Microwave ive Components: 3. Four-port networks
Wave guide Directional Coupler
Prof. D. Kannadassan, School of Electronics Engineering
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In general…. • Basic requirements for 4-port n/w – Matched – Reciprocal – Lossless.
• Such 4-port devices are possible, but with some limitations
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Matched and reciprocal 4-port network
• S matrix will be,
1.1
For lossless network, the matrix will lead to 10 possible equations… In this, we shall take multiplication of row-1 and row-2, and multiplication of row-3 and row-4 1.2 (a) 1.2 (b)
• •
Multiply the equation 1.2(a) by S24* and equation 1.2(b) by S13* When we subtract them, 1.3 (a)
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Similarly we will get by selecting the other possible combinations… 1.3(b) Which imply that
S14 = S23 = 0, S21 2
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S31
S41 4
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Such possible 4 port network is “Directional Coupler” 4
Directional coupler • • •
A directional coupler, of the 4 ports, 2 of them are outputs [port 2 and 3] 4th port is isolated by S14=S23=0. Further design specification can be included by introducing angles between port 2 and 3.
That:
Here α, β are real variables, where θ, φ are angles. And we can argue that, [product of row-2 and row-3] To get this relation, Thus, the addition of both angle must be equal to π always. 5
This is possible in two cases, Symmetric coupler,
θ= φ = π/2
Anti-symmetric coupler
θ=0, φ = π.
α, β are not independent,
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Basic coupler-properties
Coupling factor, Directivity, Isolation, These are called “Coupling factor indices”, they are related by
I=D+C
[dB] 7
Types • • • • •
Wave guide Bethe Hole coupler Quadrature hybrid or 90o hybrid coupler 180o hybrid coupler Coupled line coupler Lange coupler Hybrids are special couplers, coupling will be 3dB always..
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Bethe Hole Coupler • The simplest directional coupler, waveguide based, is bathe hole coupler. The two version are shown below
Parallel waveguide- DC
Skewed waveguide- DC
• The small aperture theory can explain the working of this directional coupler
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Small Aperture theory • A plane wave is traveling near and parallel to a conducting wall. A small discontinuity is giving a positive and negative polarization of magnetic moment, will result in secondary radiation y x
z
x0, y0, and z0 are specifying the position of hole from the origin α is polarizability of respective fields
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Relating the coupling and aperture radius • The field incident at the port-1 (TE10)
Ey
Hx
• Due to the aperture, the generated polarization current (electric/magnetic) at x0=s, y0=b
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• At the secondary waveguide, the coupled components To port-4
To port-3
αe and αm are electric and magnetic polarizability, respectively
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• Coupling factor
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s-0.909cm, f-8.75 GHz
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Multi-Hole Directional coupler • The single hole directional coupler is narrow band with respect to directivity. To improve, multi-hole directional couplers have been introduced.
ECE102 - Microwave Engineering Fall 2012_13
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Two hole Directional coupler: For understanding • The simplest multi-hole directional coupler is two-hole one • The two hole are identical and separated by a distance of λg/4
• Cancellation of backward component at port 4 • Addition of component in port 3
ECE102 - Microwave Engineering Fall 2012_13
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Multi-Hole DC
ECE102 - Microwave Engineering Fall 2012_13
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Numerical • For a lossless directional coupler, the measured coupling coefficient and Isolation are -10dB and -62dB. Calculate the following – Directivity – Insertion loss from port-1 to port-2 – Scattering matrix
Clues: Coupling factor, Directivity, Isolation, These are called “Coupling factor indices”, they are related by
I=D+C
[dB]
ECE102 - Microwave Engineering Fall 2012_13
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Numerical • For a directional coupler, the measured coupling coefficient and Isolation are -10dB and -62dB. Calculate the power delivered to all output ports (when all ports are matched properly) • Also calculate the reflected power at port-1 and delivered powers at other ports when ports are connected with load mismatch of Γn, where n is respective to port number. Clues:
ECE102 - Microwave Engineering Fall 2012_13
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