Microstrip Transmission Lines
[file: mstrip.mcd]
Formulas included in this spreadsheet:
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Effective relative permittivity EEFF() (used internally)
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Effective electrical trace width WE() (used internally)
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Microstrip characteristic impedance ZMSTRIP()
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Microstrip propagation delay PMSTRIP()
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Microstrip trace inductance LMSTRIP()
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Microstrip trace capacitance CMSTRIP()
Formulas from: I. J. Bahl and Ramesh Garg, "Simple and accurate formulas for
microstrip with finite strip thickness", Proc. IEEE, 65, 1977, pp. 1611-1612.
This material is nicely summarized in T. C. Edwards, "Foundations of Microstrip
Circuit Design," John Wiley, New York, 1981, reprinted 1987.
(Watch out for Edward's error in Equation 3.52b, where he omits a ln()
function.)
Variables used:
Effective relative permittivity as a function of microstrip trace geometry:
For skinny traces (w < h)
For wide traces (w > h)
Composite formula picks skinny or wide model depending on w/h ratio:
Special adjustment to account for trace thickness:
When w/h is skinny, you get the average of the PCB permittivity, er, and the
permittivity of air.
When w/h is wide, (the trace is very close to the ground plane) you get er.
Effective trace width as a function of other parameters (in.):
For skinny traces (2pw < h)
For wide traces (2pw > h)
Composite formula picks skinny or wide model depending on w/h ratio:
Characteristic impedance as a function of trace geometry (W):
Accuracy of better than 2 percent is obtained under the following conditions:
0 < t/h < 0.2
0.1 < w/h < 20
0 < er < 16
For skinny traces (w < h)
For wide traces (w > h)
Composite formula picks skinny or wide model depending on w/h ratio:
Microstrip propagation delay (s/in.):
Inductance of microstrip (H):
(Use a dummy er value of 1. It doesn't matter for inductance calculations.)
Capacitance of microstrip (F):
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Example microstrip wire calculations
Height above ground (in.)
Width of trace (in.)
Thickness of trace (in.)
 (1-oz
copper plating weight)
Length of wire (in.)
Relative electric
permeability (affects
capacitance, but not
inductance)
Impedance (W):
Total inductance (H):
Same result in nH:
Inductance per in. (H):
Total capacitance (F):
Same result in pF:
Capacitance per in. (F):
Tolerance effects
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