Doublebox
branchline coupler
New for February
2006: we've added a separate
page on the doublebox coupler, which explores this topic
further!
As with the
Wilkinson power splitter,
the bandwidth of a branchline coupler can be improved by adding
sections. The next figure shows a "doublebox" branchline
coupler with its ideal impedances. We've never seen this in
a text book, have you? Microwaves101 rules!
In a 50ohm
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.
Ideal doublebox
branchline coupler

The next three
figures show the frequency response of the ideal doublebox
branchline coupler, centered at 10,000 MHz (10 GHz). In this
case, the 1dB 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
doublebox branchline coupler

Return loss (blue)
and isolation (red) of ideal doublebox
branchline coupler

Phase response of
ideal doublebox branchline coupler

As a final illustration
of improving the bandwidth of the branchline coupler, a doublebox
structure was tuned to increase the frequency bands for 1dB
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 1dB band is now 55.6%, while the 14 dB
return loss band is 58.4%.
Doublebox
hybrid coupler tuned for more bandwidth

Power split of
tuned doublebox hybrid coupler

Return loss (blue)
and isolation (red) of tuned
doublebox branchline coupler

Lumped
element branchline coupler
New for March 2007:
here's a page on lumped
element Wilkinsons!
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 Sband) and not
have to deal with huge transmission line lengths.
Below we present a lumpedelement
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 lumpedelement
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 12 and 13. 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.
Here's a branchline coupler
in MMIC representation, with the quarter wavelength arms changed
into lumped inductive and capacitive elements. It's a doublebox
structure on fourmil GaAs. It worked great at Sband, with
less than 1 dB resistive loss in spite of all those spiral
inductors! Such a structure can make an efficient power combiner
for the IF output of a higherfrequency imagerejection mixer.
Lumpedelement
branchline coupler (MMIC representation)

Unequalsplit
branchline couplers
By varying the
impedances of the opposite arms in a branchline coupler, unequal
power splits can be obtained, as shown in the figure below.
Unequal branchline
power splitter

The equations
for the line impedances Z_{0A} and Z_{0B} are
given below, as functions of the power split PA/PB and the system
impedance Z_{0}.
The plot below
shows the characteristic impedances Z0A and Z0B, for a fifty
ohm system, as a function of the coupling ratio PA/PB expressed
in dB. Note that two very different topologies result when P_{A}
is greater than P_{B} (Z_{0A} and Z_{0B}
are higher impedance than in an equalsplit branchline) and
when P_{A} is less than P_{B} (Z_{0A}
and Z_{0B} are lower impedance than in an equalsplit
branchline).
Line
impedances of unequalsplit branchline coupler

The chart above
does not completely tell the story of the tradeoffs made when
you select which port provides the most power. Check out the
power split responses for PA/PB=0.25 and PA/PB=4.0 below. The
bandwidth for PA/PB=4.0 is far superior.
Unequalsplit
branchline frequency response, PA/PB=0.25

Unequalsplit
branchline frequency response, PA/PB=4.0

Check out our
unequalsplit
power divider calculator, it handles Wilkinsons, ratraces
and branchline couplers!