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KCC's Quizzes: AQQ239 about a High gain & high input resistance inverting amplifier

High input resistance and high gain Inverting amplifier can be needed in some applications.

In such case an even larger feedback resistor is required. Too large resistors have issues like precision, availability and excessive stray capacitance.

The here below circuit is a way to maintain both a high input resistance, a high gain and still using not too large feedback resistors.

Questions:

  1. What is the input resistance of the above circuit?
  2. What is the gain Vout/Vin ?

Good luck and try to be among the first!

And communicate this around you (colleagues, partners, customers and friends)!

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[edited by: StephenV at 4:26 PM (GMT -4) on 14 Jul 2023]
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  • So, and here are the official (and hopefully) correct answers:

    1. Rin = 100k. Justification: by assuming the opamp is well in its linear mode, the potentials at V- and V+ are equal. Since there is no current in the 51k resistor, V+ is 0 voltTherefore, Vin/In is 100k.

    2. At node V’, the current flows must be balanced:

    Vin/100k = V’/1k +(V’-Vout)/100k (eq 1)

    V+ being equal to V- we have then V’ = -Vin (eq 2)

    By injecting eq2 in eq 1 we get : Vin/100k = -Vin/1k – Vin/100k – Vout/100k

    By multiplying by 100 the whole expression and by simplifying: 102 Vin = -Vout

    We have the gain = Vout/Vin = -102

    So congratulation to all the ones having found the solutions and big applause for the 4 first ones:

     from Cavite, Philippine

     from Germany

     from Bangalore, India

     from Milan, Italy

    Now, be prepared for the next coming challenge!

    Kuo-Chang

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  • So, and here are the official (and hopefully) correct answers:

    1. Rin = 100k. Justification: by assuming the opamp is well in its linear mode, the potentials at V- and V+ are equal. Since there is no current in the 51k resistor, V+ is 0 voltTherefore, Vin/In is 100k.

    2. At node V’, the current flows must be balanced:

    Vin/100k = V’/1k +(V’-Vout)/100k (eq 1)

    V+ being equal to V- we have then V’ = -Vin (eq 2)

    By injecting eq2 in eq 1 we get : Vin/100k = -Vin/1k – Vin/100k – Vout/100k

    By multiplying by 100 the whole expression and by simplifying: 102 Vin = -Vout

    We have the gain = Vout/Vin = -102

    So congratulation to all the ones having found the solutions and big applause for the 4 first ones:

     from Cavite, Philippine

     from Germany

     from Bangalore, India

     from Milan, Italy

    Now, be prepared for the next coming challenge!

    Kuo-Chang

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