CROSSTALK - Advanced Signal Integrity for High-Speed Digital Design - page 160

3 . 592

×

10 − 7 H / m

Z 0 , isolated =

10 − 11 F / m =

65 . 0

8 . 501 ×

1

ν p, even = [ ( 35 . 92

10 − 8 H / m][ ( 85 . 01 10 − 12 F / m] + 3 . 218 ) × − 2 . 173 ) ×

10 8 m / s

= 1 . 756 ×

1

ν p, odd = [ ( 35 . 92

− 3 . 218 ) × 10 − 8 H / m][ ( 85 . 01 + 2 . 173 ) × 10 − 12 F / m]

10 8 m / s

= 1 . 873 ×

1

ν p, isolated = 3 . 592

× 10 − 7 H / m8 . 501 × 10 − 11 F / m

10 8 m / s = 1 . 810 ×

Step 2 : Calculate the even-mode waveform. Calculate the values for the initial
voltage and current waves, reflection coefficients, final voltage and current levels,
and propagation delay as preparation for a lattice diagram analysis.

Z 0 , even
R S + Z 0 , even V S =

68 . 7
65 +

v(t = 0 ,z = 0 ) =

68 . 7 ( 1V )

= 0 . 514 V

v(t = 0 ,z = 0 ) 0 . 514 V

68 . 7 =

i(t = 0 ,z = 0 ) = = 7 . 48 mA

Z 0 , even

R S − Z 0 , even
R S + Z 0 , even

65 − 68 . 7

(z = 0 ) = =

68 . 7 =−

0 . 028

65 −

R T − Z 0 , even 65 − 68 . 7

(z = l) =

=

68 . 7 =−

0 . 028

R T + Z 0 , even 65 +

R t
R S +

65
65

v(t =∞ ) =

R t V S = 65 ( 1V ) =

0 . 500 V

+

v S
R S + R t =

1 . 000
65 +

i(t =∞ ) =

65 =

7 . 69 mA

l
ν p, even

11 in m

39 . 37 in. =

t d, even = = 1 . 592 ns

1 . 756 × 10 8 m / s

The corresponding lattice diagram is shown in Figure 4-11.
Step 3 : Calculate the odd-mode waveform. Repeat the analysis for the
odd-mode propagation, with the lattice diagrams shown in Figure 4-12.

Z 0 , odd
R S + Z 0 , odd V S =

61 . 2
65 +

v(t = 0 ,z = 0 ) =

61 . 2 ( 1V )

= 0 . 485 V