# Two-section branchline coupler

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

Here is original content from the early 2000s. The plots were made using an old version of Eagleware, they are kind of like fossils and should be preserved for future microwave engineers...

The term "double-box" applied to a brainchine coupler is a colloquialism. The academic term is "two-section".

As with the Wilkinson power splitter, the bandwidth of a branchline coupler can be improved by adding sections. The next figure shows a "double-box" branchline coupler with its ideal impedances. We've never seen this in a text book, have you? Microwaves101 rules!

In a 50-ohm system, the line impedances of the end vertical segments work out to be 120.71 ohms, and the center vertical segment 70.71 ohms. In practice, it may be hard to accurately achieve the 120.71 ohm impedance lines accurately.

**Update September 2017:** the lower right port should show +90 degrees, not -90 degrees. Thanks to Chih-Jung! If you think about it, the path goes through three -90 degree legs, or -270 degrees, which is +90 in microwave-land. One of these days we will fix it.

Ideal double-box branchline coupler |

The next three figures show the frequency response of the ideal double-box branchline coupler, centered at 10,000 MHz (10 GHz). In this case, the 1-dB response of the coupled arm is 35%, the 14 dB return loss band (1.5:1 VSWR) is 41%, and the +/-10 degrees phase difference is 50%. However, the tradeoff for the extra bandwidth in real life will be added loss of the second box section, not to mention the added size.

Power split of ideal double-box branchline coupler |

Return loss (blue) and isolation (red) of ideal double-box |

Phase response of ideal double-box branchline coupler |

As a final illustration of improving the bandwidth of the branchline coupler, a double-box structure was tuned to increase the frequency bands for 1-dB coupling and 14 dB return loss. Note that the equal 3 dB power split at the center frequency must be somewhat corrupted as a tradeoff. The arm impedances of this coupler are now 38 ohms for the series arms and 100 ohms and 65 ohms as shown for the three shunt arms, as shown below. The figures speak to the results. The 1-dB band is now 55.6%, while the 14 dB return loss band is 58.4%.

Double-box hybrid coupler tuned for more bandwidth |

Power split of tuned double-box hybrid coupler |

Return loss (blue) and isolation (red) of tuned |

## Additional material dating back to 2006

We took a closer look at the double-box branchline coupler, a.k.a. the three-section hybrid according to Pozar's *Microwave Engineering* book (order it here!) There is precious little in the literature about this, but you can trace it back to the 1950s when it was described in a MTT paper.

We had seen more than one solution to the impedances, the picture in Pozar's book clearly show fifty-ohms as the predominant impedance Z_{1}. But we had also seen 35.35 ohms. What gives?

We tried varying the three impedances to get different values, using Agilent's ADS. We looked for solutions that gave equal split (-3 dB), infinite return loss and isolation of the fourth port. It turns out there is more than one way to skin this cat! We found that the "end" impedances Z_{2} of the box must remain at [1+sqrt(2)] x Z_{0} (120.8 ohms in a fifty-ohm system), but Z_{1} and Z_{3} can be varied according to:

Z_{3}=sqrt(2)x(Z_{1}^2)/Z_{0}

Thanks for the correction, Steve!

Here we will plot the four solutions we came up with to compare their frequency responses. This one has Z_{1}=25 ohms.

This one has Z_{1}=35.35 ohms:

This one has Z_{1}=50 ohms:

This one has Z_{1}=70.7 ohms:

Now that's something you won't learn anywhere else but Microwaves101.com!

**Author : **Unknown Editor