# 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]) Calculates the electrical length of a section of transmission line. zl_2_Gamma0(z0, zl) Reflection coefficient from a load impedance. Gamma0_2_zl(z0, Gamma) Input impedance from a load reflection coefficient. 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. 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.

### 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, …) 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. 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.

## Distributed Circuit and Wave Quantities¶

 distributed_circuit_2_propagation_impedance(…) Convert distrubuted 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.