1. Passive Devices (3 port network) S-matrix of 3 port networks (1) All ports are matched and network is reciprocal (2) can be lossless? 3 Port Network can not be lossless, reciprocal, and match at all port

2. Matched, lossless, and nonreciprocal 3 port network Circulator

3. Reciprocal, matched, and lossy 3 port network Reciprocal, lossless, and only 2 ports matched Port 3 is isolated Lossy power divider

4. Passive Devices (4 port network) S-matrix of reciprocal and matched network For lossless, S-matrix must be unitary matrix

6. Hybrid Coupler(3 dB Coupler)

7. Even-Odd Mode Circuit Analysis If circuit can be decomposed into the superposition of an even-mode excitation and odd- mode excitation Adding two sets( even & odd) of excitations produces the original excitation

8. 3-Port Network: Power Divider (1)Reciprocal and Lossless -> some ports mismatched Lossless Power Divider: Input Admittance at Input Port for Input Port Matching, B=0 and Port #1 Port #2 Port #3 Ex) 1:2 divider (with B=0 & Port #1 matched: ) Reflection at Port #2 : Reflection at Port #3:

9. (2)Resistive Divider – All ports are matched - output ports are not isolated

10. Wilkinson Power Divider( equal power division) Resistive divider -all ports are matched -out-ports are isolated Microstrip Wilkinson Power Divider Equivalent Circuit

11. Wilkinson Power Divider even mode odd mode Equivalent Circuit in normalized and symmetric form

12. Wilkinson Power Divider: even mode Voltage on transmission line

13. Wilkinson Power Divider: odd mode All power from Port #2 is delivered to r/2 resister, and all dissipated No power is delivered to Port #1

14. Wilkinson Power Divider: input port Wilkinson Power Divider: S-matrix All ports are matched Reciprocal Lossy Output ports are isolated Symmetric Not Unitary

15. Wilkinson Power Divider: unequal power division Wilkinson Power Divider: N-way Divider

16. 4-Port Network: Quadrature Hybrid 3 dB Directional Coupler with Quadrature Phase Difference between two output ports Reciprocal, Lossless, and all ports are matched.

17. Even-mode

18. Odd-mode

20. Coupled Line Theory Propagating Modes on Symmetric Coupled Line Even ModeOdd Mode ground

21. Even Mode Line Characteristics for even mode propagation Capacitance per unit length w/o dielectrics: Inductance per unit length: Capacitance per unit length with dielectrics: Characteristic Impedance: Propagation Constant:

22. Odd Mode Line Characteristics for even mode propagation Capacitance per unit length w/o dielectrics: Inductance per unit length: Capacitance per unit length with dielectrics: Characteristic Impedance: Propagation Constant:

24. (1)Voltage and Current Waves of Even Mode Excitation

25. (1)Voltage and Current Waves of Odd Mode Excitation

26. Voltage and Current Waves on Coupled Lines (1)Voltage and Current Waves on Line #1(2)Voltage and Current Waves on Line #2

28. Impedance Matrix Z 11 = Z 22 =Z 33 = Z 44

29. Impedance Matrix Z 12 =Z 21 =Z 34 =Z 43

30. Impedance Matrix Z 13 = Z 31 = Z 24 = Z 42

31. Impedance Matrix Z 14 = Z 41 = Z 32 = Z 23

33. 4-Port Network: Coupled Line Coupler

34. Single Section Coupled Line Coupler Boundary Condition at each Port