Updated May 16,
here to go to our main page on power splitters and couplers
here to go to our main page on Gysel power splitters
here to go to our main page on rat-race power splitters
New for April 2011! Why
would you want to cascade a rat-race? Cascaded couplers are known
to provide wider bandwidth than their one-section counterparts.
Here's an example of a cascaded
90 degree coupler that achieves equal split in microstrip.
Here's two references on this
idea (provided by Steve) that describe the cascaded rat-race (it
is not original to the Microwaves101 web site). Later we'll dive
into the math and present further information.
A New Class of Multisection
180 Hybrids Based on Cascadable Hybrid-Ring Couplers, Kian
Sen Ang et al, IEEE MTT Vol. 50, No. 9, September 2002.
A New Class of Wideband
Multisection 180 Hybrid Rings Using Vertically Installed Planar
Couplers, Chun-Hsiang Chi and Chi-Yang Chang, IEEE MTT, Vol.
54, No. 6, June 2006.
The cascaded rat-race cannot
be laid out in a single plane, it requires three-D. The basic idea
is to use an unequal-split rat-race fed at the "sum port",
which is much like a Gysel splitter. Two unequal signals pass out
of the first splitter, in phase, and enter the second one. The second
splitter is set up as an unequal splitter but in the opposite sense
(Z1 becomes Z2, and Z2 becomes Z1). We arrived at the values of
Z1 and Z2 by tuning the circuit, not with fancy-pants algebra (but
we'd be delighted to present the derivation some day).
The signals exit the splitter
in phase. Does that mean it is a Gysel cascade or a rat-race cascade?
Let us know what you
think! These two couplers are indeed quite
someone can rearrange the topology to create a cascaded circuit
with outputs 180 out of phase, that's worth fifty dollars to us
for the first person who shoots
it in! No cheating allowed by adding a 180 degree section to
one of the outputs...
Contest is now over, skip down
toward the bottom of the page:
2011 contest only took a weekend to finish! Steve sent in the solution.
Here's a guy that won't have trouble finding a job even in a recession!
Nothing like coming back
from a vacation to find a brainteaser up on Microwaves101. Gave
me an excuse to goof off a little before I had to get back to
real work! I took the design and simulated it in Ansoft Designer,
using the same Z1 and Z2 you specified, and modified it to the
circuit shown in the attached zip folder. All ports are 50 ohm,
just like in yours. I moved ports 3 and 4 to take off 180 deg
of signal path, and rearranged the impedances to keep the symmetry
and retain the matching at all ports. The performance is not perfect
(just like people!), but I haven't attempted any tuning on Z1
or Z2, and I figure with this performance being fairly close to
the circuit on the website, but with 180 deg phase difference
on the output, it may be the right solution!