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New for October 2005!
The comparator network (also known as an "arithmetic network")
is what processes the four quadrants of a monopulse antenna into
the SUM, Delta AZ, Delta EL, and Delta Q signals.
A monopulse antenna has four
feeds, which can be horns or other radiators. We'll use the convention
of the Cartesian coordinate system, where the quadrants are labeled
starting in the upper right, then go counterclockwise, in this case,
can be made with either 180 degree or 90 degree hybrid couplers.
We'll show you both ways!
comparators using rat-race hybrids
Below is a schematic representation
of a monopulse comparator using 180 degree rat-race couplers. We've
labeled the signals as they go through the network, so you can follow
the arithmetic. You could try to find a better explanation of this
important antenna concept somewhere else on the web, but you never
Check it out, someone stole
this figure and published
it in Microwave Journal article!
The lengths of lines labeled
"(L1)" don't matter, but they must remain the same phase.
The same goes for "(L2)" lines. With all monopulse comparators,
anything that introduces phase or amplitude errors on the four inputs
is going to kill the response. So when you are laying this out,
pay attention to every little detail, make the four inputs EXACTLY
the same, and keep as much symmetry as possible.
We used Eagleware's Genesys
program to simulate a rat-race comparator network, including response
versus azimuth angle. We found it slightly awkward to use, especially
in perfoming the comparator circuit math, which ideally is done
using vectors but Eagleware insists that you first convert everything
to real and imaginary parts first.
Our circuit model used a 50
um GaAs substrate (Er=12.9). We used 1 mm for the quarter-wavelength,
which works out to a center frequency of about 27.6 GHz. Below is
the schematic of the rat-race hybrid that we generated in Genesys:
The plots below
shows some of the S-parameter frequency responses of this four-port
rat-race network, in this case, the magnitude of the transmission
between port 1 and the other three ports. Note that port 1 is the
"sum" port, which means that a signal into this port splits
equally to in-phase signals to ports 2 and 4. Port 3 is the "difference"
port, which would also split equally into two signals at ports 2
and 4, but they would be anti-phase (180 degree difference).
Now it's time to build the comparator
network. We know that we need a better figure below. Ports 1, 2,
3 and 4 are the antenna quadrant inputs A, B, C and D. The transmission
lines TL1, TL2, and TL3 are used to add phase when the monopulse
is tipped off of boresight (we'll explan this below). Following
the arithmetic of the rat-race, signals at ports 2 and 4 are summed
at port 1, and subtracted at port 3, for hybrid network N2 (top
Here are the equations we came
up with to compute the sum and deltas responses using Genesys:
Yikes, that was painful!
Here are the transmission coefficients
of signals into the four antenna quadrants, out the sum port.
Now let's look
at the phases of the signals, and they exit the SUM, Delta AZ, Delta
EL and Delta Q ports. The SUM port has all signals nearly in phase:
The AZ port subtracts
the left signals (ports 2 and 3) from the right (ports 1 and 4):
The EL signal subtracts
the top signals (1 and 2) from the bottom (3 and 4):
We didn't plot
the Q-channel but it subtracts diagonally. Typically this output
is not used and just terminated.
Here are the sum and difference
channels versus frequency:
Here are SUM and AZ versus added
phase in the AZ plane, at center frequency:
comparator using 90 degree hybrids
Below is a schematic
representation of a monopulse using 90 degree hybrid couplers, in
this case, branchline couplers. The trick is to add a 90 degree
section to one of the inputs of the coupler, converting it to a
180 degree coupler (click here
to learn more). The layout has an advantage over the ratrace comparator
in that none of the signals are "trapped" inside the network.
The disadvantage is the bandwidth of this approach sucks!
In this comparator,
all of the blue lines are quarterwavelength. The lengths of the
four skinny black lines labeled "(L1)" don't matter much,
but they all must be the same. Again, use care when you lay this
out, errors of a few mils can mess up the response.
We didn't simulate
the branchline coupler comparator, but if we get bored one of these
days we will!