Transistor beta repeatability

[MacGyverS2000]

The recent post on collector/emitter reversability has prompted me to ask a long-time question I've had...

In general terms, is there a family of inexpensive, small-signal transistors that has decent repeatability of gain from batch to batch?

For example, I commonly use 2N2222-style NPNs in a lot of my circuits (SOT-23 package). The gain is decent for my typical current and frequency range (<50mA, <1kHz) in the area of 120-150, and they're just so darn inexpensive (<<$0.25/pc in quantity, if memory serves).

Difference in part-to-part Beta is usually counted on one hand when comparing devices on a reel (and I would therefore assume from the same batch). However, comparing reel to reel the Beta can vary 20-30 or more, and that can cause issues with circuit repeatability.

Would there be a more appropriate line of transistors to use that are equally inexpensive, but have a tighter tolerance from batch to batch (never bothered comparing a large batch of 3906s, etc.)? Maybe a more recent process? This is more of a curiosity to me than a pressing design issue...


Dan - Owner

http://www.Hi-TecDesigns.com

 

[Skogsgurra]

That's an interesting question.

I have no idea. But since everything else in silicon is fabricated to narrow tolerances and processes are better controlled, I would think that transistors with their "gigantic" dimensions (compared to memories and such) should be very repeatable nowadays.

I haven't used transistors in applications where beta variations would be noticed for several decades. It was only *Before 709* that you had to do things like that.

Is there any application where a tight beta is needed anymore?

Gunnar Englund

http://www.gke.org

 

[IRstuff]

There's still probably a rather large variance.

We used to send devices to a company called Solecon that did a measurement of doping profiles in the transistor. Solecon used to graph the device profiles with a series of "P" and "N" to denote p-type or n-type. Using our device thick nesses, each letter represented about 150 nm of depth change. We used to joke about our "one N" bases, e.g., a base that was about 150 nm thick.

This is formed as a result a double counter-dope, i.e., starting with a n-type collector, counterdoping to get the p-type base, counterdoping that to get the n-type emitter. So doping concentration variances, coupled with processing variances almost always resulted in a larger variation of beta.

The only time you can get closely matched beta is when the devices are processed on the same wafer and essentially next to each other. There's usually enough variance across a wafer to cause some amount of mismatch in performance.

TTFN

 

[logbook]

Don't even both trying to match beta. Waste of time.

The transistors you are talking about are horrendously expensive. BC847/BC547 are much nicer. But they have always been banded in current gain because it is all over the place (factor of 4). If you need matched gains your circuit design is wrong. I just did a design for a PRT amplifier. The matched pair transistors were ok but expensive. I ended up using a pair of Darlingtons as the base current is then so low it really doesn't matter that it is not identical to the other pair.

 

[IRstuff]

Agreed, that's why a differential amp's performance is primarily dependent on its resistors

TTFN

 

[bogeyman]

The forward current tranfer charictaristic of a BJT is not a parameter that any design should rely on, it is not by any means constant and varies widely with temperature, Vce and Ic.

Contrary to popular belief the BJT is a voltage controlled device, whilst more base current will generaly increase the collector current it is the applied base emitter voltage which determines the actual collector current that flows.

BJT collector current is a logarithmic function of the voltage applied to the base emmiter junction.

It would be a gross error to design a system in which Hfe was an important or critical factor for functionality.

If you need to match pairs they should match well for Vbe at the operating collector voltage and current as well as a reasonable match for Hfe.

Try having a look here:-

http://www.dself.dsl.pipex.com/index.htm

I trust this man, he seems to know what's what.

 

[MacGyverS2000]

Contrary to popular belief the BJT is a voltage controlled device, whilst more base current will generaly increase the collector current it is the applied base emitter voltage which determines the actual collector current that flows.

I'm not quite sure what you're saying here. With emitter tied to ground, the base voltage is pretty darn constant, and I can change the collector current over a wide range with changes in base current (as designed). Considering a BJT (and not a FET) as a voltage-controlled device (at least as far as the base goes) is a very odd way of looking at it...


Dan - Owner

http://www.Hi-TecDesigns.com

 

[jimkirk]

Bogeyman is correct.

I(c) = I(sat)*[e^[V(be)/V(t)] - 1]

V(t) = k*T/q

q =~ 1.6022e-19 coulombs
k =~ 1.381e-23 joules / K
T = Absoluteo temperature
I(sat) is a function of the transistor geometry, doping, etc.

This describes the exponential response of a transistor which holds over 9 decades of collector current or more. Simple, basic.

The current that goes in when driving a BJT is just a nuisance. An important one, and one that can be exploited for many cool applications, but not a fundamental property.

The exponential relationship can be exploited for even cooler applications, transconductance amplifiers, multi-quadrant multipliers and such.

MacGyvers, if you carefully measure that base voltage, which is "pretty darned constant", you'll find it has an excellent exponential (or logarithmic, depending on your point of view) relationship with the collector current. A much simpler relationship that the collector current divided by the base current has.

Self has a good explanation at

http://www.dself.dsl.pipex.com/ampins/discrete/discrete.htm

As I recall, historcally, When Shockley, Bardeen and Brattain were working at Bell Labs, they were really trying to produce a solid state equivalent of a vacuum tube, more like a FET, (Which wouldn't have all that pesky base current) but they didn't have sophisticated enough equipment for processing that. Failing that, they figured they'd publish thir results on the bipolar junction device.

 

[Skogsgurra]

And what about the Pope's beard? ;-)

Both are right. For practical work, the BJT is mostly regarded as a current controlled device. To check if you got enough drive for a switch, you divide Ic by beta and many times a simple bias network is based on Ib and beta. But, of course, the Transistor Equation is correct (no Ib, there). And that is probably what academia thinks is valid in the engineering world, too.

Since this is Eng-Tips, not academia, I prefer to regard the BJT as being current controlled.

Gunnar Englund

http://www.gke.org

 

[MacGyverS2000]

Lucky for me I have both academia and practicalia [] in my blood. Equation aside, "viewing" the BJT as a voltage-controlled device is an odd way of looking at things. Except under extreme circumstances, looking at it that way is bound to muddle the design issue. I could keep in mind the exponential curve of a Schottky diode, the 0.3-0.4V loss, and the minor current leakage... but most of the time I can get away with ignoring those relatively minor effects and get on with the design.

To wit, the reason behind the original question. When driving LEDs, it makes little difference to the consumer if they're lit up using 30mA or 25mA, they pretty much look the same in brightness. For small units, the effect is irrelevant. But when I place them into large arrays (thousands of LEDs), I would like to characterize the panel's power draw a bit more closely than +/-20%. If I can find a transistor family whos Beta remains within a few percent of nominal, so does my power draw, and that makes my life easier (not to mention changes in brightness not seen on small units are more easily discerned on larger units).


Dan - Owner

http://www.Hi-TecDesigns.com

 

[jimkirk]

You'd be hard pressed to find even a single transistor whose beta remains within a few per cent over temperature, I(c), V(ce), phase of the moon, et cetera. As logbook and others have said, forget about it. Design so beta variations won't matter.

For your current source, by adding an emitter resistor to drop a volt or two the few tens of millivolts difference the exponential relationship will give over operating conditions generally won't matter. If they do, you can compensate with an appropriate diode drop in the base circuit which can also compensate for temperature variation, but guess what? That equation will describe what's going on.

Not even chip designers depend on I(sat); it's all in the geometry, matching, area scaling, minding temperature gradients, clever topology and such.

 

[MacGyverS2000]

<chuckle> Maybe I should explain a typical scenario for one of my circuits...

First off, I use a constant collector current... PWM (or similar), so it's on/off, but I do not change the drive current. LEDs, being what they are, prefer a specific small drive range for their specified color temperature, so dimming is performed by way on/off modulation.

Second, temperature changes are continually monitored, and the software modifies the modulation frequency to keep the LEDs within spec and drive current within tight tolerance. Temperature change is pretty consistent across an entire board, so deltas in Beta from one transistor to another remain quite small. If the Betas were fairly consistent to begin with, my regulation scheme becomes easier.

If I could place a large number of transistors on a panel that have relatively close Betas (regardless of what Beta may be), my job becomes easier. If I can make my job easier by simply changing the BOM, I declare that change worthwhile.

Dan - Owner

http://www.Hi-TecDesigns.com

 

[IRstuff]

In a high-performance op-amp, matching is still critical, particularly for getting the offset voltages and currents down. Certain op-amps have their input diff pair laid out as 4 transistors in a cross to minimize thermal gradients across a 50 mil die.

TTFN

 

[2dye4]

Many spec sheets will list a Beta min and max.
Scan through till you find one that falls in range.

Otherwise I would suggest sample testing. The dropouts
can be used elsewhere.

Put those transistors in a differential pair config and
then you do worry about their voltage dependent properties.
(transconductance) as that impacts the gain of the pair.

 

[felixc]

I agree with Cap'n Kirk. Why do you rely on the beta to control your current? Is your board already designed and you don't want to redo it? Adding a resistor at the emittor would not be real-estate efficient? I guess that there's a resistor at the base of your transistors. What about having no resistor at the base and one at the emitter instead?

 

[MacGyverS2000]

Design is on a 1.2" x 0.6" board with about 20 SMD components, including processor and 2 large LEDs. Emitter tied to ground, resistor in the collector along with the LEDs, processor tied to base through resistor. Lather, rinse, repeat 3 times.

As I said, it doesn't matter for the small boards, but for the large boards every bit of control you can get back in your posession is a goldmine.

Dan - Owner

http://www.Hi-TecDesigns.com

 

[benta]

I would do this differently:
Skip the base resistor and connect directly to your logic output.
Insert an emitter resistor instead, remove the collector resistor and place the LED directly between supply and collector.

You now have a nice constant-current drive for your LEDs, practically independent of Beta (if there's enough of it).

LED current spread is dependent on logic supply voltage and VBE only. VBE variances should be negligible, supply voltage you can make as precise as you want.

By the way, LED supply voltage needs to be higher than the logic supply, of course.

There! I just saved you a resistor per LED

Regards,

Benta.

 

[MacGyverS2000]

The resistor in the base design was from a time when they resistance was variable and micro-controlled. Once my current batch of boards is gone for each product, I'll be redesigning them one by one.

Dan - Owner

http://www.Hi-TecDesigns.com

 

[MacGyverS2000]

Oh, I should also add...

Placing a resistor in the emitter forces the voltage drop from the transistor to ground to be my digital supply voltage (5V). These are for the automotive arena, so my main supply voltage can be as low as 9-10V (though typically closer to 11V), leaving me only 4-5V to work with for the LEDs. Two LEDs are in series, and their combined forward voltages can by in excess of this... that's a problem.

I could mitigate this somewhat by moving to a 3.3V processor, but that may cause issues elsewhere finding 3.3V tolerant parts (some components are still only made in economical 5V parts, unless you want to pay a premium).


Dan - Owner

http://www.Hi-TecDesigns.com

 

[IRstuff]

Did I miss a statement of the current matching accuracy desired?

You could certainly achieve something on the order of 0.5% matching using precision resistors, precision voltage references and wrapping the LED in the feedback loop of an op amp, so something similar:

http://www.4qdtec.com/csm.html

TTFN