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Equivalent impedance (Read 4240 times)
adesign
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Equivalent impedance
May 30th, 2007, 4:53am
 
Dear all,

Please have a look at the attached circuit arrangement.
What would be the equivalent impedance at node N?

Regards,
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aamar
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Re: Equivalent impedance
Reply #1 - May 30th, 2007, 5:40am
 
Hallo,

In case of an ideal amplifier, with infinite input impedance then  at N one can see approx. A*Z2, which results from the miller effect.

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aamar
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mg777
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Re: Equivalent impedance
Reply #2 - May 30th, 2007, 6:23am
 

It's Z2/(A+1), it's only capacitances that get multiplied by (A+1) because their impedance is 1/sC.

The interesting thing is what happens when we put in a frequency response for A, including the case of positive feedback.

M.G.Rajan
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aamar
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Re: Equivalent impedance
Reply #3 - May 30th, 2007, 8:45am
 
yes you are right, thanks for the correction.

aamar
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adesign
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Re: Equivalent impedance
Reply #4 - May 30th, 2007, 9:05pm
 
mg777 wrote on May 30th, 2007, 6:23am:
It's Z2/(A+1), it's only capacitances that get multiplied by (A+1) because their impedance is 1/sC.

The interesting thing is what happens when we put in a frequency response for A, including the case of positive feedback.

M.G.Rajan


Could you explain it through circuit analysis?

I did the analysis as given in the attachment and it's coming wrong. Please correct me where I made a mistake.

Regards,
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aamar
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Re: Equivalent impedance
Reply #5 - May 30th, 2007, 11:30pm
 
Hallo,

according to the assumption which we assumed at first, the input impedance is infinite and output impedance is zero then you should ignore the first part in your current equation because it is zero, remains for you the second term, and as no current flows in Z1 then V1=V, then you can simplify the equation as follows

0+(V1+AV1)Z2= I1     =>   Zeq=V1/I1= Z2/(1+A)

but next time you should not do it this way. It is better to redraw your schematic such that your input is on the left side and output on the right side (the traditional way), then you will notice that there is a feedback in the circuit and as the gain is negative it comes in mind directly the miller effect (then use miller simplification directly rather than calculating). But in your case your forward network is not only the amplifier but also the series impedance Z1, so one should calculate the transfer characteristics of both together at first and this is the case which Rajan mentioned (I made it simpler by assuming infinite input impedance of amplifier) , but it is not always valid, as the impedance is frequency dependent and then you should consider that all these impedances including the input impedance of the amplifier will be different, that is why it is interesting to study the case.

Best regards,

aamar
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adesign
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Re: Equivalent impedance
Reply #6 - May 30th, 2007, 11:55pm
 
That's gr8 aamar. Thank you very much.
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