ECE 6130 Quadrature Coupler Text Section 7.5 What is a quadrature coupler and how does it work? Quadrature Coupler 90 degree phase shift between output ports. Power Evenly divided (-3dB) between output ports. All ports matched. No coupling to port 4 (complete isolation). Branch Line Coupler: Even-Odd Mode Analysis: Normalized Impedance Circuit Model: []Sjjjj=−⎡⎣⎢⎢⎢⎢⎤⎦⎥⎥⎥⎥1201000110001 0EVEN MODE: ODD MODE: [][][]ABCDStub TL StubYjZojZo YjjjcjjjSABCDABCDjjjee⎡⎣⎢⎤⎦⎥==⎡⎣⎢⎤⎦⎥⎡⎣⎢⎤⎦⎥⎡⎣⎢⎤⎦⎥=⎡⎣⎢⎤⎦⎥⎡⎣⎢⎤⎦⎥⎡⎣⎢⎤⎦⎥=−−⎡⎣⎢⎤⎦⎥==+−−+++=−+−+−+λλλββββ///cos sinsin cos/()/(84810110110102201011211112111lllΓ+−===+++=−+ + −=−+jSTABCDjjje1202211212121)/()/()COMBINE EVEN and ODD MODES: Incident voltage at node 1: V1e = V1o = 1/2 Incident voltage at node 4: V4e = - V4o = -1/2 Amplitudes of waves exiting each node: B1 = V1e Γe + V1o Γo = Γe /2 + Γo /2 = 0 (Port 1 is matched) B2 = V1e Te + V1o To = Te /2 + To /2 = - j / sqrt(2) (Half power, -90 degree phase shift from port 1 to 2) B3 = V4e Te + V4o To = Te /2 - To /2 = -1/sqrt(2) (Half power, 180 degree phase shift from port 1 to 3) B4 = V4e Γe + V4o Γo = Γe /2 - Γo /2 = 0 (Port 4 is isolated) This is the first row of the S matrix: [][][]ABCDStub TL StubYjZojZo YjjjcjjjSABCDABCDjjjjee⎡⎣⎢⎤⎦⎥==⎡⎣⎢⎤⎦⎥⎡⎣⎢⎤⎦⎥⎡⎣⎢⎤⎦⎥=−⎡⎣⎢⎤⎦⎥⎡⎣⎢⎤⎦⎥−⎡⎣⎢⎤⎦⎥=⎡⎣⎢⎤⎦⎥==+−−+++=+−−++λλλββββ///cos sinsin cos/()/(84810110110102201011211112111lllΓ+===+++=+++=−1202211212121)/()/()STABCDjjje[]Sjjjj=−⎡⎣⎢⎢⎢⎢⎤⎦⎥⎥⎥⎥1201000110001 0Other rows are found by transposition: Row 2 for example: 1 Æ 2 =0 2 Æ 1 =j 3 Æ 4 =1 4Æ 3
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