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

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

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4. 4 Input Through or direct Coupled Isolated Directional Coupler 1 43 2

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6. 6 Directional Couplers 12 3 4 PiPi PbPb PfPf PtPt

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9. 9 Two-hole Waveguide Couplers Port 1 Port 3 Port 4 Port 2 a1a1 0 b2b2 b4b4 b3b3 K f a 1 -L-L Kba1Kba1 -2  L K f a 1 -L-L 0 a1a1 -L-L L and reverse aperture coupling coeffiecients K f and K r are the forward PiPi PbPb PfPf PtPt

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11. 11 Multi-element Couplers To achieve good directivity over a band of frequencies, couplers With many apertures may be used. d A BbBb BfBf F0F0 B0B0 A A Let the aperture coupling in the forward direction be CnCn And the reverse coupling in the reverse direction be DnDn Input Isolated Through Coupled n=0 n=1 B1B1 A F1F1 A

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

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16. 16 Branch-Line Coupler Z 02 Z 01 l l Z0Z0 Z0Z0 Z0Z0 Z0Z0 Port 4 Port 3 Port 2Port 1 Even-mode pair Odd-mode pair a 1 /2 -a 1 /2 a 1 /2 b4b4 b1b1 b2b2 b3b3

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

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

20. 20 Z0Z0 Z0Z0 Z0Z0 Z0Z0 1 3 2 4 Z 0e Z 0o I1I1 I3I3 I4I4 I2I2 V

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22. 22 Hybrid Junctions Magic T

23. 23 Microstrip Hybrid Ring  1 2 3 4  The hybrid ring (rat-race) a a Ports 1 and 3 are uncoupled, ports 2 and 4 are uncoupled Z1Z1 ZcZc Va+Va+ V a + or -V a + Vb+Vb+ or -V b + Vb+Vb+ Even Odd 1/2 Even Odd 1/2-1/2

24. 24 jB 2 jB 1 11 Y1Y1 YcYc YcYc Va+Va+ Vb+Vb+ Equivalent circuit for one half of Hybrid ring

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26. 26   3  1/2 O.C 21 TeTe    3  1/2 S.C 21 ToTo  Even ModeOdd Mode Port 2 Port 1 Port 2

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28. 28 Power Dividers Z1Z1 Z3Z3 Z2Z2 P3P3 P2P2 P1P1 A lossless three port juntion

29. 29 R Z L2 Z L3 Z2Z2 Z3Z3 ZcZc 

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33. 33 -Y 23 -Y 22 +Y 23 -Y 33 +Y 23 G V2V2 V3V3 I2I2 I3I3 YcYc Y3Y3  Y2Y2 sc V2V2 I3I3 z3z3 z2z2 Equivalent circuit with port 2 and 3 excited Equivalent circuit between Port 2&3 with port 3 sc and R removed

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35. 35 Passive Microwave Devices Attenuators R1R1 R2R2 R1R1 ZcZc ZcZc VgVg R2R2 R1R1 R1R1  section T section

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37. 37 Phase shifters  OC Bias Current Input Bias Circuit Ground Bias Current Input Bias Circuit Ground Length l 2 l1l1 Incremental-line-type phase shifter oc inputoutput

38. 38  Bias Current Input jB  l=  V+1V+1 V-1V-1 V+2V+2 V-2V-2 V+3V+3 V-3V-3 V+4V+4 V-4V-4 OC A phase shifter using switched reactive elements

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

40. 40 Relationship among wave amplitudes: Choose V - 4 = 0, then V + 4 = V + 1 /A 11 Thus T 14 = 1/ A 11 If tan  then :

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42. 42  P P’ d d1d1 A phase shifter using open circuited stubs spaced  Apart. P and P’ are switched into the circuit when the Diodes are off and on, respectively.

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