ECE414/514 Electronics Packaging Spring 2012 Lecture 6 Electrical D: Transmission lines (Crosstalk) James E. Morris Dept of Electrical & Computer Engineering Portland State University 1 Lecture topics Inductive and capacitive coupling Forward and backward noise Far end and near end noise Incremental model and formulae Capacitive crosstalk systems No ground plane 2 1
Objectives Understand the origins of crosstalk Inductive Capacitive Calculate basic crosstalk noise levels Calculate signal crosstalk and delta-i noise in no ground systems 3 Incremental line model 4 2
Crosstalk polarities 5 Forward and backward noise 6 3
Near end and far end 7 Theory: line segment 8 4
Capacitive noise 9 Inductive noise 10 5
Incremental model 11 Far end formula 12 6
Zero far end noise 13 Far end overview 14 7
Backward wave model 15 Backward wave construct 16 8
Near end formula 17 Near end noise waveform 18 9
Near end pulse shape 19 Near end saturation 20 10
Near end saturation 21 Pulse crosstalk noise examples Driver pulse 0.5 volt amplitude 20 ns pulse width 1ns rise and fall times 22 11
Forward noise: matched 23 Backward: matched 24 12
Forward: not matched 25 Near end: not matched 26 13
Crosstalk waveforms 27 Current distribution in ground 28 14
Ground coupled crosstalk 29 Dielectric constant effect 30 15
Mutual capacitances 31 Even/odd modes 32 16
33 Development of a SPICE model: Package leads 34 17
User selectable configurations: Corner Center Balanced Uniform Power, ground, and signal line architectures 35 Analysis options 1. Delta-I noise model 2. Signal crosstalk model V P Specify: I noise i.e. set I P (I S =0) Signal & assume all power lines same current I P /n G OR signal crosstalk i.e. set I S (I P =0) & assume all signal lines same current (i.e. n S I S total) 36 18
Matrix calculations Induced voltages v i due to changing currents I i : V i = L i1 di 1 /dt + L i2 di 2 /dt +.. L ii di i /dt + L in di n /dt = ΣLij d(ij)/dt for line i = 1, 2,..., N where N = Number of leads/side V i = voltage at line i for i = 1, 2,..., N I i = current at line i for i = 1, 2,..., N L ij = mutual inductance between line i and line j for i, j = 1, 2,..., N and i j L ii = self-inductance of line i for i = 1, 2,..., N 37 v 1 L 11 L 12 L 1N I 1 v 2 L 21 L 22 L 2N I 2 v 3 = v N L n1 L NN I N L symmetrical, L ij = L ji = M ij L ii L i 38 19
[(N+1) by 1 matrix] = [(N+1) by N matrix] * [N by 1 matrix] v 1 L 11 L 12 L 1N I 1 v 2 L 21 L 22 L 2N I 2 v 3 = v N L N1 L NN I N 0 1 1 1 1 39 Model choice According to the layout specified by the user, V i s and I i s are divided into three catagories: power (V p, I p ), signal (V s, I s ), and ground (V g, I g ) For delta-i noise model, 1. set I p (assuming all power lines have the same current) 2. set I s = 0 For signal crosstalk model, 1. set I s (assuming all signal lines have the same current) 2. set I p = 0 Assuming pin 1 is ground, set V g s = V 1 40 20
A y = X x --> y = A -1 X x Rearranging the matrix equations by moving all L ij I j s (where I j is I g ) to the left side results in: [(N+1) by (N+1) matrix] * [(N+1) by 1 matrix] = [(N+1) by (N-n) matrix] * [(N-n) by 1 matrix] 1 0 0 0 0 -L 11 V 1 L 12 L 1N 1 0 0 V 2 I 2 1 0 0 V N 0 1 0 0 0 I 1 = 0 0 1 0 0 0 1 1 0 0 0 0 1 -L N1 L N2 L NN I N 0 0 0 0 0-1 -1-1 1 1 1 1 41 Inductance/ground transform (in practice for Spice, etc) Need to reference a common ground 42 21
Effective inductance v 1 =L 11 (di 1 /dt)+ L 12 (di 2 /dt)+ L 13 (di 3 /dt) v 3 =L 31 (di 1 /dt)+ L 32 (di 2 /dt)+ L 33 (di 3 /dt) and for ground return: I 3 =-(I 1 +I 2 ) v 1/ = v 1 -v 3 = (L 11 -L 13 -L 31 + L 33 ) (di 1 /dt) + (L 12 -L 13 -L 32 + L 33 ) (di 2 /dt) = L / 11(dI 1 /dt) + L / 12(dI 2 /dt) So have L / ij = L ij -L ig -L gj + L gg = 2(L ij L ig ) Use for inductive crosstalk i j L ij/ M ij / and delta-i noise I = j = s(org) L ij/ L s, (L g ) Also: Mutual capacitance crosstalk crosstalk currents (Develop voltages if impedances high) 43 Multiple co-planar lines Coplanar lines i = 1 2 3 4 5 n Ground C 12 C 23 C 34 C 45 L 1 L 2 L 3 L 4 L 5 L g 1 2 3 4 5 n plus mutual inductance M ij where L i is the self-inductance of an individual isolated wire. 44 22
Referencing all lines to v n, taken as v n = 0 to define ground L 1 L 2 L 3 L 4 L 5 ground 45 Effective L L s = L i = L i + L g -M ig -M gi M ig = M gi and if the lines are identical, L i = L g, so L i = 2(L i -M ig ) To evaluate crosstalk in the transmission line system, the mutual inductances become M ij = M ij + (L g -M ig -M jg ) The self-inductance L s includes both internal and external inductances L s = L si + L se L si varies with frequency (skin effect) 46 23
Discrete wire to line model Individual wires considered as a transmission line L ii wires L gg L ig L gi L s transmission line G 47 Coplanar lines with remote ground 4. Similarly, M ij = L ij - L ig - L gj + L gg, where 1 2 3 g n = i - j ns Co-planar lines with remote ground line 48 24
Assignment #3 1. Dally et al, Problem 3.17 (see text for τ) 2. Dally et al, Problem 3.19 3. A lossless 10cm long microstrip transmission line as shown in Dally et al Fig. 3.17, is terminated in a load R L equal to impedance Z 0 and driven by an ideal 1 volt voltage step source. Use SPICE (or any other similar program with which you are familiar) to plot the load waveforms over a period of 2.5 line delays, representing the line by: (a) a single lumped L-C section (b) 10 lumped L-C sections (c) 100 lumped L-C sections, and (d) a transmission line model. (e) Comment on your results. 4. For a transmission line of impedance 50Ω driven by a source of impedance 0Ω and terminated by load 100Ω, determine the source and load reflection coefficients. Draw the reflection diagram for a propagation time of 4T, and label all the quantities at each time interval. 5. Two identical signal lines of Z 0 = 50Ω are terminated by 50Ω loads. The signal lines are 2cm long, and the ramp-step source to line 1 changes at 10 9 V/s. The mutual inductance between the two signal lines is 2nH, and the mutual capacitance is 2pF. Determine the crosstalk magnitudes on line 2, and sketch the crosstalk waveforms. 49 25