## mathavraj 2 years ago A particularly important ramification of the property of linearity is expressed in the notion of equivalent circuits. To wit: if we are considering the response of a network at any given terminal pair, that is a pair of nodes that have been brought out to the outside world, it follows from the properties oflinearitythat,ifthe networkislinear,the output at a singleterminalpair(either voltage or current) is the sum of two components: 1. The response that would exist if the excitation at the terminal pair were zero and 2. The response forced at the terminal pair by the exciting voltage or cur

1. mathavraj

2. mathavraj

@stgreen could you help me..i cant get these points..

3. stgreen

yea it makes sense...its about natural and step response of circuits

4. mathavraj

|dw:1360488103509:dw|i found this in the explanation for thevenins theorem...V=Voc+iRth which one is the natural one and step one?

5. stgreen

when we talk about natural and steo response, we refer to capacitors/inductors mostly..natural response means the behavior of a network when there is no source...(e.g. capacitors connected in a circuit having no voltage/current source..the initial energy stored in capacitors will drive the circuit...means the circuit is source-free and its such a behaviour is said to be natural response)

6. stgreen

step response is the response when a source will try to charge the inductor/capacitors such that after a long time, the capacitors/inductors connected will be charged. if the capacitors/inductors have high initial voltage/current than what the source has to offer they can discharge until it reaches a steady charged state with a lower voltage/current.

7. stgreen

i don't know if it makes sense to you...depends on which grade you are studying

8. mathavraj

im in first year studying about thevenins theorem...

9. stgreen

ok if you didn't get it....i'll try to make it simpler.what say?

10. stgreen

thevenin theorem is little bit different thing

11. mathavraj

ok please explain..im struggling with it..

12. stgreen

ok you can look at it this way....suppose we have a network, and we are interested in the output at two terminals of it (forget what's inside the circuit...it may have resistor,capacitors,inductors and so on) the point is....the output,we are interested in,is the sum of two terms...one terms comes when we have no source voltage/current applied to the circuit and the circuit drives on the energy initially stored in the circuit (like we connected charged capacitors in the circuit and measured the output)....now the second term comes when we excite the network by a voltage/current source..and measured the output again...sum both the terms and we get the general output response...

13. stgreen

don't confuse it with thevenin theorem.... thevenin theorem is just a simplification of a circuit..it says we can replace a whole linear circuit just by a resistor and a voltage/current source

14. mathavraj

ok tnx..

15. warrenvsmith

it maybe helpful to see the math related to non electrical system to understand the dynamic, http://ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011/unit-ii-second-order-constant-coefficient-linear-equations/exponential-response/ , the 16 min video "inhomogeneous second order DEs definitions and models" explains the math using both the spring mass dash-pot physical system model and a circuit model. focusing on the key point of driven vs non-driven, basically that the equation itself is set up in such a way that the non-driven will yield zero(the natural case) and driven will yield some non-zero result(the step case), I am still learning myself so I am sure that my explanation is inadequate(possibly wrong) but the professor in the link explains it very well.

16. warrenvsmith

I should have said yield zero for the "second" term above.