# Lumped-element two-section branchline coupler

New for February 2023.  This content was split from our main branchline coupler page and is currently being expanded.

We also added a new circuit from an old friend, the "Bowtie Guy", which is further down the page.

Lumped elements can be used to approximate transmission lines in a branchline coupler. The structure for a quarter wave transmission line can be realized with a pair of shunt capacitors of equal value, separated by a series inductor (a "pi" network). By optimizing the inductor and capacitor values, different line impedances can be "faked". Why would you want to use shunt elements? So you make branchline couplers at lower microwave frequencies (UHF through S-band) and not have to deal with huge transmission line lengths.

Below we present a lumped-element quadrature coupler which was optimized to work at 100 MHz. The lumped elements are ideal; if this was a real design that we were getting paid for we would have included all of the parasitic elements into the capacitor and inductor models, which is necessary if you want a true prediction of how the circuit will perform on the bench. Note that if you want to scale the design to a different frequency, all you have to do is scale the element values with inversely with frequency (use half the values for a 200 MHz design).

 Schematic representation of 80 to 100 MHz lumped-element quadrature coupler

Below are the power splits of port 2 and port 3. Note that we managed to get them within maybe 1.5 dB of each other at the center frequency. Maybe you could do better, Mr. Smart Guy...

Below is the phase difference between the paths 1-2 and 1-3. Note that 90 degrees is achieved with less than 1 degree of error from 80 to 100 MHz. In real life it won't be as good because you will have to allow for tolerances on the parts.

Finally, we show the port matching (S11) and the isolation (S23). Note they are similar, this is true of most quadrature coupler designs.

## Bowtie Guy's redesign

New for February 2023. Bowtie Guy is Randy Rhea, who started the company that produced software that eventually evolved into Keysight's Genesys product.  He is doing well and still enjoys microwave circuit design.  and also founded the Susina Plantation Winery in Thomasville, GA. .Before you admire his design, meet Randy in the video below, where he explains how he became vintner. Fast forward to 3:45 and you will see why he is still the Bowtie Guy!

Update February 2023... turns out Randy sold off the winery back in 2017, but is staying busy in other pursuits.  You can pick up a copy of his recent book, Astronomy is Heavenly, on Amazon.    Unfortunately, the new owners of Susina Plantation bought it for the antebellum house only, and ripped out the grape vines.

Susina Plantation winery starring Randy Rhea

Editor's note: Side story:  a well-known Massachusetts defense contractor has a site that includes a very large factory and many other smaller buildings.  For years the factory was called the "Big House" until an HR woman pointed out that "Big House" is what slaves called their master's quarters in the Antebellum South.  If you want to email us about how "woke" this is, we will forward your concerns to the head of HR at the Dukes building...

Now Randy takes over...in his own words...

It’s been about 20 years since the Unknown Editor walked into Eagleware’s booth at MTT and introduced himself to me, the Bowtie guy. Well, recently I was strolling around Microwaves101 and wandered into the Branchline Couplers page with a two-section lumped version of a Branchline. Well, who could resist a challenge like “Maybe you could do better, Mr. Smart Guy.” I may not be too smart, but I developed some pretty smart software. So I set the Keysight Genesys suite to work and went and had a nice glass of Susina Plantation Wine. Here’s the design. Better amplitude and phase flatness over a slightly wider bandwidth. Oh, that was fun!

Editor - Thanks, Randy!

Author : Unknown Editor