Transmission lines take on many forms in order to accommodate particular applications.
All rely on the same basic components  two or more conductors separated by a dielectric
(insulator). The physical configuration and properties of all the components determines
the characteristic impedance, distortion, transmission speed, and loss.
See a discussion on
transmission lines and coaxial connectors.
The
following formulas are presented in a compact text format that can be copied and
pasted into a spreadsheet or other application.
For the following equations,
ε is the dielectric constant (ε = 1 for air)
Two Conductors in Parallel (Unbalanced)
Above Ground Plane
For D << d, h
Z_{0}= (69/ε^{½})
log_{10}{(4h/d)[1+(2h/D)^{2}]^{½}}

Single Conductor Above Ground Plane
For d << h
Z_{0}= (138/ε^{½}) log_{10}(4h/d)

Two Conductors in Parallel (Balanced)
Above Ground Plane
For D << d, h_{1}, h_{2}
Z_{0}= (276/ε^{½}) log_{10}{(2D/d)[1+(D/2h)^{2}]^{½}}

Two Conductors in Parallel (Balanced)
Different Heights Above Ground Plane
For D << d, h_{1},
h_{2}
Z_{0}= (276/ε^{½})log_{10}{(2D/d)[1+(D^{2}/4h_{1}h_{2})]^{½}}

Single Conductor Between Parallel Ground
Planes
For d/h << 0.75
Z_{0}= (138/ε^{½})
log_{10}(4h/πd)

Two Conductors in Parallel (Balanced)
Between Parallel Ground Planes
For d << D, h
Z_{0}=
(276/ε^{½}) log_{10}{[4h tanh(πD/2h)]/πd}

Balanced Conductors Between Parallel
Ground Planes
For d << h
Z_{0}= (276/ε^{½})
log_{10}(2h/πd)

Two Conductors in Parallel (Balanced)
of Unequal Diameters
Z_{0}= (60/ε^{½})
cosh^{1} (N)
N = ½[(4D^{2}/d_{1}d_{2}) 
(d_{1}/d_{2})  (d_{2}/d_{1})]

Balanced 4Wire Array
For
d << D_{1}, D_{2}
Z_{0}= (138/ε^{½})
log_{10}{(2D_{2}/d)[1+(D_{2}/D_{1})^{2}]^{½}}

Two Conductors in Open
Air
Z_{0}= 276 log_{10}(2D/d)

5Wire Array
For d <<
D
Z_{0}= (173/ε^{½}) log_{10}(D/0.933d)

Single Conductor in Square Conductive
Enclosure
For d << D
Z_{0}≈ [138 log_{10}(ρ)
+6.482.34A0.48B0.12C]/ε^{½}
A = (1+0.405ρ^{4})/(10.405ρ^{4})
B = (1+0.163ρ^{8})/(10.163ρ^{8})
C = (1+0.067ρ^{12})/(10.067ρ^{12})
ρ= D/d

Air Coaxial Cable with Dielectric Supporting
Wedge
For d << D
Z_{0}≈ [138 log_{10}(D/d)]/[1+(ε1)(θ/360)]^{½})
ε = wedge dielectric constant
θ= wedge angle in degrees

Two Conductors Inside Shield (sheath
return)
For d << D, h
Z_{0}= (69/ε^{½})
log_{10}[(ν/2σ^{2})(1σ^{4})]
ν = h/d
σ = h/D

Balanced Shielded Line
For
D>>d, h>>d
Z_{0}= (276/ε^{½}) log_{10}{2ν[(1σ^{2})/(1+σ^{2})]}
ν = h/d
σ = h/D


Two Conductors in Parallel (Unbalanced) Inside Rectangular
Enclosure
For d << D, h, w
∞ Z_{0}= (276/ε^{½}) {log_{10}[(4h tanh(πD/2h)/πd) ∑ log_{10}[(1+μ_{m}^{2})/(1ν_{m}^{2})]}
^{m=1}
μ_{m}=sinh(πD/2h)/cosh(mπw/2h)
ν_{m}=sinh(πD/2h)/sinh(mπw/2h)

Equations appear in "Reference Data for Engineers," Sams Publishing 1993
