Dear forum experts!
Please help explain the inconsistency between the algebraic solution and LTSpice simulation for a second order parallel circuit here. The parameters are:
\(
R=200 \Omega, L = 0.28H, C = 3.57 \mu F
\)
The capacitor ought to have an initial voltage of 50V. Hence, I us the .ic command in the sim to set the initial voltage for the identifier n001. This identifier seems to correspond with the node above the capacitor.
By calculating the circuit algebraically it can be shown that the RLC parameters result in an underdamped (oscillatory) case. The algebraic equation for the circuit is:
\( v(t) = e^{-700t} * (50 cos (714t) - 49 sin (714t)) \)
Below you can see the plot of this equation until 10 ms.
The image below shows the simulation. Besides some similarity in the curve shape, the values on the y-axis seem to be off by a factor of \( 10^6 \).
My assumption is that there is something wrong with the simulation, since the algebraic solution has been derived according to my textbook. Could someone please give a hint as to what could be wrong. Other circuits that I have simulated without the initial conditions seemed to be OK in LTSpice. Could it be that one should use the switch element in the sim, e.g., first to charge the capacitor with a source and then move a switch to a desired position?
Please help explain the inconsistency between the algebraic solution and LTSpice simulation for a second order parallel circuit here. The parameters are:
\(
R=200 \Omega, L = 0.28H, C = 3.57 \mu F
\)
The capacitor ought to have an initial voltage of 50V. Hence, I us the .ic command in the sim to set the initial voltage for the identifier n001. This identifier seems to correspond with the node above the capacitor.
By calculating the circuit algebraically it can be shown that the RLC parameters result in an underdamped (oscillatory) case. The algebraic equation for the circuit is:
\( v(t) = e^{-700t} * (50 cos (714t) - 49 sin (714t)) \)
Below you can see the plot of this equation until 10 ms.
The image below shows the simulation. Besides some similarity in the curve shape, the values on the y-axis seem to be off by a factor of \( 10^6 \).
My assumption is that there is something wrong with the simulation, since the algebraic solution has been derived according to my textbook. Could someone please give a hint as to what could be wrong. Other circuits that I have simulated without the initial conditions seemed to be OK in LTSpice. Could it be that one should use the switch element in the sim, e.g., first to charge the capacitor with a source and then move a switch to a desired position?