# Electromagnetics - Telegraphers EQs - 3 parallel lines

• VinnyCee
In summary, the homework problem involves a multisection transmission line with three lossless transmission lines connecting an ideal step source to two load resistances. The line parameters are given and the task is to sketch the voltages for given time intervals. The equations for reflection coefficients, characteristic impedance, propagation velocity, and time delay are provided. The attempt at a solution includes finding the necessary variables and creating a bounce diagram, but the presence of a mysterious 0.2V bounce in the diagram is confusing the writer. Assistance is requested to resolve the issue.
VinnyCee

## Homework Statement

A multisection transmission line consists of three lossless transmission lines used to connect an ideal step source of 5V amplitude and 6$\Omega$ output impedance to two separate load resistances of 66$\Omega$ each. All three lines are characterized by the line parameters L = 364.5 nH/m and C = 125 pF/m and length of 40cm. Sketch voltages Vs and $V_L$ versus t for 0 < t < 20 ns.

http://img23.imageshack.us/img23/5678/problem218lq7.jpg

## Homework Equations

$$\Gamma_S\,=\,\frac{R_S\,-\,Z_0}{R_S\,+\,Z_0}$$

$$\Gamma_L\,=\,\frac{R_L\,-\,Z_0}{R_L\,+\,Z_0}$$

$$Z_0\,=\,\sqrt{\frac{L}{C}}$$

$$v_p\,=\,\frac{1}{\sqrt{L\,C}}$$

$$t_d\,=\,\frac{l}{v_p}$$

## The Attempt at a Solution

http://img168.imageshack.us/img168/8978/problem218solnpu5.jpg

I found all the variables quite easily using the formulas above. I started making the bounce diagram and got a few $t_d$ into it. But when I get to 3$t_d$=8.1 ns, I am confused by one of the bounced voltages. I have the answer, but I have no idea where the writers are getting a 0.2V bounce in the diagram.

On the right side, between 8.1ns < t < 10.8ns, there are three voltages. 0.8V, -0.1V and the mysterious 0.2V. I understand that the 0.8V line comes from the 1.2V on the left, and the -0.1V line comes from the reflection of the 0.3V line above. Actually there should be two of the 0.1V lines considering the reflection from both of the right hand lines. But where is that third 0.2V line coming from?

Last edited by a moderator:
The bounce diagram is wrong? I really can't think of any other explanation. I will ask TA tomorrow I guess!

I would like to address the confusion about the third 0.2V line in the diagram. It is important to note that in a multisection transmission line, there can be multiple reflections and bounces of the voltage signal. In this case, the 0.2V bounce is a result of a second reflection from the rightmost load resistance of 66Ω. This reflection occurs at a time of 9.45ns, which is why it appears in the graph between 8.1ns and 10.8ns. I hope this clarifies your understanding of the diagram. It is also important to carefully consider all possible reflections and bounces when analyzing a multisection transmission line.

## 1. What is the purpose of telegraphers' equations in electromagnetics?

The telegraphers' equations are a set of two partial differential equations that are used to model the propagation of electromagnetic waves in a transmission line. They are particularly useful for analyzing the behavior of signals in long-distance communication systems, such as telegraph and telephone lines.

## 2. What are the three parallel lines in the context of telegraphers' equations?

The three parallel lines refer to the three components of a transmission line: the signal conductor, the return conductor, and the ground. These components are modeled as three parallel conductors in the telegraphers' equations.

## 3. How do the telegraphers' equations take into account the effects of resistance and capacitance in transmission lines?

The telegraphers' equations include terms for resistance and capacitance in the transmission line. These parameters affect the propagation of electromagnetic waves by causing attenuation (loss of signal strength) and dispersion (spreading of the signal). The equations allow for the calculation of these effects on the signal.

## 4. Can the telegraphers' equations be applied to all types of transmission lines?

The telegraphers' equations are most commonly used for analyzing the behavior of signals in uniform, lossy transmission lines. However, they can also be applied to other types of transmission lines, such as coaxial cables and waveguides, with some modifications to account for the specific characteristics of these lines.

## 5. What are some practical applications of the telegraphers' equations?

The telegraphers' equations have many practical applications in the fields of telecommunications, power transmission, and signal processing. They are used to design and analyze transmission lines in communication systems, as well as to model the behavior of signals in high-speed data transmission. They are also used in the analysis of power distribution systems and the design of filters and other signal processing devices.