Distributed element model in Transmission Lines (Part I)

In a previous post, we studied the transmission lines in the steady state. Now, keeping the assumption of no losses, we are going to study the distribution of the voltages and currents as a function of the coordinate z in an instant of time t.

Premises

  1. It’s not practical to solve the Maxwell’s equations in the transmission lines.
  2. We will develop an equivalent model from the physical characteristics of the line that will allow us working with currents and voltages.
  3. With this model, we will apply the Kirchhoff laws to a very small section of the line and, this way, we’ll obtain a system of linear differential equations.
  4. The solutions to these equations show that the relation between the incident and reflected (current and voltage) waves are characteristics of the physical parameters of the line.

Introduction to Transmission Lines

A transmission line is characterized by taking a length comparable to the wavelength of the information signal propagating through them λ.

Therefore, Kirchhoff laws are not applicable in their classic form to these dimensions. We need to to apply the distributed element model, also named, Transmission Lines Theory.

Resultado de imagen de types of transmission line

Types of transmission lines

In the following posts, we will study:

  • The transmission lines equations
  • Solve and exercise applying the equations
  • Propagation constant and characteristic impedance of the line
  • Solve and exercise calculating this parameters on a real line

After this study is complete, we will study the parameters when the line is in a transient state which analyses what happen when there is a sudden change in the conditions of the line. We’ll also solve exercises for this study, so stay tuned! 🙂

Does this sound interesting?

 

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