Is error correction inconvenient?
In an earlier post I think I recall Ovidiu suggesting that EC had a big disadvantage in regard to the fact that it needs an adjustment. I also saw something to the same effect in one of Bruce Candy's later patents.
I really don't think this is a big deal, nor a disadvantage of EC. If anything, it is a feature of EC.
First of all, no one is holding a gun to your head to put in the pot. If you design the EC circuit properly and use commonly-available 1% resistors, your output stages will fare very well in the distortion department, certainly far better than if you had not used EC. Moreover, the effectiveness of EC at the higher frequencies, where it is usually most needed, is more often limited by the speed of the EC circuit and its necessary compensation than by the resistor tolerances. Remember, Speed is King.
If you do choose to use a pot, setting it is not much more of a big deal than setting the output stage bias pot. If you don't have a distortion analyzer that can see down to 0.001% at 20 kHz, maybe you are not a good candidate for EC anyway.
I do admit that getting down to 1 ppm is a bit more involved, but that goes with the territory, whether you are using EC to get there or not.
It does make one wonder whether Halcro bothers to put each of their $40K/pr amplifiers to a good ten-minute distortion test before they ship it
.
Cheers,
Bob
In an earlier post I think I recall Ovidiu suggesting that EC had a big disadvantage in regard to the fact that it needs an adjustment. I also saw something to the same effect in one of Bruce Candy's later patents.
I really don't think this is a big deal, nor a disadvantage of EC. If anything, it is a feature of EC.
First of all, no one is holding a gun to your head to put in the pot. If you design the EC circuit properly and use commonly-available 1% resistors, your output stages will fare very well in the distortion department, certainly far better than if you had not used EC. Moreover, the effectiveness of EC at the higher frequencies, where it is usually most needed, is more often limited by the speed of the EC circuit and its necessary compensation than by the resistor tolerances. Remember, Speed is King.
If you do choose to use a pot, setting it is not much more of a big deal than setting the output stage bias pot. If you don't have a distortion analyzer that can see down to 0.001% at 20 kHz, maybe you are not a good candidate for EC anyway.
I do admit that getting down to 1 ppm is a bit more involved, but that goes with the territory, whether you are using EC to get there or not.
It does make one wonder whether Halcro bothers to put each of their $40K/pr amplifiers to a good ten-minute distortion test before they ship it
.Cheers,
Bob
Nelson Pass said:I suggest the following tutorial, particularly on the subject of standing
waves in transmission lines.
http://www.ibiblio.org/obp/electricCircuits/AC/AC_14.html#xtocid311501
Later: Here's a more amusing one
http://www.audioholics.com/education/cables/debunking-the-myth-of-speaker-cable-resonance
Perhaps, though, I am simply measuring the LC resonance
of the cables, not the EM propagation velocity.
Nelson,
Thanks for sharing that tutorial with us. I haven't read it all through yet, but it looks great. No matter how much we fool with this stuff, there is always more we can learn.
Cheers,
Bob
traderbam said:Bob wrote:
Except in the case of a duel.
Anyhow, how convenient is it for you to make measurements on your original amplifier?
Hi Brian,
If I can find it in the junk pile it may be convenient
. Otherwise, it will be a lot easier to build an up-to-date version and measure it. Those Toshiba vertical MOSFETs look very tempting, as do those bipolars that Edmond is using in his VAS. Much better than the first-generation unmatched Hexfets and MPSU07/57 I used in my VAS.Cheers,
Bob
bam's load tolerance criteria
Bob wrote:
But...this is not to say that the absence of outright oscillation means the amplifier is sufficiently stable.
Bob wrote:
Yes. I'd go further and stipulate that an amplifier must not oscillate when connected to any passive impedance whose phase shift is within +/- 90 deg.Based on the last few posts, I propose an additional stability test for power amplifiers. The amplifier should be stable with any length of 12 AWG Home Depot zip cord between 0 and 50 feet that is unterminated
But...this is not to say that the absence of outright oscillation means the amplifier is sufficiently stable.
I'd say the variable length transmission line criterion is quite equivalent to a test using a continously variable pure capacitive load from nF's to tens of uF's ... one needs to find that specific worst case capacitance for stability test.
An open line "walks through" sometimes decades of different "capacitances" in all the freq. ranges between even and odd modes (between odd and even ones it's inductive). (Capacitively) shorted line vice versa.
Unless we're talking current output amps (current pumps), inductance should not pose any problems, except SOA issues.
- Klaus
An open line "walks through" sometimes decades of different "capacitances" in all the freq. ranges between even and odd modes (between odd and even ones it's inductive). (Capacitively) shorted line vice versa.
Unless we're talking current output amps (current pumps), inductance should not pose any problems, except SOA issues.
- Klaus
Re: Is error correction inconvenient?
Bob,
I agree that by using 1% metal film resistors an Hawksford EC based OPS will deliver better THD20 performance than a regular OPS. Question is, how much better?
Some interesting math could be done here, regarding the sensitivity of the Hawksword balance to components variations. I'll look into this, time permitting.
From a strictly experimental perspective, my experience shows that indeed, Speed is King. Using very high Ft and very low Cob devices is crucial for achieving low open loop THD and 20KHz (where, as you said, it is really required).
I have experimented our EC OPS with three sets of trannies in the differential error amp, the input buffer and the drivers. Originally, it was MJE243/MJE253 in the input buffer and the differential error amp, and MJ15030/MJ15031 in the driver stage. The EC effect was there, and no fine tuning adjustment was really required. The open loop THD20 was, if memory serves, around 330ppm and that was certainly not good enough for what we were looking for. YMMV, but based on my experience with various front end configurations (yours included) if the OPS has over 100ppm open loop THD20, chances to bring the whole amp to under 1ppm are pretty slim.
The next step was in replacing the MJE243/MJE253 with 2SB649/2SD669 which brought the THD20 at around 220ppm. Still little fine tuning required, but still not good enough.
Finally, the 2SA1407/2SC3661 and 2SA1930/2SC5171 made a huge difference, with 80ppm open loop THD20. However, the adjustment is very delicate and 0.1% resistors are recommended. The THD20 minimum is not only deep but also very narrow. For example, changing the 250ohm resistors in our OPS schematic with 255ohm brings the THD20 to 130ppm! Something worth another in depth theoretical (as of why?) analysis: fortunately, the THD20 narrow minima do not seem to be very temperature dependent; my experiemental setup survived the hair dryer test with less than +/-10% variation in the THD20 number.
So I would say, it all depends to what is the target. If it's under 1ppm, then I don't think a fine and precise tuning can be avoided. Now, as I also stated on the web site: I don't think that 1ppm or 10ppm really matters to the listeners, as long as IMD, TIM, DIM, etc... are in the same range. So yes, in a design as yours, I think you could probably go to manufacturing in a well know outsourcing country with no other provisions (THD20 related) than a statistical control of the performance.
However, if our amp would go for manufacturing, a trimpot would be required. Now, how difficult would it be to trim down the THD20 to under 1ppm? This is not difficult and doesn't require very special skills once you have the proper equipment to measure such. And now it all boils down to the production size. While for small series that's not an issue, I am having troubles (due to the involved costs) imagining a QA department in a factory with 100 operators each hadling an Audio Precision based setup. What would be the production level sweet spot for a decent RTI?
One may argue that such an amp will never be manufactured on a large scale, and here's why it costs $40,000 at Halcro or Boulder. For this kind of money, given the market, I'm pretty sure that the cost of trimming individually each amp is only a small fraction of the total cost.
But then why are EC amps not widely spread today? It seems to me that today the audio market is more interested in finding ways to slice the costs for the same (mediocre) performance rather than increasing the performance at the same costs. Unfortunately, EC would add to the cost (even without any trimming) but provide little incremental performance for the average, mid-fi, customer. I don't believe you can market on the mid-fi arena THD20 numbers. That's only for the thin layer of customers, addressed by e.g. Halcro and Boulder.
The mid-fi market could be tapped if an EC amp could be integrated. I have quite some years of experience in the semiconductor industry and I can tell that, unfortunately, this is unlikey to happen. The Hawksword EC paradigm is very difficult to put in silicon (power) chips, manly because it relies on absolute precision rather than matching precision. Of course, somebody may come up with a integrable EC schema...
Bob Cordell said:In an earlier post I think I recall Ovidiu suggesting that EC had a big disadvantage in regard to the fact that it needs an adjustment. I also saw something to the same effect in one of Bruce Candy's later patents.
I really don't think this is a big deal, nor a disadvantage of EC. If anything, it is a feature of EC.
First of all, no one is holding a gun to your head to put in the pot. If you design the EC circuit properly and use commonly-available 1% resistors, your output stages will fare very well in the distortion department, certainly far better than if you had not used EC. Moreover, the effectiveness of EC at the higher frequencies, where it is usually most needed, is more often limited by the speed of the EC circuit and its necessary compensation than by the resistor tolerances. Remember, Speed is King.
If you do choose to use a pot, setting it is not much more of a big deal than setting the output stage bias pot. If you don't have a distortion analyzer that can see down to 0.001% at 20 kHz, maybe you are not a good candidate for EC anyway.
I do admit that getting down to 1 ppm is a bit more involved, but that goes with the territory, whether you are using EC to get there or not.
It does make one wonder whether Halcro bothers to put each of their $40K/pr amplifiers to a good ten-minute distortion test before they ship it
Cheers,
Bob
Bob,
I agree that by using 1% metal film resistors an Hawksford EC based OPS will deliver better THD20 performance than a regular OPS. Question is, how much better?
Some interesting math could be done here, regarding the sensitivity of the Hawksword balance to components variations. I'll look into this, time permitting.
From a strictly experimental perspective, my experience shows that indeed, Speed is King. Using very high Ft and very low Cob devices is crucial for achieving low open loop THD and 20KHz (where, as you said, it is really required).
I have experimented our EC OPS with three sets of trannies in the differential error amp, the input buffer and the drivers. Originally, it was MJE243/MJE253 in the input buffer and the differential error amp, and MJ15030/MJ15031 in the driver stage. The EC effect was there, and no fine tuning adjustment was really required. The open loop THD20 was, if memory serves, around 330ppm and that was certainly not good enough for what we were looking for. YMMV, but based on my experience with various front end configurations (yours included) if the OPS has over 100ppm open loop THD20, chances to bring the whole amp to under 1ppm are pretty slim.
The next step was in replacing the MJE243/MJE253 with 2SB649/2SD669 which brought the THD20 at around 220ppm. Still little fine tuning required, but still not good enough.
Finally, the 2SA1407/2SC3661 and 2SA1930/2SC5171 made a huge difference, with 80ppm open loop THD20. However, the adjustment is very delicate and 0.1% resistors are recommended. The THD20 minimum is not only deep but also very narrow. For example, changing the 250ohm resistors in our OPS schematic with 255ohm brings the THD20 to 130ppm! Something worth another in depth theoretical (as of why?) analysis: fortunately, the THD20 narrow minima do not seem to be very temperature dependent; my experiemental setup survived the hair dryer test with less than +/-10% variation in the THD20 number.
So I would say, it all depends to what is the target. If it's under 1ppm, then I don't think a fine and precise tuning can be avoided. Now, as I also stated on the web site: I don't think that 1ppm or 10ppm really matters to the listeners, as long as IMD, TIM, DIM, etc... are in the same range. So yes, in a design as yours, I think you could probably go to manufacturing in a well know outsourcing country with no other provisions (THD20 related) than a statistical control of the performance.
However, if our amp would go for manufacturing, a trimpot would be required. Now, how difficult would it be to trim down the THD20 to under 1ppm? This is not difficult and doesn't require very special skills once you have the proper equipment to measure such. And now it all boils down to the production size. While for small series that's not an issue, I am having troubles (due to the involved costs) imagining a QA department in a factory with 100 operators each hadling an Audio Precision based setup. What would be the production level sweet spot for a decent RTI?
One may argue that such an amp will never be manufactured on a large scale, and here's why it costs $40,000 at Halcro or Boulder. For this kind of money, given the market, I'm pretty sure that the cost of trimming individually each amp is only a small fraction of the total cost.
But then why are EC amps not widely spread today? It seems to me that today the audio market is more interested in finding ways to slice the costs for the same (mediocre) performance rather than increasing the performance at the same costs. Unfortunately, EC would add to the cost (even without any trimming) but provide little incremental performance for the average, mid-fi, customer. I don't believe you can market on the mid-fi arena THD20 numbers. That's only for the thin layer of customers, addressed by e.g. Halcro and Boulder.
The mid-fi market could be tapped if an EC amp could be integrated. I have quite some years of experience in the semiconductor industry and I can tell that, unfortunately, this is unlikey to happen. The Hawksword EC paradigm is very difficult to put in silicon (power) chips, manly because it relies on absolute precision rather than matching precision. Of course, somebody may come up with a integrable EC schema...
Re: Re: Is error correction inconvenient?
Ovidiu,
Thanks for this detailed and informative reply. I agree with almost everything you have said here.
With fairly conventional compensation, or even mild two-pole compensation, I agree that the open loop output stage distortion with EC probably needs to be under 100 ppm to reach a final target of 1 ppm.
What was your open-loop output stage THD-20 without EC? This helps give me a calibration, since I believe that in my amp the EC dropped the THD-20 by about a factor of 30.
I agree that we may need to look more closely at the sensitivity of the HEC technique to component tolerances and trimpot setting. I never looked real hard at this, and always just assumed that in rough terms, 1% components would give a 40 dB distortion reduction at low frequencies with HEC. This does not appear to square with your reported experience in regard to the sensitivity of your pot. I'm sure Andy_c would have some thoughts on this.
I probably have not thought about it hard enough, but I am surprized to hear you assert that the proper balance and optimum performance of the HEC circuit depends on absolute resistor values as opposed to just relative matching precision. Perhaps you only meant the term matching in regard to identical pairs of resistor values? Could you elaborate here?
Those are some very nice transistors that you have chosen to use, and I've looked at their spec sheets and am impressed. Can you share with us the SPICE models you used for these transistors?
I agree that the manufacturing adjustment & QA would be much more significant for a 1 ppm amplifier than for a 10 ppm amplifier, whether EC is used to get there or not.
I don't think a 10 ppm amplifier would be particularly difficult or expensive to manufacture using HEC, especially if one were willing to go down from a 3/8 Aluminum front panel to a 1/4 Aluminum panel.
Thanks!
Bob
syn08 said:
Ovidiu,
Thanks for this detailed and informative reply. I agree with almost everything you have said here.
With fairly conventional compensation, or even mild two-pole compensation, I agree that the open loop output stage distortion with EC probably needs to be under 100 ppm to reach a final target of 1 ppm.
What was your open-loop output stage THD-20 without EC? This helps give me a calibration, since I believe that in my amp the EC dropped the THD-20 by about a factor of 30.
I agree that we may need to look more closely at the sensitivity of the HEC technique to component tolerances and trimpot setting. I never looked real hard at this, and always just assumed that in rough terms, 1% components would give a 40 dB distortion reduction at low frequencies with HEC. This does not appear to square with your reported experience in regard to the sensitivity of your pot. I'm sure Andy_c would have some thoughts on this.
I probably have not thought about it hard enough, but I am surprized to hear you assert that the proper balance and optimum performance of the HEC circuit depends on absolute resistor values as opposed to just relative matching precision. Perhaps you only meant the term matching in regard to identical pairs of resistor values? Could you elaborate here?
Those are some very nice transistors that you have chosen to use, and I've looked at their spec sheets and am impressed. Can you share with us the SPICE models you used for these transistors?
I agree that the manufacturing adjustment & QA would be much more significant for a 1 ppm amplifier than for a 10 ppm amplifier, whether EC is used to get there or not.
I don't think a 10 ppm amplifier would be particularly difficult or expensive to manufacture using HEC, especially if one were willing to go down from a 3/8 Aluminum front panel to a 1/4 Aluminum panel
.Thanks!
Bob
Well, I can't just let go of the cable propagation thing until
I see some reconciliation between my experience and the
observations by Syn08. Inductance and capacitance of a cable
have to be the electromagnetic properties in question.
So if you'll bear with me...
I went to Horowitz and Hill, and confirmed that propagation
for a coaxial cable having an insulator with ordinary dielectric
values is on the order of .66 times the speed of light in a
vacuum.
The speed of light is 186,000 miles/sec, or (rounding slightly)
1 foot per nanosecond. Down a length of coax we could reasonably
expect .66 ft/ns.
For a 40 foot length of coax we get 61 nanoseconds, which corresponds
to a frequency of about 16 megaHertz.
So we would not be surprised at a 1/4 wave resonance at 16 Mz down a
10 foot length of coax.
The Mogami wire I tested in 1980 is in fact a coaxial cable, and ought
to conform to this. I had measured it as .0042 ohms/ft, 170 pF/ft, and
.023 uH per foot.
I used Microcap to simulate 10 ft of this, and saw a 1/4 wave resonance
at 12 megaHertz. The phase response down the line also fit, with a 90
degree delay at that frequency.
That's about a 25% error. Maybe the dielectric of Mogami was particularly
crappy, maybe it's not a good coax construction, maybe my figures are off
a bit, maybe all those things.
With the simulation of 18 gauge zip cord at .014 ohm/ft, 28 pf/ft, and
.21 uH/ft, I got 10 megaHertz. That's slower propagation, but then it's
not coax construction.
Polk's "Cobra" cable with .0075 ohm/ft, 500 pf/ft, and .026 uH/ft has a
10 ft resonance at 6.7 megaHertz. It's construction is of the fine
interwoven strand variety similar to Litz wire, and it appears to have
1/2 the propagation velocity.
I can't help but conclude that the "0.66 * C" figure applies to coax
cable only.
30 feet of the Polk cable definitely puts us in the ballpark for having
a serious effect on a wide bandwidth power amp, and that has been observed
historically.
This still leaves us with the mystery of why the Mogami cable drove
amplifiers crazy in the 70's. It's resonant frequency would have been
higher than the other products on the market.
Have I made any errors here?
I see some reconciliation between my experience and the
observations by Syn08. Inductance and capacitance of a cable
have to be the electromagnetic properties in question.
So if you'll bear with me...
I went to Horowitz and Hill, and confirmed that propagation
for a coaxial cable having an insulator with ordinary dielectric
values is on the order of .66 times the speed of light in a
vacuum.
The speed of light is 186,000 miles/sec, or (rounding slightly)
1 foot per nanosecond. Down a length of coax we could reasonably
expect .66 ft/ns.
For a 40 foot length of coax we get 61 nanoseconds, which corresponds
to a frequency of about 16 megaHertz.
So we would not be surprised at a 1/4 wave resonance at 16 Mz down a
10 foot length of coax.
The Mogami wire I tested in 1980 is in fact a coaxial cable, and ought
to conform to this. I had measured it as .0042 ohms/ft, 170 pF/ft, and
.023 uH per foot.
I used Microcap
to simulate 10 ft of this, and saw a 1/4 wave resonanceat 12 megaHertz. The phase response down the line also fit, with a 90
degree delay at that frequency.
That's about a 25% error. Maybe the dielectric of Mogami was particularly
crappy, maybe it's not a good coax construction, maybe my figures are off
a bit, maybe all those things.
With the simulation of 18 gauge zip cord at .014 ohm/ft, 28 pf/ft, and
.21 uH/ft, I got 10 megaHertz. That's slower propagation, but then it's
not coax construction.
Polk's "Cobra" cable with .0075 ohm/ft, 500 pf/ft, and .026 uH/ft has a
10 ft resonance at 6.7 megaHertz. It's construction is of the fine
interwoven strand variety similar to Litz wire, and it appears to have
1/2 the propagation velocity.
I can't help but conclude that the "0.66 * C" figure applies to coax
cable only.
30 feet of the Polk cable definitely puts us in the ballpark for having
a serious effect on a wide bandwidth power amp, and that has been observed
historically.
This still leaves us with the mystery of why the Mogami cable drove
amplifiers crazy in the 70's. It's resonant frequency would have been
higher than the other products on the market.
Have I made any errors here?
Hi Ovidiu,
-Chris
Edit: TI is also in there fighting for market share.
I think we are in complete agreement here. One reason DiyAudio even exists.
Now that is an interesting point. Perhaps National may incorporate that into some of their driver chips or complete amp assy's. They are putting a large effort into cornering the audio market on every level, wouldn't you say?
-Chris
Edit: TI is also in there fighting for market share.
Nelson,
My only problem was with that 1MHz resonance This time I have no issues with your calculations and conclusions, except for this one:
The value of 0.66 has nothing magic in it. Disregarding the transmission line type and geometry (coax, parallel, microstrip, waveguide, etc...) the wave propagation velocity in an homogenous dielectric is only a function of the dielectric relative permittivity k. To be more rigurous, the relative propagation velocity is exactly v/c=1/SQRT(k*u) where u is the relative magnetic permeability (which is approximately 1 for dielectrics) and c is, of course, the speed of light. This being said, v is 0.66*c for a dieletric permittivity of about 2.3 which is typical for a large range of plastics used in cable construction. A lower propagation velocity would translate in a higher permittivity, which in turn translates to a higher specific capacitance, hence (in an equivalent RLC distributed model) a lower resonance. Most likely the coax you measured is built using a high(er) k dielectric material.
My only problem was with that 1MHz resonance
This time I have no issues with your calculations and conclusions, except for this one:The value of 0.66 has nothing magic in it. Disregarding the transmission line type and geometry (coax, parallel, microstrip, waveguide, etc...) the wave propagation velocity in an homogenous dielectric is only a function of the dielectric relative permittivity k. To be more rigurous, the relative propagation velocity is exactly v/c=1/SQRT(k*u) where u is the relative magnetic permeability (which is approximately 1 for dielectrics) and c is, of course, the speed of light. This being said, v is 0.66*c for a dieletric permittivity of about 2.3 which is typical for a large range of plastics used in cable construction. A lower propagation velocity would translate in a higher permittivity, which in turn translates to a higher specific capacitance, hence (in an equivalent RLC distributed model) a lower resonance. Most likely the coax you measured is built using a high(er) k dielectric material.
Re: Re: Re: Is error correction inconvenient?
Bob,
What was your open-loop output stage THD-20 without EC? This helps give me a calibration, since I believe that in my amp the EC dropped the THD-20 by about a factor of 30.
Unfortunately I don't know precisely. I haven't in particular measured this, but I may do it ASAP. All I seem to recall is the open loop THD20 with the EC grossly mistuned, about 0.12% at 10V output for the same Ibias= 150mA/device.
I probably have not thought about it hard enough, but I am surprized to hear you assert that the proper balance and optimum performance of the HEC circuit depends on absolute resistor values as opposed to just relative matching precision. Perhaps you only meant the term matching in regard to identical pairs of resistor values? Could you elaborate here?
I don't have the time to get into details right now, but very shortly have you ever wondered why the Hawksford balance R1=(1-k)*R2 is not really true in practice, when it comes to the resistor lumped values? Obviously that's because the rest of the circuit is interacting with the balance. These interactions are unfortunately impacting the balance on a "common mode" rather than differential mode. Which means that if you insert a dual pot (as we did) the two optimal values are going to be identical (because the circuit is symetrical) but out of what the Hawksford model predicts. As an example of such a "common mode" imbalance is the emitter areas which are typically +/-10% off and hence Ic can be off by about the same amount, hence rbe can be off by about the same amount. There are other fine points here, like the relative high power dissipation of an EC amp, and hence the high thermal gradient on the chip, hence the need to place the critical resistors on the same izotherm, the need to make the Hawksford balange adjustment bias independent, etc... Of course, one could imagine a EC externally tunable chip, or an on chip tuned resitor process either by laser (as Burr Brown did) or by zener zap (as Analog Devices did). Again, I may be back on this topic. I'll need soon another life to keep track of everything I promised here.
Those are some very nice transistors that you have chosen to use, and I've looked at their spec sheets and am impressed. Can you share with us the SPICE models you used for these transistors?
Here you go. I would really appreciate if andy_c or anybody else would look into these models and further refine them.
.MODEL Q2SA1407 PNP (
+ IS=15.2F
+ NF=1
+ BF=416
+ VAF=254
+ IKF=90M
+ ISE=3.66P
+ NE=2
+ BR=4
+ NR=1
+ VAR=20
+ IKR=.135
+ RE=7.63
+ RB=30.5
+ RC=3.05
+ XTB=1.5
+ CJE=22P
+ VJE=1.1
+ MJE=.5
+ CJC=7.1P
+ VJC=.3
+ MJC=.3
+ TF=397P
+ TR=276N)
.MODEL Q2SC3601 NPN (
+ IS=15.2F
+ NF=1
+ BF=416
+ VAF=254
+ IKF=90M
+ ISE=3.66P
+ NE=2
+ BR=4
+ NR=1
+ VAR=20
+ IKR=.135
+ RE=5.63
+ RB=22.5
+ RC=2.25
+ XTB=1.5
+ CJE=18.3P
+ VJE=1.1
+ MJE=.5
+ CJC=5.91P
+ VJC=.3
+ MJC=.3
+ TF=397P
+ TR=276N)
.MODEL Q2SA1930 PNP(
+ IS=10.000E-15
+ BF=210
+ VAF=78
+ IKF=10.000E-3
+ XTB=1.5
+ BR=.1001
+ VAR=100
+ IKR=10.000E-3
+ ISC=10.000E-15
+ CJE=3.252E-12
+ CJC=63.196E-12
+ MJC=.33333
+ TF=83.239E-12
+ XTF=10
+ VTF=10
+ ITF=1)
.MODEL Q2SC5171 NPN(
+ IS=10.000E-15
+ BF=210
+ VAF=100
+ IKF=10.000E-3
+ XTB=1.5
+ BR=.1001
+ VAR=100
+ IKR=10.000E-3
+ ISC=10.000E-15
+ CJE=2.0000E-12
+ CJC=38.866E-12
+ MJC=.33333
+ TF=83.239E-12
+ XTF=10
+ VTF=10
+ ITF=1)
Bob,
What was your open-loop output stage THD-20 without EC? This helps give me a calibration, since I believe that in my amp the EC dropped the THD-20 by about a factor of 30.
Unfortunately I don't know precisely. I haven't in particular measured this, but I may do it ASAP. All I seem to recall is the open loop THD20 with the EC grossly mistuned, about 0.12% at 10V output for the same Ibias= 150mA/device.
I probably have not thought about it hard enough, but I am surprized to hear you assert that the proper balance and optimum performance of the HEC circuit depends on absolute resistor values as opposed to just relative matching precision. Perhaps you only meant the term matching in regard to identical pairs of resistor values? Could you elaborate here?
I don't have the time to get into details right now, but very shortly have you ever wondered why the Hawksford balance R1=(1-k)*R2 is not really true in practice, when it comes to the resistor lumped values? Obviously that's because the rest of the circuit is interacting with the balance. These interactions are unfortunately impacting the balance on a "common mode" rather than differential mode. Which means that if you insert a dual pot (as we did) the two optimal values are going to be identical (because the circuit is symetrical) but out of what the Hawksford model predicts. As an example of such a "common mode" imbalance is the emitter areas which are typically +/-10% off and hence Ic can be off by about the same amount, hence rbe can be off by about the same amount. There are other fine points here, like the relative high power dissipation of an EC amp, and hence the high thermal gradient on the chip, hence the need to place the critical resistors on the same izotherm, the need to make the Hawksford balange adjustment bias independent, etc... Of course, one could imagine a EC externally tunable chip, or an on chip tuned resitor process either by laser (as Burr Brown did) or by zener zap (as Analog Devices did). Again, I may be back on this topic. I'll need soon another life to keep track of everything I promised here.
Those are some very nice transistors that you have chosen to use, and I've looked at their spec sheets and am impressed. Can you share with us the SPICE models you used for these transistors?
Here you go. I would really appreciate if andy_c or anybody else would look into these models and further refine them.
.MODEL Q2SA1407 PNP (
+ IS=15.2F
+ NF=1
+ BF=416
+ VAF=254
+ IKF=90M
+ ISE=3.66P
+ NE=2
+ BR=4
+ NR=1
+ VAR=20
+ IKR=.135
+ RE=7.63
+ RB=30.5
+ RC=3.05
+ XTB=1.5
+ CJE=22P
+ VJE=1.1
+ MJE=.5
+ CJC=7.1P
+ VJC=.3
+ MJC=.3
+ TF=397P
+ TR=276N)
.MODEL Q2SC3601 NPN (
+ IS=15.2F
+ NF=1
+ BF=416
+ VAF=254
+ IKF=90M
+ ISE=3.66P
+ NE=2
+ BR=4
+ NR=1
+ VAR=20
+ IKR=.135
+ RE=5.63
+ RB=22.5
+ RC=2.25
+ XTB=1.5
+ CJE=18.3P
+ VJE=1.1
+ MJE=.5
+ CJC=5.91P
+ VJC=.3
+ MJC=.3
+ TF=397P
+ TR=276N)
.MODEL Q2SA1930 PNP(
+ IS=10.000E-15
+ BF=210
+ VAF=78
+ IKF=10.000E-3
+ XTB=1.5
+ BR=.1001
+ VAR=100
+ IKR=10.000E-3
+ ISC=10.000E-15
+ CJE=3.252E-12
+ CJC=63.196E-12
+ MJC=.33333
+ TF=83.239E-12
+ XTF=10
+ VTF=10
+ ITF=1)
.MODEL Q2SC5171 NPN(
+ IS=10.000E-15
+ BF=210
+ VAF=100
+ IKF=10.000E-3
+ XTB=1.5
+ BR=.1001
+ VAR=100
+ IKR=10.000E-3
+ ISC=10.000E-15
+ CJE=2.0000E-12
+ CJC=38.866E-12
+ MJC=.33333
+ TF=83.239E-12
+ XTF=10
+ VTF=10
+ ITF=1)
Here's a bit more info on the transmission line stuff. For a lossless transmission line, the velocity of propagation is given by:
v=1/sqrt(LC)
where L and C are the inductance and capacitance per unit length, respectively. The units of v, of course, come out corresponding to the chosen length units of L and C. For a coaxial line, L and C (per meter) are given by:
C=2*pi*epsilon/(ln(b/a))
L=mu*ln(b/a)/(2*pi)
Substituting these into the velocity formula above, you get:
v=1/sqrt(mu*epsilon)
where mu and epsilon are the dielectric permeability and permittivity respectively. Since the dielectric is non-magnetic,
mu=mu_zero (free space value)
also,
epsilon=epsilon_rel*epsilon_zero
where epsilon_zero is the permittivity of free space and epsilon_rel is the unitless relative dielectric constant of the material. For a uniform plane wave in free space, the velocity vfs is given by:
vfs=1/sqrt(mu_zero*epsilon_zero)
Thus it's clear that for coax, the velocity of propagation is given by the free space velocity divided by the square root of epsilon_rel, as Ovidiu already mentioned.
But the propagation velocity is also given by 1/sqrt(LC). Let's compute this for the Mogami cable.
v=1/sqrt(.023e-6*170e-12)
=5.0572e8 ft/sec
=1.5414e10 cm/sec
Now the speed of light in a vacuum is 3e10 cm/sec, so the propagation velocity in the cable is 0.51381 times the speed of light. From this we can calculate the relative dielectric constant:
epsilon_rel=1/(.51381*.51381)=3.788
Likewise, we can compute the characteristic impedance of the cable (assuming it's lossless) as:
Z=sqrt(L/C)=sqrt(.023e-6/170e-12)=11.6 Ohms
That's a pretty low characteristic impedance (due to the large capacitance per unit length).
v=1/sqrt(LC)
where L and C are the inductance and capacitance per unit length, respectively. The units of v, of course, come out corresponding to the chosen length units of L and C. For a coaxial line, L and C (per meter) are given by:
C=2*pi*epsilon/(ln(b/a))
L=mu*ln(b/a)/(2*pi)
Substituting these into the velocity formula above, you get:
v=1/sqrt(mu*epsilon)
where mu and epsilon are the dielectric permeability and permittivity respectively. Since the dielectric is non-magnetic,
mu=mu_zero (free space value)
also,
epsilon=epsilon_rel*epsilon_zero
where epsilon_zero is the permittivity of free space and epsilon_rel is the unitless relative dielectric constant of the material. For a uniform plane wave in free space, the velocity vfs is given by:
vfs=1/sqrt(mu_zero*epsilon_zero)
Thus it's clear that for coax, the velocity of propagation is given by the free space velocity divided by the square root of epsilon_rel, as Ovidiu already mentioned.
But the propagation velocity is also given by 1/sqrt(LC). Let's compute this for the Mogami cable.
v=1/sqrt(.023e-6*170e-12)
=5.0572e8 ft/sec
=1.5414e10 cm/sec
Now the speed of light in a vacuum is 3e10 cm/sec, so the propagation velocity in the cable is 0.51381 times the speed of light. From this we can calculate the relative dielectric constant:
epsilon_rel=1/(.51381*.51381)=3.788
Likewise, we can compute the characteristic impedance of the cable (assuming it's lossless) as:
Z=sqrt(L/C)=sqrt(.023e-6/170e-12)=11.6 Ohms
That's a pretty low characteristic impedance (due to the large capacitance per unit length).
That's very educational, thank you. I still can't reconcile this
the value for the Polk (Litz type) wire which has an apparent
propagation half that of the Mogami. The capacitance on it
is through the roof at 500 pF/ft, but the material is your standard
"magnet wire" coating. Can the dielectric figure for this enamel
be that high, or is there a geometric dependency?
the value for the Polk (Litz type) wire which has an apparent
propagation half that of the Mogami. The capacitance on it
is through the roof at 500 pF/ft, but the material is your standard
"magnet wire" coating. Can the dielectric figure for this enamel
be that high, or is there a geometric dependency?
Nelson Pass said:
It could be geometric. To tell you the truth, I'm only familiar with the kind of transmission line structures used in RF applications, so I don't have a good answer. I do know that the relationship that the prop velocity is that of free space divided by sqrt(epsilon_rel) holds for more than just coax. It holds for stripline and simple plane wave propagation through a dielectric medium of dielectric constant epsilon_rel. It doesn't hold for microstrip though, as microstrip has to contend with differing dielectric constants above and below the conductor (air and substrate respectively). That leads to a prop velocity that depends on frequency (dispersion).
The guy who does know this stuff is jneutron. He's very familiar with structures made from wires. My knowledge of this is limited to the distributed structures.
Hi,
Like Nelson did, I modelled that mogami coax, taking the tml values that andy_c provided as derived from Nelson's data.
I modelled, with LTSpice's "lossless tline" part (very "first order" ;-), 10m (30feet) mis-terminated x10 with 100R, looking into what an amp would see...
Bottom plot:
Green: impedance magnitude
Blue: real (resistive) part thereof
Red: imaginary (reactive) part thereof
Unit dB ref. 1Ohm
Center plot:
Impedance magnitude ("sawtooth") and phase ("square")
Unit dB ref. 1Ohm
Top plot:
Purple: equivalent "inductance"
Green: equivalent "capacitance"
Units: Henrys and Farads, per meter (unit length)
I checked with the terminated case and found those L=68nH/m(22nH/ft), C=511pF/m(170pF/ft) values when I "measure" at ~26MHz, which sounds reasonable and matches the data (as it should be, being the sanity check for the sim). Plotted Z_char also matched. Still I'm not sure about that "per meter" stuff. It is per some unit length (doesn't change with cable length), but why meters?
Looking at the top plot, shortly below the first resonance at 4Mhz, say at 3Mhz, the cable "capacitance" will be ~"100nF" with -70deg phase, compared to the 5nF of DC capacitance. Between 8Mhz and 12Mhz the next capacitive area (-90deg) shows up, with load "capacitances" ranging from ~4nF to ~60nF.
I hope this sim illustrates the topic in a helpful way (and I hope I didn't overlook or grossly misinterpret something, I never did that equivalent L/C stuff with transmission lines so far, with regular networks it works pretty well ).
- Klaus
Like Nelson did, I modelled that mogami coax, taking the tml values that andy_c provided as derived from Nelson's data.
I modelled, with LTSpice's "lossless tline" part (very "first order" ;-), 10m (30feet) mis-terminated x10 with 100R, looking into what an amp would see...
Bottom plot:
Green: impedance magnitude
Blue: real (resistive) part thereof
Red: imaginary (reactive) part thereof
Unit dB ref. 1Ohm
Center plot:
Impedance magnitude ("sawtooth") and phase ("square")
Unit dB ref. 1Ohm
Top plot:
Purple: equivalent "inductance"
Green: equivalent "capacitance"
Units: Henrys and Farads, per meter (unit length)
I checked with the terminated case and found those L=68nH/m(22nH/ft), C=511pF/m(170pF/ft) values when I "measure" at ~26MHz, which sounds reasonable and matches the data (as it should be, being the sanity check for the sim). Plotted Z_char also matched. Still I'm not sure about that "per meter" stuff. It is per some unit length (doesn't change with cable length), but why meters?
Looking at the top plot, shortly below the first resonance at 4Mhz, say at 3Mhz, the cable "capacitance" will be ~"100nF" with -70deg phase, compared to the 5nF of DC capacitance. Between 8Mhz and 12Mhz the next capacitive area (-90deg) shows up, with load "capacitances" ranging from ~4nF to ~60nF.
I hope this sim illustrates the topic in a helpful way (and I hope I didn't overlook or grossly misinterpret something, I never did that equivalent L/C stuff with transmission lines so far, with regular networks it works pretty well ).
- Klaus
