Estimation of electric circuits

Successive combination (impedances), current is the same

U=summation of voltages

Parallel connection of the impedances, the applied voltage is the same

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Important corrections

Operator equations for each closed circuit

How to close this system of operator equations?

For any branching point

And usage of the second Kirhhoff’s law

The role of the Duhamel integral

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Z(L)

U0

The first example and its solution.

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Z(R)

Z(R2)

Z(R1)

The second example and its solution

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The third example

The electromotive force (e.m.f) is acting on RLC circuit on the time segment 0<t< / and equals U0sin t.

Then it equals to zero. Find the current after the time t > / . For this case it is necessary to use the H-function

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Mathematical Appendix: How to solve the difference equations?

Example – Fibonacci numbers

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**Let us come back to “our” Filter. In this case it is convenient to find a solution of difference equation in the form

The constants are obtained from the first and the last difference equations:

After some algebraic manipulations we obtain finally

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In order to obtain the partial solution of the general formula we consider choke output filter

(дроссельный фильтр):

For it we have Z’=R+Ls, Z=1/Cs, U=U0

We find the original with the help of expressions given in pages 3 and 4.

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