[andy_c]

One point that may be helpful for others reading along who aren't familiar with the subject matter is to define terms that you use that aren't everyday terms.

Oops.  Wikipedia has a pretty decent page on feedback amplifiers here:

http://en.wikipedia.org/wiki/Feedback_amplifier

In the block diagram they show, A is the open-loop gain and B (actually Greek beta) is the feedback factor.  In general, A and B are complex numbers (meaning they have a magnitude and phase which depends on frequency).  Often B is just a constant, given by the ratio of resistors in a resistive voltage divider, which sets the gain.  The bandwidth of A can't be infinite.  "A" must approach zero as the frequency becomes large.  So there is going to be some frequency at which the magnitude of the product A*B is equal to one.  If the phase of A*B at this frequency is 180 degrees (A*B=-1), the closed-loop gain Acl, given by:

Acl=A/(1+A*B)

will be infinite.  This is how an oscillator works.  In practice, the frequency response of A is usually made to look like a first-order low-pass filter, making the phase shift of A*B close to -90 degrees at the frequency for which the magnitude of A*B is one (that is, the unity loop gain frequency).  This approach keeps the amplifier stable, and is called frequency compensation.

The stability problem being discussed here stems from the fact that "A" is affected by the amplifier load.  So, when considering stability, it's necessary to look at the amplifier load at or near the unity loop gain frequency.

[opaqueice]

I'd be interested in looking at the math, as I haven't looked at the problem in that way myself.  Could you scan it?  It's always nice to see how others approach a problem, especially someone taking a fresh approach.  A Physics person is likely to look at it in a more fundamental way than a typical engineer might.

When I have time I'll try to write or tex it up legibly and post it.  Meanwhile you might be able to follow it yourself - just start from the general solution to the telegrapher's equations I posted earlier and impose boundary conditions (i.e. fix the voltage at the amp and use Ohm's law at the load).

[jneutron]

Nice.

An RLC model runs flat from DC to daylight?   How did you model that?

If daylight means infinite frequency, it isn't - it's just almost flat from DC to omega^2 L C of order 1.

As andy c points out, the principal issue stems from the upper limits of the amplifier, not the audio band..

Looks like you have to put the C first or it won't work.  Not sure what to say about that.

I do.  It means the the model is an approximation to reality.  Course, we all knew that from the jump.  The concern is, is the model sufficient for the need. 

Model the settling time by varying the line to load ratio.  It must produce a cusp minima at unity....zero if you offset the transit time.

You'll have to translate that into physics - or English, take your pick  .

You are correct, I deserve that...

Let's start with some understoods..

1.  For a transmission line of any length or characteristic impedance, if the load matches the line, then the amplifier sees ONLY the "resistance" of the load.  This is independent of the frequency used.  A simple lumped element RLC model does not predict this.

2.  T-line theory predicts a propagation velocity for the signal.  The simple RLC does not predict this.

3.  For a t-line, if the load impedance is above the line impedance, the primary energy storage is capacitive in nature.

4.  For a t-line, if the load impedance is below the line impedance, the primary energy storage is inductive in nature.


Number 1 predicts that if you cause an amplifier to become unstable as a result of using a low impedance speaker cable, the stability can be re-established by making the load match the cable impedance, especially in the realm of frequency where the amplifier gets into trouble. Another interesting point here is:  this is independent of the actual values of the capacitance and inductance of the cable...increase both two orders of magnitude, and the amp still sees only a resistance..

Note: one of the posters pm'd that in practice it didn't work...but it is not clear to me if the components and hookup used were up to the task at the freq range of 1-2 Mhz...I note it should not be easy to do anyway..guidelines would have to be established..

Historically, this instability concern has been attributed to the capacitance of the cable, not the characteristic impedance.  To date, it's not been a difference worth considering.

Number 2, that of transit time (and my obscure question).

Take an amp, a 10 ohm t-line 1 uSec long, and a pure resistive load...at time t=0, bring the amp output to 10 volts instantly... and leave it there..

As the signal "fills" the line, the amplifier sees exactly 10 ohms...one ampere...and the front edge of the signal heads towards the load at prop speed.. The inductive storage within the line is some value of joules per foot, and the capacitance storage is also that exact same joules per foot...that is what "characteristic impedance" refers to..

At t=1 uSec, the entire line has charged to a value of 10 volts, and there is one ampere flowing through the entire line.  At this time, the signal hits the load.  If the load is exactly 10 ohms, the voltage goes up to 10 volts, it sees exactly 1 ampere, and the event has completed...  The system will remain exactly as it stands now, forever.  And the cable has stored the exact same joules per foot that was in it just before 1 usec was up.

So, for the matched case, the signal risetime at the load is the same as what the amp did, and it took exactly 1 uSec for the load to see this.

Now, lower the load resistance to 1 ohm and repeat.

At t=1 uSec, the 10 volt one ampere signal hits the load, and the storage energy is the same joules per foot as the previous example.  Ohms law at the load says that one ampere of current will produce one volt..so at 1 uSec, the load will have 1 volt on it....and there will be a -9 volt signal reflected back to the amp, leaving behind it 1 volt steady state on the line.  At t = 2 uSec, that -9 volts hits the amp, inverts, and heads to the load again, filling the cable back to the 10 volt level.

At 3 uSec, the 9 volt moving signal plus 1 volt steady state  hits the load, the load current bumps to 1.9 amperes, the load is 1.9 volts, and another wave heads to the amp, this time -8.1 volts leaving 1.9 volts in it's wake...

This action continues until we die of boredom..  But in the end, there will be 10 amperes flowing in the line and load, and 10 volts on both.

Now, lets look at the energy stored in the line..

The 10 volts is the same as always, so the capacitive storage is exactly the same now as all the other cases.  BUUUUT, the current is now 10 times the origional example.   The energy stored is E = 1/2 L I^2...the cable is now storing 100 times the energy in the magnetic field as the matched case..it appears to be an inductor for the most part.

Now repeat with 100 ohms as a load...in the end, the inductive energy is 1/100 th of the first example, and the capacitive is the same, or 100 times the inductive energy...so the line essentially has stored energy as a capacitor..it in essence looks like a capacitor.

(the cap energy is the same in the examples because I used the same voltage..)

Note that for mismatch, the end voltage goes through a stepwise process to the final value.  For a match, this does not happen...

If one plotted the time to settle to say, within 1% of the final value, the matched case does this instantly plus the 1 uSec.  Mismatched takes multiple transit times to do this. Hence the term "cusp minima", as the settling time is zero only when the ratio is 1.

This cusp is not predicted by a simple lumped element approximation.  By working the RLC math, I think the capacitive/inductive nature of all cases of mismatch seen by t-line analysis can be somewhat predicted.

My feeling is...the use of some t-line concepts afford a better "feel" for the impact of speaker wires to "hot" amps.  It predicts behaviour with respect to the cable's impedance, the load impedance, and how the amp sees the system..but concur that for the most part, it is much easier and productive to use RLC approximations where they apply, as long as the "approximations" are understood.

Daryl's statements were t-line in nature, which is what I agreed to conceptually..

I apologize for not having pictures and graphs to aid in the discussion..I've not proofed this well, hope I didn't toss any gaffs in..

Cheers, John

[opaqueice]

I do.  It means the the model is an approximation to reality.  Course, we all knew that from the jump.  The concern is, is the model sufficient for the need. 

Sure, but what's a little unclear to me is why the order matters so much.

Let's start with some understoods..

1.  For a transmission line of any length or characteristic impedance, if the load matches the line, then the amplifier sees ONLY the "resistance" of the load.  This is independent of the frequency used.  A simple lumped element RLC model does not predict this.

Wrong, as I thought I had already explained.  So long as the capacitor is the one connected in series, for audio frequencies and reasonable L C values the single RLC model predicts exactly that. 

I just redid the calculation for a general load (before I had assumed it was purely resistive).  It still works, but now the linear term in omega cancels if Z_L^2 = L/C, which is precisely what the exact TL treatment gave (when I ignored the cable resistance, as I am also doing here).

2.  T-line theory predicts a propagation velocity for the signal.  The simple RLC does not predict this.

Yes, of course.  But my point all along has been that the corrections due to that are very small.

3.  For a t-line, if the load impedance is above the line impedance, the primary energy storage is capacitive in nature.

4.  For a t-line, if the load impedance is below the line impedance, the primary energy storage is inductive in nature.

This is true also in the single element model.  For small load impedance Z_L the correction comes primarily from inductance; and from capacitance for large Z_L.

Number 1 predicts that if you cause an amplifier to become unstable as a result of using a low impedance speaker cable, the stability can be re-established by making the load match the cable impedance, especially in the realm of frequency where the amplifier gets into trouble. Another interesting point here is:  this is independent of the actual values of the capacitance and inductance of the cable...increase both two orders of magnitude, and the amp still sees only a resistance..

Same with the single element model.

This cusp is not predicted by a simple lumped element approximation. 

OK, now I know what you mean.  But of course the single element approx can't capture that - it doesn't know about finite signal propagation velocity.

By working the RLC math, I think the capacitive/inductive nature of all cases of mismatch seen by t-line analysis can be somewhat predicted.

That's what I've found, yes.

My feeling is...the use of some t-line concepts afford a better "feel" for the impact of speaker wires to "hot" amps.  It predicts behaviour with respect to the cable's impedance, the load impedance, and how the amp sees the system..but concur that for the most part, it is much easier and productive to use RLC approximations where they apply, as long as the "approximations" are understood.

Agreed.

[jneutron]

I do.  It means the the model is an approximation to reality.  Course, we all knew that from the jump.  The concern is, is the model sufficient for the need. 

Sure, but what's a little unclear to me is why the order matters so much.

As I said, a simple lumped element RLC is overly simplified for the general case of a transmission line.  I mentioned the "chicken and the egg" because the use of one cap and one inductor forces the decision as to where each element goes in the model.  Putting it at one end means the model may be "more correct" in one direction, but at the sacrifice of the other direction.  The t-line model is accurate in both.

Remember, we are not talking about audio frequencies.  The amplifier instability is over a Mhz.

What configuration are you using for the RLC model?




Here's the meat...so I put both my statements and yours in one spot.
me:

2.  T-line theory predicts a propagation velocity for the signal.  The simple RLC does not predict this.

Yes, of course.  But my point all along has been that the corrections due to that are very small.

me:

This cusp is not predicted by a simple lumped element approximation.

OK, now I know what you mean.  But of course the single element approx can't capture that - it doesn't know about finite signal propagation velocity.

The RLC model does not include prop velocity at all.  For the mismatched example previously cited, consider two cables of identical impedance but one created coaxially with a nitrogen dielectric (dc=1) and the other a parallel wire pair with an effective dielectric coefficient of 16. The prop velocity of the first is a foot per nanosecond, the second is a foot per 4 nanoseconds. The lumped model cannot distinguish these two cables if the load is matched.
 
For a 10 meter cable, the transit time is 32.8 nSec vs 131 nSec.  The previous mismatched load example described shows how these cables will differ in overall response, I'll do up a spreadsheet to show the diff...and this diff is one that cannot be obtained by RLC.

By working the RLC math, I think the capacitive/inductive nature of all cases of mismatch seen by t-line analysis can be somewhat predicted.

That's what I've found, yes.

As have others over the years.  The RLC model is extremely valid for the audio modelling, but where the amp can get into trouble, the t-line model is simpler...  All it requires is knowing the characteristic impedance of the cable, as opposed to worrying about the equations you've taken the time to work with.

I'll get that excel graph up soon.

Cheers, John

[opaqueice]

Remember, we are not talking about audio frequencies.  The amplifier instability is over a Mhz.

I somehow missed Any's comment on that.  That changes things considerably, although Mhz frequencies are still lowish....   Let's see: the characteristic frequency is (L C)^{1/2).  So for your numbers from earlier and a pretty long (10 m) cable I get somewhere around 100MHz.  That means the corrections to my single element RLC at 1MHz will be of order .0001.  But Andy mentioned the frequency can be as high as 100MHz, in which case the RLC analysis is toast  (plus there are various factors of order 1 floating around that could change things in various ways).

What configuration are you using for the RLC model?

Just inductor in series with the load, capacitor in parallel (there's a typo in my last post on that).

As have others over the years.  The RLC model is extremely valid for the audio modelling, but where the amp can get into trouble, the t-line model is simpler...  All it requires is knowing the characteristic impedance of the cable, as opposed to worrying about the equations you've taken the time to work with.

Sounds like we're on the same page  .

So what happens when you include the resistance of the cable, or the reactance of the load?  One thing I noticed in my telegrapher equation solution was that impedance matching only occurs when the load is purely resistive (the condition is that Z_L = (L/C)^{1/2}, which is a real number, rather than |Z_L|^2 = L/C).  Did I make a mistake somewhere there?  If not, it might just mean you need a resistive cable to precisely match a reactive load, but I haven't checked (the equations look much uglier when you include cable resistance).

[jneutron]

Did a quick looksee, found a hojo article which kinda relates..


http://www.sigcon.com/Pubs/news/6_06.htm

Note the pi model he used..fyi only.

He uses the equation 1/4 * 1/t_d for the resonant frequency of an unloaded line, a rough approximation of what we are speaking of..

From my example, DC = 5.57, Lz = 8, length = 10 meters, the calculated transit time is about 80 nSec, 80 e-9. (ten power -9)

Hojo calcs: 1/(4*80) times e9
1/320 e+9
.0031 e+9
3.1e +6, or 3.12 Mhz.

Dead on w/r to what andy spoke of..

But significantly off your numbers..

Did one of us miss a decimal place, or is this the discrepancy in model I am thinking of..?

ps..lossy cable and reactive load??  Shirley you jest...aren't we having enough analytical problems with the simplest example we are coming up with???

Sheesh, I though I was bad...

Cheers, John

[opaqueice]

Did one of us miss a decimal place, or is this the discrepancy in model I am thinking of..?

Nah - I didn't notice your numbers were Farads per foot.  What century are we in again?   

So my numbers were for 10 foot cables (which is probably a little more realistic anyway), and doing it more carefully I get 41 MHz in that case which looks consistent with you (factor of about 3.3 between feet and meters).

In any case, whatever that frequency happens to be for a given cable, the RLC analysis has corrections of order the ratio of the driving frequency to that frequency squared.

[jneutron]

Did one of us miss a decimal place, or is this the discrepancy in model I am thinking of..?

Nah - I didn't notice your numbers were Farads per foot.  What century are we in again?   

So my numbers were for 10 foot cables (which is probably a little more realistic anyway), and doing it more carefully I get 41 MHz in that case which looks consistent with you (factor of about 3.3 between feet and meters).

In any case, whatever that frequency happens to be for a given cable, the RLC analysis has corrections of order the ratio of the driving frequency to that frequency squared.

Ah, units...they'll get ya everytime..

Hey, don't mess with the good ol'  USA's choice of numerology.  12  is a golden number, as is 36, and 5280...and don't forget 212..

(pssst..my spreadsheet has meters length, pF per foot, nH per foot, nSec per meter and per foot..the only units that are consistent are "ohms" and nSec..

A factor of 3.3 gets me up to 10 Mhz, you are at 41?  We are still off by a factor of 4, is that where your corrections come in? (Note..just realized C and L are both in units per foot, did you use 3.3 once or twice?)
Honestly, I would trust HoJo on this one..but I had to laugh at his text:  ""Without worrying too much about math, let me just tell you that the resonant frequency fr of an unloaded line driven by a low-impedance source works out to (1/4)(1/td).""  Prof's would do that in the guise of either "it's obvious to even the most casual observer", or "I leave it as an exercise for the reader", or "it's intuitively obvious"...leaving guys like me scratching their head..

Cheers, John

 

[opaqueice]

A factor of 3.3 gets me up to 10 Mhz, you are at 41? 

From the 1/4 in (1/4)(1/td)? 

It works like this:  Z_T = R + i (L - C R^2) w + (2 C L R - C^2 R^3) w^2 + order w^3.  Here R is the resistance of the load (assumed to be real), and L and C are the totals for the cable.  For R^2 = L/C this becomes Z_T = R(1 + (C R w)^2) = R (1 +  L C w^2).  There's no prefactor to the w^2 term, so I don't know about that 1/4.  Note that w is the angular frequency (i.e. the driving voltage is e.g. V(t) = V_0 sin wt ).

For your values I again get (LC)^{-1/2} = 41 MHz for a 10 foot cable, as I said.  This scales as 1/length of the cable, so there's only one factor of 3.3 if you take a 10 meter cable.

[jneutron]

A factor of 3.3 gets me up to 10 Mhz, you are at 41? 

From the 1/4 in (1/4)(1/td)? 

Honestly don't know...HoJo put up the equation, I only reported it and used it.  So the discrepancy is between what HoJo writes and what you calculated. 

I was just guessing as to where the discrepancy lies.  I figured that if you missed the conversion of 3.3 in the farads per foot, you may have also missed the conversion of henries per foot.  That would put the LC product off by about 10 instead of 3.

Cheers, John

[Occam]

.......
or "I leave it as an exercise for the reader", or "it's intuitively obvious"...leaving guys like me scratching their head..

Cheers, John

Hey Jimmy,

How true, but to be honest, the whole thread makes me think folks are scratching something substantially south of their heads.

As PLMONRORE stated in the originating post of this thread -

....... Yes I had tried changing everything in the would even fuses, well ALMOST everything. I had not changed speaker cables and I had gotten new cables at the same time I had changed speakers! But what the heck can be the effect of a piece of wire? Well I unhooked the speaker cables - Acoustic Zen Holograph IIs which are nice cables and replaced them with a set of Kimber Kable 8TCs. The amp loved them !!! So the amplifier is OK with Kimber Kables, Audioquest Pike Peaks, plain lamp cord and everthing else except the Acoustic Zens......

and the conclusion in following posts has been that the obvious cause is capacitive cables. But on that same first page Gordy pointed out -

What I find odd is that the TC'8's worked well.  I've been under the impression that the heavily braided Kimber Kable and the Alpha Core ribbon cables were among highest capacitance cables around.

and a quick link to Kimber Kable yields the fact that TC8s have 100pf+ of capacitance for foot.
http://www.kimber.com/Products/LoudSpeakerCables/8TC/8TC_Spec.aspx

Don't get me wrong, the ensuing discussion using intro control theory, transmission line analytics and multivariate calculus is impressive and certainly merits its own thread. But ignoring empirical facts, although providing an ideal segue for such a facile discussion, leaves me 

Regards,
Paul

[jneutron]

.......
or "I leave it as an exercise for the reader", or "it's intuitively obvious"...leaving guys like me scratching their head..

Cheers, John

Hey Jimmy,

How true, but to be honest, the whole thread makes me think folks are scratching something substantially south of their heads.

As PLMONRORE stated in the originating post of this thread -

....... Yes I had tried changing everything in the would even fuses, well ALMOST everything. I had not changed speaker cables and I had gotten new cables at the same time I had changed speakers! But what the heck can be the effect of a piece of wire? Well I unhooked the speaker cables - Acoustic Zen Holograph IIs which are nice cables and replaced them with a set of Kimber Kable 8TCs. The amp loved them !!! So the amplifier is OK with Kimber Kables, Audioquest Pike Peaks, plain lamp cord and everthing else except the Acoustic Zens......

and the conclusion in following posts has been that the obvious cause is capacitive cables. But on that same first page Gordy pointed out -

What I find odd is that the TC'8's worked well.  I've been under the impression that the heavily braided Kimber Kable and the Alpha Core ribbon cables were among highest capacitance cables around.

and a quick link to Kimber Kable yields the fact that TC8s have 100pf+ of capacitance for foot.
http://www.kimber.com/Products/LoudSpeakerCables/8TC/8TC_Spec.aspx

Don't get me wrong, the ensuing discussion using intro control theory, transmission line analytics and multivariate calculus is impressive and certainly merits its own thread. But ignoring empirical facts, although providing an ideal segue for such a facile discussion, leaves me 

Regards,
Paul

The point I am making is that it is not necessarily the value of the cable capacitance that can cause instability, but the fact that the characteristic impedance of the cable coupled with the unloaded condition at the upper reaches of the amplifier may more indicative of the problem.  In fact, I believe we have already agreed that regardless of the capacitance of the cable, if the end is terminated in such a way that above the audio band the cable sees an impedance match, then the amp should not become unstable..somebody mentioned Zobel..

You mention 100 pf per foot...but yet how many people have ever reported an overly long cable causing oscillation? That is the implication of using bulk capacitance.

You point out Gordy as mentioning the tc8-s as high capacitance, there again it is assumed it's just the total capacitance. 

Don't blame me for control theory and multivariate calculus, I'm just a simple farmboy..

But it would be really nice to be able to plop an excel spreadsheet on this forum that allowed everybody else to work out the cable parametrics I "spew".  It would allow anybody to design a coaxial cable or flat ribbon cable of any inductance, capacitance, or impedance (of course, there are inter-parameter constraints).  And then, look at the resultant parametrics, resonance, and performance..

I tried to find the characteristics of the zen cables to no avail. Can anybody provide them?

For the TC-8's, 100 pf per foot doesn't strike me as particularly high, and 42 nH per foot isn't particularly low.

I ran the numbers on the spreadsheet..  The cable impedance is about 20 ohms, the DC is 4.06, the transit time is 17 nSec,  the self resonance unloaded is 14.8 Mhz, and the effective risetime is about 30 nanoseconds.

What would be of great importance, IMHO, is...given a cable with a characteristic impedance, transit time, and DC, what is the highest frequency that would have to be guaranteed loaded at cable z in order to guarantee amplifier stability?  The unity gain point of the amp?  The unloaded resonance fequency?  If it's just related to the cable, it would be trivial to add the value of R and C required to do so for any design cable.   If related to the amp, same deal..


Cheers, John

[opaqueice]

Honestly don't know...HoJo put up the equation, I only reported it and used it.  So the discrepancy is between what HoJo writes and what you calculated. 

I was just guessing as to where the discrepancy lies.  I figured that if you missed the conversion of 3.3 in the farads per foot, you may have also missed the conversion of henries per foot.  That would put the LC product off by about 10 instead of 3.

As I said, there's only one factor of length (don't forget, it's the square root of LC).  Anyway the ratio of our results is 3.99, so I'm pretty sure it's that factor of 1/4.  Why it's there I have no idea. 

I'm quite sure my calculation is correct as far as it goes, and I don't have any more time spend on this now.

[jneutron]

As I said, there's only one factor of length (don't forget, it's the square root of LC).  Anyway the ratio of our results is 3.99, so I'm pretty sure it's that factor of 1/4.  Why it's there I have no idea. 

Yah, me either.  HoJo knows.

I am guessing it is because of a low Z source and a high Z load.  The low Z source inverts the returning reflection, the high Z reflects uninverted.  It would appear that those two boundary conditions setup a resonance that is supported by two full signal passes, which is 4 lengths of the cable..

My guess..

Cheers, John

[JoshK]

""Without worrying too much about math, let me just tell you that the resonant frequency fr of an unloaded line driven by a low-impedance source works out to (1/4)(1/td).""  Prof's would do that in the guise of either "it's obvious to even the most casual observer", or "I leave it as an exercise for the reader", or "it's intuitively obvious"...leaving guys like me scratching their head..

Ha!  I had a professor of mathematics at the university of Chi-town that would quite often through the course of the lecture, while detailing a rather opaque topic, pause and say, "is that obvious? Let's see...hmmm...is it obvious? [pause for about 20 secs staring at his math]...yes, that is obvious."  Meanwhile there was noone in the student body that was thinking anything was close to obvious.

[Occam]

Josh,

According to my son, its even worse in England. The profs at the Trippos at Cambridge couldn't be bothered to explain much of anything, consistently just transcribing their lecture notes onto the blackboards. They apparently wern't concerned whether something was obvious or not.

FWIW,
Paul

[Daryl]

I just wrote an Excel macro to calculate the input impedance of wire and load combinations.

Here a wire with a characteristic impedance of 10 ohms is loaded with 1, 3, 10, 30 and 100 ohms.

It shows how the amplifier can see capacitance only when the load impedance exceeds the wires characteristic impedance and the amplifier can see inductance only when the load impedance is below the wires characteristic impedance.

When the load impedance is equal to the characteristic impedance of the wire then neither capacitance nor inductance can be seen by the amplifier.

[andyr]

OK guys,

I'd like some input ... hopefully, some of you will actually agree in your responses! 

I'm afraid most of the above discussion is outside my knowledge area (I'm a mathematician - we're much more exact than either physicists or engineers!  ) but I would like to understand one point (which I'll come to, soon).  However, I must say first, I certainly have experienced one amp blowing its output stage when connected up to a 15m pair of speaker cables which another amp (Naim) took in its stride.  Yes, I know 15m speaker cables is an unconscionable length but sometimes that's what you have to have!  And in this case, it was not the particular design of speaker cable which made it high C ... it was simply that the particular design of amp (Harmon Kardon "high bandwidth" amp) couldn't cope with the capacitance induced by 15m of that cable.

OK my Qu is fourfold; and this comes about because I have a 3-way active system (so there are no 'random' effects produced by a passive XO, and each amp sees a constricted frequency range) with 3 DIY monoblocks located in the one case (separate PSes, separate on/off switches & fuses), directly behind each speaker.  In terms of the original Post Heading - "Amplifier and Speaker Cable Incompatibility":

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?)

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? 

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?

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. 

So is this related to jneutron's post about "line impedance matching the load"?

Thanks,

Andy

[jneutron]

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??

This graph is just what the amp terminals see, yes?  I've been considering how to express the differential capacitance resulting from the mismatch, with baseline being the matched energy storage..

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 cannot see 8 to 12 inches having any effect at all.  Worst case would be what, 200 to 300 pf?  And when you think about the terminals themselves, they toss 1 to 2 uH into the fray anyway, so that kinda trashes any characteristic impedance thing.

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? 

Line impedance is = sqr(L/C).   That is not to be confused with the total resistance of the wires, which is in the milliohm range.  (btw, "he" is here, and certainly open to questions of any nature..so you can ask me directly... )

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?

No, I would not consider it as relevent for such small wires.

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. 

So is this related to jneutron's post about "line impedance matching the load"?

Thanks,

Andy

Yes, reflections are in essence the entire gist here.  However, I certainly take exception to the concept of "muddies up the sound" as a result of reflections which occur in the tens of nanosecond regime.  Those speeds are many orders of magnitude faster than that which any human can respond to.

Where I would worry is in what the amp does with reflections, as some amps are "hot" with respect to speed capability, and if the amp has problems with the reflections, it is not known exactly how the amp will respond. (one must keep in mind that the "primary signal" charges the line exactly as the line's characteristic impedance would wish it to be with the load matched, and that the reflections are what charges the line to the final current as a result of the load mismatch.  It is therefore the reflection stuff that is responsible for the line looking either capacitive or inductive in nature in response to the load....no reflection (match condition), no inductance or capacitance is seen by the amp.

If a poor cable choice caused an amplifier instability, then it is indeed possible that sound quality could be degraded.  Oscillation of this nature can easily trash the amp, or even the tweet and crossover.  John Curl was good enough to have his design detect and shutdown for this condition..

Cheers, John