One of the unique products that we have at Marki Microwave is our broadband, high isolation 3-way and 4-way power dividers. In this blog post we will answer some common questions we receive, including:

- How to make a 5 way power divider
- How to make a 6 way power divider
- How to make a 7 way power divider
- How to make an 8 way power divider
- How to make a 10 way power divider
- How to make a 12 way power divider
- How to make a 16 way power divider
- How to make a 32 way power divider
- How to make an
*n*way power divider

Generally the application for this device is a large scale local oscillator distribution system, some kind of phased array radar test system for example. Note that in this blog post we will only consider power *splitting *and not power *combining, *as these two applications have very different requirements*.* Before we address the ways to solve this problem, we need to consider the required performance metrics we need one at a time.

**Figures of Merit**

__Insertion Loss:__ Generally this is the most important spec for an LO distribution splitter. By law (of conservation of energy), an *N *way power split will have a loss of at least log_{2}(N)·3 dB. Therefore an 8 way power split will have a minimum loss of 9 dB, plus excess circuit losses. Determining how much output power is required and how much noise addition is acceptable will determine where you need to put amplifiers to compensate for these circuit losses. In general if you put them earlier you will be able to use fewer, but may have less output power at the end.

__Isolation:__ This is the classic figure of merit for a power divider, but in this case it may not be that important. Generally two non-adjacent output ports from an N-way power divider will have good isolation just from circuit losses. For example, examining the isolation for the PD4-0140 we see that the typical isolation from port 1-2 or 3-4 is 22 dB or so, while between all other ports it is generally better than 30 dB.

The other thing that relieves the isolation spec is that in power splitting applications, especially at a single frequency as with an LO, there is little penalty for bad isolation as long as the loads are reasonably well matched. If the loads are poorly matched then the reflected waves could corrupt adjacent channels, but if they are well matched then the signals match at all points and there will be no power transmission from one channel to another. I would estimate that if you have input return losses better than 12 dB or so, then isolation will not improve the signal distribution significantly.

__Phase Balance:__ In most LO distribution applications phase balance is strictly required. This is a bummer, since as we will see later maintaining phase balance in a usable form factor imposes significant extra cost on the circuit. If no phase balance is required, the problem becomes much easier. Generally better than 5˚ across all outputs is what we try to maintain.

__Return Loss:__ Similar to isolation, return losses can be important, or they can just be a small adder to the insertion loss. We try to be better than 15 dB, since this relieves a lot of problems.

__Size, Form Factor, and Cost:__ These are the most closely related elements, along with insertion loss. If the form factor is totally negotiable, then a small, cheap, and low insertion loss power divider can be made. If the form factor has to be a block of metal with SMA connectors evenly spaced across one side (as is typically the case), then the size gets much larger and insertion loss and cost both increase.

**6 Ways to Implement an N way Power Divider**

**1: **Direct *N* Way Wye Resistive Power Splitter

Direct *N* Way Wye Resistive Power Splitter

R = Z_{0}·(N-1)/(N+1)

**2:** Branched Wye resistive power splitter

Branched Wye resistive power splitter

R2 = 2·R1 = 2·Z_{0}/3 = 33.3

**3: **Branched Delta resistive power splitter

Branched Delta resistive power splitter

R = Z_{0} = 50

The __Resistive Power Divider__ is the simplest circuit topology, the smallest, the easiest to implement, and the most broadband. Unfortunately it also has the highest losses. The resistors need to be carefully selected (generally 0201 resistors for high frequency applications) and assembled for resonance-free performance. You can either build it as a series of two way branches of either Wye or Delta power dividers, or a direct *N* way Wye splitter, as shown above.

It is obvious from examining the branched couplers that they have two major problems:

- They can only create a power split that is a power of 2 (2,4,8,16…)
- They have a nominal insertion loss equal to 6 dB per split (8 way split = 18 dB loss)

The direct Wye splitter appears to have none of these problems, but when you work out the math it actually has just as much loss as the branched power divider does. It also has a further problem, which is that all of the power dissipation occurs in fewer resistors, so each resistor has to handle more power dissipation. Therefore the total circuit power limit decreases. Finally there is the obvious layout problem (the circuit looks pretty much like the schematic).

Given all of these problems, it appears that a resistive N-way power split can be used in some limited applications where a small, very broadband power divider is required. If it is a 2^{N} split, then a branched power splitter is preferred due to the improved power handling and layout. For other values a combination of branched and N way Wye splitters can be used.

**4: **__Branched Bridge Power Combiners__

If a broadband, high isolation split is required, then our bridge combiners (parts beginning with PBR) can be used. These will offer tremendous isolation across a broad bandwidth (down to kHz), but with high loss and no phase balance. For this reason, they are generally not used for LO splitting applications where low loss and phase balance are important, but isolation is less relevant. The layout of the PBR-0006SMG makes the layout very straightforward for this application, however.

**5: **__Branched Wilkinson Power Dividers (Connectorized Module)__

If the bandwidth is acceptable, this is the best solution. When the bandwidth is not acceptable, this *still* is probably the best solution, since the bandwidth limitation of a Wilkinson is the isolation, and LO splitting applications typically require low loss and phase balance. Wilkinsons have low loss and phase balance *even out of band*. Unlike the resistive power divider, the Wilkinson is ideally lossless in a power splitting application. The phase balance is only limited by the fabrication tolerance of making the microstrip lines the same length. Also the power handling of a Wilkinson power divider used as a splitter is very high, since there should be no power dissipated in the isolation resistors. So if Wilkinson power dividers are so great for LO power distribution, why don’t we make N way Wilkinson power dividers?

Marki Microwave is unique in offering 3 way Wilkinson power dividers to start with. This comes from the difficulty in laying out a 3 way Wilkinson power divider. Although the circuit diagram for it is simple, the *layout* is very challenging. Edge coupling tends to cause havoc, which is one of the reasons that we do not offer 3 way power dividers above 26 GHz.

The way that we build 4 way power dividers is with a branched line section of two way power dividers. This is fairly straightforward, since we basically just have to copy our two way power dividers onto the circuit three times, and then wire them together with microstrip lines. We do some optimization to improve the return loss and isolation above the basic design, but that is pretty much it. So why not make this an 8 way power divider?

Lets try to design an 8 way X-band power divider as an example. A single section Wilkinson centered at 10 GHz will have better than 15 dB of isolation from 8-12 GHz, as you can see below:

Then we just cut and paste to get four ports:

And then eight ports:

The insertion loss increases with the splitting losses, but otherwise this design looks pretty much like you would expect it to, maintaining acceptable performance over the band.

The problem, however, is that this is not a physical circuit. We have provided no lateral separation for the connectors along the edge of the housing. Male connectors require 0.350” of separation to turn, and we prefer to have at least 0.440” to allow a wrench to turn them. If we have 0.440” of separation, then our 8 way power has to be at least a realistic 3” along one side. Note that the active power divider sections are quarter wave, or 0.218” at 10 GHz, so now we have a power divider that is a total of around 1” long, and 3” wide, a very odd aspect ratio indeed. If we add all of the T sections and microstrip lines necessary to do the layout, things get ugly:

As you can see, resonances start to occur, and the insertion loss increases dramatically, although the isolation can stay fairly good. The isolation isn’t that important for LO splitting applications though, so the parts that matter get really bad. In real life we would optimize this design both in our circuit solver (Microwave Office) and in 3D FEM software to improve on this performance significantly, but you can see the fundamental problem with the layout here. This is without even including the bends in the microstrip, which further degrade the performance.

Compare this to the simulated performance you would expect by connecting 7 PD-0426 power dividers to get the same effect:

A low loss microstrip line has losses on the order of .2 dB/inch at low frequencies, while coaxial cable has losses on the order of 0.02 dB/inch. In practice the microstrip loss comes from a both basic per unit length loss, and additional loss due to bends and curves. Coaxial cable losses tend to come from the connectors. In practice the loss due to connectors tends to be less than the loss due to microstrip bends, making coaxial cable the preferred interconnect.

Note that the return loss ripple in the eight way power divider above comes from standing waves on the coaxial cables between each power divider. This can be tuned somewhat with the selection of cable length. Although each section needs the same cable length for phase matching, different sections can have different cable lengths.

A coaxial cable assembly has other benefits as well. The improvement in layout is obvious, as power dividers can then be stacked or arranged in three dimensions in an arbitrary fashion. It also saves significant cost and size, as in a branched power divider most of the space is taken up by interconnections. This makes the aluminum housing large, expensive, difficult to fabricate, and difficult to test.

**6: **Branched__ Wilkinson Power Dividers (Surface Mount)__

The story for surface mount LO distribution is similar to connectorized: it comes down to size. There may be some improved performance from integrating multiple surface mount power divider sections without surface mount transitions, which typically limit the performance of our surface mount parts. However, any benefits would be offset by the difficulty and reliability issues associated with mounting and assembly of such a large board. We do, however, recommend using the PD-0530SMG down to much lower frequencies than 5 GHz to perform LO power splitting functions, since it will operate out of band with reduced isolation.

**Conclusion**

For higher order power splitting, our recommendation is for customers to buy our off the shelf power dividers (even out of band) and provide their own phase matched cables or microstrip transmission lines between the parts. This allows the minimum loss, lowest cost, best layout flexibility, and smallest size solution possible.

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