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keantoken 28th November 2009 05:05 AM

BJT Hfe Curves
Hello everyone.

I have a funny question I need to ask...

I've seen 2 general types of Hfe graphs in BJT datasheets:

1: Hfe remains constant until a point where it rolls off.

2: Hfe starts low, then rises steadily until it crests and rolls off.

I need to know if these two types of graphs are taken by the same method, or whether they are different, as I have been trying my hand at designing models for BJTs. A possible distinction is that 1 is "pulsed" current gain where the device stays at the same temperature all along, where as 2 is continuous current gain where the transistor heats up with higher Ic and therefore the Hfe rises as indicated with temperature.

- keantoken

sawreyrw 3rd December 2009 05:43 PM

First, let me clear up some confusion. Often time people use the terms hfe and Beta(B) interchangably, but that is wrong. Strictly speaking hfe is the small signal AC current gain. It is given by hfe=change in ac collector current/change in ac base current. Sometimes people define Bac as being the same as hfe which is ok I suppose. In addition Bdc is given by Ic/Ib. So Bac and Bdc are not the same.

If you look at figures 11 and 15 the Onsemi data sheet for the 2N3904 you will see different curves for ac and dc current gains. Onsemi seems to define the ac gain as hfe, and the dc gain as hFE.

Now, the general answer to your question is condition 2 and device heating effects are not included. Pusle testing will be used to avoid significant self heating. Note that there are 3 different temperature curves in figure 15.

wahab 3rd December 2009 06:01 PM

with a logarithmic vertical scale for the Hfe , you can
have a curve that is fairly flat at first look...

keantoken 3rd December 2009 10:43 PM

Thanks for the information.

But... Why are the 2N4124 and 2N3904 datasheet graphs pixel copies of each other!? Scroll down to the graphs and compare yourself... I seems these graphs are just placebos to make it look professional; do they really convey any accurate data?

Almost the only difference is voltage ranges and noise...

I've been thinking for some time a curve tracer would be a worthwhile investment.

- keantoken

sawreyrw 4th December 2009 12:07 AM

I don't know, but obviously they are the same die. What does this have to do with your original question about Bdc, Bac, hFE and hfe?

keantoken 4th December 2009 12:13 AM

It has nothing to do with the original topic, but I do have another question.

How is the measured small signal AC and DC gain any different? I'm talking about the Ic graphs. Beta is always Ic/Ib isn't it, so how can the graphs be any different? At 1KHz, any Cj would be negligible...

Thanks for your patience, Sawrey
- keantoken

godfrey 4th December 2009 09:32 AM

Hi all

Re: DC current gain (hFE) and small-signal current gain (hfe):

Say you measure Base current = 0.01mA, Collector current = 1mA.
The DC current gain (hFE) is 100 (Ic / Ib).

Then you increase Base current to 0.011mA, and the collector current rises to 1.12mA.
The small signal-current gain (hfe) is 120 (change in Ic / change in Ib).

Datasheets normally give hFE and sometimes hfe.
I don't remember seeing "beta" used in ages.

Beware: often textbooks and articles will use the terms differently or ignore the difference between DC current gain and small-signal current gain.

e.g. I just looked up "beta" in Wikipedia and it says DC current gain = beta = hfe.

Then I looked up hfe and it says: "hfx = hfe = The current-gain of the transistor. This parameter is often specified as hFE or the DC current-gain (βDC) in datasheets."

Hmm - maybe there's a difference between the "proper" academic definitions and normal usage.

Anyway, the example at the top of this post reflects the normal usage in datasheets.

Hope that adds more clarity than confusion:)

Cheers - Godfrey

godfrey 4th December 2009 11:58 AM

4 Attachment(s)
Hi keantoken

I've also noticed the two "flavors" of curve mentioned in your first post. First, many years ago, I saw datasheets for BD139 and BD140 where the BD140 had the "starts flat" curve and the BD139 had the humped curve. That got me thinking that the BD140 would be better than the BD139 for a VAS in an amp. i.e. use an NPN input LTP and a PNP VAS, rather than the other way round.

Your post awhile ago somewhere else about biasing transistors on the hump of the curve for minimum distortion got me thinking about this again. I got to wondering if PNP devices are inherently more linear in their current gain than their NPN complements, just as they tend to be slower.

I googled around for some datasheets now to check that out. Couldn't find any BD139 or BD140 datasheets with curves, but the TIP3055/TIP2955 curve below shows the effect.

Then I decided to look at BC547 and BC557. The curves below from Fairchild show the two shapes you mentioned but blow my theory totally. Their NPN has the flat curve and the PNP has the humped curve. (and yes - I've at least triple checked to make sure I didn't mix them up:))

The Motorola data sheet shows a "hump" curve for the BC547, though! Unless somebody screwed up their datasheet, it looks like the "same" part from different manufacturers can be totally different.:(

Looked at another two BC547 datasheets to check.
The Vishay one is almost a classic "hump" shape, but flattening out at very low Ic. The Philips one is almost a classic "starts flat" curve, but droops down at very low Ic.

That's four manufacturers with four different shape curves :bawling:

Maybe more modern / exotic transistors are more predictable?

Maybe it's just that the decades-old ones have been refined differently by different manufacturers over the years?

I like cheap non-exotic parts, though because:
a) They're cheap and easy to find
b) You don't have to worry about counterfeits


Cheers - Godfrey

andy_c 4th December 2009 05:58 PM


Originally Posted by keantoken (
I've seen 2 general types of Hfe graphs in BJT datasheets:

1: Hfe remains constant until a point where it rolls off.

2: Hfe starts low, then rises steadily until it crests and rolls off.

I need to know if these two types of graphs are taken by the same method, or whether they are different, as I have been trying my hand at designing models for BJTs.

Hello keantoken,

I've addressed this issue to some extent on this web page. In terms of SPICE modeling, it's best understood in terms of the so-called "Gummel Plots".

The rationale of these plots comes from the assumption that, for an ideal BJT, IC vs. VBE is an exponential function. If beta (=IC/IB) were constant over all collector current, then IB vs. VBE would also be an exponential function for this idealized BJT.

This idea is combined with two properties of logarithms. The first is that ln(x) and exp(x) are inverse functions, that is, ln(exp(x)) = x. Therefore, for the ideal BJT above, plots of ln(IC) and ln(IB) vs. VBE should look like straight lines. This is shown in Figure 8 on the page linked above. The second property of logarithms that comes into play is ln(x/y) = ln(x)-ln(y). Since beta = IC/IB, ln(beta) = ln(IC/IB) = ln(IC) - ln(IB). That is, ln(beta) at each VBE value can be interpreted as the difference between the two curves.

Now have a look at Figure 9. The Gummel-Poon model shows that ln(IC) vs. VBE has a bend at high currents. This is what models the beta reduction at high currents. The model also shows that ln(IB) vs. VBE has a bend at low currents. This is what models the beta reduction at low currents. At both low and high currents, the curves are closer together, therefore beta is less at these extreme current values than it is at a mid range of currents.

Now, suppose at some "middle current" value (that is, some middle range of VBE), both ln(IC) and ln(IB) vs. VBE have become straight lines - that is, they don't bend. These lines will be parallel, thus beta will be relatively constant over this range of currents. Further, the parameter BF will be exactly the value of beta in the region where beta is constant with current.

Consider another case, in which there is no middle range of VBE values where both ln(IC) and ln(IB) vs. VBE have become straight and parallel lines. That is, as we start from a low VBE value and work our way up, ln(IB) vs. VBE is still bending up, while ln(IC) vs. VBE is already starting to bend down. For this case, there will be no middle range of collector current for which beta is constant. Further, for such a BJT, the BF parameter will be greater than the actual maximum beta.

This leads to another interpretation of BF. Suppose we take the linear portion of these two curves and extrapolate them so each curve (ln(IC) and ln(IB) vs. VBE) looks like a straight line. IOW, we ignore the bends. Then these curves become lines, and the difference between these lines at any and all VBE values is ln(BF). The key is that for BJTs that don't have a region of constant beta, there is no range of VBE values for which the actual curves look like parallel lines.

Some great examples of these two cases are the MJL3281A and MJL1302A. The PNP has a region of IC where beta is relatively flat, while the NPN never gets to a constant beta. This is reflected in the BF values of the two, relative to the actual measured maximum beta.

keantoken 5th December 2009 10:49 PM

Thanks for the info Andy and Godfrey. I found it annoying myself to find that different manufacturers gave different curves. I think some questions can only be answered by someone with a curve tracer.

Andy, what you say confirms my experience. To model a humpier transistor, Bf must be higher than the actual value.

Thanks everyone,
- keantoken

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