Fundamentals of a Transistor

Construction and operation of NPN and PNP transistors

Biasing of BJT: CB, CE and CC configuration

Characteristics of CB, CE, CC configuration

W. Shockley, J. Barden, & W. Brattain invented transistor in 1947.

**Transistor**\(\Rightarrow\)**transfer**+**resistor**\(\Rightarrow\) transfer of an input signal from a low resistance circuit to a high resistance circuit.

A

**three-terminal**semiconductor device: emitter (E), base (B), and collector (C).

It consists of

**two p-n junctions:**the E-B and B-C junctions.It is capable of

**amplifying or magnifying**a signal.The BJT is a

**current controlled device**.When a small amplitude signal is applied to the base, it is amplified and available at the collector.

Requires an external DC source for the amplification process.

BJT is typically made using doped silicon or germanium.

Doping : Emitter (heavily), base (lightly), and collector (moderately).

Each layer thickness determines the performance of the transistor.

PNP/ NPN transistors have very closely spaced pn-junctions.

The base must be small to allow interaction between the two pn-junctions.

The flow of charge in a BJT is due to the

**diffusion of charge carriers**between the two regions belonging to different charge concentrations.The base-emitter junction is forward biased, and the base-collector junction is reverse biased.

Forward biased means p-doped region has more potential than the n-doped side.

**NPN****PNP**

There are three operating regions of a BJT:

**Active region**: operate as an amplifier.**Saturation region**: is fully on and operates as a switch such that collector current is equal to the saturation current.**Cut-off region**: is fully off and collector current is equal to zero.

For ex - PNP

**Biased
transistor**

An

**unbiased transistor**is like two back-to-back diodesHeavily doped emitter inject its free electrons into the base.

**Emitter injects free e
into base**

Lightly doped base pass emitter-injected electrons on to the collector.

**Free e from base flow
into collector**

Collector collects most of the electrons from the base.

The emitter terminal, being the source of electrons, carries the largest current.

As most of the emitter electrons flow towards the collector, the collector current is nearly equal to the emitter current.

npn-transistor

Base current is significantly smaller, often less than 1% of the collector current.

\[\begin{aligned} &\boxed{I_E = I_C + I_B}~\Leftarrow~\text{KCL} \\ I_C & \approx I_E \\ I_B & << I_C \end{aligned}\]

The

**dc alpha**is defined as the dc collector current divided by the dc emitter current:

\[\boxed{\alpha = \dfrac{I_C}{I_E}}\]

Low-power transistor, \(\alpha>0.99\) and high-power transistor \(\alpha>0.95\)

The

**dc beta**is defined as the ratio of the dc collector current to the dc base current:

\[\boxed{\beta = \dfrac{I_C}{I_B}}\]

The current gain is a significant advantage of a transistor and has paved the way for various applications.

Low-power transistors (under 1 W) \(\Rightarrow\) current gain 100 to 300.

High-power transistors (over 1 W) \(\Rightarrow\) current gain 20 to 100.

\[\boxed{\alpha = \dfrac{I_C}{I_E} = \dfrac{\beta}{1+\beta}}\] \[\boxed{\beta = \dfrac{I_C}{I_B} = \dfrac{\alpha}{1-\alpha}}\]

**Derivation**

\[\begin{aligned} I_E & = I_B + I_C \\ \Rightarrow~\dfrac{I_E}{I_C} & = \dfrac{I_B}{I_C}+1\\ \Rightarrow~\dfrac{1}{\alpha} & = \dfrac{1}{\beta}+1\\ \Rightarrow~&\boxed{\alpha = \dfrac{\beta}{1+\beta}} \end{aligned}\]

**Relating formulas**

\[\begin{aligned} I_E & = \dfrac{I_C}{\alpha} = I_B \cdot (1+\beta) \\ I_C & = \beta \cdot I_B = \alpha \cdot I_E\\ I_B & = \dfrac{I_C}{\beta} = \dfrac{I_E}{1+\beta} = I_E \cdot (1-\alpha) \end{aligned}\]

Since BJT has three leads, there are three possible amplifier types:

**Common-Base** \[\begin{aligned}
\text{Voltage gain}~A_v & = \dfrac{V_{out}}{V_{in}}=
\dfrac{I_C \times R_L}{I_E \times R_{in}}
\end{aligned}\]

**Common-Emitter**
\[\begin{aligned}
\alpha & = \dfrac{I_C}{I_E} \qquad \beta = \dfrac{I_C}{I_B}\\
I_E & = I_C+I_B\\
\alpha & = \dfrac{\beta}{\beta+1} \quad \beta -
\dfrac{\alpha}{1-\alpha}
\end{aligned}\]

**Common-Collector**
\[\begin{aligned}
A_i & = \dfrac{I_E}{I_B}
= \dfrac{I_C+I_B}{I_B}\\
& = \dfrac{I_C}{I_B}+1
= \beta +1
\end{aligned}\]

**Characteristics of the main configurations :****Common Emitter**– has both voltage and current gain**Common Collector**– has no voltage gain but has a current gain**Common base**– has no current gain but has a voltage gain

**Common Base**

**Common Emitter**

**Common Collector**