RL Switching Theorm
RL Switching Theorm
(OP)
Any one knows about the 'RL Switching theorem',where a complicated RL switching circuit can be reduced to a single loop of resistance and inductance in series ?
i'm trying to use this theorem to find the circuit's time constant using step input function.
Any reference available?
Thanks for help
i'm trying to use this theorem to find the circuit's time constant using step input function.
Any reference available?
Thanks for help





RE: RL Switching Theorm
RE: RL Switching Theorm
TTFN
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RE: RL Switching Theorm
RE: RL Switching Theorm
TTFN
FAQ731-376: Eng-Tips.com Forum Policies
RE: RL Switching Theorm
RE: RL Switching Theorm
But how this arrangement can be reduced furthe to one resistor in seires with one inductor ?
RE: RL Switching Theorm
Every linear system has one. It gives the same sinusoidal steady state response, by superposition must also provide the same transient response (provided initial conditions are properly translated).
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(2B)+(2B)' ?
RE: RL Switching Theorm
1)Circuit one:
R1 in parallel with L1 and the combination in series with R2.
2)Circuit two:
R3 in series with L2.
RE: RL Switching Theorm
In the specific case you cited, if we tried to solve
R1*s*L1/(R1+s*L1) + R2 = R3 + s*L2
We cannot find R2 and L2 to satify the relation for all values of s.
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(2B)+(2B)' ?
RE: RL Switching Theorm
RE: RL Switching Theorm
We could analyse by Laplace transform as shown attached to determine the analytical form of the step response for systems 1 and 2. The Laplace form is not the same function of s and so the time form is not the same function of t. We cannot determine any R3 and L2 parameters for circuit 2 that will match general R1, L1, R2 (only in special cases like L1-> infinity could we get an exact match).
So, I guess I have not heard of an R-L switching theorem that allows reducing a general R/L circuit into a simple R-L circuit which performs the same under transients like step response. I don't think such a theorem exists if the requirement is exact match. I'll be interested to hear what you find.
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(2B)+(2B)' ?