It looks obvious that there is a decent correlation between VAF and BF.
But it's a bit hard to see clearly because the curve would be a hyperbola if VAF * BF is constant.
Could you plot inverse of VAF and BF?
That should be nice line, make it easier to estimate the correlation coefficient and variance.
Best wishes
David
Bob's book does discuss Spice models and transistor performance in some detail, so I expect he considers this relevant.
Perfectly happy to move the discussion if he wishes.
Yes, some transistor types are better than others, the question here was constancy of VAF*BF within a type.
It is hard for human eyes to interpolate a hyperbolic curve but Mark's plot shows an obvious correlation.
If it's in a spreadsheet and not too much trouble to do a simple statistical fit then that would be nice.
Best wishes
David
Actually, Mark's data shows VAF*BF is far less variable than either parameter alone.
The lowest BF has the maximum VAF. the lowest VAF has the maximum BF
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I have a premonition that when somebody posts corresponding data for NPN transistors, the "spread" will be wider than for PNPs. However you choose to define spread: standard deviation, (max /min), distance between hand-drawn, eyeball estimated "upper" and "lower" envelope boundaries, etc.
Nothing but a feeling, a vibration, a palpable sensitivity. Might be mistaken of course.
Nothing but a feeling, a vibration, a palpable sensitivity. Might be mistaken of course.
It doesn't seem as though asking Mark to plot VAF*BF for his data on different scales would answer your question, because the data he plots covers multiple types.
Separately I did inspect the FoM on different gain grades of a certain transistor, and armed with all of two data points could see that there is plausibility in the 'VAF*BF is stable for a type' hypothesis.
I did find that each batch of transistor was also within a few percent if not a couple of percent of each other in terms of vaf and bf, so obtaining such a robust data set to test the hypothesis with would appear to either require a lot of time or a transistor type made by a manufacturer that somehow produces batches with wide production spread.
I took it that his scatter plot was in response to Matze's question and covered only one type.
I have now looked at the link you posted and it makes me think you are correct.
If so then the variation within a type will practically certainly be even less.
Which tends to support Matze's thesis even more.
As does your own, admittedly small, data set.
Thank you for the additional data and correction.
Best wishes
David
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Thanks for these links.
It seems clear that there is a correlation between VAF and BF within one transistor type. Whether their product varies to a large extend, might be another question.
I only wanted to clarify, if some of the models heavily used by some of us are a bit too optimistic, depending on concrete application.
Matthias
Early voltages for BC550/560 of gain group "C"
This thread is not exactly concerned with Early voltage, but again the results seem to agree with different manufacturer models. Reasonable VAF values could be in the range 50 to 100 for BC550, gain group "C".
Many thanks for these comprehensive measurements, Mark and other contributors.
Matthias
From this thread and models of different manufacturers, one could conclude a VAF of order 25 to 50 for BC560, gain group "C".
This thread is not exactly concerned with Early voltage, but again the results seem to agree with different manufacturer models. Reasonable VAF values could be in the range 50 to 100 for BC550, gain group "C".
Many thanks for these comprehensive measurements, Mark and other contributors.
Matthias
I had a sudden Aha! realization while brewing coffee this morning: When you perform Linear Regression, you automatically get a "Goodness Of Fit" statistic called R-Squared. This might shed some additional light, when trying to judge how well or how poorly Bob Cordell's Figure Of Merit (Figure 1) fits the measured Beta and Vearly of 52 different PNP transistor part-numbers.
To perform Linear Regression, we need a linear equation in canonical form: y = mx + b . Starting with Bob's FOM equationwe multiply both sides by (1/Beta):and then, for perfect matching with the canonical form, add zero:There it is, an ideal textbook linear equation: y = mx + b, where (y = Vearly), (m = FOM), (x=(1/Beta)), and (b = 0).
I put these into Excel, made a new scatter plot, and told Excel to overlay its fitted Linear Regression line (Figure 2). Excel says the best fit value of FOM, for these 52 different PNP transistors, is 33490. Call it thirty three thousand. The R-Squared statistic is 0.65, which suggests to me that the model fits the data moderately well, although the scatter plot in Figure 2 does show there is often quite a large error (> 300% !!) between Predicted_Vearly from the equation (dotted line), and Measured_Vearly from the curve tracer (red diamonds). We can see why Bob's book says that the FOM of real transistors usually falls somewhere within a ten-to-one (!!) range.
_
To perform Linear Regression, we need a linear equation in canonical form: y = mx + b . Starting with Bob's FOM equation
- Beta * Vearly = FOM
- Vearly = FOM * (1/Beta)
- Vearly = FOM*(1/Beta) + 0
I put these into Excel, made a new scatter plot, and told Excel to overlay its fitted Linear Regression line (Figure 2). Excel says the best fit value of FOM, for these 52 different PNP transistors, is 33490. Call it thirty three thousand. The R-Squared statistic is 0.65, which suggests to me that the model fits the data moderately well, although the scatter plot in Figure 2 does show there is often quite a large error (> 300% !!) between Predicted_Vearly from the equation (dotted line), and Measured_Vearly from the curve tracer (red diamonds). We can see why Bob's book says that the FOM of real transistors usually falls somewhere within a ten-to-one (!!) range.
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From the discussions in the nice thread on measurement of Early voltage for pnp devices, I learnt that Early voltage is less controlled during manufacturing process, and that it depends on certain design conditions and targets, for instance the base spreading resistance.
This leads to the conclusion that one will find devices (of different type) with comparable current / voltage ratings as well as current gains, but different mean Early voltages.
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Nice work, Mark; an r^2 of 0.65 and how it slices through the data suggests there are other variables at play that are unaccounted (looks almost like a fractional power law would greatly improve your regression, note how everything is below the regression for low 1/Beta and above the line for high 1/Beta). So I'd definitely say there's a relation between Beta and V_early, but would be reluctant to use Beta*V_early as a figure of merit unto itself, unless very loosely. None of this is a criticism of your work, just my interpretation of the plots.
BLT
Is there a buildable, listenable and testable power amp design at the end of the wonderfully delightful discussion about transistors? I am learning a lot, but want to experience an audible delight at some point. Not trying to rush anyone, but hoping for an amplifier to close and my eyes and enjoy it singing. Thanks
Is there a buildable, listenable and testable power amp design at the end of the wonderfully delightful discussion about transistors? I am learning a lot, but want to experience an audible delight at some point. Not trying to rush anyone, but hoping for an amplifier to close and my eyes and enjoy it singing. Thanks
I tried all of the regression models that come with Excel: Linear, exponential, logarithmic, power, moving average, polynomial. None of them were any better than the linear model. Fourth order polynomial fit, did give some erroneous and hilarious local minima and maxima, but scant improvement.
The scatter plot shows the data is: scattered. There does not exist a smooth curve which goes through each datapoint.
The scatter plot shows the data is: scattered. There does not exist a smooth curve which goes through each datapoint.
Hello Krisfr, welcome to the discussion thread about Bob Cordell's Power amplifier book. In my opinion, Bob's amplifier design shown in Figure 3.13 of the book (p.70 of the paperback edition) is Buildable, Listenable, and Testable. Have you had a chance to study that amp design? It employs all of the circuit design improvements which Bob has methodically described and analyzed, up to that point. Chart 3.9, four pages later, shows Bob's steady progress in reducing distortion, as he adds each of these circuit improvements, one by one.
Fair enough, Mark. And, yes, it's definitely easy to overfit the data, so the simplest regression that gets the job done is usually the best one.
The current LTSpice standard library contains LSK489. Capacities still appear to be a bit low, but this is already better than the standard value CGD=CGS=1p in the model from the Web page of Linear Systems.
Matthias
Sometimes those models comes from libraries where the model was never intended to be used without the corresponding package parasitics model. So the Jfet model would have accurate capacitances, but you would need to use it with the TO92 package parasitics model to get reasonable capacitance.
Often what people do is open up the library, find the .model statement, change the name appropriately and use it that way. This does not always work well since the surrounding subcircuit sometimes accounts for things such as quasi-saturation, extra capacitances and so on.
Often what people do is open up the library, find the .model statement, change the name appropriately and use it that way. This does not always work well since the surrounding subcircuit sometimes accounts for things such as quasi-saturation, extra capacitances and so on.
This all might be true, but I would not expect that from a manufacturer offering models for the complete products to his customers. In the concrete case, I do not think that datasheet capacities mainly stem from package parasitics. After all, they have to be voltage-dependent according to FET behaviour.
It is in line with the very good impression many have of this free software that LTSpice does provide a model someone thought about.
Matthias
Transistor models can be a tough thing these days, partly because of changes that may have resulted from some mergers among semiconductor manufacturers. Even with manufacturers, they have likely tried to retire some of the older processes and consolidate processes. Given that transistor datasheet specs are often pretty loose, if they choose, they can fit new versions of an older transistor into the spec windows of their original versions. If they do that, they will likely not do new plots of the typical characteristics that are most helpful to us in the absence of doing our own measurements.
Lately I have spent some time looking at ways of determining VAF numbers in the lab using ac measurements to find essentially small-signal VAF numbers at different operating points for a given small-signal transistor. I've had some success, but more verification of my results needs to be done, perhaps with two different small-signal measurement techniques for a sanity check. In doing those measurements, I also wanted to see how much VAF was a function of operating point voltage and current, to get a better idea of nonlinearity in the Early effect.
Finally, as we have often been taught, especially in the linear IC design business, we want to design circuits that are inherently less sensitive to transistor parameters to the extent possible. Since Early effect is largely seen as an effect on transistor current gain, circuits that are less dependent for their performance on transistor beta are a good way to go.
Cheers,
Bob