output stage thermal stability
Hi,
could someone please check my numbers?
3pair output stage using 200W devices, Rth j-c 0.625C/W
On each device Re=0r1, Rb=2r2
Vre = 15mV
Ibias = 150mA / device
hFE~110 @ 30 to 300mA of Ic
Supply voltage +-50.5Vdc
RE = External Re + internal Re + [Rb+Rbb]/hFE
Rex=0.1, estimated Reint=0.005 to 0.02, Rb=2.2, Rbb=? is it insignificant if external Rb is fitted?
RE=0.1 + 0.01 + [2.2/110] = 0.13
Gm0 = Ibias / 0.025V = .15/.025 = 6A/V
Actual Gm = Gm0 / [1 + Gm0 * RE] = 6 / [1 + 6*0.13] = 3.37A/V
Bob's stabilty criteria
0.5>Beta> [Rth j-c + Rth c-s] * Vce * 0.0022 * Gm = [0.625 + 0.3] * 50.5 * 0.0022 * 3.37 = 0.35 <0.5, Bob is satisfied, or is he?
Are the few assumptions close to reality?
Are the 3pair irrelevant to the calculation? Each device is considered alone.
Any mistakes in the formulae used?
Is the arithmetic correct?
Hi,
could someone please check my numbers?
3pair output stage using 200W devices, Rth j-c 0.625C/W
On each device Re=0r1, Rb=2r2
Vre = 15mV
Ibias = 150mA / device
hFE~110 @ 30 to 300mA of Ic
Supply voltage +-50.5Vdc
RE = External Re + internal Re + [Rb+Rbb]/hFE
Rex=0.1, estimated Reint=0.005 to 0.02, Rb=2.2, Rbb=? is it insignificant if external Rb is fitted?
RE=0.1 + 0.01 + [2.2/110] = 0.13
Gm0 = Ibias / 0.025V = .15/.025 = 6A/V
Actual Gm = Gm0 / [1 + Gm0 * RE] = 6 / [1 + 6*0.13] = 3.37A/V
Bob's stabilty criteria
0.5>Beta> [Rth j-c + Rth c-s] * Vce * 0.0022 * Gm = [0.625 + 0.3] * 50.5 * 0.0022 * 3.37 = 0.35 <0.5, Bob is satisfied, or is he?
Are the few assumptions close to reality?
Are the 3pair irrelevant to the calculation? Each device is considered alone.
Any mistakes in the formulae used?
Is the arithmetic correct?
don't know where the .0022 comes from. I haven't seen Bob's post in a while.
However, you might be using too much resistance in the Gm correction.
The usual nomenclature is re for internal resistance and RE for external resistance.
Also, your Gm0 already takes into account re., as re=1/Gm0
However, you might be using too much resistance in the Gm correction.
The usual nomenclature is re for internal resistance and RE for external resistance.
Also, your Gm0 already takes into account re., as re=1/Gm0
Andrew,
Would you give us Bob's post number?
Also, not sure what you are doing for "actual Gm".
I assumed your Gm0 was the Gm without an external resistor, but it is not. You are getting the 150ma bias with RE in place, so the 150ma is for re+RE already.
I don't think the reflected Rs comes into play, here.
Would you give us Bob's post number?
Also, not sure what you are doing for "actual Gm".
I assumed your Gm0 was the Gm without an external resistor, but it is not. You are getting the 150ma bias with RE in place, so the 150ma is for re+RE already.
I don't think the reflected Rs comes into play, here.
I think these will give you sufficient memory jogging:
http://www.diyaudio.com/forums/showthread.php?postid=1275669#post1275669
http://www.diyaudio.com/forums/showthread.php?postid=1278164#post1278164
http://www.diyaudio.com/forums/showthread.php?postid=1278169#post1278169
http://www.diyaudio.com/forums/showthread.php?postid=1275669#post1275669
http://www.diyaudio.com/forums/showthread.php?postid=1278164#post1278164
http://www.diyaudio.com/forums/showthread.php?postid=1278169#post1278169
Andrew,
Bob's examples already seem to play in to your scenario.
He uses 3.7 as a conservative value of gm ignoring internal resistance, and 2.7 assuming an internal resistance of .1. Also, it appears that his TCvbe and beta equation already account for Vt.
Not sure where you got the "assumed" value for your re, or how Bob got his.
However, if you just use his 2.7 which accounts for re, instead of your 3.37 value, your beta would be an even better .28
Bob's examples already seem to play in to your scenario.
He uses 3.7 as a conservative value of gm ignoring internal resistance, and 2.7 assuming an internal resistance of .1. Also, it appears that his TCvbe and beta equation already account for Vt.
Not sure where you got the "assumed" value for your re, or how Bob got his.
However, if you just use his 2.7 which accounts for re, instead of your 3.37 value, your beta would be an even better .28
Perhaps Bob could elaborate on his math in the first link in Andrew's last post.
If intrinsic re= Vt/Ic(ma), then re=25/150=.167
As this resistance is in series with external RE=.1 with 15mv across it, then as I understand it,
Gm= 1/(re + RE)=3.7, yet Bob uses this value for Gm when NOT? including the intrinsic resistance.
This is unclear Bob. At first, you stated you got 3.7 under these conditions:
"To be conservative, we use the ideal gm of the transistor at 150 mA to arrive at a net gm of 3.7 S."
which appears to take the intrinsic resistance into account.
But then you state:
"Finally, let’s assume that the real transistor gm is degraded by an effective internal RE of 0.1 ohm. This is the same effect that reduced the optimum bias from 260 mA to 150 mA. For gm we now have about 2.7 S. "
Is this "effective internal RE" due to something OTHER than the intrinsic re?
If intrinsic re= Vt/Ic(ma), then re=25/150=.167
As this resistance is in series with external RE=.1 with 15mv across it, then as I understand it,
Gm= 1/(re + RE)=3.7, yet Bob uses this value for Gm when NOT? including the intrinsic resistance.
This is unclear Bob. At first, you stated you got 3.7 under these conditions:
"To be conservative, we use the ideal gm of the transistor at 150 mA to arrive at a net gm of 3.7 S."
which appears to take the intrinsic resistance into account.
But then you state:
"Finally, let’s assume that the real transistor gm is degraded by an effective internal RE of 0.1 ohm. This is the same effect that reduced the optimum bias from 260 mA to 150 mA. For gm we now have about 2.7 S. "
Is this "effective internal RE" due to something OTHER than the intrinsic re?
I suggest the thermal stability calculation also be done with the maximum Gm of the transistor to investigate what happens at overload. I like the output stage to be able to recover from a short overtemperature instead of the bias current snowballing until meltdown.
A 2SC5200 has a pretty constant Gm of 30A/V above 2A for example due to the internal base and emitter resistances. The MJL3281 doesn't have a linear-linear Vbe/Ic graph but I guess it is similar.
Maximum Hfe = 160.
Total transresistance: 1/30 + Re + Rb/160 = .15 ohms (or transconductance of 7S) for .1 ohm emitter resistor, 2.2 ohm base resistor.
Gain = Gm * Rth * Vce * Tc = 7 * 1 * 50 * .0022 = .77
So it will recover
I'll try to post something more thorough later.
A 2SC5200 has a pretty constant Gm of 30A/V above 2A for example due to the internal base and emitter resistances. The MJL3281 doesn't have a linear-linear Vbe/Ic graph but I guess it is similar.
Maximum Hfe = 160.
Total transresistance: 1/30 + Re + Rb/160 = .15 ohms (or transconductance of 7S) for .1 ohm emitter resistor, 2.2 ohm base resistor.
Gain = Gm * Rth * Vce * Tc = 7 * 1 * 50 * .0022 = .77
So it will recover
I'll try to post something more thorough later.pooge said:
Hi Pooge,
Sorry, I've been out of town on business, and now back with a terrible cold, probably caught on the plane. Can't think straight right now. When my head clears, I'll try to give this all a look over. I fly to LA tomorrow, but hope to be in internet contact.
Cheers,
Bob
OK Bob, after struggling through Oliver again, I now gather your last .1ohm is that "effective internal RE" contribution of the base circuit resistance that contributes to the output impedance for which Oliver tries to minimize the variation of vs. current, and that your "effect of reducing optimum bias" is somehow related to the 13 to 26mv being "measured" across the entire output impedance rather than just the external emittier resister. (I got a little distracted by you "effect that reduces optimum bias" statements.) I'm wondering about the practical implications of setting the optimum bias is, if one wanted to follow these constraints, as the betas of each half of the output transisters can be somewhat hard to match. I haven't attempted any math, so can we assume that instead of theory, Self's optimum bias determined from measured voltage across the external resistances that reduces measured distortion is sufficient?
I also see that Oliver states that the most practical solution to the temperature stability problem is to make the external emitter resistance large compared to the internal emitter resistance. (I know all this stuff has been mentioned before, I'm just trying to see the forest again before I can get a handle on your thermal beta.)
Since we would not want to raise the value of this external emitter resistor arbitrarily, I gather your beta is a thermal sensitivity function of the various circuit parameters related to temperature stability for given resistances, for which you indicate a beta value of .5 or less is preferred. While I do not question your function, I think we do not appreciate fully how to interpret it. You indicated that .5 or less is preferred, while ~.45 is marginal, etc. I realize you'd like beta as low as possible, but when do you feel entirely "comfortable" with whatever real world gm is plugged in?
I also see that Oliver states that the most practical solution to the temperature stability problem is to make the external emitter resistance large compared to the internal emitter resistance. (I know all this stuff has been mentioned before, I'm just trying to see the forest again before I can get a handle on your thermal beta.)
Since we would not want to raise the value of this external emitter resistor arbitrarily, I gather your beta is a thermal sensitivity function of the various circuit parameters related to temperature stability for given resistances, for which you indicate a beta value of .5 or less is preferred. While I do not question your function, I think we do not appreciate fully how to interpret it. You indicated that .5 or less is preferred, while ~.45 is marginal, etc. I realize you'd like beta as low as possible, but when do you feel entirely "comfortable" with whatever real world gm is plugged in?
Bob, you were planning to reply to this and my enquiry, I hope.
What are your thoughts on Pooge's and my discussion on using your output stage thermal stability formula?
Hi Andrew,
I am once again out of town and in limited contact. Let me get caught up with the discussion here that was going on and I'll try to give a good answer in the next day or so.
Thanks for your patience and continued interest in this topic.
Best regards,
Bob
Hi Andrew,
I’m sorry I took so long getting back to this, but I actually had to go back and read several posts to get back in sync. Recall that I asserted that
Beta = Theta_JS * Vce * TCvce * gm
Was an indicator of local output stage thermal stability, and that Beta was actually a positive feedback factor. I suggested that a value of Beta greater than about 0.5 was cause for significant concern. A Beta value of 0.5 will mean that any thermal disturbance will be magnified by a factor of two due to the positive feedback.
In the equation above, Theta_JS is the thermal resistance from junction to heat sink, and we assume for purposes of this analysis that the heat sink does not move in temperature because of its very large thermal inertia.
One question you raised was in regard to what the proper value of gm is to use for this equation, and that in a couple of places I was a bit unclear about what the constituent components of gm were. I think I began to confuse matters when I brought into the discussion the non-ideality introduced by base resistance. I confused things further by having the value of excess emitter resistance (mainly RB/beta) be the same as the value of external emitter resistance I was using in the example be the same 0.1 ohm.
In the first example, I had an “ideal” transistor biased at 150 mA and an external emitter resistance of 0.1 ohm. By ideal, I meant that the gm of the transistor was only governed by the exponential junction relationship; in other words, emitter resistance was only equal to re’ as defined by re’ ~ Vt/Ic. In this case any effect of internal excess emitter resistance was not included. Effective gm was thus determined by the sum of re’ and RE = 0.167 + 0.1 = 0.267 ohms => 3.75S.
In the second example I went on to include the non-ideality of excess emitter resistance contributed largely by base resistance divided by beta. I assumed RB=5 ohms and beta=50, arriving at excess emitter resistance of 0.1 ohm. The excess emitter resistance, being ohmic in nature, it is functionally no different than the resistance from the external emitter resistor; it is just inside the power transistor. As a result, the effective value of total ohmic resistance in the emitter path became 0.2 ohms. Operational transconductance then became governed by a total resistance of 0.167 + 0.1 + 0.1 = 0.367 ohms => 2.7S.
In accordance with Oliver, we want the re’ component of total emitter path resistance to be equal to the ohmic part of the total emitter path resistance. In the case above, the re’ component is 0.167 ohm while the ohmic part is 0.2 ohm. This is not too bad, but does suggest that the output stage is slightly over-biased relative to the Oliver criterion. If we reduce Ib to 125 mA, then re’ becomes 0.2 ohms and we meet the Oliver criteria. In this case, the total voltage across the total ohmic resistance in the emitter path will be 26 mV. Half of this 26 mV will appear across the external emitter resistor.
One other point about Oliver. As you pointed out, Oliver states that the most practical solution to the temperature stability problem is to make the external emitter resistors large in comparison to the internal emitter resistance.
My recommendation is to increase temperature stability by using reasonable value emitter resistors (e.g. 0.22 ohm) in combination with multiple pairs of output transistors, all biased at optimum quiescent current. At the same time, the output stage should be made as stable as possible against local HF parasitic oscillations with the minimum required amount of base stopper resistance.
Cheers,
Bob