Primary Constants & Parameter Calculations

Comms 4 Primary Constants & Formulas

Characteristic Impedance (Two-Wire, Physical)

Zo = (276 / square root of e) * log10(2D / d); where D is spacing and d is diameter.

Resistance per 100ft (Two-Wire)

R = (square root of F) / (5 * d); where F is in MHz and d is in inches.

Characteristic Impedance (Coaxial, Physical)

Zo = (138 / square root of e) * log10(D / d); where D is outer conductor inner diameter and d is inner conductor outer diameter.

Resistance per 100ft (Coaxial)

R = 0.1 * ((D + d) / (D * d)) * square root of F; where F is in MHz.

Attenuation per 100ft (dB)

Attenuation = 4.35 * (R / Zo).

Characteristic Impedance (Primary Constants)

Zo = square root of ((R + jomegaL) / (G + jomegaC)).

Characteristic Impedance (Low Frequency)

Zo = square root of (R / G).

Characteristic Impedance (High Frequency)

Zo = square root of (L / C).

Velocity Factor (VF)

The ratio of the actual velocity of propagation in a medium to the velocity of propagation in a vacuum (VF = Vp / c = 1 / square root of epsilon_r).

Dielectric Constant (epsilon_r)

The relative permittivity of a material.

Propagation Constant (gamma)

Describes the distribution of voltage and current with distance; gamma = alpha + jbeta = square root of ((R + jomegaL) * (G + jomega*C)).

Attenuation Constant (alpha)

The real part of the propagation constant; measured in nepers/unit length or dB/unit length.

Phase Shift Constant (beta)

The imaginary part of the propagation constant; measured in rad/unit length or degrees/unit length.

Neper to dB conversion

1 neper = 8.686 dB.

Phase Velocity (Vp) Formula using beta

Vp = omega / beta = lambda * f.

Phase Velocity (TEM wave)

Vp = 1 / square root of (mu * epsilon) = c / square root of epsilon_r.

Beta (TEM wave)

beta = omega * square root of (mu * epsilon) = 2 * pi / lambda.

Time Delay (td)

The time it takes for a signal to travel from one end of a line to the other; td = square root of (L * C).

Primary Line Constants

Electrical parameters based on dimensions: Series Resistance (R), Series Inductance (L), Shunt Capacitance (C), Shunt Conductance (G).

Series Resistance (Coaxial) Formula

R = (Rs / (2 * pi)) * ((1/a) + (1/b)); where Rs is surface resistance.

Series Inductance (Coaxial) Formula

L = (mu / (2 * pi)) * ln(b / a).

Shunt Conductance (Coaxial) Formula

G = (2 * pi * sigma) / ln(b / a).

Shunt Capacitance (Coaxial) Formula

C = (2 * pi * epsilon) / ln(b / a).

Series Resistance (Two-Wire) Formula

R = Rs / (pi * a).

Series Inductance (Two-Wire) Formula

L = (mu / pi) * ln(2D / d) (approx).

Shunt Conductance (Two-Wire) Formula

G = (pi * sigma) / ln(2D / d) (approx).

Shunt Capacitance (Two-Wire) Formula

C = (pi * epsilon) / ln(2D / d) (approx).

Intrinsic Resistance (Rs)

Surface resistance of a conductor; Rs = square root of ((pi * f * muc) / sigmac).

Electrical Permittivity of Free Space (epsilon_o)

8.854 x 10^-12 F/m.

Magnetic Permeability of Free Space (mu_o)

4 * pi * 10^-7 H/m.

Series Resistance (PWTL) Practical Formula

R = (0.1 * square root of fMHz) / rin; Unit: Ohms/100 ft.

Series Inductance (PWTL) Formula

L = (mu / pi) * ln(2S / d); Unit: H/m.

Shunt Capacitance (PWTL) Formula

C = (pi * epsilon) / ln(2S / d); Unit: F/m.

Series Resistance (Coax) Practical Formula

R = 0.1 * square root of fMHz * ((1/Din) + (1/d_in)); Unit: Ohms/100 ft.

Series Inductance (Coax) Formula

L = (mu / (2 * pi)) * ln(D / d); Unit: H/m.

Shunt Capacitance (Coax) Formula

C = (2 * pi * epsilon) / ln(D / d); Unit: F/m.

Parallel-Plate Resistance (R')

(2 * Rs) / w.

Parallel-Plate Inductance (L')

(mu * h) / w.

Parallel-Plate Conductance (G')

(sigma * w) / h.

Parallel-Plate Capacitance (C')

(epsilon * w) / h.