to a complete impedance mismatch. When there is a complete impedance mismatch there is a complete reflection, which is what will happen to the two waves. They will both completely reflect back to the output ports, which is bad because it will create standing waves in the system. 

In real applications reflections are rarely all odd mode. The benefit of this model, however, is that any arbitrary reflections can be decomposed into a ratio of even mode and odd mode reflections at each frequency. Similarly when used as a combiner it is clear to see that two different inputs (different frequencies or modulations) will be half even mode and half odd mode, leading to a reflection of half the input power back into the output arms. This is where the lack of isolation comes from. It can be seen as a reflection of the odd mode component of the input waves. 

Fortunately there is a way to combat this effect. Since there is a voltage drop between the two arms, a resistor placed between them will dissipate the energy in this mode. If the resistor values are chosen correctly, the wave can be completely dissipated (at a given frequency) prior to reaching the split. This is the basis of the Wilkinson Power Divider, which is the most common type of power splitter used at microwave frequencies. 

In our next note, we'll examine how the Wilkinson Power Divider eliminates the problems with reactive splitters, and look at the tradeoffs inherent in its design.