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For the inverting op amp, I've seen the equation Vout/Vin = Hf/Hr

Hr is the same as Vr but without Vout. Why isn't Hf the same as Vf but without Vin?

What I mean is that

Vr = Vout[R1/(R1+R2)] and Hr = [R1/(R1+R2)]
Vf = Vin[R2/(R1+R2)] but Hf = -[R2/(R1+R2)]

V- = Vr + Vf.

But why Hf is negative ?

schematic

simulate this circuit – Schematic created using CircuitLab

Why is it like that? I've seen in the comments that it is about the input network but I didn't understand it. Can someone explain it to me a little bit differently?

Here is also the link for the last post I am referring to:
How does feedback factor works in equation V-/Vout

user331990
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  • Please define your terms. What do you mean by "Hf", "Hr", "Vf", and "Vr"? – The Photon Aug 07 '22 at 15:07
  • The only thing I know is that Vf is a forward factor and Vr is a feedback factor where V- = Vf+Vr. Also Hf and Hr I don't know. I took it from the post I linked. – user331990 Aug 07 '22 at 15:17
  • To include that the gain is negative (inverting amplifier). You could have Hf positive but then you have to have Aol (opamp open loop gain) negative. – G36 Aug 07 '22 at 16:12
  • I don't get it. So Vf and Hf aren't the same ? Where can I find Hf ? And why Hr and Vr are the same ? – user331990 Aug 07 '22 at 16:21
  • It is the same. But notice that we are dealing here with an inverting amplifier. Thus, Aol is negative. This "minus" only informs us that the output voltage is the 180-degree phase shift with respect to the input voltage. – G36 Aug 07 '22 at 17:03
  • Yes but as you said Vf is the same as Hf so what Aol has to do with Hf, as well as with Vf ? is Aol in the equation of Hf ? Also Aol as I remember is the open loop gain which was positive as I remember. – user331990 Aug 07 '22 at 17:11
  • Hf is positive but Aol is negative due to inverting amplification action. And if you assume that Aol is infinity. We can't forget about the "minus" sign. So we add "-" to Hf, because this is the input. – G36 Aug 07 '22 at 17:18
  • What I meant is that where Aol in some equations apply to Hf ? Because now I understand that Hf is positive. For example here : Vout/Vin=Hf[Aol/(1+Aol*Hr)]=Hf/[(1/Aol)+Hr]. Aol isn't negative. Also I don't know where this equation came from. – user331990 Aug 07 '22 at 17:26

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