 Lesson Explainer: Transistors | Nagwa Lesson Explainer: Transistors | Nagwa

# Lesson Explainer: Transistors Physics

In this explainer, we will learn how to describe how transistors can be used as electrical switches in circuits.

The most important property of a transistor is that it can act like a switch. More precisely, a transistor can make a small change in current cause a much larger change in current to occur.

A transistor contains three doped semiconducting regions.

An n-type doped semiconductor consists of an atomic lattice that contains more free electrons than it contains atoms with vacancies in their outer shells.

A p-type doped semiconductor consists of an atomic lattice that contains more atoms with vacancies in their outer shells than it contains free electrons.

A transistor can be formed by placing a p-type semiconductor between two n-type semiconductors. A transistor can also be formed by placing an n-type semiconductor between two p-type semiconductors.

These types of transistors are shown in the following figure.

Both NPN and PNP transistors consist of three regions.

When connected to a circuit, a transistor has a connection to the circuit from each of its regions.

The three regions of a transistor are called

• the emitter,
• the collector,
• the base.

The base is much less strongly doped than the emitter.

A circuit that connects these three regions in this way is called a common emitter configuration circuit. This is shown in the following figure.

We see that the transistor in the circuit is an NPN transistor.

For there to be current in this circuit, there must be potential difference across some part of the circuit. In a transistor circuit, there is in fact a potential difference source in each loop of the circuit. A resistor is also included in each loop of the circuit.

The circuit including all its components is shown in the following figure.

A transistor circuit can also be represented using a transistor circuit symbol. This is shown in the following figure.

For a PNP transistor, the symbol is slightly different, as the following figure shows.

We recall that applying a potential difference across a boundary of p-type and n-type semiconducting materials applies either a forward bias or a reverse bias across the boundary of the materials.

Let us look at an example involving a transistor circuit.

### Example 1: Identifying the Regions of a Transistor

An NPN transistor is connected to two direct current sources, as shown in the diagram. The two n-regions are identical.

1. Which of the regions of the transistor is the collector region?
2. Which of the regions of the transistor is the emitter region?

Part 1

The positive terminal of the source that connects to both and is connected to .

For a common emitter NPN transistor, the positive terminal of the source that connects to both and connects to the collector.

Therefore, is the collector.

Part 2

The negative terminal of the source that connects to both and is connected to .

For a common emitter NPN transistor, the negative terminal of the source that connects to both and connects to the emitter.

Therefore, is the emitter.

The current in a transistor circuit is affected by the biases at the boundaries of the base and the regions adjacent to it.

The following figure shows how the p-type and n-type materials in an NPN transistor respond to the potential difference sources in the circuit. Free electrons are shown by blue circles. Vacancies are shown by red rings.

The diagram shows four important things:

• The base region is thinner than the collector and emitter regions. For a real transistor, the base region is extremely thin compared to the other regions. The difference in thickness is much greater than is shown in the diagram.
• The concentration of vacancies in the base region is much lower than the concentration of free electrons in the emitter and collector regions.
• The emitter is forward biased, and the collector is reverse biased.
• The negative terminals of both potential difference sources are at the same potential.

The currents in different parts of this circuit depend on the semiconducting properties and dimensions of the emitter, base, and collector regions.

In the circuit, the current directions for each connection of the transistor are as follows:

• There is a current out of connection to the emitter region. This can be denoted .
• There is a current into the connection of the collector region. This can be denoted .
• There is a current into the connection of the base region. This can be denoted .

These currents are shown in the following figure. The flow of free electrons is also shown.

We see that is due to free electrons moving from the emitter into the base region.

Free electrons that travel from the emitter to the base are accelerated by the forward bias at the emitter, toward the collector. Most of these electrons have sufficient energy to overcome the effect of the reverse bias across the collector and pass into the collector region.

A small portion of the electrons from the emitter region recombine with vacancies in the base. The base current consists of these electrons.

The magnitude of compared to depends on the thickness of the base region and on the difference in the doping concentration of the emitter and base regions.

There is a formula relating the currents in a transistor circuit.

### Formula: The Relation between the Emitter, Base, and the Collector Currents

The values of the collector current, , the emitter current, , and the base current, , are related as follows:

The ratio of to is an important value for a transistor circuit. For a common emitter transistor circuit, the value of is usually much less than that of . This is because the base region has a low doping concentration and thickness compared to the collector region.

The ratio of to can be determined by expressing as a fraction of . The constant of proportionality between and is called . This means that

It must be therefore that

The ratio of to is therefore given by where is called the current gain of the circuit.

### Formula: Current Gain in Common Emitter Connection

The current gain of a transistor circuit, , is given by where is the collector current and is the base current.

The magnitude of compared to depends on the thickness of the base region and on the difference in the doping concentration of the emitter and base regions.

For a circuit where it must be the case that and hence that is a very large value.

The following figure shows a common emitter transistor circuit, with various circuit values labeled.

The currents , , and are shown, as are

• , the potential difference supplied across the collector and the emitter,
• , the potential difference across the collector and the emitter,
• , the potential difference supplied across the base and the emitter,
• , the resistance to the collector current,
• , the resistance to the base current.

The emitter region contact of the transistor is at zero potential compared to both and .

is called the input potential, and is called the output potential.

Let us look at an example involving the currents in a transistor circuit.

### Example 2: Determining Currents in a Transistor Circuit

An NPN transistor is connected to a power supply with voltage . A power supply with voltage is connected across the transistor’s emitter and base terminals, as shown in the diagram. There is a current between and the collector terminal, a current between and the emitter terminal, and a current between and the base terminal.

1. Calculate .
2. Find the rate at which free electrons diffusing through the base region recombine with holes. Use C for the charge of an electron. Answer in scientific notation to one decimal place.

Part 1

The currents in the circuit are related by the equation Substituting the values stated in the question, we see that

Part 2

The base current is assumed here to entirely consist of free electrons that recombine with holes in the base. The current in the base region is 0.5 mA, which is A. One ampere is equal to one coulomb per second.

The number of electrons, , recombining per second to produce this current is given by

In scientific notation, to one decimal place, is s−1.

Let us look at an example involving the current gain in a transistor circuit.

### Example 3: Determining the Current Gain for a Transistor Circuit

An NPN transistor is connected to a power supply with voltage . A power supply with voltage is connected across the transistor’s emitter and base terminals, as shown in the diagram. There is a current between and the collector terminal, a current between and the emitter terminal, and a current between and the base terminal.

1. Calculate .
2. The dc current gain of the transistor is equal to the ratio of to . Calculate the dc current gain of the transistor.

Part 1

The currents in the circuit are related by the equation

We can make the subject of this equation, giving us

Substituting the values stated in the question, we see that

Part 2

The base current gain, , is given by the equation

Substituting the values stated in the question, we see that

We can see from Kirchhoff’s second law that, in a transistor circuit,

We know that, in such a circuit, the collector current and base current are related by the current gain according to

This means that can be changed by increasing the input potential, as increasing increases .

We can call the input current and call the output current.

For a constant , the ratio of to is a constant for a transistor. We see then that increasing the input current increases the output current.

Let us look at an example involving the current changes in a transistor circuit.

### Example 4: Relating Current Changes in a Transistor Circuit

An NPN transistor is connected to a power supply with voltage . A power supply with voltage is connected across the transistor’s emitter and base terminals, as shown in the diagram. There is a current between and the collector terminal, a current between and the emitter terminal, and a current between and the base terminal. An external resistance is placed between and the collector terminal, and an external resistance is placed between and the base terminal. The potential difference across the collector and emitter terminals is .

1. If the value of is reduced, which of the following most correctly describes the effect on the value of ?
1. increases.
2. decreases.
3. is constant.
2. If the value of is increased, which of the following most correctly describes the effect on the value of ?
1. is constant.
2. increases.
3. decreases.

Part 1

Decreasing increases .

From the equation we see that, for a constant , increasing will increase .

Part 2

Increasing decreases .

From the equation we see that, for a constant , decreasing will decrease .

The relationship between the input and output values of current are not directly proportional.

This means that the value of the current gain is not actually constant but is approximately constant for some values of and .

To show how the change in the value of corresponds to a large change of , let us show the effect of a small change in a small number that is used to divide a much larger number.

For example, consider the equation

Let and let .

We have then

Now, let us suppose we have a value

Let be 0.001.

This means that increases by 0.001 and decreases by 0.001.

We have then

We see that a change of of 0.001 has increased by 501.

Now, suppose that we let be 0.0015.

We have then

We see that a change of of 0.0015 has increased by 1‎ ‎503.

A graph of vs shows how much greater the change of can be than the change in .

We can see that this graph mostly consists of two regions. In one region, the value of is approximately constant as the value of changes, and in the other region, the value of is approximately constant as changes. These regions correspond to approximately constant values of current gain for a transistor when it is acting as a closed switch and as an open switch.

We can also consider the input and output potentials instead of the input and output currents.

From the equation we see that, for the maximum value of , the minimum value of output potential is obtained.

If the input potential is decreased, both the input current and the output current decrease. The output current is zero for zero input current.

For zero output current, the maximum value of output potential is obtained.

A graph of the change of output potential of a transistor with its input potential is shown in the following figure.

Let us now summarize what has been learned in this explainer.

### Key Points

• A transistor consists of either two n-type semiconductors on either side of a p-type semiconductor (NPN) or two p-type semiconductors on either side of an n-type semiconductor (PNP).
• A transistor has collector, emitter, and base terminals. There is one terminal for each semiconductor region.
• A transistor is used in a circuit that contains two potential difference sources. The potential difference sources forward bias the emitter and reverse bias the collector.
• The currents in different parts of a transistor circuit depend on the semiconducting properties and dimensions of the emitter, base, and collector regions.
• The currents at the emitter, , collector, , and base, , terminals are related by the formula
• The currents at the emitter, , and collector, , terminals are related by the formula where is a constant.
• The current at the collector, , and base, , terminals are related by the formula where is the current gain of the circuit.
• A small change in can cause a much greater change in , allowing a circuit with a transistor to effectively switch on or off.