Does cable impedance add to source or load impedance? - Page 1
Forum section: electronics / beginners

author: fonograph
author_rank: Frequent Contributor
timestamp: February 14, 2019, 10:45:15 pm
content: Lets imagine we have amplifier with 2 ohm output impedance connected to 8 ohm impedance load, headphone for example. Becose the amp impedance is 2 and headphone is 8, then the damping factor is 4.How will the cable affect our system? If the cable has 2 ohm resistance, does it add up to the source impedance and decrease damping factor from 4 to 2 becose 2 ohm source + 2 ohm cable = 4 ohm output impedance divides 8 ohm load = 2x damping factor.Or does it add to the load impedance and increase the damping factor becose 8 ohm headphone + 2 ohm cable = 10 ohm load divided 2 ohm amp output impedance = 5x damping factor?

author: Doctorandus_P
author_rank: Super Contributor
timestamp: February 15, 2019, 12:05:17 am
content: Damping factor gets worse (lower) by cable resistance.If high resistance would increas damping factor everybody would use open connections between the amplifier and speakers.

author: Audioguru
author_rank: Super Contributor
timestamp: February 15, 2019, 12:10:06 am
content: Simply try it. A modern audio amplifier has an output impedance at low frequencies of 0.04 ohms or less for excellent speaker resonance damping. A pulse sounds like a "thump". With a poor damping factor caused by the amplifier output or cable resistance then the pulse sounds boomy like a bongo drum.The amount of damping required depends on the speaker and on your hearing.Your example of a 2 ohm amplifier or cable resistance feeding an 8 ohm speaker also reduces the maximum undistorted output level a little.

author: Richard Crowley
author_rank: Super Contributor
timestamp: February 15, 2019, 12:15:15 am
content: Remember that series resistance has nothing to do with cable impedance.Cable impedance is of no importance down at audio frequencies.OTOH, series resistance does indeed affect damping factor:Quote

author: fonograph
author_rank: Frequent Contributor
timestamp: February 15, 2019, 04:02:27 am
content: So cable impedance adds up to and counts as source output impedance? I expected it will add up to load impedance.

author: David Hess
author_rank: Super Contributor
timestamp: February 15, 2019, 04:24:32 am
content: If it added to the load impedance, then it would also be interacting with the magnetic field in the driver to produce EMF counteracting the increase in resistance.

author: Richard Crowley
author_rank: Super Contributor
timestamp: February 15, 2019, 04:25:55 am
content: Quote from: fonograph on February 15, 2019, 04:02:27 amYou still seem to be confused about cable IMPEDANCE vs. cable RESISTANCE.NO, cable IMPEDANCE does NOT count as source output impedance.YES, cable RESISTANCE is frequently added to source impedance.Cable IMPEDANCE is IRRELEVANT down at audio frequencies.Now, if you are talking about radio frequencies (RF), that is a completely different scenario.

author: fonograph
author_rank: Frequent Contributor
timestamp: February 15, 2019, 10:27:34 am
content: Quote from: Richard Crowley on February 15, 2019, 04:25:55 amCable impedance, cable resistance... does it matter? Its almost the same thing. I cant imagine how one part cable impedance, the resistance, adds up to source output impedance but the cable reactance does not. That doesnt make any sense, not saying its wrong, I need explanation why its like that.Also, I am aware that most headphone cables have very low reactance at audio frequencies. I brought the headphone and amp example for no reason other than that I am familiar with headphones and head amps.No need to repeat that cable reactance doesnt matter in audio, I know it, I am not audiophool who buys 10K cables, its just example to paint the picture about my impedance question.

author: fonograph
author_rank: Frequent Contributor
timestamp: February 15, 2019, 10:37:32 am
content: Quote from: David Hess on February 15, 2019, 04:24:32 am

author: Richard Crowley
author_rank: Super Contributor
timestamp: February 15, 2019, 10:39:56 am
content: There are several resources online that explain cable impedance. For example:http://www.epanorama.net/documents/wiring/cable_impedance.htmlDown at audio frequencies, there is no practical IMPEDANCE in cables.There is only RESISTANCE (series resistance, to be precise).It is only up at radio frequencies (MHz, GHz, etc.) that cable has impedance.If you only stick to audio frequencies and use the word "resistance" when talking about cable, you will be OK and others will understand what you are talking about. But if you start playing with RF, then at least you will need to understand that they are different things.

author: ggchab
author_rank: Frequent Contributor
timestamp: February 15, 2019, 11:07:04 am
content: Isn't impedance the sum of resistance and reactance ?So, I believed resistance is a special case of impedance where reactance is close to 0 ?Am I wrong ?

author: fonograph
author_rank: Frequent Contributor
timestamp: February 15, 2019, 11:12:19 am
content: Quote from: Richard Crowley on February 15, 2019, 10:39:56 amI understand your point, I will avoid using the audio frequency example in future.But just to make it clear, I DONT care about the amount of impedance average audio cable has in audio frequencues. You say there is no practical impedance, I say label it as you want there is still impedance and its amount is completly irrelevant in the context of this question.I am not aware of any real world conductor that has only resistance, sure you can name billion examples where its so small that nobody gives a funk about it but we are not solving real world problem here, we are trying to make me understand how impedance counts.I understand that you meant good by telling me audio cables dont care about reactance, I just want to concentrate about how the impedance adds up and not if this is real world problem. We can change my example to 140 GHz phased array radar antenna and cryogenic HEMT based amplifier if you prefer.

author: vealmike
author_rank: Regular Contributor
timestamp: February 15, 2019, 12:01:45 pm
content: Richard is correct.Impedance is relevant only when you are dealing with a transmission line.The usual test for a whether or not you have a transmission line is whether the propagation delay of the line is more than 1/3 the 10% to 90% time of your signal. It's a rule of thumb, but a very good one.For a 20KHz audio signal, let's approximate that rise time to 1/2 the period. 1/20KHz is 50us, half that is 25us.Lets assume a very rough 200ps/inch propagation velocity in your cable. 25us/200ps = 125,000 inches. 1/3 of that is 3472 feet.Below a length of 3472 feet, you can ignore the effects of cable impedance at 20KHz. If you have a little over half a mile of speaker cable, sure, you have a transmission line. You will need to start worrying about what we normally term "high speed" effects.You'll also find that the CD will have finished playing by the time you've walked from the hi-fi to the speaker.If you move to rf, then a shorter cable becomes a transmission line.A mismatch of impedances in the channel will cause a reflection. The signal bounces off the mismatch, some of the signal does an about face and heads back to the transmitter. This means less of the signal gets to the receiver.But if you keep everything even, a transmitter with a 50Ohm impedance, a 50Ohm transmission line and a 50 Ohm load then 100% of your transmitted energy gets to the load.This is different to the way that cable series resistance adds to the load in exactly the way you'd expect at dc. This doesn't stop happening in a transmission line, its still there and we still have to take it into account.The two are totally different things, with confusingly similar terminology. I didn't get it when I was a student either, it wasn't until I started working with high speed stuff and playing with a TDR that the penny dropped.I suggest you look online for articles written by Dr. Howerd Johnson. He's really good at explaining this stuff.

author: Doctorandus_P
author_rank: Super Contributor
timestamp: February 15, 2019, 12:31:20 pm
content: It seems that different kinds of impedance are getting intermixed here.A loudspeaker definately has an impedance because it has a resistive and an inductive component, which combine to form the impedance vector.Impedance of a transmission line is a whole other beast, and Richard keeps hammering on it that it is not relevant. But why then bring it up? The dog with it's paw's on the keyboad does not even know what it is.

author: Zero999
author_rank: Super Contributor
timestamp: February 15, 2019, 01:42:05 pm
content: Quote from: ggchab on February 15, 2019, 11:07:04 amIt's the vector sum.Z = √(X2+R2)Yes, when X is near zero, then we might as well just use R.Quote from: fonograph on February 15, 2019, 11:12:19 amI don't see what all the fuss is about. At low frequencies and DC, then impedance and resistance are often used interchangeably. True, this may not always be strictly correct, but who cares? We all know what people mean when they talk about the impedance of a battery or audio amplifier.

author: vealmike
author_rank: Regular Contributor
timestamp: February 15, 2019, 02:02:01 pm
content: Quote from: Doctorandus_P on February 15, 2019, 12:31:20 pmI suspect, because when someone asks about the impedance of a cable that is what they are referring to. They may be mistakenly using the wrong terminology, but that is the question conveyed by the words used.To the OP.At dc or low frequencies (compared to the length of the line), you can use lumped elements to model the cable. Just as we consider a capacitor model to have a small R & L element as well as a C. A cable will have a small C & L as well as a R.You can draw those in series with the cable's resistance and calculate the effect using standard ac analysis. Or if you're feeling lazy, put it into PSPICE and simulate.I think the point being made is that these stray inductances and capacitances are usually so tiny compared to the cable and load that they do not need to be taken into consideration.If you were driving a very high impedance load, then maybe. But it would usually be far simpler to just reduce the impedance of the load.I challenge the OP to measure the self inductance and capacitance of a 10m length of speaker wire.1/ Because it's bloody difficult, the values are small, and it will give him a sense of proportion.2/ Because it will answer his questions in a way that we're not going to be able to and help him understand what's going on.

author: Dave
author_rank: Super Contributor
timestamp: February 15, 2019, 02:14:09 pm
content: Quote from: Doctorandus_P on February 15, 2019, 12:31:20 pmWhen we talk about transmission lines, we're usually interested incharacteristic impedance.We simply call it impedance to save us an extra word, but the two are not simply interchangeable.Quote from: Richard Crowley on February 15, 2019, 12:15:15 amA bit of a misleading statement.Characteristic impedance of a cable is:The resistance, inductance, conductance and capacitance are all specified per unit length.It is only because resistance and conductance usually have a negligible effect at RF frequencies, that we tend to ignore them and simplify the equation to:

author: David Hess
author_rank: Super Contributor
timestamp: February 15, 2019, 03:28:44 pm
content: Quote from: fonograph on February 15, 2019, 10:27:34 amAt high frequencies where the signal does not have time to reach the end of the cable, only the cable's impedance is seen by the source. At low frequencies, the impedance seen is the load plus the cable's series resistance and the cable's parallel capacitance.In audio applications, both can be relevant. At audio frequencies, the cable impedance is practically irrelevant except for the parallel capacitance which can cause instability however at high frequencies, the source must be designed to handle the cable impedance plus load mismatch to prevent instability.The above leads to an interesting problem in some poorly designed amplifiers where they work fine with short or long cables but oscillate with medium cable lengths. Look for something like a pi network which includes a pair of Zobel networks to avoid this problem. This also serves to suppress RFI pickup in the output leads.

author: ArthurDent
author_rank: Super Contributor
timestamp: February 15, 2019, 03:40:41 pm
content: Some of the typical values of inductance and capacitance per foot of speaker wire I've seen are around .2 microhenry and a few picofarad, small enough to be ignored.If you model speaker wire as an RLC network it will look like a speaker crossover network. A typical speaker crossover network could have around a 10uF capacitor and a 1 mH inductor, many orders of magnitude greater than any speaker wire you could use. So to make a crossover network with just speaker wire you would probably need over a mile of two conductor wire and the resistance of that length of wire could be in the range of 70 ohms. No matter how you look at it, resistance is the major problem with long or smaller diameter wires.Here are a couple of links that help explain some of the stuff to consider. One concludes with: "The bottom line is the resistive losses are far more a dominant factor to consider when choosing loudspeaker cables. The associated electrical delay of a "long" cable vs a "short" cable is simply not a real issue to concern yourself with."https://www.audioholics.com/audio-video-cables/speaker-cable-length-differences-do-they-matter

author: Richard Crowley
author_rank: Super Contributor
timestamp: February 15, 2019, 04:08:03 pm
content: Indeed, over on GearSlutz audio forum cable series resistance and especially parallel capacitance is a very frequent topic of discussion. But cable (characteristic) impedance is only a topic when referring to high-frequency signals. Like digital audio, digital video, or RF like wireless microphones, etc.Electrified string instruments (guitars, bass, etc.) still use a half-century old connection protocol/standard. High-source-impedance, low-level, unbalanced. Impedances on the order of 100K to 1M ohm. Now, in more modern times some (many?) pickup coil assemblies are lower impedance, and some instruments have battery-powered buffer amplifiers which provide a lower source impedance.Cable parallel capacitance has the effect of creating a high-cut/low-pass filter (in interaction with the source impedance). For that reason many manufacturers still make "instrument cable" which is specifically designed for low parallel capacitance.And because the high-impedance nature of the source (and by necessity load impedance), the typically cables tend to be microphonic and sensitive to movement. For that reason many instrument cables have a conductive coating on the outside of the insulation dielectric which attenuates the triboelectric voltages. And sometimes even around the inner conductor.In order to reduce the capacitance, they frequently use a very small center conductor. But since the signal is such a very low voltage (and low power) the series-resistance of the center conductor is of no practical significance over the relatively short distances (a few meters). For instrument cable, parallel capacitance is the important factor, not series resistance.OTOH, at the other end of the audio chain, for a connection between a power amplifier and a speaker, we are talking about very low source and load impedance (on the order of 10 ohms) In that scenario, parallel capacitance is of no practical significance. However, series resistance is of very significant importance because it will attenuate the signal at such low (source and destination) impedance. Which is why speaker cables tend to be large gauge for low series resistance.

author: David Hess
author_rank: Super Contributor
timestamp: February 15, 2019, 05:31:33 pm
content: Quote from: Richard Crowley on February 15, 2019, 04:08:03 pmThe cable capacitance has no significance to the low impedance driver at audio frequencies but it can cause the output stage to oscillate above the audio band if not properly handled.

author: Kleinstein
author_rank: Super Contributor
timestamp: February 15, 2019, 05:45:50 pm
content: The damping of the speaker depends on the speaker impedance at resonance, the speakers own ohmic resistance, that cable resistance and the amplifiers output resistance. If there is a passive cross over network this also can add quite a bit.Here the resistance insider the speaker, wire and amplifier are added. Quite often of the resistance is due to the speaker itself so some 2 Ohms of wire resistance would not add that much and the actual damping factor would not change very much. The extra resistance still have a slight effect on the cross over network.With modern speakers the ohmic resistance may be quite a bit lower than the speaker impedance, but it's usually still more than the wire or amplifier.

author: larry42
author_rank: Regular Contributor
timestamp: February 15, 2019, 07:44:21 pm
content: Quote from: fonograph on February 14, 2019, 10:45:15 pmMy understanding (after 2 decades of RF design) is:The characteristic impedance, Z0, of a transmission line, such as coaxial cable, is a notional concept that relates the current flowing through the line with the voltage across it. Heaviside and later Maxwell showed that a transmission line can be considered as a concatenation of short RLGC sections (series R and L, shunt G and C) and Z0 is given byZ0 = sqrt((R+j*w*L)/(G+j*w*C))where j = sqrt(-1)w = 2*pi*frequency (omega)and R,L,G,C are per unit lengthFor practical cables made from good conductors and good insulators the physical values of the R,L,G,C work out mean that for f>100kHz, say, Z0 ~= (sqrt(L/C))Thus at HF the char. impedance is real and fairly constant.At medium and audio freq. it is complex and varying.with RG-58R = 39mOhm/mL = 250nH/mC = 100pF/mAt f> 250kHz, j*w*L ~= 10*R and Z0 is quite constant 50Ohm.At audio frequencies therefore the char. impedance is complex and a function of freq (i.e. Z0(f))But what is the effect of this impedance? Modeled as a two port:https://en.wikipedia.org/wiki/Transmission_lineThen using ABCD parameters, you will probably be able to see how the output inpedance of the amplifier (Port 1) is transformed viahttps://en.wikipedia.org/wiki/Two-port_networkto V1, I1 = ABCD V2, I2and so see how much of an effect your tx line has. It's not a simple resitive addition, as the shunt capacitance is usually non negliable.This will give you an effective Zsource that is connected to your load.But Zsource is a function of freq. (due to the tx line) and because your amplifier will have a damping factor (output impedance) that rises with freq.So... basically, IMO damping factor is just a fairly meaningless marketing term (which is is freq. dependent). Your speaker network as funkloads of resonances, and will be 8Ohm restive at 1 single point probably and unless you are using very long (say >5m) lines the tx line's characteristics are not interesting to consider, and cannot be regarded as a simple resistance in any case.

author: larry42
author_rank: Regular Contributor
timestamp: February 15, 2019, 07:46:30 pm
content: I just want to add - that this all assumes that you are at a freq. such that jwL is >> R and jwc >> G. below that you may need to think about transmission line effects, but the char. impedance is not constant.

author: Johnny B Good
author_rank: Frequent Contributor
timestamp: February 15, 2019, 08:03:25 pm
content: Quote from: fonograph on February 14, 2019, 10:45:15 pmThe term "Damping Factor" must be the most abused "Figure of Merit" invented by the amplifier manufacturing industrys' marketing departments since the advent of transistorised power amplifiers with output impedances two to three orders of magnitude lower than the one to three ohms output impedance typical of the valve (tube) amplifiers of the day.A myth was created that the 'Damping Factor" (DF) was the ratio of speaker load impedance to that of the amplifier's output impedance, neglecting the inconvenient truth that some 95% or more of the typical moving coil speaker's impedance was simply the ohmic resistance of its voice coil which is effectively in series with that of the amplifier's output Z and the connecting cable's loop resistance.All such signal carrying cables (two wire balanced circuits or unbalanced shielded co-axial circuits) have a "characteristic impedance" (not to be confused with "loop resistance") which, in the case of Hi-Fi wiring, is typically not a critical matter. That's not to say there isn't any need to consider its impact on audio frequency circuits such as the telephone trunk lines of old and local land line circuits which can be several miles in length. In this case, a more accurate phrasing of your question in the subject line would have been achieved by replacing the the first occurrence of the word "impedance" with the word "resistance" since in this case, the cable "impedance" is immaterial to this question.The myth that an amplifier with an output impedance of 0.02 ohms provides a damping factor of 400 on an 8 ohm speaker load is just that, a myth. At best you might see an effective DF of circa 4 on the typical 32 ohm resonant impedance (the characteristic behaviour that is being damped) of an eight ohm voice coil driven speaker cone (roughly the sum total of amplifier impedance plus maybe half an ohm loop resistance of cable plus 7.5 ohms or so of voice resistance versus the 32 or so ohms resonant impedance of the speaker).Such wonderful transistorised amplifiers do NOT improve the DF a hundredfold over that of a valved (tubed) amp with an output Z of 2 ohm with a half ohm loop resistance cable driving the same speaker voice coil load. In the transistorised amp case, the actual DF is only around 4 versus the valved (tubed) amp case of 3.2 which is a mere 25% improvement by the transistorised amp over that of its valved predecessors.In short, the DF figures published by the solid state amplifier manufacturers were (are still?) pure marketing bullshit designed to persuade their target demographic to give up their treasured valved amps for these nice shiny new wonders of solid state technological excellence in amplification. Unfortunately for those who fell for the false advertising claims back in the 1970s, those solid state technological wonders of amplification had far worse vices than the less than perfect valved amplifiers they were supposedly superior to.However, in the intervening four decades or so since those dark days, the industry has learnt a lot of valuable lessons and high power mosfet transistors became available many years since (two decades or so?) to address the limitations of the early bi-polar power transistors such as the classic 2N3055s so commonly employed in those early designs. Modern solid state amplifiers are a world away from those early amplifier designs and do now offer genuine improvements over the classic valved amplifiers from the late 20th century.The short answer to your question btw, is that unless you're planning on using several hundreds of yards of the thinnest of thin headphone cables, I wouldn't worry about it. it'll make bugger all difference. It's only the resonant impedance of the drive unit as explained above that's being damped everything else, the voice coil resistance (typically 95% or more of the drive unit's nominal impedance), the cable loop resistance and the amplifier's output impedance are all effectively in series across the resonant impedance which, for a speaker drive unit might be as high as 4 or 5 times its nominal impedance (headphone drive units may be even lower than this). It's not the nominal drive impedance you're trying to damp out but its much higher resonant impedance.Your main concern with the additional 2 ohms will be over the matter of the dB or so loss this will introduce, not the imperceptible reduction in damping effect on the resonance peak at the bottom end of the drive unit's frequency response plot.HTH & HANDJBG

author: fonograph
author_rank: Frequent Contributor
timestamp: February 15, 2019, 09:23:17 pm
content: I have never seen a thread being derailed so hard in my entire life. All I asked is if cable impedance adds up to source or load, a extremly simple question that can be answered in one sentence and somehow this turned into discusion about audio, a topic I foolishly chosen believing it will be obvious to everybody that I used it merely to give a example to help deliver my question and that this topic of audio is in context of this thread and purpose of my question completly irrelevant, and unimportant.That is like if you had 6 year old son and he came to you asking how many apples does Bob have if he picked 10 from tree, gave away 2 to grandma and 3 to sister, a first grade homework question that any adult not suffering from brain damage should be able to clearly answer in one sentence yet you would then go on hour long rant about pesticides, fructose intolerance, global warming and its impact on apple yields, stupid politicians making retard laws about imported apples, morals of genetical modification of apples, apple pie recipes and your neighbour who steals apples from your tree in garden by reaching over the fence.

author: Audioguru
author_rank: Super Contributor
timestamp: February 15, 2019, 10:06:56 pm
content: Cheap intercoms and TVs sound very boomy at the resonant frequency of the speaker and its enclosure. I think because its amplifier has a fairly poor damping factor. I think they will sound much better if the amplifier has a high damping factor.

author: Johnny B Good
author_rank: Frequent Contributor
timestamp: February 16, 2019, 12:29:22 am
content: Quote from: Audioguru on February 15, 2019, 10:06:56 pmI'm afraid to say that you're quite wrong in thinking that a low Z output amplifier will have any noticeable effect on the audio quality of such speaker arrangements. The poor quality is essentially down to enclosure resonances with just one significant contribution from the drive's own resonance which can only be damped by the voice coil resistance in series with the amplifier's output impedance which can easily be less than an ohm even with a cheap amplifier meaning an effective DF of just 4 or less regardless of how high a DF is claimed for the amp. The other resonances created by the enclosure will remain unaffected by the DF rating of the amplifier since they're effectively decoupled from the drive unit's voice coil and cone assembly.To give fonograph the short answer he was seeking, the loop resistance of the cable simply adds to that of the amplifier's impedance and the voice coil resistance since they're all effectively in series across the drive unit's impedance at resonance, typically some three to five times its nominal impedance. It is this resonance impedance that's being damped, not the nominal 4 or 8 or 15 ohm (or whatever) given for the drive unit.The damping factor figures of merit often quoted in the glossy brochures' advertising copy back in the 1970s were/are simply marketing bullshit designed to emphasise out of all proportion the importance of the ultra low output impedance figures that could be so readily achieved with voltage negative feedback in these new fangled DC coupled solid state amplifiers. The importance of lo-Z was grossly overstated as it relates to any drive unit damping effect, limited as it is by the series resistance of the drive unit's voice coil.HTH & HANDJBG

author: Zero999
author_rank: Super Contributor
timestamp: February 16, 2019, 10:55:43 am
content: Quote from: fonograph on February 15, 2019, 09:23:17 pmDon't worry about it. This is fairly common, especially with audio. As I said above, as far as power audio amplifier are concerned resistance = impedance. Although some may find the extra information useful, it can be a pain filtering it.From the amplifier's perspective, the resistance of the cable adds to the load resistance. If the cable is 1Ω and speaker is 8Ω, then the amplifier sees a 9Ω load.From the load's perspective, the resistance of the cable adds to the amplifier's resistance. If the speaker is 8Ω, the cable 1Ω and the amplifier has an output impedance of 0.5Ω, then the speaker sees a voltage source with an impedance of9.5Ω1.5Ω.I hope that answers the question.

author: fonograph
author_rank: Frequent Contributor
timestamp: February 16, 2019, 11:47:56 am
content: Quote from: Zero999 on February 16, 2019, 10:55:43 amThis is excellent answer, thank you very much Zero999.

author: macboy
author_rank: Super Contributor
timestamp: February 16, 2019, 12:59:44 pm
content: Quote from: fonograph on February 15, 2019, 04:02:27 amActually it is both.From the perspective of the load (speaker), the source has an additional 2 ohms. From the perspective of the amplifier, the load has an additional 2 ohms.

author: unitedatoms
author_rank: Frequent Contributor
timestamp: February 16, 2019, 01:42:55 pm
content: Quote from: macboy on February 16, 2019, 12:59:44 pmFor completeness of model, you may choose to consider 4 impedances of 3 devices. Single port source Zs, two port cable with Zin and Zout, and single port load Zl.My estimate is that typical speaker cable (two thick wires as air line) is about hundred ohms. With insertion loss of -0.00x dB at low Hz frequencies.edit: I looked up for formulations.For 1 meter loslsess cable with characteristic impedance of 100 Ohm, 4 Ohm active load the cascade at 1000Hz will look like4 Ohm plus 0.002 imaginary ohms.http://www2.ece.ohio-state.edu/~johnson/311/week3.pdfhttps://www.wolframalpha.com/input/?i=z%3D100*((4%2B0.002096i)%2F(100%2B0.0000838i))https://en.wikipedia.org/wiki/Vacuum_permittivitylost link to value of mu, it is 1.257e-6Henries/meterThe reactance value can be represented as lumped component , inductance about 300nanoHenriesSo to answer the topic. You may choose to add very small inductance to load impedance.Also equally valid to add inductance to source impedance instead.But to be absolutely correct, the cable should be considered a lossy line and must be not added to either and model should be of 3 devices.edit 2: Coming from VNA metrology lingo. It looks like for cables with load there is a general intuitive rule. The loads lower than characteristic impedance of line will make input of a cable to look like inductance, the matching loads will look like active load and the loads higher than characteristic impedance will look like capacitance. That sounds very intuitive and with agreement to calibration standards story for VNAs.With assumption that line is very short. Lines longer than some portion of lambda will look very different.

author: Zero999
author_rank: Super Contributor
timestamp: February 18, 2019, 08:30:22 am
content: Quote from: fonograph on February 16, 2019, 11:47:56 amExcept for the fact I made a mistake, which I've corrected.