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 total resistance is doubled in the simulations since there are two wires in each pair (+ and -). 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.
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.
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).
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 (a0), planar-dynamic (a1), hybrid ESL (a2), and second hybrid (a3, 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.
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.
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.
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:
SS Amp:
Tube amp:
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.
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.
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
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 total resistance is doubled in the simulations since there are two wires in each pair (+ and -). 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.
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.
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).
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 (a0), planar-dynamic (a1), hybrid ESL (a2), and second hybrid (a3, 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.
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.
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.
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:
SS Amp:
Tube amp:
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.
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.
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
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