Quadrature Coupler and Rat-Race Coupler Notes 1

ECE 5317-6351 Microwave Engineering Fall 2019 Notes 21 Quadrature Coupler and Rat-Race Coupler 1 Quadrature (90o) Coupler “A quadrature coupler is one in which the input is split into two signals (usually with a goal of equal magnitudes) that are 90 degrees apart in phase. Types of quadrature couplers include branchline couplers (also known as quadrature hybrid* couplers), Lange couplers and overlay couplers.” Taken from “Microwaves 101” This coupler is very useful for obtaining circular polarization: There is a 90o phase difference between ports 2 and 3. Note: The term “hybrid” denotes the fact that there is an equal (3 dB) power split to the output ports. 2 Quadrature Coupler (cont.) 2 1 90o Coupler 4 3 0 j 1 0   −1  j 0 0 1  [S ] = 2 1 0 0 j    0 1 j 0    The quadrature hybrid is a lossless 4-port (the S matrix is unitary ).  All four ports are matched.  The device is reciprocal (the S matrix is symmetric.)  Port 4 is isolated from port 1, and ports 2 and 3 are isolated from each other. 3 Quadrature Coupler (cont.) The quadrature coupler is usually used as a splitter: 2 1 90o Coupler 4 +90o out of phase φ2- φ3 = 90o -90o out of phase φ2- φ3 = -90o 3 Note: A matched load is usually placed on port 4. The signal from port 1 splits evenly between ports 2 and 3, with a 90o phase difference. S21 = jS31 Can be used to produce right-handed circular polarization. The signal from port 4 splits evenly between ports 2 and 3, with a -90o phase difference. S24 = − jS34 Can be used to produce left-handed circular polarization. 4 Quadrature Coupler (cont.) Branch-Line Coupler A microstrip realization of a quadrature hybrid (branch-line coupler) is shown here. 1 2 4 3 Notes:  We only need to study what happens when we excite port 1, since the structure is physically symmetric.  We use even/odd mode analysis (exciting ports 1 and 4) to figure out what happens when we excite port 1. An analysis of the branch-line coupler is given in the Appendix. 5 Quadrature Coupler (cont.) Summary 1 2 4 3 0 j 1 0   −1  j 0 0 1  [S ] = 2 1 0 0 j    0 1 j 0   The input power to port 1 divides evenly between ports 2 and 3, with ports 2 and 3 being 90o out of phase. Note: A matched load is usually placed on port 4. 6 Quadrature Coupler (cont.) A coupled-line coupler is one that uses coupled lines (microstrip, stripline) with no direct connection between all of the ports. Please see the Pozar book for more details. Port 1 Port 3 Port 2 λg / 4 Port 4 This coupler has a 90o phase difference between the output ports (ports 2 and 3), and can be used to obtain an equal (-3 dB) power split or another split ratio. 7 Quadrature Coupler (cont.) Circularly-polarized microstrip antennas can be fed with a 90o coupler. One feed port produces RHCP, the other feed port produced LHCP. Note: This is a better way (higher bandwidth) to get CP than with a simple 90o delay line. 8 Rat-Race Ring Coupler (180o Coupler) “Applications of rat-race couplers are numerous, and include mixers and phase shifters. The rat-race gets its name from its circular shape, shown below.” Taken from “Microwaves 101” Photograph of a microstrip ring coupler Courtesy of M. D. Abouzahra, MIT Lincoln Laboratory 9 Rat-Race Coupler (cont.) 2 1 180o Coupler 4 0 1  − j 1 0 [S ] = 2 1 0  0 −1 3 1 0 0 −1  0 1  1 0  The rat race is a lossless 4-port (the S matrix is unitary).  All four ports are matched.  The device is reciprocal (the S matrix is symmetric).  Port 4 is isolated from port 1, and ports 2 and 3 are isolated from each other. 10 Rat-Race Coupler (cont.) The rat race can be used as a splitter: Σ 2 1 In phase 180o Coupler ∆ 4 180o out of phase 3 Note: A matched load is usually placed on port 4. The signal from the “sum port” Σ (port 1) splits evenly between ports 2 and 3, in phase. This could be used as a power splitter (alternative to Wilkinson). S21 = S31  The signal from the “difference port” ∆ (port 4) splits evenly between ports 1 and 2, 180o out of phase. This could be used as a balun. S24 = − S34 11