I'd like to calculate algebraically the DC behaviour of various bipolar transistor circuits that used matched pairs or quads (exponential converters, current mirrors etc.), taking into account the imperfect matching between transistors and deviations from exponential behaviour. The aim of this is to see when cheap matched pairs (e.g. DMMT3904W) will suffice for a particular application, and when precision parts (e.g. SSM2212) are required.
Two of the parameters specified for the above parts are the offset voltage and bulk resistance (\$r_{be}\$). In the context of an Ebers-Moll model, where the emitter current is given by
$$I_e = I_s (e^{V_{be}/V_t} – 1)$$
how should I model these parameters?
- Should I model the offset voltage just by specifying a different \$I_s\$ for each transistor in the pair?
- As I understand it the bulk resistance is effectively a resistance in series with the base-emitter diode – but is the voltage drop across this resistor equal to \$r_{be}I_b\$ or \$r_{be}I_e\$?
Best Answer
The offset voltage can be modeled with different Is, as you suggest. The Rbe, usually, is dominated by Rbb (the base spreading resistance); in low-noise transistors (high beta) this will have less effect, so you might want to use beta-selected transistor pairs in order to make this parameter predictable. So, it's Ib * Rbb...
In transistors intended for high-ish currents (500 mA and up) it is not unusual to see deliberately added emitter resistance (it prevents hot spots). And, in PNP transistors (because N material has higher mobility) the Rbb value might be smaller than in NPN ones.
Two manufacturers may use the same name, but don't always make the same transistor. Even from a trusted manufacturer, a geometry or process change can happen without notice. It's safest to avoid using off-datasheet info.