## Transmission Line Impedances

See also the page on the "transmission line equation", which describes the behavior a transmission line in a system, once you know the characteristic impedance, etc. There is also some information on waveguides.

### Microstrip

#### Characteristic impedance, given dimensions

Z0 = 60/ sqrt(0.475*epsilonr + 0.67) * ln(4 * h/(0.67 * (0.8 * w+t)

if w < 2h (max error ca. 3%)

#### Width for given impedance

w = 7.463 * h / exp(Z0*sqrt(0.475*epsilonr + 0.67)/60) - 1.25*t

where:

w = tracewidth in cm
h = dielectric thickness in cm
epsilonr = relative dielectric constant

### Stripline

#### Impedance, given dimensions

Z0 = 60/sqrt(epsilonr) * ln( 4 * b/(0.67 * pi * (0.8 *w + t)))

best accuracy for (b-t)>2w and b>4t

#### Line width for given impedance

w = 2.375 * b / exp( Z0 * sqrt(epsilonr)/60) - 1.25 *t

where:

b = dielectric thickness between ground planes
others as defined above

### Differential Impedance

For microstripline

Zdiff = 2 * Z0 * (1 - 0.48 * exp(- 0.96 * s / h))

For stripline

Zdiff = 2 * Z0 * (1 - 0.374 * exp( -2.9 * s / h))

where:

s = spacing between striplines

These functions derived from empirical data. Error could be +/- 10%. Practical ranges for Z0 and Zdiff are 20 to 150 ohms.

### References:

#### Stripline Equations taken from:

Mears, James A., "Transmission Line RAPIDESIGNER (c) Operation and Applications Guide", National Semiconductor Application note AN-905, May 1996 ( http://www.national.com/an/AN/AN-905.pdf) This application note cites 7 further references and provides some useful advice on where the formulae are applicable.

radio/tlz.htm - 3 June 2002 - Jim Lux
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