Derivation of telegrapher's equations

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In summary, the conversation is about deriving telegrapher's equations using Kirchhoff current/voltage laws and the confusion surrounding the placement of shunt capacitance and conductance in parallel. The person is also unsure about the use of voltage 'u' in the calculations for losses through the resistor and capacitor. They are seeking clarification on whether u(x,t) is used for both components and if the voltage at u(x+dc,t) is also considered. The link provided offers a resource for further understanding.
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When deriving telegrapher's equations using Kirchhoff current/voltage laws (this equivalent circuit), are the shunt capacitance and shunt conductance in parallel? I assume not, and if not, are they in parallel with the voltages at each corresponding end? I am confused by this; in Pozar's derivations, he assumes the latter when using Kirchhoff current law. I always have trouble determining what is parallel with what, especially in ICs. Can anyone elucidate this for me?
 
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Thanks for the derivation although I think my questions are still unanswered. When calculating the losses through the resistor and capacitor, he uses voltage 'u' for both. Is this u(x,t)? Both the capacitor and resistor are at this voltage, so in parallel? What about the voltage at u(x+dc,t)?
 
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FAQ: Derivation of telegrapher's equations

What are the telegrapher's equations and why are they important?

The telegrapher's equations are a set of partial differential equations that describe the propagation of electrical signals along a transmission line. They are important because they allow us to analyze and design electrical systems such as telegraph and telephone networks, as well as modern communication systems.

What is the history behind the derivation of telegrapher's equations?

The telegrapher's equations were first derived in the mid-19th century by British mathematician Oliver Heaviside. He was working on improving the telegraph system and realized that the equations governing the transmission of electrical signals could be simplified into a single set of equations.

What are the assumptions made in the derivation of telegrapher's equations?

The derivation of telegrapher's equations is based on three main assumptions:

  1. The transmission line is infinitely long, meaning there is no loss of signal due to the length of the line.
  2. The line is uniform, meaning the electrical properties (resistance, capacitance, and inductance) are constant along the entire length of the line.
  3. The line is lossless, meaning there is no energy dissipation due to resistance.

How are telegrapher's equations used in practical applications?

Telegrapher's equations are used in a variety of practical applications, including the design of telecommunication systems, power systems, and high-speed data transmission lines. They are also used in electromagnetic compatibility analysis and in the study of signal propagation in electronic circuits and antennas.

What are the limitations of the telegrapher's equations?

The telegrapher's equations have some limitations, including the assumption of an infinitely long and uniform transmission line, which may not accurately represent real-world systems. They also do not take into account non-linear effects, such as distortion and interference, which can occur in high-frequency signals. Additionally, the equations do not account for the effects of dispersion, which can impact the speed and quality of signal transmission.

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