Electric circuit how to check linearity

[Physicslearner500039]

Hi all,

I found the following equations for the electric circuit shown
Vc(t) = - 1/(R2*C) * Vc(t) – 1/C * i(t) --------------------1
Vt(t) = Vc(t) – R1*i(t) ------------------------------------ 2

I have the following questions
1.The first equation should be dVc(t)/dt = -1/(R2*C) * Vc(t) – 1/C * i(t) . Am I correct on this?
2.The discrete time equations are given in the documents as
Vc,k+1 = exp(-T/(R2*C)Vc,k – R2 * (1 – exp(-T/R2*C)*ik --------------- 3
Vt,k = Vc,k – R1*ik; ------------------------------------------------------------- 4

I can understand the 4th equation, but I cannot understand the 3 equation, could someone guide me how to do this conversion from continuous to discrete.
What is the “T” that is used?

3.Is this system linear? From little understanding I have, when an exponent is involved generally it is nonlinear. What is the methodology I should adopt to check whether a system is linear or nonlinear?

thanks in advance,
Regards

 

[anorlunda]

I can understand the 4th equation, but I cannot understand the 3 equation, could someone guide me how to do this conversion from continuous to discrete.
What is the “T” that is used?

The T is probably time step size.

There is no general way to transform continuous to discrete. For example, the Euler approximation difference equation is:

df(t)/dt = f(T)-f(0)/T where T is the time step size, t is time, and f(t) is any function of t.