thylantyr

12-11-2006, 01:12 PM

I've noticed alot of people on forums jumping on the CAT5 speaker wire

bandwagon. They are taking networking wire and making into speaker

wire as they think it's superior.

To make matters worse, these guys did a wire test;

http://www.audioholics.com/techtips/setup/interconnects/DIYSpeakerCablesp1.html

This test is misleading to the consumer as they rank cables implying that

certain brands aren't good as speaker wire.

I did some basic electronics math to see what the skinny is all about.

Wire has resistance, capacitance and inductance. They measured those

variables and formed a conclusion. But there is more to the story than

what was told. How does the particular wire perform in it's 'line driving'

application ?

How much resistance, capacitance and inductance is ok before your

speaker wire behaves like a low pass filter which will attenuate the higher

audio frequencies? We can look at wire gauge and know it's current

ratings per foot, so I don't need to talk about this as we already know.

Preamp Line Driving

This Rane article "Practical Line-Driving Current Requirements" is a good read.

http://www.rane.com/note126.html

It talks about small signal line driving {preamp level}, but the same is true

for large signal line driving, ie amplifier to speaker.

Look at figure 2.

Ro = Source output impedance

Cw = Total cable capacitance

RL = Input impedance of the load.

Look at figure 3. The formula.

You use this to analyze your signal path, either preamp or power amp.

For instance, lets say you bought some cable to make your own RCA

or XLR preamp cables. If you know the cable capacitance, source output

impedance, and destination input impedance, you can see if that cable

you chose will will in the audio range with no low pass filter effects in

the audio range.

Lets say your preamp is 100 ohms output impedance, and your amplifier is

10,000 ohms input impedance and the cable you chose has a rating of

50 pF {pico Farads} per foot. You decide you need a 100 foot cable.

Math.

Ro = 100 ohms

Cw = 50 pF x 100 foot = 5000 pF {or 0.005 uF, or 0.000000005 Farads}

RL = 10,000 ohms

Because the Ro is significantly less than RL, you can use the short formula.

Fc = 1 / (2 pi Ro Cw)

Fc = 318 khz

318khz is way higher than the audio range, 20khz so this cable would

work in this application.

Power Amp Line Driving

Amplifier output impedance is very low vs. the speaker load. Amplifier damping factor gives you a clue on how low output impedance is. Damping factor is

a ratio.

DF = load / amp output impedance.

or

amp output impedance = load / DF

If your amp has a damping factor of 100 {assume @ 20khz} driving an 8 ohm

load, then the amp output impedance is about 0.08 ohms.

Fc = -3dB point, cutoff frequency.

Ro = 0.08 ohms

Cw = 50 pF x 100 foot = 5000 pF {or 0.005 uF, or 0.000000005 Farads}

RL = 8 ohms

Lets use the same 50pF capacitance and lets say you are running a 100 foot

speaker wire.

Because the Ro is significantly less than RL, you can use the short formula.

Fc = 1 / (2 pi Ro Cw)

Fc = 379 Mhz

This is way outside the audio range.

Speaker Wire Inductance

Speaker wire is like an inductor and when you connect your amplifier

to speaker wire to the speaker, it's as if you are adding an inductor in

series just like a first order woofer crossover.

The math is simple.

Fc = RL / (2pi L)

Fc = -3dB point, cutoff frequency.

L = cable inductance

RL = speaker load

The worse speaker wire of the bunch tested has an inductance of 0.3 uH

per foot. Lets assume you are going run 100 foot between amp and speaker.

L = 0.3uH x 100 feet = 30 uH

RL = 8 ohm speaker

Fc = 42.4khz

This is way outside the audio range of 20khz

Conclusion

Unless I analyzed wrong, cable capacitance even using cheap cables doesn't play

a big role in affecting the audio signal. Even cheap speaker wire with high inductance

and a 100 foot run is still 2x beyond the audio range where you have low pass filtering effects.

To add, inductance in preamp cables connecting to high input impedance equipment doesn't

play a big role either.

bandwagon. They are taking networking wire and making into speaker

wire as they think it's superior.

To make matters worse, these guys did a wire test;

http://www.audioholics.com/techtips/setup/interconnects/DIYSpeakerCablesp1.html

This test is misleading to the consumer as they rank cables implying that

certain brands aren't good as speaker wire.

I did some basic electronics math to see what the skinny is all about.

Wire has resistance, capacitance and inductance. They measured those

variables and formed a conclusion. But there is more to the story than

what was told. How does the particular wire perform in it's 'line driving'

application ?

How much resistance, capacitance and inductance is ok before your

speaker wire behaves like a low pass filter which will attenuate the higher

audio frequencies? We can look at wire gauge and know it's current

ratings per foot, so I don't need to talk about this as we already know.

Preamp Line Driving

This Rane article "Practical Line-Driving Current Requirements" is a good read.

http://www.rane.com/note126.html

It talks about small signal line driving {preamp level}, but the same is true

for large signal line driving, ie amplifier to speaker.

Look at figure 2.

Ro = Source output impedance

Cw = Total cable capacitance

RL = Input impedance of the load.

Look at figure 3. The formula.

You use this to analyze your signal path, either preamp or power amp.

For instance, lets say you bought some cable to make your own RCA

or XLR preamp cables. If you know the cable capacitance, source output

impedance, and destination input impedance, you can see if that cable

you chose will will in the audio range with no low pass filter effects in

the audio range.

Lets say your preamp is 100 ohms output impedance, and your amplifier is

10,000 ohms input impedance and the cable you chose has a rating of

50 pF {pico Farads} per foot. You decide you need a 100 foot cable.

Math.

Ro = 100 ohms

Cw = 50 pF x 100 foot = 5000 pF {or 0.005 uF, or 0.000000005 Farads}

RL = 10,000 ohms

Because the Ro is significantly less than RL, you can use the short formula.

Fc = 1 / (2 pi Ro Cw)

Fc = 318 khz

318khz is way higher than the audio range, 20khz so this cable would

work in this application.

Power Amp Line Driving

Amplifier output impedance is very low vs. the speaker load. Amplifier damping factor gives you a clue on how low output impedance is. Damping factor is

a ratio.

DF = load / amp output impedance.

or

amp output impedance = load / DF

If your amp has a damping factor of 100 {assume @ 20khz} driving an 8 ohm

load, then the amp output impedance is about 0.08 ohms.

Fc = -3dB point, cutoff frequency.

Ro = 0.08 ohms

Cw = 50 pF x 100 foot = 5000 pF {or 0.005 uF, or 0.000000005 Farads}

RL = 8 ohms

Lets use the same 50pF capacitance and lets say you are running a 100 foot

speaker wire.

Because the Ro is significantly less than RL, you can use the short formula.

Fc = 1 / (2 pi Ro Cw)

Fc = 379 Mhz

This is way outside the audio range.

Speaker Wire Inductance

Speaker wire is like an inductor and when you connect your amplifier

to speaker wire to the speaker, it's as if you are adding an inductor in

series just like a first order woofer crossover.

The math is simple.

Fc = RL / (2pi L)

Fc = -3dB point, cutoff frequency.

L = cable inductance

RL = speaker load

The worse speaker wire of the bunch tested has an inductance of 0.3 uH

per foot. Lets assume you are going run 100 foot between amp and speaker.

L = 0.3uH x 100 feet = 30 uH

RL = 8 ohm speaker

Fc = 42.4khz

This is way outside the audio range of 20khz

Conclusion

Unless I analyzed wrong, cable capacitance even using cheap cables doesn't play

a big role in affecting the audio signal. Even cheap speaker wire with high inductance

and a 100 foot run is still 2x beyond the audio range where you have low pass filtering effects.

To add, inductance in preamp cables connecting to high input impedance equipment doesn't

play a big role either.