CROSS TALKECE 6130 Cross TalkPortfolio:What is cross talk? What causes it? How do you maximize, minimize it? Given a pair of coupled lines, what signals do you receive from the forward and reverse cross talk?Read Chapter 5 in Black Magic textbook.CROSS TALKExamine effect of capacitive coupling on a small segment of line (dz) starting at z.From capacitor equation:di(z,t) = (C) (dz) (dv(z,t) /dt)This differential cross talk current feeds the victim line. We can model the current as either direction.Differential Forward Voltage:dv_f(z,t) = ( di(z,t) /2) (Zo) = (C) (dz) (dv(z,t) /dt) (Zo) /2Differential Reverse Voltage:dv_r(z,t) = dv_f(z,t)Analysis of Inductive Coupling:Lenz’s Law:(1) When the switch is closed, a transient (changing) current ia appears on lineA. (2) This induces a changing magnetic flux density, a around line A. (3) Flux a also wraps around (couples to) line B.(4) Lenz Law states that line B will try to oppose the CHANGE in a . So, Line B produces a current ib in the opposite direction.(5) Current ib creates an opposing magnetic flux b .(6) After the transient has died away flux b will be gone.dv(z,t) = L (dz) (di(z,t) /dt)Differential Forward Current:di_f(z,t) = (L) (dz) (di(z,t)/dt) / (2 Zo)Differential Reverse Current:di_r(z,t) = - di_f(z,t)Differential Forward Voltage:dv_f(z,t) = -(Zo) di_f(z,t) = -(L) (dz) (di(z,t)/dt) / 2Differential Reverse Voltage:dv_r(z,t) = - dv_f(z,t) = (L) (dz) (di(z,t)/dt) / 2Add components from Inductive and Capacitive Coupling:dv_f(z,t) = ( C Zo – L / Zo) (dv(z,t) /dt) (dz) /2dv_r(z,t) = ( C Zo + L / Zo) (dv(z,t) /dt) (dz) /2Cross talk Coefficients::K_f = ( C Zo – L / Zo)/2 (seconds/meter)K_r = vp( C Zo + L / Zo)/4 (dimensionless)Forward Cross Talk Equation:Assume voltage starts at z=0 at time t=0. It propagates down the line to z=z at time t=t + dt, where dt = z/vpdv_f(z,t) = (K_f) (dv(t – dt) /dt) (dz)= (K_f) (dv(z, t – z/vp) /dt) (dz)This cross talk voltage will propagate down the line to an observer located at zo. It is then given by:dv_f(zo,t) = (K_f) (dv( t – z/vp – (zo – z)/ vp) /dt) (dz)= (K_f) (dv( t – zo / vp) /dt) (dz)In the limit as (dz) goes to zero:v_f(zo,t) = (K_f) int (0 to zo) (dv( t – zo / vp) /dt) (dz)Integrand is not a function of dz, so:V_f(zo,t) = (K_f) (z) (dv (t- z / vp) /dt)Reverse Cross Talk Equation:dv_r(z,t) = (2/ vp) (K_r) (dv (t- z / vp) /dt) (dz)Wave travels to the left to zo.dv_r(z,t) = (2/ vp) (K_r) (dv (t- z / vp – (z – zo)/ vp)) /dt) (dz)=(2/ vp) (K_r) (dv (t + (zo-2z)/ vp) /dt) (dz)In the limit as (dz) goes to zero:v_r(z,t) =(2/ vp) (K_r) integral (zo to L) (dv (t + (zo-2z)/ vp) /dt) (dz) = -K_r v(t + (zo – 2z)/ vp) from z to Lv_r(z,t) = (K_r) [ v(t-z/ vp) – v(t – 2T + z/ vp)