gm matching of BP transistors

[yeeshkul]

Can please someone tell me what so called gm matching of bipolar transistors means? I tried to goggle it out but no success.

[George Giblet]

gm is the small signal transconductance of the transistor.

     gm = ic / vbe

where ic small signal collector current and vbe is the small signal base-emitter voltage.

It is another form of gain for a transistor ie. how much the collector current changes for a given input voltage.

You can calculate gm from,

     gm = IC / VT

where IC is the DC operating collector current and VT is called the "thermal voltage"; it is about about 25.8mV but can also be calculated (do a google).

A more accurate form is

     gm = IC /  (n * VT)

where n is usually between 1 and 1.1 for transistors.

You can read up about it by searching for "hybrid pi" model of the transistor.  Here is a more detailed reference,

http://ece-www.colorado.edu/~bart/book/book/chapter5/ch5_6.htm

With gm matching you are essentially trying to match gm's, at a given operating point.

[yeeshkul]

thanks George!

[JDoyle]

You can calculate gm from,

     gm = IC / VT

where IC is the DC operating collector current and VT is called the "thermal voltage"; it is about about 25.8mV but can also be calculated (do a google).

A more accurate form is

     gm = IC /  (n * VT)

where n is usually between 1 and 1.1 for transistors.

George,

Not to nitpick, but I'd just go ahead and say that the thermal voltage is 26 mV, because that seems to be the standard used in every text I've read up on and is the thermal voltage at 300 degrees Kelvin, or room temp.

And I thought that 'n' for a germanium transistor was 2?

------------------------

yeeshkul,

by looking for gm matching I'm assuming that you are actually working on something with matched transistors. The individual transistors available in an IC transistor array are matched because they are 'grown' on the same substrate at the same time and there thermal voltages track because of their proximity...

But the important fact for your case is that the vbe of each transistor are also normally matched withing +/- 5%, which if you look at George's first equation, would match the gm's as well as long as the transistors are operating at the same current.

Most of those ICs are unavailable not, and the MPQ series aren't matched transistors, just four transistor types in an IC. Your best bet may be to look for matched pairs...

Hope this helps...

Jay Doyle

[JDoyle]

Oh yeah, with the BMP circuit, I really don't think that matching would make a difference, they are capacitively coupled so the qualities of one have no effect on the one previous or after...

Matching is a fortunate byproduct of the planar process of making ICs. It really comes in handy because large caps are prohibitively expensive to create on a chip and take up a TON of space, so there are ways of using the matching characteristics to preform the same job as a cap...

In short, I don't think matching the transistors would change anything...

Jay Doyle

[Sir H C]

In general when all the transistors are on the same piece of silicon and properly oriented, they match pretty darn well.  That is what makes IC designs work as the absolute values often change by 50% or more.

[JDoyle]

In general when all the transistors are on the same piece of silicon and properly oriented, they match pretty darn well.  That is what makes IC designs work as the absolute values often change by 50% or more.

Right, the ratios of all the components scale equally no matter the error factor. So while you don't know what the value of a specific resistor is going to be at the end of the process you DO know that two of them in different parts of the circuit, with the same dimensions, will have the same value, even though you have no clue what that value will be. Or that three in series will be three times the resistance of one of them.

The exception comes with the MPQXXXXX series of transistor arrays, those are absolutely isolated from each other and not grown into the same substrate so they won't match.

Jay Doyle

[George Giblet]

> Not to nitpick, but I'd just go ahead and say that the thermal voltage is 26 mV, because that seems to be the standard used in every text I've read up on and is the thermal voltage at 300 degrees Kelvin, or room temp.

No worries Jay.

Vt can be calculated from first principles:

  Vt = k T /  q

where k = Boltzmanns contant = 1.38e-23, q = electron charge = 1.602e-19 and T = temperature in Kelvin.

At 300K you get 25.84mV.  Yes lot of books quote 26mV, it's right to two decimal places but I suspect that started from the 60's where less siginifcant figures were easier to work with.

>And I thought that 'n' for a germanium transistor was 2?

My understanding is if you separate leakage, resistance and the exponential terms you end up with n near 1 for transistors - but I'm not 100% sure.  Most Si and Ge diodes are close to 2.  If you start curve fitting you can end-up with larger n's which aren't necessarily physically correct because the "wrong" terms get used to make the curve fit better. That's why you will see *silicon* transistor models with dodgy looking n values (so don't rely on spice models from the web to give you the right answer).

[JDoyle]

No worries Jay.

Vt can be calculated from first principles:

  Vt = k T /  q

where k = Boltzmanns contant = 1.38e-23, q = electron charge = 1.602e-19 and T = temperature in Kelvin.

At 300K you get 25.84mV.  Yes lot of books quote 26mV, it's right to two decimal places but I suspect that started from the 60's where less siginifcant figures were easier to work with.

I'll flat out admit that I was and am entirely too lazy to ever actually plug in the numbers! 

When I read the same value in several texts, I figured, hey, if it was good enough for Widlar, it's good enough for me! 

Plus, the 1/Vt values end up pretty close as well (obviously):

Your actual, non-lazy value: 38.699 (I'd call that 38.7)
My lazy value: 38.461

Though in the end, isn't Vt more important for discretes rather than integrated? 

>And I thought that 'n' for a germanium transistor was 2?

My understanding is if you separate leakage, resistance and the exponential terms you end up with n near 1 for transistors - but I'm not 100% sure.  Most Si and Ge diodes are close to 2.  If you start curve fitting you can end-up with larger n's which aren't necessarily physically correct because the "wrong" terms get used to make the curve fit better. That's why you will see *silicon* transistor models with dodgy looking n values (so don't rely on spice models from the web to give you the right answer).

OK, you helped clear me up there, I was confusing transistors and diodes, my understanding is that for silicon diodes they start out with an n of 1 that approaches 2 when the Vd gets significant (of course, the text I am remembering from never definied 'significant' but I'd guess 10V or so) and that Ge diodes have an n of 2. Does that ring any bells or am I nuts?

Thanks!

Jay Doyle

[George Giblet]

The 26mV figure is good enough.  There's a lot of secondary effects which change the behaviour more than any differences in Vt.

> Though in the end, isn't Vt more important for discretes rather than integrated? 

Vt is really just a number, it is what it is.  Pspice for example doesn't use a fixed Vt it effectively calculates it from the first principles equation.  If you plug in a different Vt number like 26mV into the equation all it does is make your answers look like the transistor is a little hotter.  Whether or not that small error is important is up to you.  I wouldn't say it is more important or not for discretes or IC's.

> start out with an n of 1 that approaches 2 when the Vd gets significant (of course, the text I am remembering from never definied 'significant' but I'd guess 10V or so) and that Ge diodes have an n of 2. Does that ring any bells or am I nuts?

Pretty much.  According to the theory diodes start with n=2 (recombination) then as curent is increased go through a region where n=1 then they go back to n=2 (high injection).   At the transitions the regions blend together.  The resistive drop of the diode also makes n look artificially larger and some books confuse/mix the high injection n=2 and IR drop but they are different things.   With silicon diodes the initial n=2 region occurs at very low currents so most applications won't see it.  I think what happens with Ge diodes is the recombination region occurs at higher currents and the high injection region occurs at lower currents and that makes the n=1 regions hard to see - but don't quote me on it, my deeper understanding of this stuff is slowly eroding away.

It's applications like this where you really need to know what the real n is (that's where you will see the curve fitted pspice models fail to give the correct answers)
http://pdfserv.maxim-ic.com/en/an/AN1057.pdf