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I'm studying for an exam and as a part of a question I am given a transimpedance amplifier and need to explain/show how the current gets converted to voltage.

Task

That's fairly easy, however, the op-amp has a Vb connected to the non-inverting input, which makes my answer differ from the official one.

My logic says that the inverting input is virtually on Vb, and then when we add the voltage drop over R1, output is V1 = Vb - I * R1.

The official answer just says V1 = - I * R1.

Is my understanding flawed? Does the non-ground reference affect the output?

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    \$\begingroup\$ Simplest answer is to specify that Vb is the reference point for measuring V1. \$\endgroup\$ Mar 28, 2016 at 21:11
  • \$\begingroup\$ That is why the answers differ! Thanks! Due to a language barrier I didn't think that Vb was used as a reference to the answer as well. When I read the question again, it is oh-so clear :) \$\endgroup\$
    – Alfis
    Mar 28, 2016 at 21:16

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Yes your answer is correct. if Vb was grounded then Vb=0, substitute this in your equation you get the equation below which matches.

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  • \$\begingroup\$ I'll accept this as an answer, but as I noted in another comment, when we Vb is taken as a reference for the V1, the official answer is correct. I assumed that 0V was a reference for a final answer. Thanks! \$\endgroup\$
    – Alfis
    Mar 28, 2016 at 21:17
  • \$\begingroup\$ Yeah if Vb=0 then you do get the needed answer that you have specified. Also try simple nodal analysis videos related to opmaps in YouTube, you might understand it better. This video series in youtube is good for a start. youtube.com/watch?v=Q3RMFpGGcZM Simple nodal analysis are explained here with the opamp basics. \$\endgroup\$ Mar 28, 2016 at 21:45
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There is a simple and logical way for finding the answer: Superposition. We have two "signal" sources - and the corresponding output voltages must be superimposed.

1.) VB=0: Vout1=-I*R1

2.) I=0 (open circuit): Classical nin-invereting gain with 100% feedback (unity gain): Vout2=VB.

3.) Vout=VB-I*R1

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