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Having trouble with Double Null Injection for nEET

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Andrew_K:
Hi,

I'm trying to learn about the Extra Element Theorem, and the N Extra Element Theorem.

In general, this method makes sense to me. But I'm having some trouble understanding Double Null Injection, particularly a few cases that I get when I try to use this method.


1) According to "Fast analytical techniques for electrical and electronic circuits" by Vorperian Vatche, we should never need to deal in terms of the input voltage. However, there are a few cases where I get something like this:



Conveniently, in the books and videos, and even in other books or courses, the circuits are always constructed such that this is never an issue.

2) There are a few situations I can think of where the null injection impedance won't make sense for the given term. For example:



If the "extra element" here is an inductor, this makes perfect sense.

$$i_{t} = 0$$, therefore $$\mathscr{Z} = \frac{v_{t}}{0} = \infty $$

For an inductor, this term will make sense:

$$\frac{L}{\infty} = 0$$

But for a capacitor,

$$C * \infty$$

Which does not make sense.

Benta:
I survived the first two slides of this:
https://www.coursera.org/lecture/techniques-of-design-oriented-analysis/introduction-to-n-extra-element-theorem-neet-ui2rq
and then killed it.
To me it's just a really convolved way of presenting something bleedingly obvious.
I your place, I wouldn't pursue it. I can imagine that someone finds it "pedagogically valuable", but so is plasticine.
And going to the lengths of introducing special symbols places it... well, I don't know where.

SuperFungus:
It's been too long since I've messed with this for me to be able to follow your example, but I thought I recall that for the nEET there were "choices" of which pairs of elements to include in each step.  Either choice would usually be equivalent, but it's also possible that one of the choices would introduce a singularity which mean you would have to choose the other pair. Maybe that's what you're hitting?  I was coincidentally thinking I should review my notes on this at some point, if I do that I'll re look at this and maybe have something more helpful to offer.

Something more immediately useful: If you didn't know already, Vorporian has a YouTube channel with some helpful lectures https://www.youtube.com/channel/UCXOe8OLJT92XC56MMvbHUfA

Andrew_K:

--- Quote from: Benta on June 25, 2022, 07:47:29 pm ---I survived the first two slides of this:
https://www.coursera.org/lecture/techniques-of-design-oriented-analysis/introduction-to-n-extra-element-theorem-neet-ui2rq
and then killed it.
To me it's just a really convolved way of presenting something bleedingly obvious.
I your place, I wouldn't pursue it. I can imagine that someone finds it "pedagogically valuable", but so is plasticine.
And going to the lengths of introducing special symbols places it... well, I don't know where.

--- End quote ---

Very useful, thanks! :clap:

It's a tool to derive simpler transfer functions from circuits without a ton of algebra. Not surprised you don't see the value in this.

Andrew_K:

--- Quote from: SuperFungus on June 25, 2022, 11:51:05 pm ---It's been too long since I've messed with this for me to be able to follow your example, but I thought I recall that for the nEET there were "choices" of which pairs of elements to include in each step.  Either choice would usually be equivalent, but it's also possible that one of the choices would introduce a singularity which mean you would have to choose the other pair. Maybe that's what you're hitting?  I was coincidentally thinking I should review my notes on this at some point, if I do that I'll re look at this and maybe have something more helpful to offer.

Something more immediately useful: If you didn't know already, Vorporian has a YouTube channel with some helpful lectures https://www.youtube.com/channel/UCXOe8OLJT92XC56MMvbHUfA

--- End quote ---

I think you're right, I think the first example I had can be resolved by swapping the order.

Still, I'm not so sure about the second one.

It should be 0. I know that from looking at the total transfer function solved from matlab.

I just don't know how this issue is resolved in the neet theorem.

I reached out to Dr. Vorporian on his youtube account. Hopefully he's receptive to questions.

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