IDEAL TRANSMISSION-LINE FUNDAMENTALS - Advanced Signal Integrity for High-Speed Digital Design - page 84

w

e r = 1

t

e r

h

(a)

w h 2

e r

t

h 1

(b)

Figure 3-12 Dimensions used in the impedance and effective dielectric constant for-
mulas: (a) microstrip line; (b) stripline.

3.3.4 Simple Formulas for Calculating the Characteristic Impedance
For maximum accuracy it is necessary to use one of the many commercially avail-
able two-dimensional electromagnetic field solvers to calculate the impedance of
the PCB or MCM traces for design purposes. The solvers will typically provide
the impedance, propagation velocity, and the L and C elements per unit length
using many of the concepts that will be presented in Section 3.4. In the absence
of a field solver, the formulas presented here will provide approximations to the
impedance values of typical transmission lines as a function of the trace geometry
and the dielectric constant ε r , where the dimensions are as shown in Figure 3-12.

Microstrip: Infinitely Thin Conductors (t h) [Hammerstad and Jensen,

1980]

1

2

2 h
w

η
2 π ln

ξh
w +

Z 0 = +

(3-36a)

6 )e − ( 30 . 666 h/w) 0 . 7528 ξ = 6 + ( 2 π −

377
√ ε eff η =

Microstrip: Finite Thickness [Collins, 1992] The formulas below are accurate
for 1 <ε r ≤ 6. Note that ε eff in this equation set accounts

for the finite thickness of the signal conductor when calculating the effective
dielectric constant for the microstrip. The term w e is an effective width that
accounts for the extra capacitance caused by the finite thickness of the signal
conductor. Since electric field lines will be established between the edge of the
conductor and the reference plane, thicker signal conductors will exhibit increased

16 and 0 . 25 ≤ w/h ≤