The What and Why of Circuit Analysis Assumptions - Comments

Greg Bernhardt submitted a new PF Insights post

The What and Why of Circuit Analysis Assumptions


Continue reading the Original PF Insights Post.

A good topic to discuss! There are certainly many cases in real circuits where non-ideal behavior can have a huge affect. Just to offer a few suggestions:

I think the main point you are making here is that there are non-ideal behaviors in real circuits which do not fit the assumptions of CA. You gave some of these assumptions, so maybe you could show some explicit cases where the assumptions are violated and what the correct solution would be.

I think the references to QED and FT somewhat detract from your main point. Perhaps the focus should be on how EM fields from one part of a circuit can alter the operation of another part, such as with the multiple inductors in the schematic shown.

NFuller said:

Perhaps the focus should be on how EM fields from one part of a circuit can alter the operation of another part,

Thanks for the kind words, but that was not my focus. Non ideal behavior would make an interesting Insights article, but others like @berkeman who designs circuits, or @jim hardy who troubleshoots misbehaving ones are better qualified than I to write it. My expertise in on the tools that analyze circuits that do follow CA assumptions.
You may have heard of Spice. That is the kind of tool I mean. In power system analysis PSS/E is the tool. I wrote the first version of that software in 1971.

Analysts have tricks to use CA even when circuit behavior is non ideal. Consider the following picture showing two three phase circuits sharing the same transmission towers. The mutual coupling between the two circuits violates the CA assumptions big time. But analysts simply adjust the values of series reactance for both lines to compensate, then put them into the analysis as if they weren't mutually coupled. In other words, they fudge the data to avoid the need to use Maxwell's equations to model the entire power grid (which would be impossibly difficult.) The practice is akin to the transformer equivalent circuit that I showed in the article. Non-ideal behavior is approximated by ideal components and standard CA methods are used to solve the circuit.

Great article. A classic CA example are batteries.

It can be simplified to an ideal voltage source. But as you need more and more accuracy you add capacitance, inductance, and non linear elements. Before you know it you have a fourth order non-linear filter. That is before add series and parallel cells.

It might be needed, depending on your application, but if you are making a pwm based low power led driver run off a voltage regulator, is all that really necessary. Making assumptions simplifies design and analysis so much, as long as one is aware of the conditions of the assumption.

Another common CA that greatly simplifies things, but can cause disastrous results if mismanaged...
Forgetting that PCB traces and wire harnesses and wires can and will act as transmission lines, not ideal 0 impedance connections.

Great Insight and great comments!

From the thread on helical antennas: How about the fact that between its 1/4WL self resonant frequency and 1/2WL self resonant frequency, an inductor exhibits capacitive reactance? So much for inductance being proportional to the square of the turns.

anorlunda said:

The What and Why of Circuit Analysis Assumptions

Great insight article! That was also my first circuit analysis textbook, and I remember that introductory chapter with its explicit list of assumptions to this day! Personally, I wish that every textbook would start off with such an explicit list of the simplifying assumptions used in the theory.

As far as when to teach these assumptions, I think that it doesn't make sense to teach QED first, you would lose a vast number of students many of which can make good use of CA throughout their life but will never use QED. So CA needs to come first in a program of study. But even if a student never learns the more advanced courses, they should still know these assumptions. That way the students can tell if a given physical scenario is one that they can model with these tools or not. They may not know how to treat assumption-violating scenarios, but they will at least know that their familiar tools may not be up to the task.

CA as used by electronic engineers has some rather strange implications when applied to active devices like transistors.

There is a device called a 'diamond' amp - its a little IC that acts like an ideal transistor - current can flow both ways through the base-emitter. The current is then amplified and appears at its collector.

It's sometimes used as the buffer for a current output DAC chip that likes to see a virtual earth.. What you do is you clamp the base to ground and the emitter to the output of the DAC chip and have a load such as a resistor on the collector. Because the current flows both ways and it has gain it will always try to keep emitter also at Earth - if not current will flow through the collector and whatever is connected to the emitter until it is. This is since the base is clamped to the Earth it can't go there - no potential difference so it must flow through the collector and its load - yet still sees a virtual earth. I have shown the circuit to a number electronic engineers I know - one even incorporated it in a DAC he built - but it takes a while to see it, its just a simple application of current laws - current must go somewhere.

That of course is the 'naive' analysis - what's really going on I have tried and failed to understand - it is rather tricky.

Just as an aside I always thought the best output for a DAC chip was just a simple transformer. I got one of my electronic friends to try it - it failed miserably with the PCM1704. But he told me when he switched to an AKM chip it worked great. Interesting.

Thanks
Bill

bhobba said:

There is a device called a 'diamond' amp -

That was interesting. Thanks. Are you able to make an equivalent circuit for a diamond amp?

Dale said:

anorlunda said:

The What and Why of Circuit Analysis Assumptions

Great insight article! That was also my first circuit analysis textbook, and I remember that introductory chapter with its explicit list of assumptions to this day! Personally, I wish that every textbook would start off with such an explicit list of the simplifying assumptions used in the theory.

As far as when to teach these assumptions, I think that it doesn't make sense to teach QED first, you would lose a vast number of students many of which can make good use of CA throughout their life but will never use QED. So CA needs to come first in a program of study. But even if a student never learns the more advanced courses, they should still know these assumptions. That way the students can tell if a given physical scenario is one that they can model with these tools or not. They may not know how to treat assumption-violating scenarios, but they will at least know that their familiar tools may not be up to the task.

I am friendly with a number of electronic engineers in the audio field and believe me they know circuit analysis backwards. I have tried and failed miserably to explain QM to them - they just don't get it. QED - well that's way off the landscape for them. Yet of course transistors rely on holes that are really quasi particles. They understand well how transistors and diodes work using the hole idea - but quasi particles - that they have great difficulty with.

Thanks
Bill

anorlunda said:

That was interesting. Thanks. Are you able to make an equivalent circuit for a diamond amp?

For the gory detail of what is actually inside a diamond transistor see:
https://www.edn.com/electronics-blogs/analog-bytes/4438881/Quest-for-the-Ideal-Transistor-

In a circuit diagram it has the same symbol as a normal transistor but with two arrows in each direction - one from base to emitter and the other emitter to base indicating current can flow both ways - see fig 3 in the above link.

It's also sold as a little IC eg the OPA 860:
http://www.ti.com/lit/ds/symlink/opa860.pdf

For some reason its not actually used much by the electronic guys I know, and when I was into electronics many many moons ago none of the circuits I mucked around with or saw in magazines used it, so may be out of production these days - but has some advantages - so I don't know why.

Understanding what's going on at the naive level is a bit tricky as I explained - but it's simple when looked at the right way - its just current must go somewhere - if the base is clamped to Earth it can't go there so must go through the collector and its load. Of course when you look at the actual circuit of one of these things as in the above link its not that at all - that's the tricky bit I have never really been able to figure out. Abstraction hides all sorts of difficulties.

Thanks
Bill

I would assume the diamond transistor is not very popular because what you describe it being able to do can be done easily with op amps. Unless I misinterpret what you are describing.

I thought a diamond amp was a transconductance amplifier.
To boil it down to one line, it would be an op-amp with a current output instead of a voltage output

donpacino said:

I thought a diamond amp was a transconductance amplifier.

That's another name for it.

The advantage is you do not have to bias it on - current travels both ways.

Don't know why for sure, but if you use it instead of an a normal op amp for current to voltage conversion it tends to sound better according to those that have tried it - possibly because its better slew rate -
'Another dynamic advantage of CFAs is their relative immunity from slew-rate limitations because Cc is driven directly by the input buffer, which can supply virtually any current to rapidly charge/discharge Cc.'

Thanks
Bill

Regarding the "Diamond Transistor": I think, the device we call "transconductance ampolifier , OTA" has two high-resistive inputs.
In contrast, the device called "Diamond Transistor" has one high-resistive as well as one low-resistive input.
That`s why it is a kind of current conveyor (CCII).

Interesting stuff! I'd like to clarify my understanding of the CA assumptions.

My previous understanding of a lumped element, was that you could imagine putting the circuit element inside a tiny 'black box', with two terminals at either end. The electric and magnetic fields produced by the circuit element would be approximated to be contained entirely within that black box. That would mean, we can derive the constitutive equations for our circuit elements using ordinary electromagnetism, but we can ignore the other effects the elements might have on the larger circuit.

But this article seems to go one step further, that we should completely ignore fields and charges. Does that mean that CA is a purely mathematical formalism? That's to say, we take all of our constitutive equations - like Ohm's Law, the inductor/capacitor laws, whatever - as axioms, and start writing equations, using our analytical tools.

Is that along the right lines, or am I missing something more subtle?

etotheipi said:

Does that mean that CA is a purely mathematical formalism?

No. You can experimentally measure voltage and current, and CA predicts the outcome of such measurements. It is a fully legitimate physical theory.

etotheipi said:

Is that along the right lines, or am I missing something more subtle?

It's more a matter of teaching strategy rather than accuracy.

We can teach students CA before they ever heard of fields or charges or electrons. And we should tell students to suppress any knowledge of fields when studying closed circuits depicted by neat schematics with unspecified distances and square corners. When they try to blend CA and fields, they can get horribly confused. On PF, we see that frequently from people attempting self-teaching of basic electromagnetics.

But it is also true what @Dale said, that CA is fully legitimate. Countless electrical engineers can get through entire careers analyzing circuits without the need for anything deeper than CA, (if they don't design transformers or RF, or transmission lines, or semiconductor devices). Physicists need the deeper understanding, but physicists may never need to confront the schematic of a closed circuit.

Thanks for the Article - I do not recall having Lumped Abstraction, specifically taught or defined in uni and came across this lecture many years later via MIT Open courseware. ( https://cosmolearning.org/video-lectures/introduction-and-lumped-abstraction-9569/)

I think you could call this defining of the system of higher order models, the philosophy of engineering, vs the practical matter of solving the problems.

When taught CA, we generally know there is more to the story of what is going on in a circuit but we do not need to know or use that info to do the analysis. But often, I agree, many question here, and in other related forums, are people/students asking - in a way trying to "see it all at once" - and yes, ha, if they bring up electrons it is often a red flag.

Windadct said:

the philosophy of engineering, vs the practical matter of solving the problems.

Of course, I agree with what you said. But that way of saying it understates the motivations. Using CA, we can easily solve real life circuits with millions of nodes, and branches. For example, the power grid. Those would be unthinkably hard to solve, and in practice impossible, using rigorous physics.

In addition to simplicity, CA offers scalability.

My philosophy comment was related to the entire concept of lumped abstraction, and the different layers it is applied. "Above" CA may be digital logic, for example, we then do not need to think about how to build a nand gate to use a nand gate. EEs move through these layers or environments easily, or without necessarily thinking about it.

anorlunda said:

Thanks for the kind words, but that was not my focus. Non ideal behavior would make an interesting Insights article, but others like @berkeman who designs circuits, or @jim hardy who troubleshoots misbehaving ones are better qualified than I to write it. My expertise in on the tools that analyze circuits that do follow CA assumptions.
You may have heard of Spice. That is the kind of tool I mean. In power system analysis PSS/E is the tool. I wrote the first version of that software in 1971.

Analysts have tricks to use CA even when circuit behavior is non ideal. Consider the following picture showing two three phase circuits sharing the same transmission towers. The mutual coupling between the two circuits violates the CA assumptions big time. But analysts simply adjust the values of series reactance for both lines to compensate, then put them into the analysis as if they weren't mutually coupled. In other words, they fudge the data to avoid the need to use Maxwell's equations to model the entire power grid (which would be impossibly difficult.) The practice is akin to the transformer equivalent circuit that I showed in the article. Non-ideal behavior is approximated by ideal components and standard CA methods are used to solve the circuit. Although I did manage to ship a couple complex SCADA designs with remote control well before Allen Bradley in the late '70's with lots of logic uC analog and robotics. I never got famous or rich from it.

View attachment 214066

That's amazing cmd-line programming PSS/E in 1971. I've never used it but we did cmd-line lunar landing simulations between classes in 1971. (albeit, very primitive game) I see this app became part of Siemens tools, and I like the trademark of Manitoba Hydro's App, "If you can dream it, you can simulate it"

https://www.eepowerschool.com/softwares/10-must-learn-electrical-engineering-software/

In my career, I rarely had access to S/W simulation tools, I was never in R&D for power, yet everything else. I was lucky to have all best Test Equipment to analyze the task, from VNA's, BER and phase margin analyzers, Laser Particle Counters, a wide variety of HASS (vibe and e-noise) tests, Modal Analyzers, Bode Analyzers , FET Diff Probes and SEM scope in-house. My legacy was to learn how to design/test and develop Design Verification Tests with margin testing under stress then apply this to Doppler Navigation, RF communication channels, magnetic recording (HDD Mfg), and DOE for CMS soldering processes.

Anecdotal
I have often observed the physical phase-rotation of power lines every 1km and knowing the Magnetosphere wobble effects on mutual coupling to power lines, I imagined this was to reduce the effect of Solar Flare induced Carrington Events One that occurred more than once a century go, but today might induce a total grid failure or shutdown. Although there would be a large CM induction from the magnetosphere, the isolation of DELTA wound distribution lines helps with the CMRR or common mode rejection ratio using the twisted pair effects every 1 km. Essentially I imagined this was to have a common- mode LC coupling to earth ground plane for each phase equidistant to each other in a triangle. The final leg of power is earth-grounded Neutral using step-down Delta to Y transformers.

Every year many oil-filled power transformers explode (nasty) due to lack of adequate monitoring for Partial Discharge, PD due to contaminants which create a breakdown into dissolved combustible gases , only tested in expensive Transfo's using DGA on oil samples, when PD technology has expanded so much and reduced in cost. There are other causes but by simply measuring the PD pulse rate just like listening to lightning on a quiet AM channel tells you how close a storm is. Being an ionization pulse within the insulation only detonations a tiny number of molecules which can either get rid of minimal contaminants or escalate from 1 pulse/min to many pulses per AC cycle before trouble begins. I once discovered a factory epidemic of 5 MVA units in the field , used on many megawatt wind farms in Ontario, CAN. and traced the contaminants down to invisible silicate-coated CRGOS transfomer steel lamination particles from rolls going into an anvil sheet cutter. The particles were both magnetic and insulator coated materials and would take a cluster to be visible. It took me 3 mos, since I started learning this from scratch testing 50 kV 5 MVA transformer units testing to 150 kVdc and doing oil sample breakdown slow ramped up AC voltage tests. For those that do this breakdown voltage test, the stoichastic (random) breakdown results with std. dev and level of performance are direct indicators of all the contaminants in the insulation. They can be re-processed to raise from 25 kV/mm to 75 kV/mm with special equipment. A perfectly clean insulator will have the same current-limited breakdown voltage (BDV) every time like a precision vacuum air gap. But even space has contamination and astronomic stoichastic events "bang" occur frequently just like magneto-flux solar flares. Yet scientists have have learned how to predict flare eruptions better than earthquakes.

Sorry I digressed from Circuit Analysis.

I'll leave you with a simulation of a spark plug.

or a variation https://tinyurl.com/2djlouhe