Power Dividers and Directional Couplers

1. Power Dividers and Directional Couplers Divider or coupler Divider or coupler Power combining Power division

2. Four-Port Network (Directional Couplers) Assume all ports are matched

4. 1 2 Input Through or direct Isolated Coupled 4 3 Directional Coupler

6. Directional Couplers 4 3 Pf Pb Pi Pt 1 2

9. -2bL -bL -bL 0 Kf a1 Kf a1 Kb a1 Kf a1 Directional Couplers Two-hole Waveguide Couplers Pf Pb Port 3 b4 Port 4 b3 L b2 Port 1 a1 0 a1 -bL Port 2 Pi Pt Kf and Kr are the forward and reverse aperture coupling coeffiecients

11. Multi-element Couplers To achieve good directivity over a band of frequencies, couplers With many apertures may be used. Coupled Isolated B1 A B0 A F1 A Bb F0 A Bf Input n=1 n=0 A Through d Cn Let the aperture coupling in the forward direction be And the reverse coupling in the reverse direction be Dn

14. Chebyshev Response In order to obtain an equal-ripple characteristics in the pass band The array factor F is made proportional to Chebyshev polynomial.

16. Branch-Line Coupler Z02 Z0 Z0 b2 Port 1 Port 2 Even-mode pair Odd-mode pair l b1 Z01 l Z01 a1/2 a1/2 a1/2 Port 3 -a1/2 Port 4 Z0 Z02 Z0 b3 b4

17. Short circuits Open circuits Even-mode excitation Odd-mode excitation

19. Parallel-Coupled Lines Directional Coupler L Direct Port 2 Input Port 1 Isolated Port 4 Coupled Port 3 a1/2 L Direct Port 2 Input Port 1 H wall a1/2 Isolated Port 4 Coupled Port 3 Even Mode excitation

20. Z0 I3 Z0 I4 3 4 Z0e Z0o I2 I1 2 Z0 1 Z0 V

22. Hybrid Junctions Magic T

23. Even Odd Vb+ 1/2 1/2 Microstrip Hybrid Ring Even Odd a 3 2 Vb+ 1/2 -1/2 l/4 or -Vb+ l/4 l/4 Va+ 1 4 Va+ or -Va+ Zc Z1 3l/4 a The hybrid ring (rat-race) Ports 1 and 3 are uncoupled, ports 2 and 4 are uncoupled

24. q1 Vb+ Va+ jB2 jB1 Y1 Yc Yc Equivalent circuit for one half of Hybrid ring

26. Port 2 Port 2 l/4 l/4 1/2 1/2 2 1 2 1 Port 1 Port 1 To Te Ge Go l/8 l/8 3l/8 3l/8 O.C S.C Even Mode Odd Mode O.C S.C

28. P2 Z2 P1 Z1 Z3 P3 Power Dividers A lossless three port juntion

29. R l/4 Z2 Zc ZL2 Z3 ZL3

33. G z3 z2 I3 -Y23 I3 I2 Yc sc V2 V2 V3 -Y33+Y23 -Y22+Y23 Y3 Y2 ,q ,q Equivalent circuit between Port 2&3 with port 3 sc and R removed Equivalent circuit with port 2 and 3 excited

35. Passive Microwave Devices Attenuators R1 R1 R2 Zc Zc R1 R1 R2 Vg T section p section

37. OC l/4 Bias Current Input l/4 input output l1 l/4 l/4 Length l2 Bias Circuit Ground Bias Circuit Ground l/4 Bias Current Input l/4 oc Incremental-line-type phase shifter Phase shifters

38. Bl=q V+1 V+2 V+3 V+4 V-1 V-2 V-3 V-4 l/4 Bias Current Input jB jB l/4 OC A phase shifter using switched reactive elements

39. Transmission matrix of a normalized shunt suceptance jB: Transmission matrix of a section of transmission line of Electrical length q:

40. Relationship among wave amplitudes: Choose V-4 = 0, then V+4 = V+1 /A11Thus T14 = 1/ A11 If tanq = 2/Bthen :

42. l/4 d1 P’ P d A phase shifter using open circuited stubs spaced l/4 Apart. P and P’ are switched into the circuit when the Diodes are off and on, respectively.