Microwave Passive Components: 3. Four-port networks Wave guide Directional Coupler Prof. D. Kannadassan, School of Electronics Engineering 1 In general…. • Basic requirements for 4-port n/w – Matched – Reciprocal – Lossless. • Such 4-port devices are possible, but with some limitations 2 Matched and reciprocal 4-port network • S matrix will be, 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 1.1 1.2 (a) 1.2 (b) • Multiply the equation 1.2(a) by S 24 * and equation 1.2(b) by S 13 * • When we subtract them, 1.3 (a) 3 1 4 2 3 S 21 S 31 S 41 Similarly we will get by selecting the other possible combinations… 1.3(b) Which imply that S 14 = S 23 = 0, 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] • 4 th port is isolated by S 14 =S 23 =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, 6 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 90 o hybrid coupler • 180 o hybrid coupler • Coupled line coupler • Lange coupler Hybrids are special couplers, coupling will be 3dB always.. 8 Bethe Hole Coupler • The simplest directional coupler, waveguide based, is bathe hole coupler. The two version are shown below • The small aperture theory can explain the working of this directional coupler Parallel waveguide- DC Skewed waveguide- DC 9 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 α is polarizability of respective fields x 0 , y 0 , and z 0 are specifying the position of hole from the origin 10 x y z Relating the coupling and aperture radius • The field incident at the port-1 (TE 10 ) • Due to the aperture, the generated polarization current (electric/magnetic) E y H x 11 at x 0 =s, y 0 =b • At the secondary waveguide, the coupled components To port-4 To port-3 α e and α m are electric and magnetic polarizability, respectively 12 • Coupling factor 13 s-0.909cm, f-8.75 GHz 14 15 16 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 17 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 λ g /4 • Cancellation of backward component at port 4 • Addition of component in port 3 ECE102 - Microwave Engineering Fall 2012_13 18 Multi-Hole DC ECE102 - Microwave Engineering Fall 2012_13 19 Numerical Coupling factor, Directivity, Isolation, These are called “Coupling factor indices”, they are related by I=D+C [dB] ECE102 - Microwave Engineering Fall 2012_13 20 • 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: Numerical ECE102 - Microwave Engineering Fall 2012_13 21 • 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 Γ n , where n is respective to port number. Clues: