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.

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

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]) Calculates the electrical length of a section of transmission line.
zl_2_Gamma0(z0, zl) Returns the reflection coefficient for a given load impedance, and characteristic impedance.
Gamma0_2_zl(z0, Gamma) calculates the input impedance given a reflection coefficient and
zl_2_zin(z0, zl, theta) input impedance of load impedance zl at a given electrical length,
zl_2_Gamma_in(z0, zl, theta)
Gamma0_2_Gamma_in(Gamma0, theta) reflection coefficient at a given electrical length.
Gamma0_2_zin(z0, Gamma0, theta) calculates the input impedance at electrical length theta, given a

Long-names

distance_2_electrical_length(gamma, f, d[, deg]) Calculates the 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, …) calculates the input impedance given a reflection coefficient and
reflection_coefficient_2_input_impedance_at_theta(z0, …) calculates the input impedance at electrical length theta, given a
input_impedance_at_theta(z0, zl, theta) input impedance of load impedance zl at a given electrical length,
load_impedance_2_reflection_coefficient(z0, zl) Returns the reflection coefficient for a given load impedance, and characteristic impedance.
load_impedance_2_reflection_coefficient_at_theta(z0, …)

Distributed Circuit and Wave Quantities

distributed_circuit_2_propagation_impedance(…) Converts distrubuted circuit values to wave quantities.
propagation_impedance_2_distributed_circuit(…) Converts wave quantities to distributed circuit values.

Transmission Line Physics

skin_depth(f, rho, mu_r) the skin depth for a material.
surface_resistivity(f, rho, mu_r) surface resistivity.