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Example – Coupled Lines

Example – Coupled Lines. Subscripts 1,2,C,D line 1, line 2, common mode, differential mode 0, l position: x=0, x=l f, r forward wave, backward wave, no f or r indicates total voltage. + –. 1 V 0 V. 0ns 1ns. Coupled Lines. V 1l. V 2l.

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Example – Coupled Lines

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  1. Example – Coupled Lines Subscripts 1,2,C,D line 1, line 2, common mode, differential mode 0, l position: x=0, x=l f, r forward wave, backward wave, no f or r indicates total voltage

  2. + – 1 V 0 V 0ns 1ns Coupled Lines V1l V2l (Rx is the equivalent R in the terminated case) R1 = 50Ω 50Ω 50Ω R2 = 250Ω V10 V20 l/vD = 5ns 50Ω l/vC = 4.5ns

  3. 250 V10 V20 + – 50 50 50 0ns 1ns t = 0+ x = 0 1 V 0 V V10 1/11 V 0 V V20=25/275V Equivalent Z Model Line 2 Rs 0ns 1ns 6/11 V 0 V Remember: Vc = (V1+V2)/2 Vd = (V1-V2)/2 5/11 V 0 V

  4. t = l/v+ x = l 250 V1l V2l + - 50 50 50 50 + – + – 2·VClf 2·VClf Line 1 Rt Line 2 Rt 4ns 4.5ns 5ns 5.5ns 6ns 6/11 V 0 V VClf 5/11 V 0 V VDlf

  5. 4ns 4.5ns 5ns 5.5ns 6ns 6/11 V VCl 0 V (7/6)·(5/11) V 0 V VDl (6/11)+(35/66) = 71/66 V V1l 3/11 V V2l 3/11 V + (1/66)

  6. 250 If matched termination t = l/v+ x = l VDlf·2·7 250 + - 50 50 50 50 + – + – 2·VClf 4ns 4.5ns 5ns 5.5ns 6ns 6/11 V VClf 5/11 V VDlf 1 V V1l 3/11 V V2l 1/11 V

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