**Transmission Lines**
======================

A *transmission line* is a specialized cable or other structure designed to conduct
electromagnetic waves in a contained manner. The term applies when the conductors
are long enough that the wave nature of the transmission must be taken into account.

.. _transmission_matrix_def:

**Transmission matrix**

The **transmission matrix** is one of the ways to describe a microwave device. The
:math:`ABCD`-parameters of the device act as elements of this matrix. The matrix
equation relates the input voltage and input current to the output voltage and output
current.

.. _scattering_matrix_def:

**Scattering matrix**

The **scattering matrix** is one of the ways to describe a microwave device. The
:math:`S`-parameters of the device act as elements of this matrix. The matrix equation
relates the waves reflected from the input and output to the waves incident on the input
and output.

.. py:currentmodule:: symplyphysics.electromagnetism.circuits.transmission_lines

**Contents:**

.. toctree::
    :maxdepth: 4

    electromagnetism.circuits.transmission_lines.coplanar_lines
    electromagnetism.circuits.transmission_lines.microstrip_lines
    electromagnetism.circuits.transmission_lines.coefficient_standing_wave_from_reflection_coefficient
    electromagnetism.circuits.transmission_lines.coefficient_standing_wave_from_voltages
    electromagnetism.circuits.transmission_lines.hybrid_parameters_matrix
    electromagnetism.circuits.transmission_lines.impedance_matrix_equation
    electromagnetism.circuits.transmission_lines.impedances_pi_type_circuit_of_transmission_line
    electromagnetism.circuits.transmission_lines.impedances_t_type_circuit_of_transmission_line
    electromagnetism.circuits.transmission_lines.input_impedance_from_parameters_transmission_matrix
    electromagnetism.circuits.transmission_lines.input_impedance_lossless_transmission_line
    electromagnetism.circuits.transmission_lines.input_impedance_lossy_transmission_line
    electromagnetism.circuits.transmission_lines.ratio_of_average_power_to_incident_power_from_reflection_coefficient
    electromagnetism.circuits.transmission_lines.ratio_of_average_power_to_incident_power_from_standing_wave_coefficient
    electromagnetism.circuits.transmission_lines.reflection_coefficient_from_load_and_transmission_line_impedances
    electromagnetism.circuits.transmission_lines.scattering_matrix_equation
    electromagnetism.circuits.transmission_lines.scattering_matrix_to_transmission_matrix
    electromagnetism.circuits.transmission_lines.total_conductivities_matrix
    electromagnetism.circuits.transmission_lines.transmission_matrix_equation
    electromagnetism.circuits.transmission_lines.transmission_matrix_for_a_parallel_load_in_line
    electromagnetism.circuits.transmission_lines.transmission_matrix_for_a_series_load_in_line
    electromagnetism.circuits.transmission_lines.transmission_matrix_lossless_transmission_line
    electromagnetism.circuits.transmission_lines.transmission_matrix_lossy_transmission_line
    electromagnetism.circuits.transmission_lines.transmission_matrix_of_pi_type_circuit
    electromagnetism.circuits.transmission_lines.transmission_matrix_of_t_type_circuit
    electromagnetism.circuits.transmission_lines.wave_resistance_of_microstrip_line_for_effective_width_greater_thickness
    electromagnetism.circuits.transmission_lines.wave_resistance_of_microstrip_line_for_effective_width_less_thickness