K
Kevin Aylward
- Jan 1, 1970
- 0
Pooh said:These devices which I currently use for example are pre-graded by the
manufacturer. Worst case match is 2:1 in either gain grade.
http://www.profusionplc.com/cgi-bin/gex/pcatdtl?ipartno=2SC5200-O
A simple low value emitter ballast resistor overcomes the bulk of beta
mismatch anyway and I would never fail to use them. You can't depend
on paralled device temps being identical - in fact quite the reverse
- never mind thermal runaway !
Well, it might be useful to explain just why beta/hfe matching is
important, considering that that the bipolar transistor is a voltage
controlled device!
The issue is the internal base resistance, rbb', from the external base
terminal to the actual junction.
Lets say, the output in a device is 5A, with a hfe of 100. This is 50ma
base current. Typically, rbb' might be 5 ohms for a power device (or
less). This
results in 250 mv across rbb', that is, the applied voltage is
reduced by 250mv. If the hfe was half due to mismatch, there would be a
net 250mv difference in applied base emitter voltage *iff* the current
stayed the same. It don't, as the current will be reduced resulting in
less drop. The calculation actually gets a bit messy.
Essentially, we have:
IB1.RB1 + Vt.ln(IC1/Io1) = IB2.RB2 + Vt.ln(IC2/Io2)
simplifying with RB1=RB2 and Io1=Io2 we get
Vt.ln(IC1/IC2) = (IC2/Hfe2 - IC1/Hfe1).R
or
IC1/IC2 = exp((IC2/Hfe2 - IC2/Hfe1)R/Vt)
Which is still a bit tricky to solve, hence the introduction of
SuperSpice
We can actually do something more with the above with a bit of
rearranging:
IC1.exp(IC1.R/Hfe1.Vt) = IC2.exp(IC2.R/Hfe2.Vt)
Which the more astute readers will recognise can be expresed in terms of
our friend the Lambert W function,
http://www.anasoft.co.uk/EE/widlarlambert/widlarlambert.html, to wit:
IC1 = Vt.hfe1/R . W( R/(Vt.hfe1) . IC2.exp(IC2.R/Hfe2.Vt) )
So given, IC2 we can calculate IC1.
Emitter resisters introduce negative feedback, but I think I will stick
to SS for the sums...
It should be noted that 2:1 hfe variations, without emitter degeneration
can typically be of the order of 10:1 in current ratios.
Kevin Aylward
[email protected]
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.