The Impact of Speaker Wires on Frequency Response

[DonH56]

I added an addendum to the first post to show the effect of cable length using the second SS amp and 12 AWG cables that are 3', 10', and 20' long.

 

[Bruce Morgen]

Thanks Jim, Adam, et. al.! Not sure I can live up to that last sentence...

Don't doubt that for a nanosecond, Don. You've been a great resource for the non-EEs among us -- yours truly included -- even if some of us techno-dilettantes tend to lose patience and go "TL;DR" from time to time. IMO your contributions are invaluable!

 

[antcollinet]

they are to help explain and show things to less technical folk.

Exactly - they tell us what we already know, but give us something to point at when trying to explain what it is we know. As always a picture's worth 1K words.

Thanks for the effort you've put into this.

 

[NTTY]

Thank for the effort, this is a reference article indeed!

One note though, you wrote:

All the results show the frequency response at the speaker terminals with the amp connected directly to the speaker (“a_”), via 10’ of 18 AWG cable (“a_w1”), and 10’ of 18 AWG cable ("a_w2”).

"a_w1" is the 10 AWG lower resistance cable, right?

————
Flo

 

[notinuse]

Engineers are welcome to look up Richard Greiner and Fred Davis's work from about 40 years ago. Non-engineers can get the same thing in more understandable form from Don and Pavel.

If that is the same Richard Greiner that taught engineering at UW-Madison, he was one of my professors in the late '70s.

 

[SIY]

If that is the same Richard Greiner that taught engineering at UW-Madison, he was one of my professors in the late '70s.

Yep. I met Dick several times while I was working at Nicolet. Super smart guy and damn nice as well.

 

[notinuse]

Yep. I met Dick several times while I was working at Nicolet. Super smart guy and damn nice as well.

He was really smart, and a very nice guy. So you worked at Nicolet Instrument? They used to bring new products to our lab classes sometimes, so we could check out the upcoming 'scopes.

 

[DonH56]

Thank for the effort, this is a reference article indeed!

One note though, you wrote:

All the results show the frequency response at the speaker terminals with the amp connected directly to the speaker (“a_”), via 10’ of 18 AWG cable (“a_w1”), and 10’ of 18 AWG cable ("a_w2”).

"a_w1" is the 10 AWG lower resistance cable, right?

————
Flo

Yes, corrected, sorry. I originally had 18 AWG then 10 AWG but realized it made more sense to reverse the order so the plots were easier to follow visually. Source (no wire), 10 AWG, then 18 AWG drops the curves in order so easier to see and track the changes. Had to repeat all the durn simulations, of course.

 

[sam_adams]

@DonH56, nice writeup. Thanks for putting in the time on this. Another great resource to have on hand when the question comes up again. Could you zip up the sim files and attach them to the first post?

 

[SIY]

So you worked at Nicolet Instrument

Yes, it was a terrific experience. I shared an office with their Chief Scientist, with whom I'm still close friends. One of the most professionally productive and educational times of my career, and I really liked Madison.

 

[DonH56]

@DonH56, nice writeup. Thanks for putting in the time on this. Another great resource to have on hand when the question comes up again. Could you zip up the sim files and attach them to the first post?

Thanks.

The files are a bit of a mess but I can just attach them for anybody who really wants to see how the sausage is made. It's been a while since I used LTSpice so had to figure out a few dumb mistakes first, and never did figure out how to pass parameters into a model call (LTSpice might not allow that; some others do, and I have used a dozen or so different simulators so get them mixed up). Consider them "as-is" and I do not want to know about any (more) errors.

 

[DonH56]

Yes, it was a terrific experience. I shared an office with their Chief Scientist, with whom I'm still close friends. One of the most professionally productive and educational times of my career, and I really liked Madison.

A company I worked for had some Nicolet stuff, and Dick ??? (forgot the last name, sorry) stopped in one time to see how things were going. Great guy, polite and passionate all in one.

 

[sam_adams]

for anybody who really wants to see how the sausage is made.

Mmmm . . . sausage!

 

[Cool Runnings]

This article is to look at the impact speaker cables may have on frequency response. For this study three amplifiers driving four speakers using no cables and 10’ (~3 m) of 18 AWG or 10 AWG cables are modeled and the frequency response at the speaker terminals simulated. The implicit assumption is that frequency deviations at the terminals can affect the acoustic output of the speakers given they are designed to be driven by an ideal voltage source (a perfect amplifier). In general, real amplifiers are used, so speakers may be designed using a particular amplifier (or set of amplifiers), but in practice these simulations will still show how frequency response can change with different cables.

The amplifiers are a wideband solid-state (SS) AVR amplifier with very low output impedance (and thus very high damping factor), another SS amplifier with more modest output impedance and bandwidth, and a relatively high-impedance (low damping factor) tube amplifier.

The speaker models are the Stereophile speaker load and three models based upon previously-measured speakers: a planar dynamic (e.g. Magnepan, a two-way model and not my MG-IIIa three-way speaker) model with mostly resistive impedance, a hybrid ESL speaker (e.g. Martin Logan), and an old hybrid speaker that I think is another ESL (I had thought it a ribbon, but the phase looks ESL’ish). The latter has a pretty severe impedance peak in the midrange and is one I have used for many years as a “heavy” load. Note that, due to the coupling transformer, the phase of ESLs is often inductive at high frequencies despite the panel itself being one big capacitor.

These are the same amplifier and speaker models I have used in previous articles.

The wires are 18 AWG and 10 AWG twin lead copper (not CCA) cables typical of speaker wire you buy at a store (or online). Resistance per conductor is 6.385 m-Ohms/ft for 18 AWG and 0.9989 m-Ohms/ft for 10 AWG, so the resistance is doubled in the simulations. I used a simple distributed model for capacitance and inductance, with 18 AWG having 15 pF/ft and 0.2 uH/ft, while the 10 AWG cable has 25 pF/ft and 0.1 uH/ft. These are typical numbers for standard “zip cord”. I choose two sizes that bound typical runs of speaker cable in my experience, though today most knowledgeable people are probably running 12 or 14 gauge cables.

Here are the output impedance and damping factor (into 8 ohms) of the three amplifiers. I have included phase since that question has been previously asked, though it is very small within the 10 Hz to 20 kHz audio band of interest. The plots go to 200 kHz so we can see the rising output impedance as feedback is reduced and output devices become more inductive (note the phase is trending positive). The models do not reflect the amplifier’s bandwidth past the audio band, it is a constant voltage, so the rising output impedance will not interact as much with the speakers as shown in simulations since the output will be much lower. The SS AVR has very wide bandwidth and output impedance changes little even to 200 kHz. The other SS amp has less bandwidth (though still well above the audio band) and thus higher impedance at higher frequencies, again still low within the audio band. The tube amplifier has high output impedance with bandwidth falling between the SS amplifiers.

View attachment 392334

Damping factor follows the output impedance as shown below. Ignore the units; they are an artifact of the simulation. You can see the SS AVR has very high damping factor, the second SS amp starts high but falls more quickly (though still 60 at 20 kHz, plenty for tweeters or most any speaker), and the tube has very low but fairly flat damping factor.

View attachment 392335

Next are the speaker impedances. The first (top) is the Stereophile test load as presented on their web site (and magazine; I originally pulled this long ago from the printed magazine). It is 8-ohm nominal with a low around 4 ohms. The planar-dynamic model is almost a purely resistive 4-ohm load. The hybrid ESL is not too bad until dropping over 10 kHz, though this particular model is still 3 ohms at 20 kHz (other ESLs drop to 1-2 ohms). You can see why the other hybrid (bottom) is such a hard load; it dips low in the bass and at high frequencies, with the aforementioned peak around 1.3 kHz. The phase in these plots is useful to show relative variation over frequency but ignore the absolute values (a consequence of phase unwrapping and the test probe).

View attachment 392336

For the first simulations, the speaker wire is modeled as purely resistive, with no capacitive or inductive components in the wire models. All the results show the frequency response at the speaker terminals with the amp connected directly to the speaker (“a_”), via 10’ of 10 AWG cable (“a_w1”), and 10’ of 18 AWG cable ("a_w2”). The speakers from top to bottom are the same as above: Stereophile model, planar-dynamic, hybrid ESL, and second hybrid (worst-case).

For the SS AVR, variation is less than 0.5 dB for all speakers, even with the 18 AWG wires. You can see, however, that 10 AWG wire is much closer to the amp without cables (directly driving the speakers), with just a fraction of dB loss and variation over frequency.

View attachment 392337

The second SS amp exhibits more variation as expected, though still <1 dB for all cases even with 18 AWG wires. Again we see that 10 AWG results in performance almost identical to that with no wires between amp and speaker.

View attachment 392338

Finally, this is the response using the tube amplifier. Because its output impedance is high, speaker cables have little impact on the response, since the cables are in series with the amplifier’s output impedance. I could zoom in to show the effect, but it is essentially buried by the output impedance, so the curves practically overlie. This is an example of why people might choose particular amp and speaker combinations to meet their preferences.

View attachment 392339

Here are the results with distributed RLC models of the speaker cables. The main change is a slight peaking in high-frequency response of the SS amplifiers, especially with the ESL speakers; there is essentially no change with the tube amp.

SS AVR amp:

View attachment 392340

SS Amp:

View attachment 392341

Tube amp:

View attachment 392342

Finally, here are the results for the second SS amplifier comparing the purely-resistive 10 AWG model (w1) to the RLC models (w2). This makes it easy to see how reactive elements change the response, and how it interacts with the amp and speaker impedances. In all cases, the resistive and RLC models essentially overlie until 1 kHz or above. The Stereophile model causes slightly higher response, though negligible at less than 0.05 dB. The planar-dynamic has very little change. The two ESL hybrids exhibit about 0.2~0.3 dB change at 20 kHz from the purely resistive wire to the RLC models.

View attachment 392343

These simulations indicate that ten feet of cable can have some impact, though likely inaudible unless the cable is small, and if the amplifier has sufficiently low output impedance so that the cable’s added impedance is significant. The results also show the effect of cables is primarily due to their resistance, although adding capacitance and inductance can influence the higher-frequency response significantly (not sure if audibly, leave that to you).

HTH - Don

Edit: For actual speaker measurements, Pavel @pma has this excellent thread: https://www.audiosciencereview.com/...er-cables-in-frequency-and-time-domain.22894/

Addendum: The plot below shows the second SS amplifier driving the same four speaker loads but now using 12 AWG cables that are 3’ (top), 10’ (middle), and 20’ (bottom) long. This allows us to assess how length affects the response.

View attachment 392517

Addendum 2: I attached a zip file with the LTSpice schematics and plot files. Consider them "as-is", though the filenames are somewhat descriptive, but hopefully looking at the schematics will tell you what they do. I also included the older speaker impedance files for reference.

See attachment 20240916_Amp_plus_wires.zip

LTSpice: https://www.analog.com/en/resources/design-tools-and-calculators/ltspice-simulator.html

Thank you for this Don. I am definitely your non-tech target audience. Even then I could probably understand 50% of this at best.

Perhaps you could help laymen like me further by putting in a few simple summary thoughts.For eg Speaker cables do make a theoretical FR difference under certain conditions. However, these differences are highly unlikely to be audible unless (insert qualifiers). For all practical intents and purposes, any decent 18 AWG and above cable will do just fine. Don't need to spend more than $50 bucks for each cable unless you're spending for audio jewelry purposes. That essentially is my takeaway haha

 

[DonH56]

Thank you for this Don. I am definitely your non-tech target audience. Even then I could probably understand 50% of this at best.

Thanks, but I was hoping for more understanding... These articles are really a no-win for me; for engineers and such they are far too basic, and for people with no technical background they are too hard. Like any compromise, I figure if nobody likes them, but half are on one side and half on the other, I've done the best I can.

Edit: I do not know if there is already a thread, but if you have questions, ask here, or open a generic thread to answer basic questions we (techies) take for granted? After decades of doing this stuff, it is far too easy to forget or miss a basic term obvious to me but incomprehensible to laymen.

Perhaps you could help laymen like me further by putting in a few simple summary thoughts.For eg Speaker cables do make a theoretical FR difference under certain conditions. However, these differences are highly unlikely to be audible unless (insert qualifiers). For all practical intents and purposes, any decent 18 AWG and above cable will do just fine. Don't need to spend more than $50 bucks for each cable unless you're spending for audio jewelry purposes. That essentially is my takeaway haha

Close enough. I tend to go light on "audible" because it always ends up in a huge debate about what is audible and I'd rather just present the data and let y'all duke it out. I usually put in a comment or two and inevitably get told I am wrong. Blah.

I added the last plot because length is important. My front stage is within 6' or so of the amplifiers, though I think I have 10' or so cables because that's what I had on hand, but the rears are pushing 40' runs since they have to run along a side wall and across the back due to a door in the way. The fronts are on 12 AWG, the rears 11 AWG, and the heights (not sure length but not short) 14 AWG. I have a 500' spool of 10 AWG cable for the bed layer that I've never gotten around to using, it cost me about $200 at the time.

The only thing I tend to quiver about (aside from grandiose claims for expensive cables) is the use of CCA. Half the price but too many drawbacks for me. Speaker cable is usually a one-time buy that lasts many years so any decent pure copper 14~12 AWG is what I would suggest.

 

[Cool Runnings]

Thanks, but I was hoping for more understanding... These articles are really a no-win for me; for engineers and such they are far too basic, and for people with no technical background they are too hard. Like any compromise, I figure if nobody likes them, but half are on one side and half on the other, I've done the best I can.

Edit: I do not know if there is already a thread, but if you have questions, ask here, or open a generic thread to answer basic questions we (techies) take for granted? After decades of doing this stuff, it is far too easy to forget or miss a basic term obvious to me but incomprehensible to laymen.


Close enough. I tend to go light on "audible" because it always ends up in a huge debate about what is audible and I'd rather just present the data and let y'all duke it out. I usually put in a comment or two and inevitably get told I am wrong. Blah.

I added the last plot because length is important. My front stage is within 6' or so of the amplifiers, though I think I have 10' or so cables because that's what I had on hand, but the rears are pushing 40' runs since they have to run along a side wall and across the back due to a door in the way. The fronts are on 12 AWG, the rears 11 AWG, and the heights (not sure length but not short) 14 AWG. I have a 500' spool of 10 AWG cable for the bed layer that I've never gotten around to using, it cost me about $200 at the time.

The only thing I tend to quiver about (aside from grandiose claims for expensive cables) is the use of CCA. Half the price but too many drawbacks for me. Speaker cable is usually a one-time buy that lasts many years so any decent pure copper 14~12 AWG is what I would suggest.

Nah it’s all good man. Turns out I got most of your message Appreciate you and all the other techies here always being patient with us non tech folks.

 

[tomtoo]

Nothing will change,there are the people that can read the graphs and say speaker cables are not a problem. And there are the people that cant read the graphs and say speaker cables under 5$/inch sound horrible. The hifi industrie loves the second sort much more.

 

[pogo]

My experience with LTspice almost 20 years ago was that a good result depends on realistic models and stimulus. I see the biggest deficits here in the speaker models, which tend to be static.
This topic is not trivial and good information can be found here, but it certainly does not cover everything:
'High Performance Audio Power Amplifiers' by Ben Duncan
7.4.3 Damping factor & 2.3.2 What speakers are looking for

 

[DonH56]

My experience with LTspice almost 20 years ago was that a good result depends on realistic models and stimulus. I see the biggest deficits here in the speaker models, which tend to be static.
This topic is not trivial and good information can be found here, but it certainly does not cover everything:
'High Performance Audio Power Amplifiers' by Ben Duncan
7.4.3 Damping factor & 2.3.2 What speakers are looking for

The use of any simulator depends upon the models (and the simulation algorithm, of course). I used distributed RLC (lossy transmission line) models for the wires, which should be more than adequate at audio frequency (I have used similar models to 100+ GHz, though over 1-10 GHz tend to use S-parameters instead as the lossy line model is limited and distributed subcircuit models get complicated). Static (linear) speaker models are more than good enough for frequency response, and dynamic (behavioral) speaker models I do not have and have not had in years (at the time I had access to SABER, a very good mixed-signal simulator with extensive electromechanical models). Note the speaker models I use are based upon either recognized standards (Stereophile's) or my own measurements (the other three).

I always try to encourage you or anyone who wants to dig deeper to do so and create a thread with more advanced models and simulations to illustrate more facets of the problem. Most of my articles do not go that deep, not necessarily due to my own ignorance (though speaker design is not my day job!), but rather to attempt to bring some engineering and physics to laypeople on ASR wishing to learn a bit more about the technical side of things. I do not consider any of these topics trivial, but folk with an engineering or related degree will likely know all of this and/or dig deeper on their own, whilst your average audiophile not having years of technical courses and experience needs a starting point.

That is probably the most frustrating part of these articles; trying to present technical information in a manner most people can follow, while knowing those with technical backgrounds will find much to critique, with implicit (sometimes explicit) references to the competence and credibility of the author. As I have said many times, as long as both sides are equally dissatisfied, I've done my best.

 

[pogo]

extensive electromechanical models

Back-EMF, ...