# Serial coupled combiner

Here's a power combiner that we have not discussed before. The serial-coupled combiner provides a compact layout but does not have the problems of the traveling wave combiner, which needs lower and lower impedance lines as you add more sections. You won't ever have to leave Z0 for the feed line!  And it also features full isolation of all of the amplifiers. It provides moderate bandwidth, but there are certainly other combiner structures that beat it in that regard.

Below is a figure from the 1994 paper that is referenced at the bottom of this page for a 47-way power-combined amplifier, the first publication we could find on the serial coupled combiner. It uses waveguide to feed and collect the signals from the amplifiers, with cross-guide couplers feeding individual amps.  The couplers provide good isolation, and the feed line happily in standard WR-90 rectangular waveguide throughout.

Here's a six-way example serial-coupled divider that we made up of whole cloth. Note that only N-1 couplers are needed, as the final coupler feeds two amplifiers with a 3dB (equal) split.  The first coupler removes 1/6 of the power, the second 1/5, the third, 1/4.  Do a little algebra in the other columns and you find out that each amplifier gets 1/6 of the power.  Analyzing something this simple so quickly will make you look like a genius at design reviews, but keep in mind the coupler values will have to be adjusted slightly for loss in the feed line. Like Jody in Steinbeck's masterpiece novella "The Leader of the People", don't get "too big for your britches".  Read this synopsis of the tale and learn how to use "anagnorisis" in a sentence.

 Coupler number Coupler power fraction Coupler value (linear) Coupler value (dB) Remaining signal % Coupled signal % 0 100.00% 1 1/6 0.17 -7.78 83.33% 16.67% 2 1/5 0.20 -6.99 66.67% 16.67% 3 1/4 0.25 -6.02 50.00% 16.67% 4 1/3 0.33 -4.77 33.33% 16.67% 5 1/2 0.50 -3.01 16.67% 16.67% 6 1 1.00 0.00 0.00% 16.67% Sum 100.00%

Now think about that 47-way power divider... you will discover that the differences in ideal coupling values for the first few couplers are in the noise: 1/47., 1/46, 1/45 are all between 16.72 and 16.53 dB.  This would be a manufacturing nightmare if you actually had to nail them exactly.  It turns out you can be off a little and the scheme will still work.  More on this at a later date.

Now we will look at a five-way serial coupled divider (a divider is equivalent to a combiner but it seems easier to study).  It is nice to be able to use any number of power amplifier in your SSPA, n'est ce pas?

Here, we modelled it the divider in Microwave Office and instead of waveguide we used ideal coupled line couplers.  If you can't read the coupler values, they are -7dB, -6 dB, -4.77 dB and -3 dB, which you should have committed by memory by now for 5, 4, 3 and 2-way power splits. We center most Microwave101 designs at 10 GHz, because in Microwave Engineering, 10 GHz is historically the center of the universe, before millimeter-wave was ever a thing.

Here's a view of the coupled line model we used as a sub-circuit.  The port numbers match up with the image of the coupler we used in the full schematic.

Here are the divider's amplitudes.  The red trace is the final power division and is what is left over after passing through four couplers, so it is quite different than the others. Down at 0Hz and up at 20 GHz, all of the power flows to this arm. At center frequency, all of the arms receive -7dB of the input signal at center frequency (1/5 of the power).

You don't need to look at return losses or isolations for this example.  As it uses ideal couplers and resistors, these parameters are all perfect at all frequencies, like -200dB in Microwave Office, if you actually plotted them.

Let's look at transmission phases.  You could force and transmission phase between elements by adding some line between the couplers, but if you left it with just back to back couplers the phases are all 90 degrees apart.  This will come in handy for SSPAs employing an even number of amplifiers, to achieve reflection coefficient cancellation.

Let's mockup a five-way SSPA. Here we used ideal amplifiers with 20 dB gain from DC to light, with the aforementioned five-way divider on the input and the same network on the output, rotated 180 degrees.

Let's look at the bandwidth that this design offers. Coupled-line couplers are generally described to be good for up to an octave (100% BW). Here we arbitrarily selected the 1dB points, which shows 78% bandwidth.  Bandwidth is in the eye of the beholder, your business development guy/gal can brag that it has 120% BW at 3dB points (4 to 16 GHz).

Now let's look at a slightly more real example.  We loaded in S-parameters from a Qorvo TGA2235 GaN power amp, and backed off to a four-way design. Noting that the final coupler in the divider is always 3dB, and 3dB couplers are hard to obtain using coupled lines (yeah, we know anout the Lange coupler, but what if you wanted to make this design on a circuit board?) so we replaced the final coupled line with a 3dB Wilkinson power divider for fun. If you don't think this is fun, become a program manager and read books on how to hold a "scrum" for entertainment.

Below the SSPA gain is plotted, along with the gain of the constituent amplifier TGA2238. Voila, there is no difference in the part of the band that you care about!  We also plotted the input reflection coefficients.  The TGA2238 has crappy return loss, which is improved with the divider, because two pairs of  amplifier reflections come back 180 degrees out of phase.  This will occur so long as you use and even number of amplifiers in this style combiner, but there will also be some improvement with three and five-way designs.

The original reference for this combiner showed how it was used to combine 47, 10W power amplifiers to get 400W, an excellent achievement in 1995. You can also find a more recent use of the technique in a University Colorado Boulder (UCB) doctoral thesis posted on-line, where post-grad candidate Mauricio Pinto employed Lange couplers make a five-way power-combined amplifier at W-band. Just google "Millimeter-Wave GaN Solid-State Arrays" and you will be rewarded with a copy of this work from the Colorado.edu web site. If anyone knows the student, tell him we'd ,love to have permission to cut and paste an image of his awesome five-way MMIC design here on this page!

Update January 2023: when this page went live, it only took a couple days for Mauricio Pinto to contact us about his thesis. Here's an image of one of his serial-coupled designs, used with permission, showing a five-way series-coupler MMIC power amplifier operating across W-band. He used Lange couplers on a fifty-micron GaN-on-SiC design. You can see how the coupling changes through the divider (or combiner). In the coupler nearest the input (lower left) the fingers are spread wide apart (lighty-coupled) and in the fourth and final coupler the fingers are so closely spaced you cannot distinguish them. The design provides 1.27W from 75 to 108 GHz.  Bravo, and thanks!

Here's a further interesting point about the above power amplifier design.  It uses an experimental 90 nanometer Tee-gate process at Qorvo, so-called GaN-09.  Universities often get first crack at new process nodes.  It is just a matter of time before the 90 nanometer process gets released and you will be able to order 1W GaN MMICs at W-band yourself. Meanwhile, Qorvo's GaN15 should take us all to Ka-band and beyond.

## References

M. Knox et al., "400 W X-band GaAs MMIC CW amplifier," Proceedings of 1995 IEEE MTT-S International Microwave Symposium, 1995, pp. 1605-1608 vol.3.

Mauricio E. Pinto, "Millimeter-Wave GaN Solid-State Arrays", doctoral thesis at university of Colorado Boulder, submitted 2019.

Author : Unknown Editor