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Directional couplers are four-port
circuits where one port is isolated from the input port. Directional
couplers are passive reciprocal networks, which you can read more
about on our page on basic network
theory. All four ports are (ideally) matched, and the circuit
is (ideally) lossless. Directional couplers can be realized in microstrip,
stripline, coax and waveguide. They are used for sampling a signal,
sometimes both the incident and reflected waves (this application
is called a reflectometer, which is
an important part of a network analyzer). Directional couplers generally
use distributed properties of microwave circuits, the coupling feature
is generally a quarter (or multiple) quarter-wavelengths.
Lumped element couplers can be constructed as well.
What do we mean by "directional"?
A directional coupler has four ports, where one is regarded as the
input, one is regarded as the "through" port (where most
of the incident signal exits), one is regarded as the "coupled"
port (where a fixed fraction of the input signal appears, usually
expressed in dB), and one is regarded as the "isolated"
port, which is usually terminated. If the signal is reversed so
that it enter the "though" port, most of it exits the
"input" port, but the coupled port is now the port that
was previously regarded as the "isolated port". The coupled
port is a function of which port is the incident port.
Forward-wave versus backward-wave couplers
New for January 2013: we will further describe the simple difference between forward and backward wave coupling. In the forward-wave coupler, energy that propagates down transmission line starts a parallel wave down transmission line 2 as shown below. The most common forward coupler is the multi-hole coupler realized in waveguide. In this case the holes are spaced a quarter wave apart so that the reverse wave cancels out. Flat coupling across a wide bandwidth is possible, using a lot of math to specify the sizes and positions of each coupling hole.
In the backward, or reverse coupler, energy that propagates down transmission line starts a reverse wave down transmission line 2, as shown below. Single-section coupled transmission lines are always backward-wave couplers (and outputs are in quadrature), the Lange coupler is one example. Asymmetric multi-section coupled structures provide forward-wave, in-phase response, while symmetric multi-section couplers provide backward-wave, quadrature response. Try to remember that for the upcoming quiz...
Don't get hung up on the port nomenclature, there is no "standard" way to number the ports. We have used a clockwise notation and we will attempt to remain consistent, at least on this page. Also, there is no perfect coupler, in a forward coupler there will be reverse coupling to some degree, and vice-versa.
Most waveguide couplers couple in
the forward direction as they rely on multiple coupling holes; a signal incident
on port 1 will couple to port 3 (port 4 is isolated in our clockwise notation). Microstrip
or stripline couplers are backward wave couplers because they rely on coupled lines: for a signal incident on port 1,
port 4 is the coupled port (port 3 is isolated in our clockwise notation).
The coupled port on a microstrip or stripline directional coupler
is closest to the input port because it is a backward wave coupler.
On a waveguide broadwall directional coupler, the coupled port is
closest to the output port because it is a forward wave coupler.
Here's a "bonus" rule of thumb:
Forward couplers are in-phase couplers. Backward couplers couple in quadrature (the coupled port phase is 90 degrees more negative than the direct port). We attempt to explain why the phases are in quadrature on our coupled-line coupler page.
The Narda coupler below is made
in stripline (you have to cut it apart to know that, but just trust
us), which means it is a backward wave coupler. The input port is
on the right, and the port facing up is the coupled port(the opposite
port is terminated with that weird cone-shaped thingy which voids
the warrantee if you remove it. Luckily Narda usually prints an
arrow on the coupler to show how to use it, but the arrow is on
the side that is hidden in the photo.
On the waveguide coupler below,
the input is on the left, while the coupled port is on the right,
pointing toward your left ear. There is a termination built into
the guide opposite the coupled port, although you can't see it.
Generic directional coupler schematic symbol
Looking at the generic directional
coupler symbol below, if port 1 is the incident port, port 2
is the through port (because it is connected with a straight line).
Port 3 is the coupled port, and port 4 is the isolated port. For
a signal incident on port 2, port 1 is the through port, port 4
is the coupled port and port 3 is the isolated port. Just follow
the lines! The symbol below is for a forward coupler. Note: this paragraph was corrected in November 2011
thanks to Jim!
If you ever have
any schematic questions, there is an IEEE standard that you can
probably find with a google search:
Graphic Symbols for Electrical
and Electronics Diagrams, IEEE Standard 315-1975.
Directional coupler definitions
Let's first look at some definitions
using S-parameters. Let port 1 be
the input port, port 2 be the "through" port, and let's assume we are talking about a forward wave coupler (port 3 is the coupled port and port 4 is the isolated
port in clockwise notation, thanks to Tuomo for pointing out an inconsistency, January 2013!) Ideally, power into port 1 will only appear at ports 2 and
3, with no power at port 4, but in real couplers some power leaks
to port 4. For an incident signal at port 1 of power P1 (and output
powers P2, P3 and P4 at ports 2, 3 and 4), then:
Insertion Loss (IL) = 10*log(P1/P2)=-20*log(S21)
Isolation (I) = 10*log(P1/P4)=-20*log(S41)
Coupling (C) = 10*log(P1/P3)
Directivity (D) = 10*log(P3/P4)=20*log(S31/S41)
Note: these equations were corrected on October 5, 2012, thanks to Sushia. It seems when we corrected the figure back in 2012 we didn't check that the ports had changed. The equations are now in agreement with Pozar's Microwave Engineering, 2005 edition, page 313. Pick up a copy from our book page!
Note that these numbers are supposed to be positive
in dB. Quite often, microwave engineers present these quantities
as negative numbers, it is not a great faux pas, just look at the
Note that directivity requires
two, two-port S-parameter measurements, the other quantities require
only one. Directivity is the ratio of isolation to coupling factor.
In decibels, isolation is equal to coupling factor plus directivity.
Please send us any comments on
the preceding statements, we are operating under a state of partial
dyslexia and there is a possibility that we slipped up on a minus
This topic has its own page.
Bethe-hole is a waveguide directional
coupler, using a single hole, and it works over a narrow band. The Bethe-hole is a reverse coupler, as opposed to most waveguide couplers that use multi-hole and are forward couplers.
The origin of the name comes from a paper published by H A Bethe, titled "Theory of Diffraction by Small Holes", published in the Physical Review, back in 1942. If you google it you might find it, even though it is probably subject to copyright protection. This is a tough read, unless you like to ponder equations....
In waveguide, a two-hole coupler,
two waveguides share a broad wall. The holes are 1/4 wave apart. In
the forward case the coupled signals add, in the reverse they subtract
(180 apart) and disappear. Coupling factor is controlled by hole
size. The "holes" are often x-shaped, or perhaps other proprietary shapes. It is possible to provide very flat coupling over an entire waveguide band if you know what you are doing (think "Chebychev"...)
Any directional coupler is bi-directional, that is, it performs equally well when the signal is incident on port 2 versus port 1, but the coupled and isolated ports flip. All direction couplers are bi-directional, unless you terminate one of the ports. Consider the coupled-line coupler below. Port 4 is the coupled port when a signal is incident on port 1, and port 3 is the coupled port when a signal is incident on port 2.
Here we have two couplers in series, in opposing directions,
with the isolated ports internally terminated. This component is
the basis for the reflectometer. Using internal, well-matched loads helps remove errors associated with poor terminations that might be present in real systems. We'll analyze that statement one of these days. Oops, we have violated our clockwise notation rule below!
A hybrid coupler is a special
case, where a 3 dB split is desired between the through path and
the coupled path. There are two types of hybrid couplers, 90 degree
couplers (such as Langes or branchlines) and 180 degree hybrids
(such as rat-races and magic tees). We have a separate page on this
topic, click here!
This is the component that allows
you to measure S-parameter magnitudes using a network
You can build a reflectometer using a single directional coupler to form a reflectometer and two power sensors,
but it is not recommended (use the dual-directional coupler you
cheapskate!) A reflectometer allows you to compute the magnitude (and perhaps phase) of an unknown reflection coefficient that is presented to one of the ports. For example, suppose the sample was placed at port 2 and it was excited by a signal at port 1. The magnitude of the reflection coefficient (S11 in S-parameters) would be the ratio of power at port 3 to power at port 4, given that the coupler is a reverse coupler.
Finite directivity can cause errors in reflectometry measurements, particularly is a load is not well matched. 40 dB directivity will have a very small
error, 20 dB may be unacceptable accuracy.
This topic deserves its very own Microwaves101 page, we'll post that next time we dive into reflectometry math....