Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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:

enter image description here

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!

enter image description here

share|improve this question
    
I know how painful those equations will be ; you will probably have a more successful answer if you post this on physics stack exchange or something. –  Patrick Da Silva Feb 13 '12 at 7:02
    
I agree with Patrick: I think physics.stackexchange.com would yield you better answers. –  William Feb 13 '12 at 7:16
2  
Actually from the description it sounds like the question is just asking about some algebraic manipulations, namely how to substitute $V_2$ into $V_\text{in} = V_2 + i_1R_1$ and simplify it. If that's the case it will be off topic on Physics. –  David Z Feb 13 '12 at 7:28
2  
Cross-posted to EE.SE; voted to close here. –  J. M. Feb 13 '12 at 8:31
2  
You waited less than a day, as in "Rome wasn't built in a." –  Gerry Myerson Feb 13 '12 at 11:50
show 4 more comments

1 Answer

up vote 3 down vote accepted

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?

share|improve this answer
2  
Thanks a lot! I'll check the values and report back if this is correct! –  Sean87 Feb 13 '12 at 13:06
1  
Hi Joel, thanks again your answer was correct (Checked it with LTSpice simulation) –  Sean87 Feb 25 '12 at 22:18
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.