# Nonzero initial conditions for a circuit solved using superposition theorem?

Suppose I have a linear circuit with 3 voltage sources Vin1, Vin2, and Vin3 in it, and one voltage of interest Vout. It's common practice to solve it using the superposition theorem, so this will lead to a set of 3 equations: $$V_{out,1}=f_1(V_{in1})$$ $$V_{out,2}=f_2(V_{in2})$$ $$V_{out,3}=f_3(V_{in3})$$ Then $$V_{out}=V_{out,1}+V_{out,2}+V_{out,3}$$ However, it seems each of the equations individually must have their own initial conditions, and naturally (in my case anyway) only the initial conditions relating to the total circuit are known - not their breakdown into each "layer".

What I mean is that I know $$V_{out}(t=0)=V_0 \neq 0$$ and $$\frac{dV_{out}}{dt}(t=0)=0$$ But neither $$V_{out,1}(t=0)$$ $$V_{out,2}(t=0)$$ $$V_{out,3}(t=0)$$ nor $$\frac{dV_{out,1}}{dt}(t=0)$$ $$\frac{dV_{out,2}}{dt}(t=0)$$ $$\frac{dV_{out,3}}{dt}(t=0)$$ (example of 2nd order system)

Is there a relationship between what I do not know (the initial conditions of the subcircuits) and what I do know (the initial conditions of the total circuit)?

• Sorry. But I didn't get the question. Are you asking that whether the initial condition for each 'layer' will be [Vo/3,DVDTo/3]? – nidhin Feb 23 '15 at 15:27
• My bad, reformulated the question – Mister Mystère Feb 23 '15 at 15:47