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Can we apply superposition theorem in transient analysis of circuits? I don't think it can be used since during transient state the input and output relation is not linear and is rather explained by exponential functions like in case of RL and RC circuits. Please consider a case having two different sources with different frequencies.

John Cena
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    Yes, superposition can be used for transient analysis if the system is linear. Why is the input/output relationship non-linear? What non-linear components are in the circuit? 'Linear', in the systems sense, does not mean that the signals are related by a linear graph. – Chu Nov 26 '18 at 12:25
  • @Chu I mean to say that Q and V are defined by exponential functions not linear in RC Circuits when we do DC Analysis. – John Cena Nov 26 '18 at 12:44
  • @Chu, can you illustrate with an example. – John Cena Nov 26 '18 at 13:21
  • Read about the conditions for linearity - there are a number, but as an illustration of one of them: for a linear system, if you apply a step input, $\small x(t)$, and get an exponential response, $\small y(t)$, and then apply, $\small Kx(t)$ where $\small K$ is a constant, the response will be $\small Ky(t)$. – Chu Nov 26 '18 at 13:53
  • ... also, for a linear system, if you apply $\small x_1(t)$ to give $\small y_1(t)$; and apply $\small x_2(t)$ to give $\small y_2(t)$; then, applying $\small (x_1(t)+ x_2(t))$ will give $\small (y_1(t)+ y_2(t))$. From this you can see, for example, that any circuit that includes a diode is (potentially) non-linear. – Chu Nov 26 '18 at 14:00
  • ...also interesting to note that, from the systems definition of linearity, $\small y=mx+c$ is not a linear relationship. It is, of course, linear from the algebraic perspective. – Chu Nov 26 '18 at 14:12
  • Why it is not linear? – John Cena Nov 26 '18 at 14:28
  • From a systems definition, say you have $\small y=2x+3$. Then, $\small x=1$ gives $\small y=5$, and $\small x=2$ gives $\small y=7$. Clearly, doubling $\small x$ does not double $\small y$. Also $\small x=1+2=3$ does not give $\small y= 5+7=12$ – Chu Nov 26 '18 at 14:35
  • @JohnCena I like Grant Sanderson's essence of linear algebra series as a segue on linear systems. For a transient response example involving all those functions you hinted towards, you might look over some of: source-free, under-damped, parallel RLC with 2 initial conditions. – jonk Nov 26 '18 at 18:40
  • Is Gilbert Strang's Series of MIT Lectures in Linear Algebra also good? – John Cena Nov 26 '18 at 18:42
  • The equation $y=2x+3$ is not linear because it does not satisfy the principle of additivity and proportionality. You can find more details here: http://cbasso.pagesperso-orange.fr/Downloads/PPTs/Chris%20Basso%20APEC%20seminar%202013.pdf – Verbal Kint Nov 26 '18 at 21:19
  • Yes, Gilbert Strang's lectures are excellent. – Chu Nov 27 '18 at 00:27

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