The Voltage Controlled
Bipolar Transistor
Kevin Aylward B.Sc.
Abstract
This paper addresses a very, very common misconception regarding the Bipolar transistor. This is the erroneous notion that the bipolar transistor is a current controlled current source (CCCS) when indeed the actual physics of the situation dictates that the transistor is fundamentally a voltage controlled device (VCCS).
Elementary, layman or Bantam paperback type references, and unfortunately, even some rare semi academic books often give generic reference to the base current controlling the collector or emitter current. The argument for this invariably involve no use of semiconductor physics, and rests on ad hoc arguments on the the notion of the collector current being equal to hfe or beta times the base current. The root cause of the this misconception is the inability to distinguish a functional relation from a causal relation. That is, whilst it is certainly true that in a practical transistor base current must exist, transistor action is not causally dependant on such current. Base current is an effect that results from an application of a voltage at the base emitter junction.
This paper gives the rational for the voltage controlled nature of the bipolar transistor without becoming too involved in advanced mathematics.
The Voltage Controlled Bipolar Transistor
The notion that that the transistor is a fundamentally a voltage controlled device is not open to debate in academic environments. The issue is usually considered of little relevance as it has been well established for many years. Any reasonably advanced academic physics text book directly shows that the currents of the transistor are causally related to the device terminal voltages. To this authors knowledge, there are no technical physics arguments that derive transistor collector and emitter currents from direct knowledge of the base current.
Physics Basics
The force on a charge is given by:
F = q(E + VXB)
That is, the force on a charge is the result of electric fields and or magnetic fields. If we discount the magnetic fields in the operation of the transistor, we can conclude that to instigate any motion of charge we must have an electric field. That is, it is electric fields that cause charges to move.
Basics of Bipolar Transistor Operation
1) The base emitter junction is a diode junction.
2) It can be shown that the current in a diode is causally related to the voltage across it. The relation is:
Id = Is.(exp(Vd/Vt) - 1) - (1)
where Vt is KT/q, and Is is a constant dependant on temperature.
This equation dictates that however Vd is achieved, Id through the junction will be related by the above equation.
3) A voltage instigated via the base and emitter of the transistor is, essentially, equal to Vd of (1), therefore the current that exists through such junction must be related by (1).
That is, the Emitter emits charge into the base region of the transistor, due to the application of Vbe.
4) The emitted charge, once in the base experiences the influence of the voltage at the Collector, and as the base is very thin, collects the charge at the collector terminal and thereby prevents most of the charge flow that would over wise attempt to exit out of the base terminal. Some charge does in fact "leak" out of the base, but this is incidental to the notion that the Emitter current is, essentially, a causal function of applied Vbe, via the diode equation. As most of this current is collected by the collector, the collector current may also be said to be a direct casual function of the applied base emitter voltage.
Summary
The bipolar transistor is described as a voltage controlled device that is spoilt by a non-linear resister across its base emitter junction. For some simple applications one might consider in a very loose way that the collector current is "caused" by a base current as there is indeed a functional relation, but this is only a descriptive approach of limited value that is difficult or impossible to apply in general situations.
Indeed, if one looks at ones watch and the motions of the planets, we can usually say that the sun will reappear when we see the watch hands rotate twice, but this functional relation is certainly not causal. Stopping the hands moving wont stop the planets moving!
This paper may be reproduced so long as no
charge is made
and that the paper is reproduced in full with full credit given to it's author.
Last updated 29th Sept 2007
Copyright © Kevin Aylward 1997-2007.