Inverting op amp feedback parameter B

IgnacioSS · Jul 10, 2018

I have a question:
In an Inverting op amp, Which is the feedback parameter B?
According to this source https://ocw.mit.edu/courses/electri...ent-spring-2006/lecture-notes/22_op_amps1.pdf (p. 10), is Ri/Rf (Which I think is the right answer). But according to other sources, it seems to be Ri/(Ri+Rf), like in the Non-inverting topology.
Which is the right answer?

Harald Kapp · Jul 10, 2018

Buenos dias, Ignacio.

I refer to equation 1.7 in your reference and the following paragraph where it states."The feedback parameter β depends only on the characteristics of the feedback network." This means, different feedback networks have different values for β.

When you scroll a bit further you'll find on page 10 that β = R1/R2 for the inverting circuit.
Equation 1.19 on page 15 states G = 1+R1/R2
which is equivalent to G = R2/(R1+R2) and thus β = (R1+R2)/R2

You see: different circuit topologies, different equations (values) for B.

Saludos,
Harald

IgnacioSS · Jul 10, 2018

¡Gracias!

LvW · Jul 10, 2018

Harald - I have some problems with your contribution.

* β = R1/R2 is NOT correct.

* β = (R1+R2)/R2 can also not be correct because a passive feedback factor can never be >1.

Ignacio: The expression for the feedback factor on page 10 is wrong!
In both cases - inverting and non-inverting amplifier - we have the same feedback factor β = R1/(R1+R2)

Harald Kapp · Jul 11, 2018

I don't like it but I have to confess that I was wrong. The document cited mixes feedback factor and gain.

IgnacioSS · Jul 11, 2018

This video explains it

LvW · Jul 11, 2018

Yes - and these explanations can also be found in each relevant text book.
Therefore, my recommendation: Before asking similar questions consult a serious textbook and do not blindly rely upon any internet-sources.

IgnacioSS · Jul 11, 2018

G seems to be something call "input damping factor": https://electronics.stackexchange.c...inbeta-derivation-for-the-inverting-amplifier
At the end of the day, Acl is just the superposition of the G (Rf/(Ri+Rf)) and B (Ri/(Ri+Rf)) factors:

V- = Vout B
V- = Vin G

IgnacioSS · Jul 11, 2018

Thank you very much for your recommendation.

I'm an amateur who has started studying on his own by reading "The Art of Electronics".
As this book does not usually develop the concepts mathematically, and I like to know where the formulas come from, I try to find it on the internet.
But maybe that book is not the best for me. Maybe you can recommend me a better one.

LvW · Jul 11, 2018

IgnacioSS said:

G seems to be something call "input damping factor": https://electronics.stackexchange.c...inbeta-derivation-for-the-inverting-amplifier
At the end of the day, Acl is just the superposition of the G (Rf/(Ri+Rf)) and B (Ri/(Ri+Rf)) factors:
V- = Vout B
V- = Vin G
Click to expand...

Yes - it is common practice to apply the general feedback model as shown in your post#6.
Here, the input signal Vn that arrives directly at the inverting (minus) input node of the active device (opamp) , consists of two parts (superposition): Vn=Vn1+Vn2.
One part is derived from the output called beta: Vn1=beta*Vout (assuming Vin=0)
The other part is derived from the signal input: Vn2=G*Vin (assuming Vout=0)
Note that for non-inverting opamp applications, we have G=1.
Together with the given feedback formula for the closed loop gain Acl and assuming Aol infinite, we arrive at the expression for the closed-loop gain Acl=-G/beta.
Alternatively, with infinite Aol we can set Vn=0 (Vn1=-Vn2) from the beginning and immediately arrive at the same expression.

My favorite book is Sergio Franco: "Design with Operational Amplifiers."
However, there are many similar books on the market - some of the are also availbale via internet (for example Roberge: "Operational Amplifiers").

IgnacioSS · Jul 11, 2018

Done: downloaded.
Thank you very much again for your recommendations.

Inverting op amp feedback parameter B

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