Bipolar Junction Transistor (BJT)

Bipolar Junction Transistor (BJT)

A Bipolar Junction Transistor (BJT) has three terminals connected to three doped semiconductor regions. In an NPN transistor, a thin and lightly doped P-type base is sandwiched between a heavily doped N-type emitter and another N-type collector; while in a PNP transistor, a thin and lightly doped N-type base is sandwiched between a heavily doped P-type emitter and another P-type collector. In the following we will only consider NPN BJTs.

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Description: Description: transistorBJT1.webp

In many schematics of transistor circuits (especially when there exist a large number of transistors in the circuit), the circle in the symbol of a transistor is omitted. The figures below show the cross section of two NPN transistors. Note that although both the collector and emitter of a transistor are made of N-type semiconductor material, they have totally different geometry and therefore can not be interchanged.

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All previously considered components (resistor, capacitor, inductor, and diode) have two terminals (leads) and can therefore be characterized by the single relationship between the current going through and the voltage across the two leads. Differently, a transistor is a three-terminal component, which could be considered as a two-port network with an input-port and an output-port, each formed by two of the three terminals, and characterized by the relationships of both input and output currents and voltages. Depending on which of the three terminals is used as common terminal, there can be three possible configurations for the two-port network formed by a transistor:

Common emitter (CE),
Common base (CB),
Common collector (CC).

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Common-Base (CB) configuration

Two voltages $Description: Description: $V_{BE}$$ and $Description: Description: $V_{CB}$$ are applied respectively to the emitter and collector , with respect to the common base , so that the BE junction is forward biased while the CB junction is reverse biased.

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Note that the polarity of $Description: Description: $V_{BE}$$ and direction of associated with the PN-junction between E and B are the same as those associated with a diode, voltage polarity: positive on P, negative on N, current direction: from P to N, but $Description: Description: $V_{CB}$$ and the direction of associated with the PN-junction between the base and collector are defined oppositely.

The behavior of the NPN-transistor is determined by its two PN-junctions:

The forward biased base-emitter (BE) PN-junction allows the free electrons in emitter to go through the PN-junction to arrive at the base, forming the emitter current .
As the P-type base is thin and lightly doped, only a small number of the electrons from the emitter are combined with the holes in base to form the base current .
Most of the electrons coming from the emitter become minority carriers in the P-type base, and they go through the reverse biased collector-base PN junction to arrive at the collector.
The percentage of those electrons that arrive at the collector out of the electrons from the emitter is defined as $Description: Description: $\alpha$$ (e.g., $Description: Description: $\alpha=99\%=0.99$$ , depending on the doping and geometry of the material). The total collector current is therefore $Description: Description: $I_C=\alpha I_E$$ .

The current gain or current transfer ratio is defined as the ratio between the emitter (input) current and the collector (output) current :

$Description: Description: \begin{displaymath} \frac{I_C}{I_E}\approx \alpha <1,\;\;\;\mbox{i.e.}\;\;\;\;\; I_C=\alpha I_E \end{displaymath}$

The base current is:

$Description: Description: \begin{displaymath} I_B=I_E-I_C\approx I_E-\alpha I_E=(1-\alpha)I_E, \;\;\;\mbox{i.e.}\;\;\;\;\; I_E=\frac{1}{1-\alpha} I_B \end{displaymath}$

The CB configuration can be considered as a 2-port circuit. The input port is formed by the emitter and base, the output port is formed by the collector and base. The relationships between the current and voltage of both the input and output ports are described by the following input and output characteristics.

Input characteristics:

The input current is a function of $Description: Description: $V_{CE}$$ as well as the input voltage $Description: Description: $V_{BE}$$ , which is much more dominant:

$Description: Description: \begin{displaymath} I_E=f(V_{BE}, V_{CB})\approx f(V_{BE})=\frac{1}{1-\alpha} I_B =\frac{1}{1-\alpha} I_0 ( e^{V_{BE}/V_T}-1 ) \end{displaymath}$

where

$Description: Description: \begin{displaymath} I_B=I_0 ( e^{V_{BE}/V_T}-1 ) \end{displaymath}$

This relationship between and $Description: Description: $V_{BE}$$ as the EB junction is very similar to the relationship of and of a diode. Also, we also note higher $Description: Description: $V_{CB}>0$$ can slightly increase .

Output characteristics:

The output current is a function of the output voltage $Description: Description: $V_{CE}$$ as well as the input current , which is much more dominant:

$Description: Description: \begin{displaymath} I_C=f(I_E,V_{CB})\approx f(I_E)=\alpha I_E \end{displaymath}$

Here the approximation is based on the assumption that $Description: Description: $V_{CB}>0.2V$$ (in linear region). As $Description: Description: $V_{CB}>0$$ , i.e., the CB junction is reverse biased, the current depends totally on . When , $Description: Description: $I_C=I_{CB0}$$ is the current caused by the minority carriers crossing the PN-junction. This is similar to the diode current-voltage characteristics seen before, except both axes are reversed (the polarity of $Description: Description: $V_{CB}$$ and the direction are oppositely defined). When is increased, $Description: Description: $I_C=\alpha I_E$$ is increased correspondingly. Higher $Description: Description: $V_{CB}$$ can slightly increase . As $Description: Description: $I_C=\alpha I_E<I_E$$ , CB configuration does not have current-amplification effect. However, if $Description: Description: $V_{BE}$$ is held constant, and therefore will also be held constant, i.e., CB transistor circuit can be used as a current source.

Description: Description: TransistorCBplots.webp

Common-Emitter (CE) configuration

Two voltages $Description: Description: $V_{BE}$$ and $Description: Description: $V_{CE}$$ are applied respectively to the base and collector with respect to the common emitter . As typically $Description: Description: $V_{CE} > V_{BE}$$ , the BE junction is forward biased but the CB junction is reverse biased, same as the CB configuration. The voltages of CB and CE configurations are related by:

$Description: Description: \begin{displaymath} V_{CE}=V_{CB}+V_{BE},\;\;\;\;\;\mbox{or}\;\;\;\;\; V_{CB}=V_{CE}-V_{BE} \end{displaymath}$

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The base current is treated as the input current, and the collector current is treated as the output current:

$Description: Description: \begin{displaymath} I_C=\alpha I_E = \alpha (I_C+I_B) \end{displaymath}$

Solving this equation for , we get the relationship between the output and the input :

$Description: Description: \begin{displaymath} I_C=\frac{\alpha}{1-\alpha} I_B =\beta I_B \end{displaymath}$

where we have defined the CE current gain, the ratio of the output current and the input current :

$Description: Description: \begin{displaymath} \beta=\frac{\alpha}{1-\alpha}\approx\frac{I_C}{I_B} \end{displaymath}$

The two parameters $Description: Description: $\alpha$$ and $Description: Description: $\beta$$ are related by any of the following:

$Description: Description: \begin{displaymath}\beta=\frac{\alpha}{1-\alpha},\;\;\;\;\;\;\alpha=\frac{\beta}... ...+\beta=\frac{1}{1-\alpha},\;\;\;\;\;1-\alpha=\frac{1}{1+\beta} \end{displaymath}$

For example, if $Description: Description: $\alpha=0.99$$ , then $Description: Description: $\beta=0.99/(1-0.99)=99$$ .

The CE configuration can be considered as a 2-port circuit. The input port is formed by the base and emitter, the output port is formed by the collector and emitter. The relationships between the current and voltage of both the input and output ports are described by the following input and output characteristics.

Input characteristics:

Same as in the case of common-base configuration, the EB junction of the common-emitter configuration can also be considered as a forward biased diode, the current-voltage characteristics is similar to that of a diode:

$Description: Description: \begin{displaymath} I_B=f(V_{BE},V_{CE})\approx f(V_{BE})=I_0 ( e^{V_{BE}/V_T}-1 ) \end{displaymath}$

$Description: Description: $V_{CE}$$ has little effect on .

Output characteristics:

$Description: Description: \begin{displaymath} I_C=f(I_B,V_{CE})\approx f(I_B)=\beta I_B\;\;\;\;\;\;\;\;\;\;\mbox{(in linear region)} \end{displaymath}$

Higher $Description: Description: $V_{CE}>0$$ can slightly increase .

The CB junction is reverse biased, the current $Description: Description: $I_C=\beta I_B$$ depends on the current . When , , the current caused by the minority carriers crossing the PN-junctions. When is increased, is correspondingly increased by $Description: Description: $\beta$$ fold.

Description: Description: TransistorCEplots.webp

The relationship between the input and output currents of both CB and CE configurations is summarized below:

$Description: Description: \begin{displaymath} \left\{ \begin{array}{l} I_{out}=I_C=\alpha I_E=\alpha I_{... ..._B=I_E-I_C=I_E-\alpha I_E=(1-\alpha)I_E \end{array} \right. \end{displaymath}$

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$Description: Description: \begin{displaymath} \left\{ \begin{array}{l} I_{out}=I_C=\beta I_B=\beta I_{i... ... gain}) \\ I_E=I_C+I_B=(\beta+1) I_B \end{array} \right. \end{displaymath}$

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The collector characteristics of the common-base (CB) and common-emitter (CE) configurations have the following differences:

In CB circuit $Description: Description: $I_C=\alpha I_E$$ is slightly less than , while in CE circuit $Description: Description: $I_C=\beta I_B$$ is much greater than .
In CB circuit, when $Description: Description: $V_{CB}=0$$ ; while in CE circuit when $Description: Description: $V_{CE}=0$$ (as $Description: Description: $V_{CB}=-V_{BE}$$ has the effect of suppressing ).
Increased $Description: Description: $V_{CE}$$ will slightly increase $Description: Description: $\alpha$$ but more greatly increase $Description: Description: $\beta=\alpha/(1-\alpha)$$ , thereby causing more significantly increased .
in CB is a function of two variables $Description: Description: $V_{BE}$$ and $Description: Description: $V_{CB}$$ , but the former is much more significant then the latter. in CE is a function of two variables $Description: Description: $V_{BE}$$ and $Description: Description: $V_{CE}$$ , but the former is much more significant then the latter.
in CB is a function of two variables $Description: Description: $V_{CB}$$ and . When $Description: Description: $V_{CB}$$ is small, its slight increase will cause significant increase of . But its further increase will not cause much change in due to saturation (all available charge carriers travel at the saturation velocity to arrive at collector C), $Description: Description: $I_C=\alpha I_E$$ is mostly determined by .
in CE is a function of two variables $Description: Description: $V_{CE}$$ and . When $Description: Description: $V_{CE}$$ is small ( $Description: Description: $\approx 0.3V$$ ), its slight increase will cause significant increase of . But when $Description: Description: $V_{CE}>0.3V$$ , its further increase will not cause much change in due to saturation (all available charge carriers travel at the saturation velocity to arrive at collector C), $Description: Description: $I_C=\beta I_B$$ is mostly determined by .

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Various parameters of a transistor change as functions of temperature. For example, $Description: Description: $\beta$$ increases along with temperature.