Hello everyone! Please help me to understand some doubts about this method. ( Open-circuit time constant method https://en.wikipedia.org/wiki/Open-circuit_time_constant_method).
First of all it looks like it doesn't always work for all cases. Actually this wikipedia page isn't all of it but unfortunately I don't have an english explanation for you so I hope you already know something about it.
The problem is that for a general \(W(s) = \frac{N(s)}{D(s)}\) this method allows me to find the coefficients of \(D(s)\) of this form:
\(D(s) = e_n s^n+e_{n-1}s^{n-1}+...+e_1n+1\)
or
\(D(s) = s^n+b_{n-1}s^{n-1}+...+b_1s+b_0\)
But if I have a pole in the origin? I can't know it first. I also can't use the first one because it has the known term equal to 1 but by trying out them both I could find out that in the second case \(b_0\) probably would be zero and this is possible as b are coefficients that are sums of fractions with resistance and capacitance at the denominator so it's enough to have an open circuit case (see the solving method). So it could give me the pole in the zero but then there's another problem: it has \(s^n\) with unitary coefficient which is again not true for any RC circuit.
So it seems like there's no way to use it in these cases and therefore it means that it doesn't work in general so it's useless when dealing with an unknown circuit as a simpler way to find the transfer function? But I can't find anywhere this comment. Also I know it's usually used for dominant pole approximation in passband studies as it semplifies the problem but there we know something before solving.
So I feel like I'm wrong. I hope someone could help me here.
Maybe these two polynomial forms are only particular cases of general time constant method? But these are the cases I've studied. Also that wikipedia page is explained a bit different so I can't understand it well but I put it anyway here for you maybe you know better and it's the only page in english that I found to be closer to what I know.
First of all it looks like it doesn't always work for all cases. Actually this wikipedia page isn't all of it but unfortunately I don't have an english explanation for you so I hope you already know something about it.
The problem is that for a general \(W(s) = \frac{N(s)}{D(s)}\) this method allows me to find the coefficients of \(D(s)\) of this form:
\(D(s) = e_n s^n+e_{n-1}s^{n-1}+...+e_1n+1\)
or
\(D(s) = s^n+b_{n-1}s^{n-1}+...+b_1s+b_0\)
But if I have a pole in the origin? I can't know it first. I also can't use the first one because it has the known term equal to 1 but by trying out them both I could find out that in the second case \(b_0\) probably would be zero and this is possible as b are coefficients that are sums of fractions with resistance and capacitance at the denominator so it's enough to have an open circuit case (see the solving method). So it could give me the pole in the zero but then there's another problem: it has \(s^n\) with unitary coefficient which is again not true for any RC circuit.
So it seems like there's no way to use it in these cases and therefore it means that it doesn't work in general so it's useless when dealing with an unknown circuit as a simpler way to find the transfer function? But I can't find anywhere this comment. Also I know it's usually used for dominant pole approximation in passband studies as it semplifies the problem but there we know something before solving.
So I feel like I'm wrong. I hope someone could help me here.
Maybe these two polynomial forms are only particular cases of general time constant method? But these are the cases I've studied. Also that wikipedia page is explained a bit different so I can't understand it well but I put it anyway here for you maybe you know better and it's the only page in english that I found to be closer to what I know.
Last edited:
