CROSSTALK - Advanced Signal Integrity for High-Speed Digital Design - page 171

We begin the development by applying Ohm's law at each end of line 2 to
get the amplitudes of the noise pulses at the near end ( v b ) and far end ( v f ):

v b = i b Z 0 (4-46)

v f = i f Z 0 (4-47)

Current is coupled from line to line through the mutual capacitance:

i C = C M dz dv 1
dt

(4-48)

The coupled current splits into separate branches on line 2 that flow in both
directions:

i C = i b + i f (4-49)

Combining equations (4-46) through (4-49) gives an expression for the voltage
pulses created by the coupling through the mutual capacitance,

= Z 0 C M dz dv 1
dt

v b + v f (4-50)

Next we define the capacitive coupling coefficient as the ratio of the mutual
capacitance between lines to the total capacitance of the line:

C M
C g + C M

K C ≡ (4-51)

Along with the capacitive coupling coefficient definition, we apply expressions
for the characteristic impedance of the line, Z 0

= L 0 /C g + C M , to equation

(4-50), resulting in

L 0 C 2 M
C g + C M

dz dv 1
dt

v b + v f = (4-52)

1 / L 0 (C g + C M ) and performing some algebra, we arrive
at the following expression for the sum of forward and backward crosstalk
induced by the mutual capacitance:

By substituting ν p =

ν p K C dz dv 1

1

v b + v f = (4-53)

dt

Turning now to the inductance, we note that the mutual inductance acts as a
coupling transformer. Current on line 1 induces a voltage on line 2 that travels in
the direction opposite that of the incident signal on line 1. As a result, it creates a