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The Wilkinson power splitter
was invented around 1960 by an engineer named Ernest
Wilkinson. It splits an input signal into two equal phase output
signals, or combines two equal-phase signal into one in the opposite
direction. Wilkinson relied on quarter-wave transformers to match
the split ports to the common port. Because
a lossless reciprocal three-port network cannot have all ports simultaneously
matched, Wilkinson knew he had to cheat so he added one resistor
and the rest is history. The resistor does a lot more than allow
all three ports to be matched, it fully isolates port 2 from port
3 at the center frequency. The resistor adds no resistive loss to
the power split, so an ideal Wilkinson splitter is 100% efficient.
In its simplest form, an equal-amplitude,
two-way split, single-stage Wilkinson is shown the figure below.
The arms are quarter-wave transformers of impedance 1.414xZ0
(thanks for the correction, Rod!) Here we show a three-port circuit
(the most common in practice by far, but Wilkinson described an
two-port Wilkinson splitter
of ideal 2-way Wilkinson power splitter
Here is how the
Wilkinson splitter works as a power divider: when a signal enters
port 1, it splits into equal-amplitude, equal-phase output signals
at ports 2 and 3. Since each end of the isolation resistor between
ports 2 and 3 is at the same potential, no current flows through
it and therefore the resistor is decoupled from the input. The
two output port terminations will add in parallel at the input,
so they must be transformed to 2xZ0 each at the input
port to combine to Z0. The quarter-wave transformers
in each leg accomplish this; without the quarter-wave transformers,
the combined impedance of the two outputs at port 1 would be Z0/2.
The characteristic impedance of the quarter-wave lines must be
equal to 1.414xZ0 so that the input is matched when
ports 2 and 3 are terminated in Z0.
Okay, what about as a power combiner?
Consider a signal input at port 2. In this case, it splits equally
between port 1 and the resistor R with none appearing at port 3.
The resistor thus serves the important function of decoupling ports
2 and 3. Note that for a signal input at either port 2 or 3, half
the power is dissipated in the resistor and half is delivered to
port 1. Why is port 2 isolated from port 3 and vice-versa? Consider
that the signal splits when it enters port 2. Part of it goes clockwise
through the resistor and part goes counterclockwise through the
upper arm, then splits at the input port, then continues counterclockwise
through the lower arm toward port 3. The recombining signals at
port 3 end up equal in amplitude (half power or the CW signal is
lost in resistor R1, while half of the CCW signal is output port
1. And they are 180 degrees out of phase due to the half-wavelength
that the CCW signal travels that the CW signal doesn't. The two
signal voltages subtract to zero at port 3 and the signal disappears,
at least under ideal circumstances. In real couplers, there is a
finite phase through the resistor that will limit the isolation
of the output ports.
Below we show an example of extending
the bandwidth of a Wilkinson splitter by placing a quarter-wave
transformer on the common-node and optimizing its impedance along
with the impedances of the quarter-wave legs.
Example of Wilkinson
with input transformer
for above Wilkinson with input transformer