Bipolar Junction Transistor (BJT)

(External reference on Wikipedia)

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.

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.

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).

• Common-Base (CB) configuration

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

  

  The polarity of $V_{BE}$ and direction of $I_B$ 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 $V_{CB}$ and the direction of $I_C$ 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 majority charge carriers, the electrons, in N-type emitter to go through the PN-junction to arrive at the P-type base, forming the emitter current $I_E$.

  • As the base is thin and lightly doped, only a small number of the electrons from the emitter (e.g., 1%) are combined with the majority carriers, the holes, in the P-type base to form the base current $I_B$. The percentage depends on the doping and geometry of the material.

  • Most of the electrons from the emitter (e.g., 99%), now the minority carriers in the P-type base, can go through the reverse biased collector-base PN junction to arrive at the N-type collector forming the collector current $I_C=I_E-I_B$.

  The current gain or current transfer ratio of this CB circuit, denoted by $\alpha$, is defined as the ratio between collector current $I_C$ treated as the output and the emitter current $I_E$ treated as the input:

  $$\alpha=\frac{I_C}{I_E}<1,\;\;\; \;\;\;\;\;\alpha =99\% \approx 1$$ (8)

  i.e.,
  

  $$I_C = \alpha I_E$$

  $$I_B = I_E-I_C=I_E-\alpha I_E=(1-\alpha)I_E$$

  $$I_E = \frac{I_C}{\alpha}=\frac{I_B}{1-\alpha}$$ (9)

  
  

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

    $$I_E=f(V_{BE}, V_{CB})\approx f(V_{BE})=\frac{I_B}{1-\alpha} =\frac{1}{1-\alpha} I_0 ( e^{V_{BE}/V_T}-1 )$$ (10)

    Note that $V_{CB}$ has little effect on $I_E$. Here $I_B$ and $V_{BE}$ associated with the emitter-base PN-junction satisfy the relationship for a diode:

    $$I_B=I_0 ( e^{V_{BE}/V_T}-1 )$$ (11)

    The voltage across the forward biased PN junction can be approximated by $V_{BE}=0.7\,V$.

  • Output characteristics:

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

    $$I_C=f(I_E,V_{CB})\approx f(I_E)=\alpha I_E$$ (12)

    As $V_{CB}>0$, i.e., the CB junction is reverse biased, the current $I_C$ only depends on $I_E$. When $I_E=0$, $I_C=I_{CB0}$ 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 $V_{CB}$ and the direction $I_C$ are oppositely defined). When $I_E$ is increased, $I_C=\alpha I_E+I_{CB0}\approx \alpha I_E$ is increased correspondingly. However, as higher $V_{CB}$ does not cause more electrons from the emitter, it has little effect on $I_C$.

    Note that when $V_{CB}=0$, the PN-junction between base and collector is not biased (short circuited), there is still a non-zero collector current $I_C>0$, formed by the electrons coming from the emitter, through both PN-junctions to form a closed loop current.

    

• Common-Emitter (CE) configuration

  Two voltages $V_{BE}$ and $V_{CE}$ are applied respectively to the base $B$ and collector $C$ with respect to the common emitter $E$. Typically $V_{CE} > V_{BE}$, i.e., the BE junction is forward biased while the CB junction is reverse biased, same as the CB configuration. The voltages of CB and CE configurations are related by:

  $$V_{CE}=V_{CB}+V_{BE},\;\;\;\;\; \;\;\;\;\; V_{CB}=V_{CE}-V_{BE}$$ (13)

  

  The CE 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 emitter. The current gain of the CE circuit, denoted by $\beta$, is defined as the ratio between the collector current $I_C$ treated as the output and the base current $I_B$ treated as the input:

  $$\beta=\frac{I_C}{I_B}=\frac{\alpha I_E}{(1-\alpha) I_E}=\frac{\alpha}{1-\alpha},$$ (14)

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

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

  $$\beta=\frac{\alpha}{1-\alpha},\;\;\;\;\;\;\alpha=\frac{\beta}{1+\beta}, \;\;\;\;1+\beta=\frac{1}{1-\alpha},\;\;\;\;\;1-\alpha=\frac{1}{1+\beta}$$ (15)

  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:

    $$I_B=f(V_{BE},V_{CE})\approx f(V_{BE})=I_0 ( e^{V_{BE}/V_T}-1 )$$ (16)

    The voltage across the forward biased PN junction is approximately $V_{BE}=0.7\,V$. $V_{CE}$ has little effect on $I_B$.

  • Output characteristics:

    $$I_C=f(I_B,V_{CE})\approx f(I_B)=\beta I_B\;\;\;\;\;\;\;\;\;\;$$ (17)

    The current $I_C=\beta I_B$ depends on the current $I_B$, which in turn depends on $V_{BE}$. However, as higher $V_{CE}$ does not cause more electrons from the emitter, it has little effect on $I_C$.

    

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

$$I_E=I_C+I_B,\;\;\;\;\;\;V_{CE}=V_{CB}+V_{BE}$$ (18)

• Common Base:

  
  

  $$\alpha = \frac{I_{out}}{I_{in}}=\frac{I_C}{I_E}, \;\;\;\; \;\;\;\;\;I_C=\alpha I_E$$

  $$I_E = I_C+I_B=\alpha I_E+(1-\alpha) I_E$$ (19)

  
  

• Common Emitter:

  
  

  $$\beta = \frac{I_{out}}{I_{in}}=\frac{I_C}{I_B}, \;\;\;\; \;\;\;\;\;I_C=\beta I_B$$

  $$I_E = I_C+I_B=\beta I_B + I_B$$ (20)

  
  

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

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

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