I am trying to model a simple RC circuit with one resistor and one capacitor using Simulink. I was given this equation G(jw)=1/(1+jw*tau), tau=RC, and need to convert it to this form in the image: v_dot_o = 1/RC(Vi-Vo).I have also attached a longer image with more detailed steps of how to get to the final equation, but I don't get how a derivative of Vo has appeared out of nowhere somewhere in the middle of the procedure. Please show as many steps as possible and explain the steps if necessary. I'm purely intending to learn from the process, so it'd be really nice if you could explain how each step was done! 1We are given the transfer function, G(j@) =T = RC.1+ jøt'Simulink works in the Laplace or s-domain, so make the substitu-tion:G(s)1T = RC1 + STWe know by the definition of a transfer function that v,Recall also that v, and v; vary with time in the time domain, andG(s) * Vị-are functions of s in the s-domain.So we can write our relationship asV, + sv,RC = v;Remember that sv, in the Laplace domain is the first derivative inthe time domain. So we can think of this as:Vo + v,RC = v;To build a Simulink model containing derivatives, it's often agood start to isolate the highest level derivative of the desired output. 1vo(v; – v)=RC

The transfer function of a simple R-C circuit is given as G(s)=11+sτ ...(1), here τ=RC. The…

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Introductory Circuit Analysis (13th Edition)

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Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

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I am trying to model a simple RC circuit with one resistor and one capacitor using Simulink.

I was given this equation G(jw)=1/(1+jw*tau), tau=RC, and need to convert it to this form in the image: v_dot_o = 1/RC(Vi-Vo).

I have also attached a longer image with more detailed steps of how to get to the final equation, but I don't get how a derivative of Vo has appeared out of nowhere somewhere in the middle of the procedure. Please show as many steps as possible and explain the steps if necessary. I'm purely intending to learn from the process, so it'd be really nice if you could explain how each step was done!

1
We are given the transfer function, G(j@) =
T = RC.
1+ jøt'
Simulink works in the Laplace or s-domain, so make the substitu-
tion:
G(s)
1
T = RC
1 + ST
We know by the definition of a transfer function that v,
Recall also that v, and v; vary with time in the time domain, and
G(s) * Vị-
are functions of s in the s-domain.
So we can write our relationship as
V, + sv,RC = v;
Remember that sv, in the Laplace domain is the first derivative in
the time domain. So we can think of this as:
Vo + v,RC = v;
To build a Simulink model containing derivatives, it's often a
good start to isolate the highest level derivative of the desired output.

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