Another 'Transistors' blog. I thought this one would be easy, but it turned out to be quite challenging and, in some
ways, a bit of a failure.
The current gain of a bipolar junction transistor (when the emitter is the common terminal between input and output)
is the ratio of collector current to base current. In some ways, it's the most fundamental parameter that the
transistor has, because our simplest conceptual model of the device is something that takes an input current and
produces an output current in proportion to it. Unfortunately, it's not a simple physical parameter - it depends on
other things and that's where all the complication sets in.
Here is what a multimeter shows for hFE for a particular 2N3904 transistor
That's nice and easy - a single number. But that's the DC current gain at a particular collector current, and for a
particular collector-emitter voltage, and at a particular temperature.
I decided to investigate the variation at different collector currents and for different C-E voltages.
Here's the circuit of my test set-up. This is the kind of design that accumulates as you're doing it, so some
aspects of it are a little odd and could probably be done better.
Quick talk-through. The top half is a constant-current source that defines the collector current of the device under
test. The opamp compares the voltage across the 47R resistor with the voltage that the 10k pot picks off the voltage
reference and drives the transistor so that they match. I wasn't worried about calibrating it as I had a meter
measuring the actual collector current - I just needed it to hold the current steady at the value I adjusted it to.
The odd arrangement with the two diodes is because the op-amp I used is a bipolar device and can't reach the rails
on either inputs or outputs - the diodes give the op-amp an extra volt and a bit to play with. The lower half of the
circuit might need a few moments thought to understand what it's doing. The op-amp drives the device under test so
that the collector sits at 0V. Once it has achieved that, and everything is stable, the base current is that
required to give the set collector current. The diode is just there to lift the voltage at the op-amp output so that
it doesn't have to get too close to the negative supply. Because the collector of the DUT (device under test) is now
held at 0V, the Vce value is whatever I set the negative rail PSU to. I could have used an ammeter to measure the
base current, but in practice I just measured the voltage across the 10k resistor and calculated the current.
Here's the result of my tests on the same transistor that I measured with the meter
And here is how the hFE behaves for a fixed collector current and varying the Vce voltage.
Unfortunately, I realised quite quickly that I had a major problem here. The transistor is small and has a low
thermal mass and, because the device self-heats and the hFE varies with temperature, I had readings that were moving
around even as I was trying to measure them. It was a particular problem at the higher Vce and collector current
values. The above graphs were the best I could do by letting the device cool, quickly moving to the required current
and voltage, and then taking an instant measurement. Even so, I don't manage the nice smooth curves that a
semiconductor manufacturer will show you on a datasheet. How do they do it? They use a pulse test where the
transistor is active for about 2% of the time. That would have been too complicated for me to do - I would have
needed a precision sample and hold to grab the readings - so I left things there.
If you want to get an idea of how the hFE varies with temperature, have a look at John Wiltrout's blog here (in the comments):
1) What I've been looking at here is the DC current gain in the common-emitter configuration, known as Beta or hFE.
The gain also varies with frequency and that is known as hfe.
2) Why beta rather than alpha? There is a parameter called alpha - it's the ratio of collector to emitter current.
[It's the gain when the base is the terminal that's common between input and ouput rather that the emitter.]
3) If you are designing with transistors, you just have to make the best of it (the variation of hFE). Often the
precise value doesn't matter and you just need to have a worst-case figure to work with. With amplifiers, where gain
accuracy is often important, feedback is normally used to shift the gain-setting on to accurate passive components
rather than the active devices.
4) I didn't come up with the form of the test circuit - the idea for servo-ing the base drive I stole from
"Transistor Circuit Design" by the engineering staff of Texas Instruments (published in 1963).