The symbol of an npn-transistor is shown in the figure below. Since this type of transistor is composed of three parts (emitter, base, collector), it has three leads or three connections to the outside world. As a result, three currents can be defined:
- IB, the base current
- IC, the collector current
- IE, the emitter current
The typical flow of the currents is indicated in the figure. Note that in the previous discussion on the operation of the BJT, the electron flow was considered, which flows in the opposite direction of the conventional current.
Also, three voltages can be defined.
- VBE, the voltage at the base, relative to the emitter
- VCE, the voltage at the collector, relative to the emitter
- VCB, the voltage at the collector, relative to the base
The question is now what the relations are between all these voltages and currents. Since there are three currents and three voltages, several equations are needed. The first two equations follow from Kirchhoff’s Laws.
- KCL: IE = IC + IB
- KVL: VCB = VCE – VBE
Note these equations are universal. They would be valid for any component with three leads. They simply reflect a fundamental property of currents and voltages, and so do not depend on the fact that we are dealing with a transistor here.
A second note on the current equation: Since the base current is almost always much smaller than the collector current (also in the saturation mode), KCL is often simplified to:
KCL: IE ≈ IC
Certainly in approximate calculations, the above equation will be used.
The relation between IB and VBE is a familiar one. Since the transistor behaves like a diode between base and emitter (remember the pn-junction), the characteristic of a diode shows up.
Figure 3.10 The base characteristic of the BJT transistor is similar to the diode characteristic.
When making calculations, the second diode model will be used, meaning that the base-emitter voltage is 0.7 V if the base current is non-zero, and if it is lower than 0.7 V, than there is no base current. In the transistor model (see further), a diode will appear between base and emitter.
The behavior of the transistor between collector and emitter is somewhat more complicated, and depends on the operating mode. Let’s start with the cut-off mode.
Figure 3.11 Characteristic of the transistor in cut-off mode
The characteristic reflects the relation between the voltage VCE, and the current IC. In cut-off mode, the current IC is always 0 A, whatever the voltage. The reason for this is that there is no base current, meaning that no electrons cross the pn-junction between emitter and base. Graphically, this corresponds to the red line in the figure above. This behavior corresponds to an open switch: no current, whatever the voltage is. So, in the model (see figure above), a diode shows up between base and emitter, and an open switch between collector and emitter.
In the active mode or linear mode, the transistor behaves like a current source between collector and emitter. The collector IC current depends on the base current IB only, and not on the voltage VCE. Since IC = β.IB one can conclude that the current source is current-controlled. An important constraint is that the voltage VCE is large enough, in practice larger than a few tenths of a Volt.
In the figure above, a few lines are drawn, each corresponding to another base current. The higher the base current, the higher the collector current. The lines are horizontal, meaning that the voltage VCE has no influence on the current, and the behavior is that of a current source (always the same current, whatever the voltage). Note that an infinite number of lines could have been drawn in the figure. Indeed, the base current can have any value within a certain range, resulting in another line in the graph.
Finally, in the saturation mode, the collector current will drop below it’s value in the linear mode (IC < β.IB), and the voltage across the transistor will approach 0 V, but still be positive.
Figure 3.13 Characteristic of the transistor in saturation
The exact value of the current is not known, and will be determined by the surrounding components. What is known, is that the voltage VCE is rather small and positive, so in the model a voltage source of a few tenths of a Volt is used. In quick and approximate calculations this voltage is set to 0 V. An alternative would then be to use a closed switch instead of a voltage source.
The most accurate formula to calculate the dissipated power takes both the base current and the collector current into account:
PT = VCE . IC + VBE . IB
In practice the second term can easily be ignored, leading to this approximation:
PT ≈ VCE . IC
In the cut-off mode the transistor dissipates (almost) nothing, since the collector current is (almost) 0 A. The same is true for the saturation area, where the voltage is close to 0 V. If the transistor is used as a switch, the power dissipation is practically zero. This is one of the reasons of the success of the so called switching power supplies, e.g. like in contemporary battery chargers. Only when switching from one state to the other there is some dissipation, since the transistor has to travel through the active area. In the active area, both current and voltage are higher than zero, so is the power. The active area is typically used in amplifier circuits, like the power drive for loudspeakers. In that case the transistor is consuming energy, that is converted into heat.
The figure below shows the complete collector characteristic of the BJT transistor.
Figure 3.14 Collector characteristic of the BJT transistor.