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CSE464 Coupling Calculations via Odd/Even Modes Spring, 2009 David M. Zar (Based on notes by Fred U. Rosenberger) [email protected] ‹#› - David M. Zar - 5/7/2017 Coupled Lines 1 I1 2 Here are two coupled lines I2 VD (V1 V2 )/2 I D ( I1 I 2 )/2 ( Odd, Difference ) VC (V1 V2 )/2 I C ( I1 I 2 )/2 ( Even, Common ) VC VCf VCr ‹#› - David M. Zar - 5/7/2017 VD VDf VDr Coupled Lines • Even-mode impedance, ZOE – impedance seen on each line by a common-mode signal • Odd-mode impedance, ZOO – impedance seen on each line by differential mode signal • Differential impedance, ZOD = 2ZOO – impedance seen across a pair of lines by differential mode signal • Common-mode impedance, ZOC = 0.5ZOE – impedance seen between a pair of lines and a common return by a common-mode signal. Z OE LM C Cd ‹#› - David M. Zar - 5/7/2017 1 2 Z OO LM C Cd 1 2 C = total line Capacitance (line to GND + Cd) Cd= line to line capacitance Coupled Lines Line 1 Line 2 Matched termination ( No reflection ) R1 Z OE Z Z R2 2 OO OE Z OE Z OO 2 VD Line 1 2 R1 R2 R1 Line 2 Coupled line equivalent circuit ( T-line only, no external components ) 2*VC Equivalent circuit at sending end VC VC 0 r ; VD VD 0 r Equivalent circuit at receiving end VC VClf ; ‹#› - David M. Zar - 5/7/2017 VD VDlf 2*VC Coupled Lines Matched termination (Wye) ( No reflection ) R3 Z OO Z Z OO R4 OE 2 ‹#› - David M. Zar - 5/7/2017 Line 1 Line 2 R3 R3 R4 Coupled Lines Procedure : ( Assuming V1 V2 0 t 0 ) 1. Solve for V1 & V2 at sending end ( V10 & V20 ) 2. Find VD 0 f & VC 0 f at sending end ( VD 0 r VC 0 r 0 ) 3. Find V1 & V2 at receiving end l l l at t ( V1l , V2l ) v v v 4. Find VD & VC at receiving end 5. Find VDr & VCr at receiving end VDlr VDl VDlf ; VClr VCl VClf 2l 2l , V20 from EQ circuit 6. Find V10 v v 7. Continue until exhaustion or small changes ‹#› - David M. Zar - 5/7/2017 Backward Crosstalk Next Boxes represent transmission line impedances, Resistor symbols are physical resistors. R t is an external termination resistor. V20 is the voltage coupled into Line 2 at x=0. Vc and Vd are zero in this case since the far end is matched. The voltage on line 2, and the coupling coefficient is given by the voltage divider. 2 VD Line 1 x=l VS 1 2 R1 R2 R1 Line 2 V20 Rt 2*VC 2*VC 2 x=0 1v VS 0v t=0 Tr ‹#› - David M. Zar - 5/7/2017 Rt Line 2 at x 0 : V20 VS R 1 // Rt R2 R 1 // Rt k rx R 1 // Rt R2 R 1 // Rt (Dally Eq 6 - 16) Forward Crosstalk Next For inhomogene ous media, same procedure applies but now vC vD . They do not arrive at same time so calculatio n is a little more tedious. Matched Termination x=l VClf 0.5v 1 2 x=0 1v 0.5v VDlf VS l/vC 0v l/vD t=0 Tr ‹#› - David M. Zar - 5/7/2017 Forward Crosstalk Next (cont.) V2lfx forward crosstalk V2l VCl VDl for l Tr vC l vC OR l vD l Tr vD for 1 dV 1 VElf l v 1 dVS 1 vD V2l l 1 D 1 t x S vD vC 2 dt 2 vC dt vD vC Tr ‹#› - David M. Zar - 5/7/2017 1 1 l Tr vD vC 1 1 l Tr vC vD & & vD vC vC vD 1 v (Dally, Eq 6 - 18) k fx 1 D 2 vC Configurations • vO > vE air dielectric – Microstrip • vO < vE – 300 Ohm TV or Twisted Pair or flat cable (ground alternate conductors, may have gnd plane) Conductors Flat cable dielectric • vO = vE – Ansley “Black Magic” flat cable. Note wide ground, narrow signal to reduce backward crosstalk – PC board stripline ‹#› - David M. Zar - 5/7/2017 ground signal r1 r2 Multiple Aggressors • We calculate for single aggressor, use superposition for multiple aggressor lines • Typical coupling is a little more than twice that for single agressor line Major Crosstalk Contributors Victim Small Contribution ‹#› - David M. Zar - 5/7/2017 What Else? • Simulation (SPICE) is widely used in evaluating/calculating transmission line waveforms – Can easily deal with lossy lines, non-linear termination, etc – Time consuming to setup and evaluate – Has replaced measurement for the most part (still want to get some confirmation from measurement (reality)) – You must know what questions to ask – If you don’t simulate critical cases, don’t learn much • Parameters are obtained by Field Solver programs – Maxwell, Mentor, … ($50K or so) – Describe geometry, get L, C, etc – 2D (uniform cross-section) and 3D ‹#› - David M. Zar - 5/7/2017 Crosstalk Wrapup • Non-Linear terminations: Use Bergeron method (covered later) • Backward crosstalk lasts for round-trip propagation delay and amplitude is independent of coupled length (for tr < round-trip delay) • Forward crosstalk is proportional to length, zero for homogeneous dielectric, width equal to Tr and amplitude inversely proportional to Tr. Typically small for moderate length with inhomogeneous dielectric. • Both forward and backward crosstalk will be reflected from nonmatched terminations. • Separate signals, place signals close to ground plane, use differential signals, … ‹#› - David M. Zar - 5/7/2017 Need to Mention Limits • We have not considered radiation or energy loss. • When distance between conductor and return is small with respect to rise/fall time our approximation is good. • When rise/fall time becomes comparable to signal-return spacing the system acts as antenna radiating energy. – Our model is no longer valid • Loss of signal amplitude or energy • EMI (electromagnetic interference) which is frowned on by FCC and any one with radio or tv receivers. – Not usually a problem of coupling to digital signals, energy is too small. – More complicated problem than digital crosstalk and not dealt with in CSE464. However, keep lateral dimensions and spacings small! – Electromagnetic fields and antennas ‹#› - David M. Zar - 5/7/2017