Examcrazy Logo
MBA in India CAT How to Prepare for Exams Technical Freshers Jobs
  Follow us|  twitter  Orkut  facebook
Electromagnetic Tutorials
   Magnetic circuits
   Faraday's law of induction. Lenz's law
   Faraday's law examples
   Faraday's law and moving circuits
   Displacement current and Ampère's law
   Maxwell's equations, boundary conditions
   Sinusoidal steady state, phasors
   Maxwell's equations and electrical circuits
   Non-ideal behavior of physical circuit elements. Skin effect
   Ideal transformer
   Transmission lines and distributed l and c.
   Time domain solutions to TL wave equations.
   Transmission line termination, reflections. Current waves.
   Bounce diagrams
   Pulse propagation on transmission lines. Time domain reflectometry
   Sinusoidal steady state excitation of lossless transmission lines
   Termination of transmission lines. Load reflection coefficient.
   Input impedance of TLs. Excitation and source conditions
   Generalized reflection coefficient. Crank diagram. VSWR
   Lossy transmission lines. Dispersionless TLs. Special cases of general TLs.
   Smith chart
   TL matching. Quarter-wave transformers. Resistive pads
   Single-stub tuner I-Analytical solution
   Single-stub tuner II-Smith chart solution
   Uniform plane waves. Infinite current sheets
   Plane waves in lossy materials. Skin depth
   Poynting's theorem. Power flow and plane waves
   Uniform plane waves normally incident on a lossless half space
   Example of a normally incident UPW on a lossless half space
   Electromagnetic radiation and antennas
   Hertzian dipole antenna
   Near and far fields of the Hertzian dipole antenna. Radiation resistance
   Antenna radiation patterns. Directivity and gain
   Antenna effective aperture. The Friis equation.
Other Electronics 1 Tutorials
   Diode Tutorials
   BJT Tutorials
   MOSFET Tutorials
   Electronics II Tutorials
Free Electronics Tutorials
   Diode Tutorials
   BJT Tutorials
   MOSFET Tutorials
   Electronics II Tutorials
   Applied Electromagnetics Tutorials
   Microwave Tutorials
GATE preparation tips
   GATE Books & How to prepare
   Objective Solving Tricks
   Other GATE links
   IES exam preparation
   All about DRDO-SET
More Engineering Links
   Directory of coaching Institutes
   Govt engg college rankings
   Private engg college rankings
   Admission notifications for Mtech/PhD
   All Engineering Colleges in India
Poyntings Theorem Power Flow and Plane Waves

Poyntings Theorem Power Flow and Plane Waves.
A propagating electromagnetic (EM) wave carries energy with it. Physically this makes sense to us when we listen to the radio or talk on a cell phone. These types of wireless communications are possible because EM waves carry energy.
In these examples, some of this EM energy is used to oscillate electrons in the metal parts of the receiving antenna of our radio or cell phone, which ultimately results in wireless communications.
There is a precise mathematical definition of the time rate of energy flow (i.e., power flow) for EM waves. Before getting to this, we first need to digress briefly to first discuss Poynting’s theorem.
Poynting’s Theorem
Poynting’s theorem is a hugely important mathematical statement in electromagnetics that concerns the flow of power through space. We’ll derive it now for time-domain fields. We begin with Maxwell’s curl equations

Next, we employ the vector calculus identity
Ñ(`E´ `H) = `H (Ñ´ `E)- `E (Ñ´ `H)
Substituting (1) and (2) into (3) we have:

Using the constitutive equations `B = m`H , `D =e`E , and `J =s`E in (4) gives

assuming m ¹ f (t) and e¹ f (t)

thinking of the chain rule of differentiation. Consequently, using this result and a similar one for the E E/ t term, (5) becomes

This is the point form of what is called Poynting’s theorem. Lastly, we integrate this point form equation (6) throughout a volume V bounded by the closed surface S:

where V, S, and ds are related as

Applying the divergence theorem to the LHS of this last equation gives

where in moving / t outside of the integral we’re assuming that V is not a function of time. This result is called the integral form of Poynting’s theorem.
Discussion of Poynting’s Theorem
To understand the physical significance of the LHS of (7), we’ll begin by looking at the RHS, which has elements you’ve seen before in EE 381. In particular, the first and second terms in the RHS of (7) are the time rates-of-change of the stored energy in the magnetic and electric fields inside V. The third term is the Ohmic power dissipated in V due to the flow of conduction current. We can now interpret the RHS of (7) as the rate of decrease in the magnetic and electric power stored in V, and further reduced by the Ohmic power dissipated in V.
OK, so now here is the payoff: By the conservation of energy law, all of this represented by the RHS of (7) must equal the power leaving the volume through the bounding surface S. Consequently, the quantity`E ´`H in the LHS of (7) is a vector that must represent the power flow of the EM field leaving the volume V per unit area. We define this vector

The LHS is the power flow into S. The first term in the RHS is the increase in the stored power in the `H and `E fields in V, while the second term is the increase in the Ohmic power dissipated in V.
Power Flow for UPWs
We will now apply this Poynting vector concept to uniform plane waves. In Example N25.1, we found for a certain UPW that
`E(z,1) = -ay 43.501 cos (6p´108 t – 21.780z)V/m `H(z,1) = -ax 0.1 cos (6p´108 t – 21.780z)A/m
This UPW is propagating in the +z direction:

The instantaneous Poynting vector associated with this UPW using (8) is then
`S(z,t) = `E(z,t) ´ `H(z,t)= (-ay ´ ax )4.350 cos 2 (6p ´ 108t -21.780z)W/m2
such that
`S(z,t) = az 4.350 cos 2 (6p ´ 108 t -21.780 z)W/m2
The direction of this S (z,t ) is az . This indicates that the flow of power of this UPW in the same direction as the wave propagation: in the az direction.
Time Average Power Flow
Notice in (11) that while S (z,t ) oscillates in time, it has a nonzero time average value. (As an aside, this is one of the reasons why S (z) is not a phasor quantity.) In particular, using the trigonometric identity

The second term in the RHS oscillates in time (at twice the frequency of E and H ) and has a zero time average value, while the first term is constant and does not vary with time. Consequently, the time average value of this Poynting vector in

This UPW – on time average – carries or transfers power in the direction that the wave is propagating.
Sinusoidal Steady State Time Average Power Flow
It turns out that there is another way to calculate this time average Poynting vector for sinusoidal steady state, and to calculate it directly from phasor fields. We derive this expression beginning with (8) and writing E(t ) and H (t ) in terms of their phasor forms

For evaluating (14), note that

Rather, we can employ

in (14) to give

which we can write as

We can recognize the RHS as a term plus its complex conjugate. So, once again using (15)

Integrating this expression over one time period as in (13), we find from (16) that

Using this equation, we can compute a time averaged quantity ( AV S ) directly from phasor domain quantities (`E and `H ). For the UPW of Example N25.1, the phasor form of `E and `H Are

Using (17), the time average Poynting vector is then

This is the same result we found in (13) using the time domain forms of `E and `H . Here in (17) we find a time averaged quantity directly from the phasor domain fields. Neat!

Discuss about MOSFET here
Discussion Board for MOSFET
You can discuss all your issues on MOSFET here
Thread / Thread Starter Last Post Replies Views
fourier transform
plz send me the notes for fourier transforms its very urgent.

Posted By :-
Aug 31, 12:14:03 PM 0 59813
Fourier Transform
Sir I want tutorial on Fourier Transform.........

Posted By :-
Jul 15, 3:24:49 PM 0 62827
fourier transform
sir i want tutorial on fourier transform

Posted By :-
Jul 11, 10:08:19 AM 0 59199
match filter
heloo sir ,i want a tutorial for match filter.plz send it as soon as possible it is very urgent.

Posted By :-
Jun 4, 2:25:18 AM 0 80275
Electic circuits
I want lecture notes for single phase ac & 3phase ac circuits

Posted By :-
May 21, 11:32:46 AM 1 99714
electro statics
what is the work done to move a charge? derive an expression for assembling a configuration of point charges

Posted By :-
May 12, 8:28:18 AM 0 58673
electromagnetic waves
i want lcr circiut teorems derivations

Posted By :-
May 12, 8:23:58 AM 0 58150
i want oscillator frequency derivations for all. plz let me know from where i can get that

Posted By :-
May 4, 5:21:01 PM 0 59264
Equivalent circuit Models
I've got a question in one of my revision papers,

Explain the advantages of representing a transistor by means of an equivalent circuit circuit model

The only thing i can remember is that you can take complex circuits and break them down into simpler circuits which are easier to understand,

Is this the only advantage or do you have any more?

Please help!

Posted By :-
Apr 12, 6:33:57 PM 2 126000
temperature Vs reverse satuation current
I want to know the variation of reverse saturation current with the increase in temperature for both germanium and silicon diodes

Posted By :-
Jan 28, 7:17:23 PM 0 65220
communication system
analog and digital communication system, fiber optic communication, telecommunication technique and application, mobile communication

Posted By :-
Dec 17, 10:38:27 AM 0 71425

Posted By :-
Dec 14, 3:29:22 PM 0 71036
coaching in ies in indore
what about coaching

Posted By :-
Dec 7, 5:27:52 PM 0 75466

To start your new thread you must login here.
New user signup at ExamCrazy.com Exam Crazy
To reply/post a comment you need to login, Use your user name and password to login if you are already registered else register here

(Members Login)

  About us | Privacy Policy | Terms and Conditions | Contact us | Email: support@Examcrazy.com  
Copyright © 2014 Extreme Testing House, India. All rights reserved.  1398