Coupled-line couplers

Updated September 16, 2008

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It's about time we dealt with couplers that are truly coupled lines, as opposed to "direct coupled" couplers such as the Wilkinson and the branchline.

The Lange coupler is one form of coupled line coupler.

Coupled lines occur when two transmission lines are close enough in proximity so that energy from one line passes to the other. Coupled lines are used in couplers (usually quadrature couplers) as well as transmission line filters.

Line can be coupled in three ways:

• edge coupled
• end coupled
• broadside coupled

In order to make a quadrature coupled-line coupler you need to couple a quarter-wave section; end-coupled structures are not useful in this case. That leaves two broad categories of coupled line couplers, edge coupled, and broadside coupled (and perhaps some gray territory in between!) Both can be realized in microstrip or stripline, but stripline is best.

Theory of coupled line couplers

For two coupled lines forming a four-port network, there are two things that have to occur with coupled lines to become a useable coupler with directivity and quadrature phase:

1. The coupled section must be a quarterwave
2. The product of even and odd mode impedance must be equal to Z0^2

It's time to define some port numbers. Let port 1 be the input port. The port that is directly coupled to port 2, which is one of the two output ports. The other output port is directly across from the input port, we'll call it port 3. Under ideal conditions, a signal incident on port 1 will transfer zero power to port 4; this is called the isolated port.

Advantages of coupled line couplers

Bandwidth is better than direct coupled couplers like the branchline.

Why does the coupled-line have a natural 90 degree phase split?

This is a great question, and if you've a better answer then the one provided, please send it in!

The coupling occurs via two mechanisms, voltage, and mutual inductance (current). The mutual inductance coupling has a minus sign associated with it, the voltage coupling does not. The combined effect not only reverses the signal flow in the coupled line (backward coupling) but it puts the two signals 90 degrees out of phase.

Ideal coupler ADS model

In ADS you can use an ideal coupled line, which is described by its even and odd mode impedances and center frequency. The product of the two impedances being Z0^2, you can easily create an equation to solve one from the other.

Now you can use ADS's tune feature to vary Ze until a 3 dB split is achieved. It turns out that to get a 3 dB split (equal power) in fifty ohm system impedance the even mode needs to be ~121.5 ohms and the odd mode impedance must be ~20.6 ohms (in our ADS network Zo is calculated automatically from Ze and Z0).

For the ideal coupler, you don't have to plot the phase between the two output arms (port 2 and port 3 in this case). It's automatically 90 degrees!

Analyzing coupled line couplers using Excel

As you know by now, one motto of Microwaves101 is that "anything that can be analyzed in Excel, should be analyzed in Excel". Coupled line couplers are no exception.

Here's the same coupler we analyzed in ADS, now in Excel. You can get a free copy of the spreadsheet that did this remarkable piece of work in our download area!

Here's a slightly undercoupled coupler.

Here's the coupler, slightly overcoupled.