rick campbell portland state university october...
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Directional Coupler Project
Rick Campbell
Portland State University
October 2012
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Project Example -- Directional Coupler Design
Signal Flow Graphs, Even-mode Odd-mode transmission line theory, S-matrix, Linear Algebra....
Go straight from Maxwell’s equations to basic RLC circuit theory, and from there quickly to a complete, buildable design.
Pre-CAD era:
Post-CAD era:
Then use 3D EM simulator to implement our basic understanding in guided wave hardware.
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While proceeding from the coupled Transmission Line model to the equivalent lumped element circuit model, bear in mind:
Inductance is a volume in space with Magnetic fields. We calculate inductance by integrating over the volume--not the wire.
Capacitance is a volume in space with Electric Fields. We calculate capacitance by integrating over the volume--not the metal plates.
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Project Example -- Directional Coupler Design
In the coupled region, the E fields and H fields of the transmission lines interact.
Textbook Microstrip Directional Coupler
Port 1 Port 2
Port 3 Port 4
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Port 1 Port 2
Port 3 Port 4
To analyze, terminate all ports in characteristic impedance R
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H field coupling is modeled with a coupled inductor
Now replace the microstrip version with a circuit model:
E field coupling is modeled with a capacitor
Port 1
Port 2
Port 3 Port 4
coupler model
note thesimplifications in the model
explore later using LTSpice simulation
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Now that we have an elementary circuit model, we can use superposition to treat the E and H behavior separately. Start with H:
1 2
3 4
1
2
3
4
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Bearing in mind that what we want is the voltage drop across the coupled branch inductor, start redrawing, using circuit basics and what we know about transformers:
1
2
3
4
R
R
R R
2R
2R2
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2R 2R L
ideal
Now replace the coupled inductor model with a simplified model:
Exercise: What would a more complete 1:1 transformer model include?
Note how much more information this simple transformer model provides than the usual rule of thumb xL > 10R.
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In this circuit model, voltages and currents are identical on each side of the ideal 1:1 transformer, so it may be omitted
Note: 1:1 transformers are common in cost-drivenapplications from near DC to THz. Why?
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Finally, invoke Thevenin equivalent circuit to obtain simple circuit model for the voltage drop across the inductor:
2R
2R2
R
1 L VL
+
-
Exercise: write the expression for VL in terms of R and jwL
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Now, on to Electric field coupling, bearing in mind that what we want is the voltage on the coupled branch due to the E field:
1 2
3 4
R
R
R R
C2
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R
2 R R R
C R/2
R/2
C
1
Again, invoke Thevenin equivalent circuit:
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R
C1
We obtain an equally simple circuit to find the voltage drop across the capacitor:
VC
+
-
Exercise: Using ohms law, write expressions for the voltage drop and current through each of the elements.
Exercise: write the expression for VC
R/2
R/2
C
1
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Now use the voltage drops and currents to analyze the lower branch of the directional coupler circuit.
This is a good review of basic sophomore level circuits.
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Observe the E (capacitor) and H (inductor) currents that flow in the coupled branch:
+ ++ -
Solid line is E coupling and dashed line is H coupling. Note the polarity of the resulting voltages across the resistors R
R R
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Now find the relationship between L, C and R such that the voltages cancel at port 4.
+ ++ -
The surprising result is that cancellation at port 4 isindependent of frequency over a very wide range.
R Rport 4
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Now obtain the sum voltage at port 3 under the R, L, and Cconstraint obtained in the last slide.
+ ++ -
Hint: the voltage at port 3 rises at 6 dB per octave when a small amount of signal is coupled.
R Rport 4port 3
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If the coupled port output increases at 6dB/octave, how does a Bird Wattmeter have a flat response from 3 - 30 MHz?
What’s in the black box?
The Bird Wattmeter is the industry standard portable tool for measuring forward and reflected power on transmission lines connected to HF-VHF-UHF transmitters.
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Bird Wattmeter measuring forward power into load Z
Z
50 uA meter
RC
detector diode
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Z
Bird Wattmeter measuring reflected power from load Z
Pretty cool! Now you can make your own customBird Wattmeter elements
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ZL
C
R
L = R C2Null when:
Generic Directional Coupler with Detector
Explore using an LTSpice simulation with R = 50 ohms. Start with XL = XC = R and then vary L and C.
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Design, build, and measure a forward and reflected power meter to optimize an antenna connected to the 50 MHz 10 mW classroom source.