tlineFunctions (skrf.tlineFunctions)

This module provides functions related to transmission line theory.

Impedance and Reflection Coefficient

These functions relate basic transmission line quantities such as characteristic impedance, input impedance, reflection coefficient, etc. Each function has two names. One is a long-winded but readable name and the other is a short-hand variable-like names. Below is a table relating these two names with each other as well as common mathematical symbols.

Symbol

Variable Name

Long Name

\(Z_l\)

z_l

load_impedance

\(Z_{in}\)

z_in

input_impedance

\(\Gamma_0\)

Gamma_0

reflection_coefficient

\(\Gamma_{in}\)

Gamma_in

reflection_coefficient_at_theta

\(\theta\)

theta

electrical_length

There may be a bit of confusion about the difference between the load impedance the input impedance. This is because the load impedance is the input impedance at the load. An illustration may provide some useful reference.

Below is a (bad) illustration of a section of uniform transmission line of characteristic impedance \(Z_0\), and electrical length \(\theta\). The line is terminated on the right with some load impedance, \(Z_l\). The input impedance \(Z_{in}\) and input reflection coefficient \(\Gamma_{in}\) are looking in towards the load from the distance \(\theta\) from the load.

\[ \begin{align}\begin{aligned}Z_0, \theta\\\text{o===============o=}[Z_l]\\\to\qquad\qquad\qquad\quad\qquad \qquad \to \qquad \quad\\Z_{in},\Gamma_{in}\qquad\qquad\qquad\qquad\quad Z_l,\Gamma_0\end{aligned}\end{align} \]

So, to clarify the confusion,

\[Z_{in}= Z_{l},\qquad\qquad \Gamma_{in}=\Gamma_l \text{ at } \theta=0\]

Short names

theta(gamma, f, d[, deg])

Electrical length of a section of transmission line.

zl_2_Gamma0(z0, zl)

Reflection coefficient from a load impedance.

zl_2_zin(z0, zl, theta)

Input impedance from load impedance at a given electrical length.

zl_2_Gamma_in(z0, zl, theta)

Reflection coefficient of load at a given electrical length.

zl_2_swr(z0, zl)

Standing Wave Ratio (SWR) for a given load impedance.

zl_2_total_loss(z0, zl, theta)

Total loss of a terminated transmission line (in natural unit).

Gamma0_2_zl(z0, Gamma)

Input impedance from a load reflection coefficient.

Gamma0_2_Gamma_in(Gamma0, theta)

Reflection coefficient at a given electrical length.

Gamma0_2_zin(z0, Gamma0, theta)

Input impedance from load reflection coefficient at a given electrical length.

Gamma0_2_swr(Gamma0)

Standing Wave Ratio (SWR) for a given reflection coefficient.

Long-names

electrical_length(gamma, f, d[, deg])

Electrical length of a section of transmission line.

distance_2_electrical_length(gamma, f, d[, deg])

Electrical length of a section of transmission line.

electrical_length_2_distance(theta, gamma, f0)

Convert electrical length to a physical distance.

reflection_coefficient_at_theta(Gamma0, theta)

Reflection coefficient at a given electrical length.

reflection_coefficient_2_input_impedance(z0, …)

Input impedance from a load reflection coefficient.

reflection_coefficient_2_input_impedance_at_theta(z0, …)

Input impedance from load reflection coefficient at a given electrical length.

reflection_coefficient_2_propagation_constant(…)

Propagation constant from line input and load reflection coefficients.

input_impedance_at_theta(z0, zl, theta)

Input impedance from load impedance at a given electrical length.

load_impedance_2_reflection_coefficient(z0, zl)

Reflection coefficient from a load impedance.

load_impedance_2_reflection_coefficient_at_theta(z0, …)

Reflection coefficient of load at a given electrical length.

voltage_current_propagation(v1, i1, z0, theta)

Voltages and currents calculated on electrical length theta of a transmission line.

Distributed Circuit and Wave Quantities

distributed_circuit_2_propagation_impedance(…)

Convert distributed circuit values to wave quantities.

propagation_impedance_2_distributed_circuit(…)

Convert wave quantities to distributed circuit values.

Transmission Line Physics

skin_depth(f, rho, mu_r)

Skin depth for a material.

surface_resistivity(f, rho, mu_r)

Surface resistivity.