**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.laws.electricity.circuits.transmission_lines

**Contents:**

.. toctree::
    :maxdepth: 4

    laws.electricity.circuits.transmission_lines.coplanar_lines
    laws.electricity.circuits.transmission_lines.microstrip_lines
    laws.electricity.circuits.transmission_lines.coefficient_standing_wave_from_reflection_coefficient
    laws.electricity.circuits.transmission_lines.coefficient_standing_wave_from_voltages
    laws.electricity.circuits.transmission_lines.hybrid_parameters_matrix
    laws.electricity.circuits.transmission_lines.impedances_pi_type_circuit_of_transmission_line
    laws.electricity.circuits.transmission_lines.impedances_t_type_circuit_of_transmission_line
    laws.electricity.circuits.transmission_lines.input_impedance_from_parameters_transmission_matrix
    laws.electricity.circuits.transmission_lines.input_impedance_lossless_transmission_line
    laws.electricity.circuits.transmission_lines.input_impedance_lossy_transmission_line
    laws.electricity.circuits.transmission_lines.ratio_of_average_power_to_incident_power_from_reflection_coefficient
    laws.electricity.circuits.transmission_lines.ratio_of_average_power_to_incident_power_from_standing_wave_coefficient
    laws.electricity.circuits.transmission_lines.reflection_coefficient_from_load_and_transmission_line_impedances
    laws.electricity.circuits.transmission_lines.scattering_matrix
    laws.electricity.circuits.transmission_lines.scattering_matrix_to_transmission_matrix
    laws.electricity.circuits.transmission_lines.total_conductivities_matrix
    laws.electricity.circuits.transmission_lines.total_resistance_matrix
    laws.electricity.circuits.transmission_lines.transmission_matrix
    laws.electricity.circuits.transmission_lines.transmission_matrix_for_a_parallel_load_in_line
    laws.electricity.circuits.transmission_lines.transmission_matrix_for_a_series_load_in_line
    laws.electricity.circuits.transmission_lines.transmission_matrix_lossless_transmission_line
    laws.electricity.circuits.transmission_lines.transmission_matrix_lossy_transmission_line
    laws.electricity.circuits.transmission_lines.transmission_matrix_of_pi_type_circuit
    laws.electricity.circuits.transmission_lines.transmission_matrix_of_t_type_circuit
    laws.electricity.circuits.transmission_lines.wave_resistance_of_microstrip_line_for_effective_width_greater_thickness
    laws.electricity.circuits.transmission_lines.wave_resistance_of_microstrip_line_for_effective_width_less_thickness