# Obtaining transfer function

In the above circuit j(t)=u(t)A, where u(t) is the step function. Z is a component/circuit system with no independent variables and all initial values zero. The goal is to find the transfer function Z(s).

So I think I know the transfer function here is the laplace transform of the output divided by the laplace transform of the input. The output being u1(t) and input being j(t). u1(t) is also Z*j(t) and the laplace transform Z(s)*1/s. The laplace transform of the input is 1/s. So using the equation for the transfer function (Z(s)*1/s)/1/s you get Z(s), which does not seem right at all. What am I missing here?

The goal is to find the transfer function Z(s).

Z is a component/circuit system with no independent variables

The transfer function is independent of the input so the fact that it is a current step is irrelevant.

So the only information you have to express the transfer function is the output voltage and the input current. The ratio then is an impedance Z(s)=Z.

This you have verified as: $$Z(s)=\frac{U1_{out}(s)}{J_{in}(s)}=Z$$

I think you are missing the fact that you have the right answer. Understand that the impedance of any passive element is the transfer function of the element where voltage is the output and current is the input.

• Oh that's interesting. Makes sense now lol. Only thing that I don't understand is how you write the equation for the transfer function. I have never seen t(s) or n(s) before, so I'm kind of confused on that. Commented Feb 8 at 20:03
• Just some finger trouble with MathJax. The equation should make more sense now. @JohnnyB Commented Feb 8 at 20:06
• Oh lol. Thanks for the help @RussellH Commented Feb 8 at 22:11