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I am trying to calculate the input impedance of a multiple feedback low pass filter. What I need is the simplest symbolic expression so that later I fill in the values and get the impedence itself:

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I assume that I am on the right track in calculation, the thing is I can not go any further and simplify the equation more. Can someone please help with putting calculated $V_2$ (down in the writings) into equation $(2)$ and then put $V_{in}$ into equation $(1)$ and simplify it so that $i_1$ will be removed?

So the question is how to substitute and simplify to get a clear $Z_{in}$ with no current in the final equation.

Thanks in advance!

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    I am not sure if input voltage of negative input should be 0...I just took it by guess...hope I was right otherwise I am in deep ... :D2012-02-13

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I tried answering in electronics.stackexchange.com, but it seems that LaTeX isn't supported there. The derivation seems to be correct.

$v_2=\frac{i_1}{sC_2+\frac{1}{R_3}+\frac{sC_5R_3+1}{sC_5R_3R_4}}=i_1\frac{sC_5R_3R_4}{s^2C_2C_5R_3R_4+sC_5R_4+sC_5R_3+1}$

$Z_{in}=\frac{V_{in}}{i_1}=\frac{v_2+i_1R_1}{i_1}=\frac{sC_5R_3R_4}{s^2C_2C_5R_3R_4+sC_5R_4+sC_5R_3+1}+R_1$

Is this what you are looking for?

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    Hi Joel, thanks again your answer was correct (Checked it with LTSpice simulation)2012-02-25