Branchline Couplers

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Reflection attenuators are one application of branchline couplers.

Patch coupler (similar to a branchline with the middle area filled in)

Here's a clickable index to our material on branchline couplers:

Single-box branchline couplers (this page)

Two-section ("double-box) branchline couplers (split onto new page for February 2023)

Lumped-element branchline couplers (split onto new page for February 2023)

Lumped-element two-section branchline couplers (split onto new page for February 2023, with new content from Bowtie Guy)

Unequal-split branchline couplers (split onto new page for February 2023)

Three-way branchline couplers (separate page)

Check out our unequal-split power divider calculator, it handles Wilkinsons, rat-races and branch-line couplers!

Single-box branchline couplers

The branchline the simplest type of quadrature coupler, since the circuitry is entirely planar. A ideal single-box branchline coupler is shown below. Each transmission line is a quarter wavelength. However, 3/4, 5/4 or 7/4 wavelengths (etc.) could also be used on each arm if the circuit layout requires it, the penalty is paid in decreasing bandwidth. A signal entering the top left port (port 1 in the figure) is split into two quadrature signals on the right (ports 2 and 3), with the remaining port 4 fully isolated from the input port at the center frequency. Remember that the lower output port (port 3) has the most negative transmission phase since it has the farthest path to travel. By the way, that "<" symbol in our cheesy schematics is supposed to represent "angle", as in "∠".  We can always recognize when people have ripped off this schematic for presentations by this quirk!

The next figure shows the response of an ideal branchline coupler where the each side is a quarter wavelength at 10,000 MHz (10 GHz). The first graph shows the losses from the input to the two output arms. S21 is the transmission loss from the top port to the upper right port, S31 is from the input to the lower right port. Using the ideal transmission line impedances shown above provides a equal 3 dB split at the center frequency. The markers have been aligned to show the 1-dB bandwidth of the coupler, which is 2580 MHz or 25.8%.

Here's an interesting historcal perspective... the plot shown above was made in "Eagleware" software, which originally cost $99 thirty years ago (as "SuperStar") and was great.  There was no license, the software was good so long as you could keep a DOS operating system alive and had a place to plug in the dongle.  The company that made it was originally called Circuit Busters. In 2005, Eagleware sold out to Hewlett Packard.   Soon Hewlett Packard offered free upgrades for the original software product.  The Unknown Editor fell for this bait, upgraded, and twelve months later the upgraded software expired.  At this point HP would support it, if you kicked in a yearly maintenance fee.  We never renewed it. It pays to read the fine print! At least some SuperStar plots can live on in perpetuity, on this page and other early Microwaves101 pages! One further revelation: Keysight still keeps the Eagleware product line alive, as the biblical play on words, "Genesys".

The second graph shows that the bandwidth where the device has better than 14 dB return loss (1.5:1 VSWR) is 2080 MHz, or 20.8%. The isolation (power coupled to the terminated port) is also plotted here and is very nearly equal to the return loss.

The next plot shows the phase difference between the two outputs (ideally 90 degrees, remember?) For +/-10 degrees the bandwidth is about 4300 MHz, or 43%.