[opaqueice]

1.  Does the fact that my speaker cable lengths range from 8" to 12" cause any problems to my amps?  And BTW, these amps do have series output inductors and they also have feedback!  (I have seen various pundits proclaiming that there is a minimum length of cable which is ideal for any amp?)

I can give you my opinion, based on what I know.  Let me stress that I'm not an electrical engineer, and so there may be some factors I'm not aware of.  

That said, I know of no reason why short speaker cables would be a problem.  On the contrary - the shorter the cables the less likely you are to have a problem of the type discussed in this thread, because regardless of the cable's impedance, at low frequency it always sees the load impedance.  The plots in the post above this one show that clearly - it's only at MHz frequencies that any of these effects come into play, and that frequency is proportional to (L C)^(-1/2), so it's higher for shorter cables.  That's exactly consistent with my analysis (which was really pretty trivial - I don't mean to make it sound fancy).

2.  Ignoring the effect of 'C' on the amp (since cable 'C' is tiny in my setup) and given that my amps see resistive loads of 4, 3.2 and 3 ohms (Maggie drivers), I'm wondering about the relevance of jneutron's post on 24 Sep:
"When the line impedance matches that of the load ... etc?".

The line impedance of 12" of cable certainly isn't anywhere near 4 ohms!    But neither would the impedance of 12' of cable be!    So WTF's he on about? 

The characteristic impedance is the square root of L/C.  Since both L and C are proportional to the length of the cable (at least to a decent approximation), the impedance doesn't depend on length.

3.  Expressed in a slightly different way ... if the C of the speaker cable and the L are negligible (8"), does jneutron's point have any relevance?

For the reasons stated in my response to point 1 and in this thread, unless the amp is producing frequency components near or above (L C)^(-1/2) the impedance of the cable is irrelevant.  The amp sees the load and nothing more.  So for very short cables you are safer.

4.  I have read comment about the signal in speaker cables being reflected between the speaker BPs and the amp BPs.  IE. if the setup is "wrong", you get lots of reflection between the two and this muddies up the sound. 

You simply don't have to worry about reflections, or any other wave phenomena, when the frequency is below (L C)^(-1/2).  But yes, at high frequencies you can think of impedance matching and these other phenomena as being due to reflections and waves bouncing back and forth down the cable.

[opaqueice]

Daryl..nice graph...  dB ohms and dB frequency did confuse me at first...but it does make the graph more well behaved..  It does show the match as being ruler flat through the breakpoint frequency, but can you change the freq units from dB to powers of 10 for us dummies??

That confused me too  .  I think 65 db-ohms means 65 = 10 log_10 R, so R = 10^(6.5).

You can see what I was saying in that plot, by the way - notice how Daryl's lines are flat and equal to the load impedance until you get to MHz frequencies.  That's  the part the single element analysis captures, plus the first correction.

[jneutron]

You simply don't have to worry about reflections, or any other wave phenomena, when the frequency is below (L C)^(-1/2).  But yes, at high frequencies you can think of impedance matching and these other phenomena as being due to reflections and waves bouncing back and forth down the cable.

Given HoJo's analysis using t-line as the basis, the actual resonant point can be 1/4 that of the lumped analysis...however, were still talking very high frequencies regardless of which analysis is used.(like falling out of a plane at 1000 feet vs 4000)..  I would be surprised to find amps which even run to 10Mhz.

You can see what I was saying in that plot, by the way - notice how Daryl's lines are flat and equal to the load impedance until you get to MHz frequencies.  That's  the part the single element analysis captures, plus the first correction.

Agreed.  What is not shown there is the equivalent capacitance or inductance as a result of the mismatch.  I'm workin on that..

Note:  The problem I was muddling over is:  For low loads, it's clear how the inductive energy increases with bigger mismatch, but capacitive doesn't increase as load z goes above match..So I was considering V drive below cableZ and I drive above cable Z..  Or, just normalize the output power into the load.  That way, I can subtract the matched energy storage from the mismatched, then back into the equivalent capacitance difference..

Yah, I like the normalized energy method...I'll try it that way first..

Cheers, John

[opaqueice]

Given HoJo's analysis using t-line as the basis, the actual resonant point can be 1/4 that of the lumped analysis...however, were still talking very high frequencies regardless of which analysis is used.(like falling out of a plane at 1000 feet vs 4000)..  I would be surprised to find amps which even run to 10Mhz.

Yeah, it's true that those plots look like they start to bend a bit sooner than expected...  maybe I did miss a factor of 4 somewhere.  Still, for 12 inch cables we're talking really high frequencies (multiply the frequencies in that plot by 20).

If I have a chance I'll expand the exact answer I had and make sure the coefficients match the single element approximation.

[jneutron]

Given HoJo's analysis using t-line as the basis, the actual resonant point can be 1/4 that of the lumped analysis...however, were still talking very high frequencies regardless of which analysis is used.(like falling out of a plane at 1000 feet vs 4000)..  I would be surprised to find amps which even run to 10Mhz.

Yeah, it's true that those plots look like they start to bend a bit sooner than expected...  maybe I did miss a factor of 4 somewhere.  Still, for 12 inch cables we're talking really high frequencies (multiply the frequencies in that plot by 20).

If I have a chance I'll expand the exact answer I had and make sure the coefficients match the single element approximation.

You could tell that from the plot???   I just gave up on figgerin the frequency, so carefully worded my verbage to make it seem like I understood but wanted it clearer for those "other guys"..   (I'm such a nice guy, always thinkin of others...)

Cheers, John

[opaqueice]

You could tell that from the plot???   I just gave up on figgerin the frequency, so carefully worded my verbage to make it seem like I understood but wanted it clearer for those "other guys"..   (I'm such a nice guy, always thinkin of others...)

Cheers, John

 

Just take those numbers, divide by 10, and then raise 10 to that power (e.g. 65 db-Hz = 10^6.5 Hz).  At least I'm pretty sure that's what he means.

[andyr]

Thanks, jneutron & opaqueice.

A couple of Qs for you as I'm puzzled about a coupla things.

Q1:  OK, if one has speaker cables which are low C (and in my case, low L too, as they're so short), then can the cables be considered to be "matched" to the load?

Q2:  In your reply, John, you said "no reflection (match condition), no inductance or capacitance is seen by the amp."  So does the reverse hold true ... ie. no inductance or capacitance in the cable, therefore no reflection - ie. match condition?

Thanks,

Andy

[opaqueice]

Thanks, jneutron & opaqueice.

A couple of Qs for you as I'm puzzled about a coupla things.

Q1:  OK, if one has speaker cables which are low C (and in my case, low L too, as they're so short), then can the cables be considered to be "matched" to the load?

The issue is whether the amp sees the load impedance or something else.  For very low cable L and C, the amp sees the load impedance almost exactly for a wide range of frequencies, but at very high frequency it starts to see something else...  unless L/C equals the load impedance squared.

Look at the plot a few posts up.  The height where the line hits the y axis is the load impedance.  So as you can see, in all cases the amp sees almost exactly just the load impedance for a wide range of frequencies.  The frequency where the line starts to bend is a function of LC - if it were made smaller to match your case, the whole plot would "stretch" off to the right.  The only line that doesn't bend for any frequency is the one that's matched.

[andyr]

Look at the plot a few posts up.  The height where the line hits the y axis is the load impedance.  So as you can see, in all cases the amp sees almost exactly just the load impedance for a wide range of frequencies.  The frequency where the line starts to bend is a function of LC - if it were made smaller to match your case, the whole plot would "stretch" off to the right.  The only line that doesn't bend for any frequency is the one that's matched.

Much obliged.

[Daryl]

OK, changed scales to powers of ten.

Also added a transfer function chart and line resistance can be used now as well.

[jneutron]

So far, the discussion has been good.  Thanks guys for that.  These plots however, do not clearly depict what the amplifier sees, but merely the response of the lumped elements vs freq. 

We all know that some "hot" amplifiers will oscillate when a capacitive load is presented it.  The concern with cables is really not one of resonance of the cable (as the graphs are all about), but how the amplifier sees the cable.

Here's the graph..  Note that inductive energy slopes upward as you go the the right, and capacitive slopes up as you go to the left.  A horizontal line would depict resistive, that occurs where the inductive and capacitive energy is exactly the same level, and that occurs at the match.

If you were to use zip cord, you'd be running in the 100 to 200 ohm cable impedance regime...note that location is to the right of the match, and clearly it shows as inductive in nature..

I made the plot log/log for convienience.  (oops, forgot to add that this is energy per foot of cable)



Cheers, John

[Daryl]

These plots however, do not clearly depict what the amplifier sees, but merely the response of the lumped elements vs freq. 

Hi John,

The impedance plot I provided indicates EXACTLY what the amplifier see's (that was the reason for it).

I did not include phase because it isn't necessary (phase and magnitude are related), capacitance is indicated by downward slope and inductance is indicated by upward slope.

More importantly the input impedance gives a very clear picture because it indicates at what frequencies capacitance is present and also the impedance magnitude where the load presented to the amplifier is capacitive.

All this information is important and clearly shows how easy it would be to design an amplifier that will be stable even into this 20ft, 10 ohm and 200 pF/ft wire.

You see with the 100 ohm termination capacitance doesn't begin to present until 100Khz and at 1Mhz the impedance magnitude has fallen only to 40 ohm.

The Transfer Function chart shows the response at the load and the separate traces for multiple impedances indicate how steady the output will be with the speakers varying impedance.

[andy_c]

Getting back to the original poster's problem, here's the quote that seems to give the pertinent info:

To take the mystery a bit further, my amp works fine with my speakers as long as I do not try to bi-am them  If I bi-amp and hook my amp and Acoustic Zen cables to the mid and treble portion of the speakers (and put my tube amp on the bass) everything is fine, if I just use my HCA-3500 and Acoustic Zen cables to drive the whole speaker system every thing is fine, BUT when I be-amp (with tubes on the top)  and power the bass with the HCA-3500 and Acoustic Zen cables the durn thing shuts off!

So in the passively biamped mode where the problem occurs, the amp is looking into the low frequency part of the speaker - specifically, the woofer combined with the low-pass filter of the speaker's crossover.  The first element in the low-pass is a large series inductor.  Therefore, at the unity loop gain frequency of the amp (about 1 MHz, where it would tend to oscillate with a capacitive load), the load of the woofer and its low-pass filter (minus the cable) could be approximated as an open.  Combine that with a cable of significant length having a high capacitance per unit length (low Z0) and you have a capacitive load on the amp.

If the mid/high portion of the speaker is hooked up in parallel (non-biamped mode), a decent high-frequency termination is obtained, rather than an open, so no oscillation.  If the amp is hooked up only to the mid/high portion of the speaker, everything is fine also, because of the decent high-frequency termination.  It all makes sense.

[Daryl]

Getting back to the original poster's problem, here's the quote that seems to give the pertinent info:

To take the mystery a bit further, my amp works fine with my speakers as long as I do not try to bi-am them  If I bi-amp and hook my amp and Acoustic Zen cables to the mid and treble portion of the speakers (and put my tube amp on the bass) everything is fine, if I just use my HCA-3500 and Acoustic Zen cables to drive the whole speaker system every thing is fine, BUT when I be-amp (with tubes on the top)  and power the bass with the HCA-3500 and Acoustic Zen cables the durn thing shuts off!

So in the passively biamped mode where the problem occurs, the amp is looking into the low frequency part of the speaker - specifically, the woofer combined with the low-pass filter of the speaker's crossover.  The first element in the low-pass is a large series inductor.  Therefore, at the unity loop gain frequency of the amp (about 1 MHz, where it would tend to oscillate with a capacitive load), the load of the woofer and its low-pass filter (minus the cable) could be approximated as an open.  Combine that with a cable of significant length having a high capacitance per unit length (low Z0) and you have a capacitive load on the amp.

If the mid/high portion of the speaker is hooked up in parallel (non-biamped mode), a decent high-frequency termination is obtained, rather than an open, so no oscillation.  If the amp is hooked up only to the mid/high portion of the speaker, everything is fine also, because of the decent high-frequency termination.  It all makes sense.

In the image below a 100 ohm wire and a 10 ohm wire are compared (100 ohms is a typical wire, I don't know the specs of PLMONROE's wires so I'm just being extreme here).

First we have them both loaded with a 4 ohm load across the entire spectrum (pink is the 100 ohm wire and light blue is the 10 ohm wire).

Next the same thing but this time a 2mh inductor in series with them to mimic the lowpass filter in PLMONROE's speakers (red is the 100 ohm wire and blue is the 10 ohm wire).
 
With the full spectrum 4ohm load (looking at the 'Input Impedance' chart) you see both wires show only load resistance and wire inductance up til the 6mhz 1/4 wave resonance of the wires (pink and light blue traces).

With the lowpass filter in place (again the 'Input Impedance' chart) you see that both wires present capacitance to the amplifier above about 100Khz, the difference being that the 10 ohm wires capacitance has an impedance magnitude 10 times lower than that of the 100 ohm wire (red and blue traces).

The impedance magnitude of the 10 ohm wires capacitance though 10 times lower than the 100 ohm wires isn't so bad though.

Were talking 13 ohms at 3Mhz (which is likely above the amplifiers gain bandwidth), 50 ohms at 1Mhz and 150 ohms at 300khz.

A suitable decoupling network would take care of this.

The advantage of the 10 ohm wire is clear in the 'Transfer Function' chart.

Whatever rigidity you desire at the end of your speaker wire you can see that the 10 ohm wire can maintain it to a frequency 10 times higher than the 100 ohm wire.

Or over a wire length ten times longer.

Note: the vertical scale for the 'Transfer Function' chart is amplitude (not power) over a range of +/- 10^.5 = +/- 3.16 to 1 = +/- 10db = 2db/div.

[jneutron]

These plots however, do not clearly depict what the amplifier sees, but merely the response of the lumped elements vs freq. 

Hi John,

The impedance plot I provided indicates EXACTLY what the amplifier see's (that was the reason for it).

I did not state that the plot does not provide exactly.  I said it did not clearly depict..clearly being the operative word..  (hee hee...gotcha)

You geeks drive me nuts...honestly..(note the other operative verbage...you geeks..not us, you...)

"" capacitance is indicated by downward slope and inductance is indicated by upward slope."""

Now that...that needed to be expounded upon..

Sigh...you know,  when I look back at what we've been saying, and the graphs...it's no wonder the majority of the people on this planet don't have a clue about what we talk about...why my wife gave up years ago asking me "what'd ya do at work today"...sigh...

More importantly the input impedance gives a very clear picture because it indicates at what frequencies capacitance is present and also the impedance magnitude where the load presented to the amplifier is capacitive.

All this information is important and clearly shows how easy it would be to design an amplifier that will be stable even into this 20ft, 10 ohm and 200 pF/ft wire.

You see with the 100 ohm termination capacitance doesn't begin to present until 100Khz and at 1Mhz the impedance magnitude has fallen only to 40 ohm.

It wouldn't be hard to make the amp accomodate the cable as the load unloads given the info...but if one thinks about it, it also provides the ability to terminate the cable so the amp doesn't see the capacitance.  If it is possible to bring the impedance back down in the frequency range where the amplifier would want to oscillate, that'd relax the amount of "dumbing down" needed at the amp.  After all, it's the lack of match that got us into trouble anyhoo.. An aftermarket widgit to put at the speaker would be nice.  And the best part is the fact that there really is no power to speak of up there in megafreq land, so the components don't have to dissipate much energy..

The Transfer Function chart shows the response at the load and the separate traces for multiple impedances indicate how steady the output will be with the speakers varying impedance.

As was pointed out by somebody ages ago, the  cable parameters aren't so much an issue at human hearing frequencies for single channel response, but I must admit concern of cable effects on localization stuff..

Cheers, John