Derive state space model of this circuit

the X matrix is the voltages across the 2 capacitors [2x1], so the A matrix should be [2x2] and B is [2x1].


Using nodal analysis I am getting 3 terms in my equations and I can't figure out how to eliminate vs and vout and replace it with c2.

emancole said:

Using nodal analysis I am getting 3 terms in my equations and I can't figure out how to eliminate vs and vout and replace it with c2.

Click to expand...

According to the thread title, you're likely mixing two different procedures: The "Space State" matrices are for stability analysis whereas matrices for the "Nodal Analysis" are for transient analysis and uses another completely different approach for obtaining its values, in which case it would be allowed a matrix with 3 or even more columns (eg. Modified Nodal Analysis).

By the way, you did not specify exactly what equations these are. Following the usual nomenclature for the matrices representing the state space of linear electric circuits (A,B,C,D), for matrix A one must take into account only the reactive components, in the case, the 2 capacitors above, and therefore must have dimension 2x2. The matrix representing the input/output voltage ratio, C should be built with unitary dimension (1x1) or rather, a scalar, once there is only 1 input and 1 output in the above circuit.