# Why is Hf negative while Vf is positive? Aren't they the same but without Vin?

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 ? 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

• Please define your terms. What do you mean by "Hf", "Hr", "Vf", and "Vr"? Aug 7 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. Aug 7 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 7 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 ? Aug 7 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 7 at 17:03