<< Chapter < Page Chapter >> Page >
This module introduces and derives the telegrapher's equations, which describe how electrical signals behave as they move along transmission lines.

Let's look at just one little section of the line, and define some voltages and currents .

Applying kirchoff's laws

For the section of line Δ x long, the voltage at its input is just V x t and the voltage at the output is V x Δ x t . Likewise, we have a current I x t entering the section, and another current I x Δ x t leaving the section of line. Note that both the voltage and the current are functions of time as well as position.

The voltage drop across the inductor is just:

V L L Δ x t I x t
Likewise, the current flowing down through the capacitor is
I C C Δ x t V x Δ x t
Now we do a KVL around the outside of the section of line and we get
V x t V L V x Δ x t 0
Substituting for V L and taking it over to the RHS we have
V x t V x Δ x t L Δ x t I x t
Let's multiply by -1, and bring the Δ x over to the left hand side.
V x Δ x t V x t Δ x L t I x t
We take the limit as Δ x 0 and the LHS becomes a derivative:
x V x t L t I x t
Now we can do a KCL at the node where the inductor and capacitor come together.
I x t C Δ x t V x Δ x t I x Δ x t 0
And upon rearrangement:
I x Δ x t I x t Δ x C t V x Δ x t
Now when we let Δ x 0 , the left hand side again becomes a derivative, and on the right hand side, V x Δ x t V x t , so we have:
x I x t C t V x t
and are so important we will write them out again together:
x V x t L t I x t
x I x t C t V x t
These are called the telegrapher's equations and they are all we really need to derive how electrical signalsbehave as they move along on transmission lines. Note what they say. The first one says that at some point x along the line, the incremental voltage drop that we experience as we move down the line is justthe distributed inductance L times the time derivative of the current flowing in the line at that point. The secondequation simply tells us that the loss of current as we go down the line is proportional to the distributed capacitance C times the time rate of change of the voltage on the line. As youshould be easily aware, what we have here are a pair of coupled linear differential equations in time and position for V x t and I x t

Questions & Answers

Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Mueller Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Introduction to physical electronics. OpenStax CNX. Sep 17, 2007 Download for free at http://cnx.org/content/col10114/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introduction to physical electronics' conversation and receive update notifications?

Ask