ENE 428 Microwave Engineering

ENE 428Microwave Engineering Lecture 12 Power Dividers and Directional Couplers 1

Power dividers and directional couplers • Passive components that are used for power division or combining. • The coupler may be a three-port or a four-port component • Three-port networks take the form of T-junctions • Four-port networks take the form of directional couplers and hybrids. • Hybrid junctions have equal power division and either 90 or a 180 phase shift between the outport ports. 2

Types of power dividers and directional couplers • T-junction power divider • Resistive divider • Wilkinson power divider • Bethe Hole Coupler • Quadrature (90) hybrid and magic-T (180) hybrid • Coupled line directional coupler 3

Basic properties of dividers and couplers • The simplest type is a T-junction or a three-port network with two inputs and one output. • The scattering matrix of an arbitrary three-port network has nine independent elements 4

The scattering parameters’ lossless property • The unitary matrix: • This can be written in summation form as where ij= 1 if i = j and ij= 0 if i j thus if i = j, while ifi j , 5

It is impossible to construct a three-port lossless reciprocal network. (1) • If all ports are matched, then Sii = 0, and if the network is reciprocal the scattering matrix reduces to • If the network is lossless, the scattering matrix must be unitary that leads to 6

It is impossible to construct a three-port lossless reciprocal network. (2) • Two of the three parameters (S12, S13, S23) must be zeros but this will be inconsistent with one of eq. (1a-c), implying that a three-port network cannot be lossless, reciprocal, and matched at all ports. 7

Any matched lossless three-port network must be nonreciprocal. (1) • The [S] matrix of a matched three-port network has the following form: • If the network is lossless, [S] must be unitary, which implies the following: 8

Any matched lossless three-port network must be nonreciprocal. (2) • Either of these followings can satisfy above equations, or 9

Any matched lossless three-port network must be nonreciprocal. (3) • This results show that Sij Sji for i j, therefore the device must be nonreciprocal. • These S matrices represent two possible types of circulators, forward and backward. 10

A lossless and reciprocal three-port network can be physically realized if only two of its ports are matched. (1) • If ports 1 and 2 are matched ports, then • To be lossless, the following unitary conditions must be satisfied: 11

A lossless and reciprocal three-port network can be physically realized if only two of its ports are matched. (2) • From (3a-b), , so (3d) shows that S13 = S23= 0. Then |S12|=|S33|=1. 12

A lossless and reciprocal three-port network can be physically realized if only two of its ports are matched. (3) • The scattering matrix and signal flow graph are shown below. • If a three-port network is lossy, it can be reciprocal and matched at all ports. 13

Four-port networks (Directional Couplers) • Power supplied to port 1 is coupled to port 3 (the coupled port), while the remainder of the input power is delivered to port 2 (the through port) • In an ideal directional coupler, no power is delivered to port 4 (the isolated port). 14

Basic properties of directional couplers are described by four-port networks.(1) • The [ S ] matrix of a reciprocal four-port network matched at all ports has the above form. • If the network is lossless, there will be 10 equations result from the unitary condition. 15

Conditions needed for a lossless reciprocal four-port network (1) • The multiplication of row 1 and row 2, and the multiplication of row 4 and row 3 can be arranged so that (4) • The multiplication of row 1 and row 3, and the multiplication of row 2 and row 4 can be arranged so that (5) • If S14 = S23 = 0, a directional coupler can be obtained. 16

Conditions needed for a lossless reciprocal four-port network (2) • Then the self-products of the rows of the unitary [S] matrix yield the following equations: which imply that |S13|=|S24|and that |S12|=|S24|. 17

Symmetrical and Antisymmetrical coupler (1) • The phase references of three of the four ports are chosen as S12 = S34 = , S13 = ej, and S24 = ej, where  and  are real, and  and  are phase constants to be determined. • The dot products or rows 2 and 3 gives which yields a relation between the remaining phase constant as  +  = 2n. 18

Symmetrical and Antisymmetrical coupler (2) • If 2 is ignored, we yield 1. The symmetrical coupler:  =  = /2. 2. The antisymmetrical coupler:  = 0,  = . 19

Symmetrical and Antisymmetrical coupler (3) • The two couplers differ only in the choice of the reference planes. The amplitudes  and  are not independent, eq (6a) requires that 2 + 2=1. • Another way for eq. (4) and (5) to be satisfied is if |S13|=|S24| and |S12|=|S34|. • If phase references are chosen such that S13=S24= and S12=S34=j, two possible solutions are given. First S14=S23=0, same as above. • The other solution is for  =  =0, which implies S12=S13=S24=S34=0, the case of two decoupled two-port network. 20

Directional coupler’s characterization (1) • Power supplied to port 1 is coupled to port 3 (the coupled port) with the coupling factor • The remainder of the input power is delivered to port 2 (the through port) with the coefficient • In an ideal coupler, no power is delivered to port 4 (the isolated port). • Hybrid couplers have the coupling factor of 3 dB or  =  = The quadrature hybrid coupler has a 90 phase shift between ports 2 and 3 ( =  = /2) when fed at port 1. 21

Directional coupler’s characterization(2) Coupling = C = = -20log dB, Directivity = D = = 20log dB, Isolation = I = = -20log|S14| dB. • The coupling factor indicates the fraction of the input power coupled to the output port. • The directivity is a measure of the coupler’s ability to isolate forward and backward waves, as is the isolation. These quantities can be related as I = D + C dB. 22

Ideal coupler • The ideal coupler would have infinite directivity and isolation (S14 = 0). 23

The T-junction power divider • The T-junction power divider can be implemented in any type of transmission line medium.

Lossless divider (1) • A lumped susceptance, B, accounts for the stored energy resulted from fringing fields and higher order modes associated with the discontinuity at the junction. • In order for the divider to be matched to the input line impedance Z0, and assume a TL to be lossless, we will have

Lossless divider (2) • The output line impedances Z1 and Z2 can then be selected to provide various power division ratios. • In order for the divider to be matched to the input line impedance Z0, and assume a TL to be lossless, we will have

Ex1 A lossless T-junction power divider has a source impedance of 50 . Find the output characteristic impedances so that the input power is divided in a 3:1 ratio. Compute the reflection coefficients seen looking into the output ports.

Resistive divider • A lossy three-port divider can be made to matched at all ports, although the two output ports may not be isolated.

The Wilkinson power divider • The lossless T-junction divider cannot be matched at all ports and does not have any isolation between output ports. • The resistive divider can be matched at all ports but the isolation is still not achieved. • The Wilkinson power divider can be matched at all ports and isolation can be achieved between the output ports.

ENE 428 Microwave Engineering