Direct beta measurement using current division? Possible?

[Analog Kid]

In our last episode I revealed my confusion over a simple transistor beta measurement circuit; that episode was successfully concluded by constructing just such a device.

Now I'm wanting to maybe go a bit further. I quite like the idea of a beta tester that delivers a direct measurement, with no arithmetic needed to come up with β.

I ran across this article on Stackexchange which is quite intriguing: someone built what I believe is called a Gilbert cell out of BJTs, something that can do current division. Here's the schematic:



Before getting all excited about this, I'm wondering if this might be usable as a practical circuit and not just an illustration of theory. Is there any way this could be used in a device to measure beta and display the result? Either with an analog meter or, even cooler, with a digital display, say 3-4 seven-segment LEDs?

One problem (among many!) i can think of is how do I "route" the two currents of interest (I_B & I_C) to the inputs in this circuit.

Thoughts?

[PGPG]

My advice:
Stop thinking about beta measurement - no one practically needs to measure it.
Start thinking about using transistors for other purposes.

For example. Long time ago (germanium transistors times) being a teenager I decided to build a circuit to toggle my desk lamp by clapping hands and one afternoon I did it without any (even prototype) PCB. It was build as a spider on the newspaper, which I then hid in a shelf and connected to my lamp.

[KerimF]

I agree with PGPG.
But while the measurement of beta is not important (it is a function of many factors), you likely gain knowledge about other things in electronics while thinking about it.
 

[Analog Kid]

OK, your negativity here is noted. Meantime, could someone please comment on the current-divider idea? I find this intriguing all on its own, regardless of its application. And yes, I know I can buy off-the-shelf current divider ICs. Not interested in those: I want to roll my own, see how it works.

I do understand that transistor beta is not the do-all and end-all value to measure, that it is usually inappropriate to use it as a design parameter, not the least because of unit-to-unit variations, and that good designs strive to reduce dependence on beta as much as possible; still, it is a useful measure for performance of BJT circuits.

[coppercone2]

you should probobly buy a IC, see if it even works, then attempt to make your own. starting from discrete stuff to make something that you don't know if it will work is silly

if you perform measurements on a working system and understand its behavior then making your own is much more likely to work

[Analog Kid]

In this case I disagree.

Sure, I know there are current-divider ICs that definitely do work. Have the datasheets and everything. But that's not what I'm after.

This scheme is so so simple (4 little transistors), why not try it? Not much to lose there. As it's part of my learning experience, it's all good. No need to meet production schedules or anything here (retired, but not retarded).

Still waiting for someone with knowledge of this concept to contribute here ...

[ArdWar]

First of all, this is a divider (as in doing mathematical function of division), not a current divider. It is however often simply referred as analog multiplier as the basic function is largely reversible.
Current divider on the other hand usually refer to something else, counterpart to the much more common voltage divider.

This scheme is so so simple (4 little transistors)

We all wish it was that simple. There are reasons why ADI charge $40 a pop for their analog multipliers (well, half of it is probably the ADI tax, but still)
I recommend you to familiarize yourself with the concept and working principle of such analog multiplier circuits. The principle is simple enough, but the implementation is decidedly not simple. As you take even the most cursory reading on the subject you'll likely come across those engineering limitations. After all, how hard is it to keep those 4 transistor junction temperature to be isothermal, right?

https://www.analog.com/media/en/training-seminars/tutorials/MT-079.pdf for a primer at analog multipliers

[Analog Kid]

Point taken about terminology: I shall refrain from calling it a current divider (which as you point out is a different critter altogether). Current division is what we're after here.

I still intend to pursue this despite all the (annoying) nay-saying I'm getting here, just because, well, I'm curious as well as being goddamn stubborn.

Temperature compensation? "Isothermal"? Not bothered; again, not looking to create any kind of high-precision instrument here. Those who like to DIY will understand. Good enough may be good enough.

I'll admit that my limited knowledge of electronics doesn't allow me to fully grok documents like the one you linked (the math especially). I can understand the basic concepts OK, but I'm not about to work out any equations involving calculus, for one thing.

Still looking for someone to tell me either "this might work" (and explain how) or "no way, Jose". Worst case here? "No way to make this work." In which case, next project!

[PGPG]

Still looking for someone to tell me either "this might work"

This may work provided you will have 4 identical transistor in identical temperature.

Principles are based on dependency of Ic on Vbe.
Comment says "Ignoring base currents".
So for Q1 Vbe1 has a value as it is needed to make Ic1 (Ic of Q1) being equal to I1.
For Q2 Vbe2 has a value as it is needed to make Ic2 (Ic of Q2) being equal to Iscale.
I2 is Ic3 (Ic of Q3) and Ic4 (Ic of Q4) is Iout.

From simplified Ebers-Moll model we have:
Ic=Ies0 * e ^ (Vbe/(kT/q)).
I will use symbols I0 for Ies0 and Vt for kT/q.

So I get the equation for Ic current as:
Ic=I0*e^(Vbe/Vt).
Ic/I0=e^(Vbe/Vt).
Taking the logarithm of both sides we get:
ln(Ic/I0)=Vbe/Vt so
Vbe=Vt*ln(Ic/I0).
It was for single transistor.

Now our circuit is made that way that Vbe1+Vbe2=Vbe3+Vbe4.
So:
Vt1*ln(Ic1/I01)+Vt2*ln(Ic2/I02)=Vt3*ln(Ic3/I03)+Vt4*ln(Ic4/I04)

Vt=kT/q where T is junction temperature expressed in degrees Kelvin. When you have the same junction temperature you have Vt1=Vt2=Vt3=Vt4 = Vt so we get:

Vt*ln(Ic1/I01)+Vt*ln(Ic2/I02)=Vt*ln(Ic3/I03)+Vt*ln(Ic4/I04) and after dividing by Vt:
ln(Ic1/I01)+ln(Ic2/I02)=ln(Ic3/I03)+ln(Ic4/I04).

The sum of logarithms is the logarithm of the product, therefore we get:
ln( (Ic1/I01)*(Ic2/I02) ) = ln( (Ic3/I03)*(Ic4/I04) )

Logarithms are equal when the logarithm values ​​are equal, so:
(Ic1/I01)*(Ic2/I02) = (Ic3/I03)*(Ic4/I04)

If transistors are identical Ies0 in their equations have the same value so I01=I02=I03=I04 = I0 and we have:

(Ic1/I0)*(Ic2/I0) = (Ic3/I0)*(Ic4/I0)
Ic1*Ic2/I0² = Ic3*Ic4/I0²
so:
Ic1*Ic2 = Ic3*Ic4
And using symbols from schematic:
I1*Iscale=I2*Iout
so:
Iout=Iscale*(I1/I2)

[Analog Kid]

OK, you've confirmed what I already suspected, that this circuit actually does work. (I was convinced of that initially; after all, the guy who posted it also provided a working simulation.) But thanks for the explanation anyhow (over my head, but whatever).

What I want to know is this: could this circuit, or one like it, be used practically to measure transistor beta, where one current is I_B and the other is I_C?

If so, how would you do that? I find it difficult to figure out exactly how you'd modify this to accept those two currents from the D.U.T.

[PGPG]

If so, how would you do that?

Me or we !?

It is 2:30 here and in the morning I have to go to work, so sorry...
It is your idea to use this circuit for your task so not ask us how would we do it but combine yourself how to do it.

From my point of view it is waste of time to design special circuit to measure transistor beta that you would be able to make only inside IC (it is the only way to get enough identical transistors having the same junction temperature).

[Kim Christensen]

Before getting all excited about this, I'm wondering if this might be usable as a practical circuit and not just an illustration of theory. Is there any way this could be used in a device to measure beta and display the result? Either with an analog meter or, even cooler, with a digital display, say 3-4 seven-segment LEDs?

If you were going to have a digital display, then you may as well use a microcontroller to measure the currents via it's ADC, and simply do the math in code.

If you need 4 matched transistors, then you can get transistor arrays like the 300 series from THAT Corp.
They are a bit pricey though.

What I suspect you'd really want to build is a transistor curve tracer which would be a much more useful device than just a beta readout.

What I want to know is this: could this circuit, or one like it, be used practically to measure transistor beta, where one current is I_B and the other is I_C?

Ignoring the fact that you can let the magic smoke out of the transistor or test gear, go over range, overheat, heating of DUT effecting beta, etc, etc:

Have a constant current source (Or simply the correct resistor) to limit the transistor base current to exactly 1mA. Then, with sufficient voltage across the collector-emitter, read the collector current in milliamps. Your beta will be the same as the current measured in milliamps.
Now, you can do this with other base currents. Simply scale the current meter on the collector circuit accordingly.

[PCB.Wiz]

Point taken about terminology: I shall refrain from calling it a current divider (which as you point out is a different critter altogether). Current division is what we're after here.

I still intend to pursue this despite all the (annoying) nay-saying I'm getting here, just because, well, I'm curious as well as being goddamn stubborn.

That circuit is what I'd call current ratio, which is very different from any division.
You already have a simpler circuit, that gives direct beta readout, why seek a more complex circuit to do the same thing ? 

You could design a precision base current source, if you wanted to make this battery voltage tolerant and able to be duplicated across continents by multiple users.
Given how HFE varies significantly with temperature, there does not seem much point in chasing that level of precision, or chasing a 3-4 digit readout.

If you are called Nexperia or Diodes Inc, and have good temperature control and are making parts in the millions, and want to match HFE to 2% or 5%, then a higher precision base current could be worth perusing.
 

[PGPG]

But thanks for the explanation anyhow (over my head, but whatever).

The mathematics behind it is the same as behind this device:
https://en.wikipedia.org/wiki/Slide_rule

It just says that adding logarithms of some numbers equals to multiplying that numbers (logarithms are just designed to work that way).

When I was very young (6..7 years) my parents took on additional work consisting of calculating hundreds of measurement results (there were no calculators back then). They did it using slide rules. As we had 3 slide rules at home and I was bored and I wanted to do what my parents did, so I learned how to multiply numbers using a slide rule. I was able to do one multiplication when they were already counting the whole page

[tggzzz]

But thanks for the explanation anyhow (over my head, but whatever).

The mathematics behind it is the same as behind this device:
https://en.wikipedia.org/wiki/Slide_rule

It just says that adding logarithms of some numbers equals to multiplying that numbers (logarithms are just designed to work that way).

When I was very young (6..7 years) my parents took on additional work consisting of calculating hundreds of measurement results (there were no calculators back then). They did it using slide rules. As we had 3 slide rules at home and I was bored and I wanted to do what my parents did, so I learned how to multiply numbers using a slide rule. I was able to do one multiplication when they were already counting the whole page

It feels like the OP would benefit from understanding not only how a particular circuit works, but also the errors inherent in its operation. Amateurs worry about how X works, professionals worry about how X fails; that true for just about anything, not just electronics

Once the OP has a feel for that, they can then have fun learning how to circumvent limitations.

As for slide rules, I still have my school slide rule. I also have, gulp, four slide rules that are the equivalent to such a slide rule that is 25.4m (1000inches) long

[PGPG]

As for slide rules, I still have my school slide rule.

I also still have one in case calculator batteries fails
At school we had only one lesson how to use it and as teacher at once found that I perfectly know how to use it she asked me to lead the entire lesson. We had a model about 2m long so that everyone in the class could see what was being set up.
When I was 18 I got CASIO-FX17 (powered by 4 x AA) what I also still have.

I also have, gulp, four slide rules that are the equivalent to such a slide rule that is 25.4m (1000inches) long

I don't understand. May be you can provide a link showing what it is.

[tggzzz]

As for slide rules, I still have my school slide rule.

I also still have one in case calculator batteries fails
At school we had only one lesson how to use it and as teacher at once found that I perfectly know how to use it she asked me to lead the entire lesson. We had a model about 2m long so that everyone in the class could see what was being set up.
When I was 18 I got CASIO-FX17 (powered by 4 x AA) what I also still have.

I also have, gulp, four slide rules that are the equivalent to such a slide rule that is 25.4m (1000inches) long

I don't understand. May be you can provide a link showing what it is.

Oooh, that would be too easy 

Approx 14500 were produced over 94 years, ceasing only when HP35 hit the scene.

Personally I think the 1000inches is (original) advertising puff. Strictly correct, but the scale is only 500inches long.

OK; here's a picture of several (?8?9?) in an insurance office, where they needed the 4-5 digit resolution...

[mawyatt]

Approx 14500 were produced over 94 years, ceasing only when HP35 hit the scene.

Remember when one of my fellow grad students showed up with the HP35, we had never seen one before and it blew me away. After he let me fool around with it we asked how did they get the entire CRC Tables in there

Fond memories indeed

Best

[TimFox]

Point taken about terminology: I shall refrain from calling it a current divider (which as you point out is a different critter altogether). Current division is what we're after here.

I still intend to pursue this despite all the (annoying) nay-saying I'm getting here, just because, well, I'm curious as well as being goddamn stubborn.

That circuit is what I'd call current ratio, which is very different from any division.
You already have a simpler circuit, that gives direct beta readout, why seek a more complex circuit to do the same thing ? 

You could design a precision base current source, if you wanted to make this battery voltage tolerant and able to be duplicated across continents by multiple users.
Given how HFE varies significantly with temperature, there does not seem much point in chasing that level of precision, or chasing a 3-4 digit readout.

If you are called Nexperia or Diodes Inc, and have good temperature control and are making parts in the millions, and want to match HFE to 2% or 5%[/b], then a higher precision base current could be worth perusing.
 

I assume that when Nexperia or Diodes Inc matches h_FE to tight tolerances, they force the emitter current and measure the base current, since the user will operate the devices at a given emitter or collector current.

In the Nexperia data sheet for PMP4501V dual NPN device, the ratio of the two h_FE values is specified as between 0.95 and 1.0, and the difference between the two V_be voltages as < 2 mV, both measured at V_ce = 5 V and I_c = 2 mA, where 200 < h_FE < 450.

[PGPG]

I also have, gulp,

I supposed unknown for me word 'gulp' is key here but didn't lead me anywhere.

I found:
https://osgalleries.org/longscale/background4.pdf
and
https://cacm.acm.org/blogcacm/the-worlds-largest-commercial-cylindrical-slide-rule-has-a-scale-length-of-24m/

I've never heard of this, but human ingenuity knows no limits. I was very surprised when few years ago I sow in popular science film power transmission lines for tens of kilometers that operated in Sweden several hundred years ago. The equivalent of modern high voltage lines. I've never seen this on the internet. I've tried to find it now, but I couldn't for 20 minutes.

[tggzzz]

Apologies for "gulp". It is movement your throat and lungs make when you have to admit something mildly embarrassing

And it is none of the ones you have found. These calculators are readily available on fleabay, but if you want to buy one it is worth ensuring the scale is in good condition. As with old books, the paper scale can come to have brown bottling (or worse), known in the antiques trade as "foxing". No idea why it is called that.

[Someone]

Temperature compensation? "Isothermal"? Not bothered; again, not looking to create any kind of high-precision instrument here. Those who like to DIY will understand. Good enough may be good enough.

AS mentioned in your other thread covering this topic. Quantify your errors and what is acceptable. For all the hand waving and not caring, Ib << Ic is enough to cancel the Ib contribution within your accuracy so adding that back in is entirely pointless unless you also control the other sources of error.

[TimFox]

Temperature compensation? "Isothermal"? Not bothered; again, not looking to create any kind of high-precision instrument here. Those who like to DIY will understand. Good enough may be good enough.

AS mentioned in your other thread covering this topic. Quantify your errors and what is acceptable. For all the hand waving and not caring, Ib << Ic is enough to cancel the Ib contribution within your accuracy so adding that back in is entirely pointless unless you also control the other sources of error.

If you ignore the I_b part of the emitter current, you need only add +1 (exact) to the ratio I_e / I_b to get the usual definition of {beta} = I_c / I_b.
If {beta} > 50 (for example), this is a small correction to the ratio at the value of emitter current you obtain from the circuit.

[TimFox]

I also have, gulp,

I supposed unknown for me word 'gulp' is key here but didn't lead me anywhere.

I found:
https://osgalleries.org/longscale/background4.pdf
and
https://cacm.acm.org/blogcacm/the-worlds-largest-commercial-cylindrical-slide-rule-has-a-scale-length-of-24m/

I've never heard of this, but human ingenuity knows no limits. I was very surprised when few years ago I sow in popular science film power transmission lines for tens of kilometers that operated in Sweden several hundred years ago. The equivalent of modern high voltage lines. I've never seen this on the internet. I've tried to find it now, but I couldn't for 20 minutes.

Onomatopoeia is tricky in different languages.  More examples than you need:  https://en.wikipedia.org/wiki/Cross-linguistic_onomatopoeias

[Analog Kid]

OK, let's try this: let's say that a guy, flying in the face of foolishness and all that the Godz of Electronics warn against, insists on proceeding with this project. That guy came up with this scheme:



Now I know (or am pretty sure) that this won't work. But it's by way of illustrating what I'm trying to figure out here: how would one get those two currents from the D.U.T. (I_B & I_C) into the Gilbert cell here? I'm assuming there is some way to do this. Does there need to be some intervening isolating circuitry between? maybe something like an optoisolator (thought that won't work, as it's current, not voltage, that we're trying to transmit here).

Can someone give me a clue here? C'mon, guys*, humor me: there must be one or a few of you who are at least curious about this.

* I use "guys" here with some confidence, but I wonder: have there ever been any women active here? I'm guessing not. Shouldn't there be at least a token few of the other gender here?