Chapter 7: Directional Coupler

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Chapter 7 Directional Coupler

1. Coupled Line
2. Even and Odd Mode
3. Coupled Line Even Mode
4. Coupled Line Odd Mode
5. Even and Odd Mode Analysis
6. Coupled Line Directional Couplers
7. Even and Odd Mode DC Voltage Analysis
8. Directional Coupler Example

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Coupled Line - Even and Odd Mode
A very common type of power divider used in
Microwave circuits is the coupled line. In the
structure the coupling between the ports is due
to the interaction of the electromagnetic fields
along transmission lines which have been placed
in close proximity.
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Coupled Line - Even and Odd Mode
Coupled lines
E wall - Odd mode
H wall- Even mode
Magnetic wall
Electric wall
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Even and Odd Mode Analysis
One method of analyzing multi-port transmission
line circuits such as coupled line is through
even and odd mode analysis. In this case, the
circuit input voltage is split into two, an even
or symmetric mode and an odd or anti-symmetric
mode. The total response of the circuit can then
be described as the superposition of the two
separate responses (Even and Odd).
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Coupled Line - Even and Odd Mode
C11 and C22 represent the capacitor to ground for
one strip (without the presence of the other).
C12 is the capacitance between the two lines
without any ground plane. If the strips are
identical, then C11 C22.
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Coupled Line Even Mode
In the even mode, a virtual open circuit occurs
along the axis of symmetry, which removes the C12
from the circuit. The resulting capacitance to
the ground is the even mode capacitance Ce C11
C22. If the two strips are identical, the even
mode impedance Zoe can be calculated as
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Coupled Line Odd Mode
In the odd mode, a virtual ground forms along the
axis of symmetry, which may be considered as a
ground plane through the middle of C12, resulting
in the capacitance as it shown above. The
resulting capacitance for each conductor to the
ground in the odd mode is Co Co C11 2C12. The
Zoo can be calculated as
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Coupled Lines Even and Odd Modes
Zoe is the characteristic impedance of one of the
transmission lines under even mode operation and
Zoo is the characteristic impedance of one of the
lines under the odd mode excitation. The design
relations for the dimensions of the transmission
line for given values of Zoe and Zoo have been
tabulated by Pozar, with a complete solution for
the microstrip lines. But only for ?r
10. These results are required for the design of
coupled line directional couplers.
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Coupled Lines Even and Odd Modes
Even and Odd mode characteristic impedance design
data for coupled microstrip lines on a substrate
with ?r 10.
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Coupled Line Directional Couplers
By using the even and odd mode analysis we can
show that two coupled lines can be used as a
power divider with predictable coupling ratio and
isolation.
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Coupled Line Directional Couplers
For the analysis we will use the schematic as
shown in the above figure, with the excitation at
port 1 and all other ports terminated in the
characteristic impedance.
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Coupled Line Directional Couplers- Even and Odd
Modes
Even Mode


Odd Mode
Using the superposition the excitation at port 1
can be treated as the sum of the even and odd
mode excitations.
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Coupled Line Directional Couplers- Even Mode
For the Even Mode from the symmetry we can see
that
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Coupled Line Directional Couplers- Odd Mode
For the Odd Mode from the symmetry we can see
that
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Even and Odd Mode Characteristic Impedances
The input impedance at port 1 can be written as
We can calculate the even and odd input
impedances for the line terminated in Zo using
We can define Zine and Zino as
Even mode input impedance.
Odd mode input impedance.
Note The line looks line a transmission line of
characteristic impedance Zoe and Zoo terminated
in a load impedance Zo.
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Even and Odd Modes - DC Voltage Analysis
Now we can calculate the input voltage and
current as a function of the even and odd modes
input impedances
Even mode
Odd mode
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Even and Odd Modes - DC Voltage Analysis
Substitution of these values in this equation
yields
Now if we set Then the input impedance at port
1 is matched. By symmetry all of the other ports
are matched as well. What about the other ports
voltages and currents? Can we find V3, V4 or V2?
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Even and Odd Modes - DC Voltage Analysis
From the even and odd mode voltage and current
relations we can write
V3 can also be written as a function of the input
voltage and even and odd mode impedances
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Even and Odd Modes - DC Voltage Analysis
Therefore, we could derive the voltage at port 3
as a function of input voltage and even and odd
mode characteristic impedances. Now if we define
the Coupling Factor C as Then we have By
similar reasoning
and
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Directional Coupler Performance
If ? l ? /4, then
The final step is to relate the coupling factor
to the even and odd mode impedances to determine
the dimensions of the coupler.
and
This allows us to use the even and odd mode
characteristic impedance plots to determine the
width and separation of the lines for a given
coupling coefficient.
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Directional Coupler Example
Design a 5 dB microstrip directional coupler for
an ??r of 10 (Zo200?).
The required coupling is 5 dB, So
From the figure 1, we have
SSeparation WWidth of Microstrip
lines dDielectric thickness