Input impedance of an opamp

Discussion in 'General Electronics Chat' started by mentaaal, Nov 13, 2008.

  1. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    Hey guys,

    We covered input and output impedances for an opamp and i understand the maths of it and also i can see that the formula appears to behave properly but i take issue on some things.

    A pdf containing the formula and info i am referring to can be found at: zebu.uoregon.edu/~rayfrey/431/notes9.pdf

    The main problem that i am having is with the formaul for input impedance: Zin = R1(1+BAol)
    where R1 is the input resistance of the opamp itself

    So if Rin and Rf(which is the feedback resistor) are equal, B will be 1.
    Then by this formula, Zin will be R1(1+Aol).
    In a normal inverting amplifier, following the "golden rules" the input current is (Vin - 0)/Rin

    Zin is then Vin/(Vin/Rin) = Rin

    So i dont understand how this generalised formula for input impedance can apply to an inverting amplifier?
     
  2. The Electrician

    AAC Fanatic!

    Oct 9, 2007
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    On what page of the document does this formula appear? A search of the document for the symbol Aol didn't find anything.
     
  3. mindmapper

    Active Member

    Aug 17, 2008
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    I do not agree with the document on this part:
    We can use our rules to analyze this circuit. Since input + is connected to ground, then by rule 1, input is also at ground. For this reason, the input is said to be at virtual ground.


    Input V- is not virtual ground because there is no voltage between V+ and V-. The reson why V- is at virtual ground is that the signal current from the input (through R1) is the same size as the current coming from the output of the opamp (through Rf). Since both current has different sign the resulting voltage in the meetingpoint is 0V. No current is floating between V+ and V- since the input impedans of the opamp is very high (ideal opamp).
    The voltage between V- and V+ is in this case 0V because V+ is grounded as is V- (virtual ground). If you remove the ground from V+ and connect it to a voltage (as in a summing amplifier) you can measure the voltage between V+ and V-. Rule 1 is IMHO wrong!
     
    Last edited: Nov 13, 2008
  4. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    Apologies, we refer to the open loop gain as Aol in college. Where it is referred to here as A
     
  5. mindmapper

    Active Member

    Aug 17, 2008
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    I did not se that you said that R1 is the resistans of the OP itself.

    In my explanation R1 is the resistor the signal is floating through to reach the V- input of the op. Since V- is at virtual ground it is easy to see that the input resistans that the signal sense is nothing else than R1.
     
  6. The Electrician

    AAC Fanatic!

    Oct 9, 2007
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    Again I ask, on what page is this material you are questioning?
     
  7. Distort10n

    Active Member

    Dec 25, 2006
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    It's Eq. 42 on page 7. :rolleyes:
     
  8. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    Sorry!

    The equation in question is equation 43 on page 41. We were given this exact formula today in college as well. Zin = Ri(1+AB)
    Where Ri is the input resistance to the opamp and A is the open loop gain.

    Taking a standard inverting amp like that on page 36 of this reference, the author makes the point that zin is merely R1 (due to action of virtual ground) which appears to make perfect sense. But when you utilise this supposedly generalised formull for Zin, the resistance value is likely to be ALOT bigger.

    Hence the confusion
     
  9. Distort10n

    Active Member

    Dec 25, 2006
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    The generalized impedance formula is illustrating that the negative feedback is increasing the input impedance of the amplifier. This happens regardless if it is a non-inverting or inverting configuration.

    The confusion is that R1 is not the input impedance of the amplifier when an amplifier is configured in an inverting configuration. Think of it as a system input impedance.

    In practice this can be a major difference in choice of configuration. If the low impedance (R1) of an inverting configuration can load your source then you will require a non-inverting amplifier for high input impedance.
     
  10. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    I was under the inpression that Zin was the input impedance to the whole amplifier. As in the input impedance that the signal Vin would see if it were connected to R1?
     
  11. Distort10n

    Active Member

    Dec 25, 2006
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    In the non-inverting case Zin is the actual input impedance of the amplifier. The input signal is connected directly to V+.

    In the inverting case Zin is R1 and not the input impedance of the amplifier, but the input impedance of the inverting amplifier does increase with negative feedback.

    Since Zin = Vin/Iin these must be true.

    What leads to the confusion I think is that you always see the derivation for the non-inverting configuration but never for the inverting configuration. For the inverting configuration literature states simply, but not thoroughly, Zin = R1.

    I will check one of my old op-amp books to see if the full derivation for the inverting case is shown. Honestly, the input impedance is NOT just R1 but the equations show that you can approximate it as such. I think that is because the Common mode impedance is very high and is in parallel with R1.
     
  12. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    Thanks distortion, you are most helpful. What confused me was this formula is referred to as general which suggests that it would work for inverting and non inverting.

    I do agree that the behaviour of the formula works fine as i verified this myself. It was just that particular case which sprung to mind that didnt work.

    I will see what my lecturer says on this today and post it here tonight.
     
  13. Distort10n

    Active Member

    Dec 25, 2006
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    I made a mistake which seems so obvious now. Feedback for the inverting case reduces the input impedance seen at the summing junction which is why virtual ground is so helpful. This is why the Input impedance ends up being R1.

    I have attached several pages from the IC Op-Amp Cookbook by Walter Jung. It does not fully derive the equations as I was hoping for, but at least they are mentioned.
     
  14. Distort10n

    Active Member

    Dec 25, 2006
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    I rotated the pictures for easy viewing.
     
  15. mentaaal

    Thread Starter Senior Member

    Oct 17, 2005
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    Thanks distortion. I understand now. If anyone else is following this: i asked my lecture about this as well. He was expalaining that there are four types of feedback, series-series, series-parallel,parallel-series and parallel-parallel depending on the way that the feedback is connected. For the inverting amplifier its actually parallel-parallel and the feedback equation in question is for series parallel.

    Thanks for all your help guys!
     
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