Oh dear. I have touched a nerve. I think that having treated me like a child, you expected me to just put up with it.

It's unfortunate that you think that having mistakes you are making pointed out to you constitutes being treated like a child.

So you think the internet is wrong,

As I said, that first equation in the screenshot you took has a mistake -- one of the same mistakes you made.

Do you know what the correct answer is?

Yes, because I analyzed the circuit and derived the correct result.

I've worked thru the previous example
V2 (gm - s·C)·R1·R2
---- = ---------------------------------------
I1 s·C·(gm·R1·R2 + R1 + R2) + 1
and rhat is correct.

What previous example?

As regards the three questions, V2/II should be ohms which the answer would be with, as they say, a large Kv value (1/(SC)).

The second equation they give is correct. It's the first one that has the mistake.

Again:

What do the units of V2/I1 need to be? Answered: resistance (e.g., ohms)

What are the units of the numerator (-Kv)?

What are the units of the denominator (1 + Kv·s·C)?

Hint: That last one has two terms, in order to add two things together, they must have compatible units. So are the units of '1' compatible with the units of 'Kv·s·C'?

 

Where is that?

 

Where is that?

Where is what? I'm not following what you are referencing?

 

http://www.ecircuitcenter.com/Circuits_Audio_Amp/Miller_Integrator/Miller_Integrator.htm:

Where is that?

Sorry, I was replying to ericgibbs.

I've worked thru the previous example
V2 (gm - s·C)·R1·R2
---- = ---------------------------------------
I1 s·C·(gm·R1·R2 + R1 + R2) + 1
and that is correct.
This formula can be found in URL above.

Regarding the numerator and denominator, presumably Ecircuit is reputable and should not be publishing information that is incorrect!

 

http://www.ecircuitcenter.com/Circuits_Audio_Amp/Miller_Integrator/Miller_Integrator.htm:

Where is that?

Sorry, I was replying to ericgibbs.

Thanks for the clarification.

Regarding the numerator and denominator, presumably Ecircuit is reputable and should not be publishing information that is incorrect!

If I'm reading your meaning here correctly, you are saying that you don't think you need to consider whether the numerator and denominator are dimensionally sound based on the fact that they were published by a reputable website.

But, if you are going to just accept what they publish because they are reputable, then why the thread? Wasn't your whole point of the thread to get someone to confirm the correctness of the formula? As you stated in your first post, "Of course, the formula may be incorrect, it's not unheard of."

Very few resources, be it websites or textbooks, are error free. Everyone makes mistakes, which is why it is extremely valuable to habitually be doing sanity checks on the sources we use.

If a result is not dimensionally consistent, then you know there is a problem with it. You need to be able to spot these things, otherwise you end up going down rabbit holes trying to use (or in this case prove) something that you can determine, at a glance and in just a few seconds, can't be correct. Knowing that something is demonstrably wrong is a huge first step in trying to figure out what is correct.

So, again...

What are the units of the denominator (1 + Kv·s·C)?

Hint: That last one has two terms, in order to add two things together, they must have compatible units. So are the units of '1' compatible with the units of 'Kv·s·C'?

I am doing everything I can to aim a huge, blinding spot light right at the problem for you to see!