Talk:Electrical impedance

Capacitive reactance
The mathematical equation for Capacitive Reactance in this article is wrong! It should be Rc = + 1 / (w . C), not - 1 / (w . C). With the minus-sign we are talking about Capacitive Impedance (Zc). Don't make things more complex than they are, please! — Preceding unsigned comment added by Koitus~nlwiki (talk • contribs) 12:20, 2 December 2018 (UTC)


 * There really is not a lot of agreement in sources on this. When capacitive reactance is being talked about by itself, it is often assigned a positive sign.  However, when discussing it as a component of impedance, it makes much more sense to assign it a negative quantity.  Our article is currently internally completely self-consistent.  It would be introducing more complexity, not taking it away, to implement your suggestion. SpinningSpark 12:55, 2 December 2018 (UTC)

The lede, again
Hi there. In the Voltage drop article there is : "The sum of oppositions to current flow from both resistance and reactance is called impedance". As a layperson, not yet knowing what electrical reactance is, i dislike that sentence less than the current "complex representation of a sinusoidal voltage between its terminals to the complex representation of the current flowing through" in here. &mdash;Jerome Potts (talk) 12:26, 30 January 2019 (UTC)
 * So why have you posted at this article? SpinningSpark 14:01, 30 January 2019 (UTC)

"Complex impedance"? A better title would be simply "impedance"
It's the first time I read the term complex added to the concept of impedance. This is redundant. By definition, impedance is a complex number, so there's no need to describe it as "complex", since it is already a complex number.--Alej27 (talk) 23:33, 22 February 2019 (UTC)
 * Well a quick check of gbooks shows a huge number of sources using the term, and we follow the sources. It is not entirely devoid of meaning; historically, the concept of impedance was developed many years before it was first stated in a complex representation (by Arthur E. Kennelly in 1893). SpinningSpark 00:42, 23 February 2019 (UTC)
 * Impedance is sometimes used to describe a similar quantity in non-electrical systems, such as mechanical systems. More often, it is used in the sense of impedance mismatch, but usually not in the complex sense. Impedance mismatch is sometimes also used in social mismatch sense. I am not sure that helps with the question of this section, though. Gah4 (talk) 09:35, 2 October 2021 (UTC)
 * Mechanical impedance most definitely is a complex quantity. All the electrical elements have direct analogies in the mechanical domain. SpinningSpark 10:52, 2 October 2021 (UTC)
 * Impedance is sometimes used to describe a similar quantity in non-electrical systems, such as mechanical systems. More often, it is used in the sense of impedance mismatch, but usually not in the complex sense. Impedance mismatch is sometimes also used in social mismatch sense. I am not sure that helps with the question of this section, though. Gah4 (talk) 09:35, 2 October 2021 (UTC)
 * Mechanical impedance most definitely is a complex quantity. All the electrical elements have direct analogies in the mechanical domain. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 10:52, 2 October 2021 (UTC)


 * I think Alej27 has a point, "complex impedance" is redundant and "impedance" is the common usage. I would assume in most cases "complex" is only used for emphasis.  This article only uses the term 3 times, and the uses are IMO appropriate and should not be changed.   --Chetvorno<i style="color: Purple;">TALK</i> 07:13, 3 October 2021 (UTC)

Resistance and phase
I don't think that your change from,
 * Impedance extends the concept of resistance to AC circuits, and possesses both magnitude and phase, unlike resistance, which has only magnitude. When a circuit is driven with direct current (DC), there is no distinction between impedance and resistance; the latter can be thought of as impedance with zero phase angle.

to,
 * Impedance extends the concept of resistance to AC circuits, and possesses both magnitude and phase, whereas resistance has magnitude at a zero phase angle. When a circuit is driven with direct current (DC), there is no distinction between impedance and resistance; the latter can be thought of as impedance with zero phase angle.

is helpful. First of all, the first sentence ends up repeating the second sentence. More importantly, the original version is easier for readers to understand and highlights the key difference between resistance and impedance in a way that may be just what they are looking for. I don't at all agree that there is a phase angle associated with resistance. It is a scalar quantity which by definition has no phase. The correct way of looking at it is what the second sentence says; a pure resistance is an impedance with zero phase angle. It is the impedance that has the zero phase, not the resistance. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 23:57, 3 May 2019 (UTC)
 * Agree with Spinningspark. --Chetvorno<i style="color: Purple;">TALK</i> 00:35, 4 May 2019 (UTC)
 * I agree, too.--ComandiDosEAltro (talk) 16:49, 10 June 2019 (UTC)
 * I've undone the edit. The editor has been on Wikipedia since then, but does not seem to be keen to explain his edit here. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 18:02, 10 June 2019 (UTC)


 * Is the above supposed to be a request to 'the editor' to explain my reasoning? I apologize for the breech of protocol of not explaining here as I don't spend a lot of time on Wiki and don''t have it all down pat.
 * This part is still very awkward. The first sentence of the original is false. Resistance has a zero phase angle between voltage and current (obviously with AC). Zero is a phase angle between voltage and current just as any other phase angle. Saying it has no phase angle implies there is no current to measure an angle to. There is a sine wave (typically) of current so it must have some phase relative to the voltage waveform. Zero is that difference.  Resistance can not only be 'thought of' as impedance with zero phase angle between voltage and current, it precisely IS impedance with a zero phase angle. (I should have removed that too)
 * Saying resistance is a scalar is like saying that speed is a scalar because it has no direction; we might not talk about it, but it HAS a direction. We can always use the term velocity even when talking about just the speed and impedance is the same. It is the umbrella term for any combination of X and R. Always has been.
 * Therefore, calling resistance a scalar quantity is false.
 * It is unnecessary to consider resistance something outside the general subject of impedance. It is a special case of zero phase angle (V to I), for sure, just as pure reactance with no resistive component is a special case with 90 degrees, but both are still within the definition of impedance.  Just because one component of the impedance has gone to zero does not mean you must change the term. Impedance is the (vector) sum regardless if one of those summed happens to be zero. [the previous paragraph incorrectly states: "impedance ... is the ratio of the ...voltage between its terminals to the ...the current flowing through it." If the cited reference says that, it is incorrect.
 * The term impedance refers to section of a circuit with any phase angle. For those experienced in the art, impedance includes all phase angles and it can be, and is used as a single term regardless of the phase angle. It is also not common to suddenly switch to calling it 'reactance' should the angle happen to be at 90 degrees (unless there is a specific reason to do so).
 * This is an unnecessary distinction that makes this more complicated than necessary. And, yes, I should have removed that second sentence all together as it does repeat the first.
 * In DC it makes no sense to even talk about phase nor use the term impedance (though we may commonly do so since we are just used to using it in general).
 * 'Keen' enough?
 * Regards, &#32;-- Steve -- (talk) 20:07, 10 June 2019 (UTC)
 * The ping to you right at the beginning of this thread last month was an invitation to you to take part. There is no problem with you not doing so, just a bit odd that you did not, leading to the conclusion that you were no longer interested. You are wrong that resistance is just a special case of impedance.  Unlike your speed/velocity analogy, resistance is entirely different from other causes of impedance, both historically in the development of the field and as a physical phenomenon. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 21:37, 10 June 2019 (UTC)
 * The article is about impedance. There is no need to treat resistance like it is something odd.  Just remove the phrase " unlike resistance, which has only magnitude".Constant314 (talk) 21:22, 10 June 2019 (UTC)
 * People may be coming to this article precisely to get a handle on the difference between impedance and resistance. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 21:55, 10 June 2019 (UTC)


 * That is obvious. When explaining something it is not good to put all the complexities in at the beginning.  Start with the overview, then build on the concepts  to be able to follow the more complicated things.
 * Impedance is defined as only the magnitude "Z", is expressed simply in ohms and relates to DC resistance in the same way as resistance e.g. I=E/Z. Bringing in the complex-representations and math talk up front doesn't help until you get to representing it in other ways (rectangular, polar).
 * If the assumption is that the reader arrives with some amount of understanding of resistance [a reasonable assumption], then capitalize on that, then build to the more complicated. However there are errors as it is written: Z is not a ratio; it doesn't have to be a two terminal circuit; R does have a V to I phase relationship as I explained. Using terms like "Qualitatively", "linear law", "complex voltages", "impedance matrix", just put the DC-beginner off.  At that stage, they're struggling with the whole 90 degree thing.
 * I don't know why I didn't get notified for the earlier comment(s). I'll look it over more and form better recommendations, but am pressed for time right now. Don't recall, now,  why I wandered over here earlier... &#32;-- Steve --  (talk) 19:37, 11 June 2019 (UTC)

citation not needed for DC impedance/resistance comparison?
Hi, apologies if I'm violating etiquette, I'm new. I saw the sentence When a circuit is driven with direct current (DC), there is no distinction between impedance and resistance; the latter can be thought of as impedance with zero phase angle. and saw that today a citation was requested for it. I don't feel this is necessary since it's in the lead of the article ( WP:LEADCITE ), and this statement is not controversial (regardless of debate about the wording of the relationship btwn resistance and impedance seen above ^^). MyIpIsLocalhost (talk) 03:53, 17 March 2021 (UTC)
 * Yes, I agree with you. Constant<b style="color: #1100cc;">314</b> (talk) 03:59, 17 March 2021 (UTC)

Reverted edit on Electrical impedance
Copied from User talk:Constant314.

Hi Constant. Recently, I edited the electrical impedance definition section. I wrote: "The impedance of an electrical component is defined as its voltage-to-current ratio when both are simple complex exponentials at the same frequency $ω$. Since the time-dependent factors cancel out in such a ratio, this is the same as the ratio of the corresponding voltage and current phasors (sometimes dubbed the frequency domain)."

which you reverted to "Impedance is defined as the frequency domain ratio of the voltage to the current. In other words, it is the voltage–current ratio for a single complex exponential at a particular frequency $ω$."

commenting "Time dependent factors do not, in general, cancel out. In particular, if there is any phase difference, current will go through zero when voltage is non-zero.)"

I do not understand your comment. Impedance is the ratio of two phasors; the phase effect you point to, is comprised in the phasor, not in the time-dependent factor. If the time-dependent factors are their own unique functions, then "frequency-domain ratio" needs further explanation, since the frequency-domain spectra then couldn't cancel out either. Care to elaborate? --MewTheEditor (talk) 22:52, 6 July 2021 (UTC)
 * Hi, yes, it could be better, but your edit was not, in my opinion, an improvement because it changed from something that needed improvement to something that was wrong. Time-dependent factors do not cancel out because they go to zero at times which would imply divide by zero.  The whole mechanism of phasors is about suppressing the time-dependent factors rather than canceling them.  It could be a pedantic point.  Constant<b style="color: #1100cc;">314</b> (talk) 23:25, 6 July 2021 (UTC)
 * But I don't see how they could go to zero. In the phasor regime (steady-state AC), the time-dependent factor is $$e^{j\omega t}$$, which lies on a complex circle with radius 1, not 0. On another note: I realise my edit might be incomplete in the sense that impedances can be obtained via the Laplace transform, which allows for exponentially decaying steady-state AC. If that's what "frequency domain" alludes to, that too should be clarified (but this is besides your point, which is that I'm wrong, not incomplete). --MewTheEditor (talk) 01:52, 7 July 2021 (UTC)
 * You take the real part of the complex exponential to get the time domain response. That will give you zero crossings.  You know it has to be, because AC current is a sinewave, Constant<b style="color: #1100cc;">314</b> (talk) 04:05, 7 July 2021 (UTC)
 * Well, yes, you take the real part of whichever mathematical oscillator is used in calculation when you want to know the time response, but that's not what I wrote, cfr. "when both are simple complex exponentials". We're dealing with a situation similar to how wave functions in quantum mechanics are just mathematical constructs, but they are very handy at that. Now, it seems like you're not generally disagreeing with the rest of my edit, so do you have a suggestion for how that is phrased better? I get that you're saying $$Z = \frac{\Re\{\hat V\,e^{j\omega t}\}}{\Re\{\hat I\,e^{j\omega t}\}}$$ makes no sense, but in terms of complex oscillators, it makes perfect sense to claim $$Z = \frac{\hat V\,e^{j\omega t}}{\hat I\,e^{j\omega t}} = \frac{\hat V}{\hat I}$$. In fact, I've had more than one course at university do exactly that. --MewTheEditor (talk) 09:14, 7 July 2021 (UTC)
 * Why don't you give it another try and If I object, I'll try to fix it. Constant<b style="color: #1100cc;">314</b> (talk) 01:28, 8 July 2021 (UTC)
 * I don't like $$v(t)/i(t)=Z$$ either. Yes, if one defines $$v(t)=\widehat{V} e^{i \omega t}$$ then it is a true statement.  But one has to throw away the imaginary part of that to get the actual time varying voltage so it is a horribly confusing way of writing it.  Trained engineers will probably have no trouble understnading this, but that's not who the article should be aimed at.  Similarly, starting the introduction with Laplace transforms (which probably no one below university level education will have come across) makes the subject opaque to most readers.  <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 09:54, 15 August 2021 (UTC)
 * I think it depends on whether you really believe in complex numbers, or just think of them as a trick to get the answer. It is supposed to be that when Planck first came up with his explanation of black body radiation, he thought it was a mathematical trick. It got the right answer, but the EM field was still continuous. For a long time, it was only Einstein and a few others that believed in quantization of the EM field, and the photon. Maybe some day they will make voltmeters that display complex voltage and current. Does the article properly consider frequency dependence of impedance? Gah4 (talk) 00:00, 16 August 2021 (UTC)
 * Phasors really are a complex quantity and hence have an imaginary part. Instantaneous voltage and current does not.  And they don't suddenly acquire it because we have just invented the phasor concept.  So let's look at sources – which is the Wikipedia way of doing things – does anyone write $$v(t)=\widehat{V} e^{i \omega t}$$ in a textbook? <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 13:06, 16 August 2021 (UTC)
 * I suspect so, but haven't looked recently, and might not have those books around. Maybe not for introductory books, but after a while, people get used to it enough not to be bothered by complex voltage. How many books do we need to find? Gah4 (talk) 23:21, 16 August 2021 (UTC)
 * I suspect so, but haven't looked recently, and might not have those books around. Maybe not for introductory books, but after a while, people get used to it enough not to be bothered by complex voltage. How many books do we need to find? Gah4 (talk) 23:21, 16 August 2021 (UTC)
 * I suspect so, but haven't looked recently, and might not have those books around. Maybe not for introductory books, but after a while, people get used to it enough not to be bothered by complex voltage. How many books do we need to find? Gah4 (talk) 23:21, 16 August 2021 (UTC)

Duplicate sections
The sections "Device examples" and "Resistance vs reactance" pretty much cover the same ground and should be merged. Also, I suggest moving some of the derivations in these sections into the "Formal derivation" section (which I have just created by moving some material out of the introduction). In my opinion this will make the article much more readable to the general reader. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 09:17, 2 October 2021 (UTC)

Representation of impedance
When I wrote "Impedance can be represented as a complex number" I had in mind graphical representations of impedance that don't rely on the use of complex numbers at all. This is a very old textbook, but shows a method of looking at impedance still taught to students at an early stage. One can also point to the Laplace operator representation definiton as given here which is different again. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 18:31, 6 December 2022 (UTC)
 * In the early days of radio, and tuned circuits, it was usual to use a mechanical analogy for the electrical system. Now, it is more usual to use the electrical analogy for the mechanical system. Whichever one is most used to seeing. Gah4 (talk) 22:53, 6 December 2022 (UTC)
 * In the early days of radio, and tuned circuits, it was usual to use a mechanical analogy for the electrical system. Now, it is more usual to use the electrical analogy for the mechanical system. Whichever one is most used to seeing. Gah4 (talk) 22:53, 6 December 2022 (UTC)

Sequence Impedance and DQ Impedance
Greetings, This page could be more informative for electrical systems engineering and research if it included sequence impedance as in symmetrical components impedance and DQO (Direct Quadrature and Zero) impedance. Most of the power systems protection engineering is done with positive, negative and zero sequence impedances these days. DQ impedances are also used for modeling, drives controls analysis, and stability analysis of power electronic systems. If you argue that these impedances should be under DQ0 transform or Fortesque transform it would be like saying that impedance belongs under complex numbers or the Fourier transform, since that is the mathematical origin. I think these impedances belong on this page because it covers the use cases of electrical impedance in its various forms. There is also a close tie between three phase impedance and single phase impedance. Most balanced three phase networks are treated with single phase impedance equivalents thank you. 173.66.144.197 (talk) 02:13, 29 March 2024 (UTC)
 * Putting DQ here would be like trying to put impedance under complex number. It would be WP:UNDUE.  Put it under three-phase power where it would be appropriate. <b style="color: #4400bb;">Constant314</b> (talk) 02:54, 29 March 2024 (UTC)
 * There is a page Dq0 where it might be applicable. If not, maybe it is enough for its own page. But I agree, it doesn't go here. Gah4 (talk) 06:01, 29 March 2024 (UTC)
 * There is a page Dq0 where it might be applicable. If not, maybe it is enough for its own page. But I agree, it doesn't go here. Gah4 (talk) 06:01, 29 March 2024 (UTC)
 * There is a page Dq0 where it might be applicable. If not, maybe it is enough for its own page. But I agree, it doesn't go here. Gah4 (talk) 06:01, 29 March 2024 (UTC)

time varying
Seems to me that time varying impedance works well when the varying is slow compared to the AC frequency. The time varying section could make this more obvious. Gah4 (talk) 21:18, 23 May 2024 (UTC)