Transistor Notes

Principles of Electronics

Transistor Amplification

• Input current, $I<em>E$ = Signal / $R</em>{in}$ = $500 mV / 20 \Omega$ = $25 mA$.
• Since $\alpha<em>{ac}$ is nearly 1, output current, $I</em>C = I_E = 25 mA$.
• Output voltage, $V<em>{out} = I</em>C R_C = 25 mA \times 1 k\Omega = 25 V$
• Voltage amplification, $A<em>v = V</em>{out} / V_{signal} = 25 V / 500 mV = 50$
• Basic amplifying action is produced by transferring a current from a low-resistance to a high-resistance circuit.
• Transistor: Transfer + Resistor → Transistor

Transistor Connections

• Transistors have three leads: emitter, base, and collector.
• When connecting a transistor in a circuit, four terminals are required: two for input and two for output.
• One terminal is made common to both input and output to overcome this.
• Input is fed between the common terminal and one of the other two terminals.
• Output is obtained between the common terminal and the remaining terminal.
• Three ways to connect a transistor in a circuit:
  • Common base connection
  • Common emitter connection
  • Common collector connection
• Each connection has specific advantages and disadvantages.
• Regardless of the connection, the emitter is always forward biased, while the collector always has a reverse bias.

Common Base Connection

• Input is applied between emitter and base, and output is taken from collector and base.
• The base of the transistor is common to both input and output circuits.

Current Amplification Factor ($\alpha$)

• It is the ratio of output current to input current.
• In a common base connection, the input current is the emitter current $I<em>E$ and output current is the collector current $I</em>C$.
• The ratio of change in collector current to the change in emitter current at constant collector-base voltage $V_{CB}$ is known as current amplification factor.
• $\alpha = \frac{\Delta I<em>C}{\Delta I</em>E}$ at constant $V_{CB}$
• Current amplification factor is less than unity.
• This value can be increased (but not more than unity) by decreasing the base current.
• Achieved by making the base thin and doping it lightly.
• Practical values of $\alpha$ in commercial transistors range from 0.9 to 0.99.

Expression for Collector Current

• The whole of emitter current does not reach the collector because a small percentage of it gives rise to base current as a result of electron-hole combinations occurring in the base area.

• As the collector-base junction is reverse biased, some leakage current flows due to minority carriers.

• Total collector current consists of:

  • That part of emitter current which reaches the collector terminal i.e. $\alpha I_E$.
  • The leakage current $I_{leakage}$.
    • This current is due to the movement of minority carriers across the base-collector junction on account of it being reverse biased.
    • This is generally much smaller than $\alpha I_E$.

• Total collector current: $I<em>C = \alpha I</em>E + I_{leakage}$

• If $I_E = 0$ (i.e., emitter circuit is open), a small leakage current still flows in the collector circuit.

• $I<em>{leakage}$ is abbreviated as $I</em>{CBO}$, meaning collector-base current with emitter open.

• $I<em>C = \alpha I</em>E + I_{CBO}$

• $I<em>E = I</em>C + I_B$

• $I<em>C = \alpha (I</em>C + I<em>B) + I</em>{CBO}$

• $I<em>C (1 - \alpha) = \alpha I</em>B + I_{CBO}$

• $I<em>C = \frac{\alpha}{1 - \alpha} I</em>B + \frac{1}{1 - \alpha} I_{CBO}$

• The collector current of a transistor can be controlled by either the emitter or base current.

• In CB configuration, a small collector current flows even when the emitter current is zero. This is the leakage collector current (i.e. the collector current when emitter is open) and is denoted by $I_{CBO}$.

• When the emitter voltage $V_{EE}$ is also applied, the various currents are as shown in Fig. 8.11 (ii).

• The magnitude of $I_{CBO}$ for general-purpose and low-powered transistors (especially silicon transistors) is usually very small and may be neglected in calculations.

• For high power applications, it will appear in the microampere range.

• $I_{CBO}$ is very much temperature dependent and increases rapidly with the increase in temperature.

• At higher temperatures, $I_{CBO}$ plays an important role and must be taken care of in calculations.

• Since there is no current gain, no voltage or power amplification could be possible with this arrangement, output circuit resistance is much higher than the input circuit resistance, therefore, it does give rise to voltage and power gain.

• $\alpha = \frac{I<em>C}{I</em>E}$

• $I<em>C = \alpha I</em>E$

• $\alpha I_E$ part of emitter current reaches the collector terminal.

• If only d.c. values are considered, then $\alpha = I<em>C/I</em>E$.

Characteristics of Common Base Connection

• The complete electrical behaviour of a transistor can be described by stating the interrelation of the various currents and voltages.
• These relationships can be conveniently displayed graphically and the curves thus obtained are known as the characteristics of transistor.
• The most important characteristics of common base connection are input characteristics and output characteristics.

Input Characteristic

• It is the curve between emitter current $I<em>E$ and emitter-base voltage $V</em>{EB}$ at constant collector-base voltage $V_{CB}$.
• The emitter current is generally taken along y-axis and emitter-base voltage along x-axis.
• The emitter current $I<em>E$ increases rapidly with small increase in emitter-base voltage $V</em>{EB}$. It means that input resistance is very small.
• The emitter current is almost independent of collector-base voltage $V_{CB}$. This leads to the conclusion that emitter current (and hence collector current) is almost independent of collector voltage.

Input Resistance

• It is the ratio of change in emitter-base voltage ($\Delta V<em>{EB}$) to the resulting change in emitter current ($\Delta I</em>E$) at constant collector-base voltage ($V_{CB}$).
• Input resistance, $r<em>i = \frac{\Delta V</em>{EB}}{\Delta I<em>E}$ at constant $V</em>{CB}$
• Input resistance is the opposition offered to the signal current.
• A very small $V<em>{EB}$ is sufficient to produce a large flow of emitter current $I</em>E$, therefore, input resistance is quite small, of the order of a few ohms.

Output Characteristic

• It is the curve between collector current $I<em>C$ and collector-base voltage $V</em>{CB}$ at constant emitter current $I_E$.
• Generally, collector current is taken along y-axis and collector-base voltage along x-axis.
• The collector current $I<em>C$ varies with $V</em>{CB}$ only at very low voltages (< 1V). The transistor is never operated in this region.
• When the value of $V<em>{CB}$ is raised above 1 − 2 V, the collector current becomes constant as indicated by straight horizontal curves. It means that now $I</em>C$ is independent of $V<em>{CB}$ and depends upon $I</em>E$ only.
• This is consistent with the theory that the emitter current flows almost entirely to the collector terminal. The transistor is always operated in this region.
• A very large change in collector-base voltage produces only a tiny change in collector current. This means that output resistance is very high.

Output Resistance

• It is the ratio of change in collector-base voltage ($\Delta V<em>{CB}$) to the resulting change in collector current ($\Delta I</em>C$) at constant emitter current $I_E$.
• Output resistance, $r<em>o = \frac{\Delta V</em>{CB}}{\Delta I<em>C}$ at constant $I</em>E$
• The output resistance of CB circuit is very high, of the order of several tens of kilo-ohms.
• The collector current changes very slightly with the change in $V_{CB}$.

Common Emitter Connection

• In this circuit arrangement, input is applied between base and emitter and output is taken from the collector and emitter.
• Here, emitter of the transistor is common to both input and output circuits and hence the name common emitter connection.

Base Current Amplification Factor ($\beta$)

• In common emitter connection, input current is $I<em>B$ and output current is $I</em>C$.
• The ratio of change in collector current ($\Delta I<em>C$) to the change in base current ($\Delta I</em>B$) is known as base current amplification factor.
• $\beta = \frac{\Delta I<em>C}{\Delta I</em>B}$
• In almost any transistor, less than 5% of emitter current flows as the base current. Therefore, the value of $\beta$ is generally greater than 20.
• Usually, its value ranges from 20 to 500.
• This type of connection is frequently used as it gives appreciable current gain as well as voltage gain.

Relation between $\beta$ and $\alpha$

• A simple relation exists between $\beta$ and $\alpha$

• $\beta = \frac{\Delta I<em>C}{\Delta I</em>B}$

• $\alpha = \frac{\Delta I<em>C}{\Delta I</em>E}$

• $I<em>E = I</em>B + I_C$

• $\Delta I<em>E = \Delta I</em>B + \Delta I_C$

• $\Delta I<em>B = \Delta I</em>E - \Delta I_C$

• $\beta = \frac{\Delta I<em>C}{\Delta I</em>E - \Delta I_C}$

• $\beta = \frac{\frac{\Delta I<em>C}{\Delta I</em>E}}{1 - \frac{\Delta I<em>C}{\Delta I</em>E}} = \frac{\alpha}{1 - \alpha}$

• $\therefore \beta = \frac{\alpha}{1 - \alpha}$

• As $\alpha$ approaches unity, $\beta$ approaches infinity.

• The current gain in common emitter connection is very high, which is why this circuit arrangement is used in about 90 to 95 percent of all transistor applications.

• If d.c. values are considered, $\beta = I<em>C /I</em>B$.

Expression for Collector Current

• In common emitter circuit, $I<em>B$ is the input current and $I</em>C$ is the output current.
• $I<em>E = I</em>B + I_C$
• $I<em>C = \alpha I</em>E + I_{CBO}$
• $I<em>C = \alpha I</em>E + I<em>{CBO} = \alpha (I</em>B + I<em>C) + I</em>{CBO}$
• $I<em>C (1 - \alpha) = \alpha I</em>B + I_{CBO}$
• $I<em>C = \frac{\alpha}{1 - \alpha} I</em>B + \frac{1}{1 - \alpha}I_{CBO}$
• If $I_B = 0$ (i.e. base circuit is open), the collector current will be the current to the emitter.
• This is abbreviated as $I_{CEO}$, meaning collector-emitter current with base open.
• $I<em>{CEO} = \frac{1}{1 - \alpha} I</em>{CBO}$
• $I<em>C = \frac{\alpha}{1 - \alpha} I</em>B + I_{CEO}$
• $I<em>C = \beta I</em>B + I_{CEO}$

Concept of $I_{CEO}$

• In CE configuration, a small collector current flows even when the base current is zero.
• This is the collector cut off current (i.e. the collector current that flows when base is open) and is denoted by $I_{CEO}$.
• The value of $I<em>{CEO}$ is much larger than $I</em>{CBO}$.
• When the base voltage is applied, then the various currents are :
  • Base current = $I_B$
  • Collector current = $\beta I<em>B + I</em>{CEO}$
  • Emitter current = Collector current + Base current = ($\beta I<em>B + I</em>{CEO}$) + $I<em>B$ = ($\beta + 1$) $I</em>B$ + $I_{CEO}$
• $I<em>{CEO} = \frac{1}{1 - \alpha} I</em>{CBO} = (\beta + 1) I_{CBO}$

Characteristics of Common Emitter Connection

• The important characteristics of this circuit arrangement are the input characteristics and output characteristics.

Input Characteristic

• It is the curve between base current $I<em>B$ and base-emitter voltage $V</em>{BE}$ at constant collector-emitter voltage $V_{CE}$.
• Keeping $V<em>{CE}$ constant, note the base current $I</em>B$ for various values of $V<em>{BE}$. Then plot the readings obtained on the graph, taking $I</em>B$ along y-axis and $V_{BE}$ along x-axis.
• The characteristic resembles that of a forward biased diode curve.
• As compared to CB arrangement, $I<em>B$ increases less rapidly with $V</em>{BE}$. Therefore, input resistance of a CE circuit is higher than that of CB circuit.

Input resistance

• It is the ratio of change in base-emitter voltage ($\Delta V<em>{BE}$) to the change in base current ($\Delta I</em>B$) at constant $V_{CE}$.
• Input resistance, $r<em>i = \frac{\Delta V</em>{BE}}{\Delta I<em>B}$ at constant $V</em>{CE}$
• The value of input resistance for a CE circuit is of the order of a few hundred ohms.

Output characteristic

• It is the curve between collector current $I<em>C$ and collector-emitter voltage $V</em>{CE}$ at constant base current $I_B$.
• Keeping the base current $I<em>B$ fixed at some value say, 5 µA, note the collector current $I</em>C$ for various values of $V<em>{CE}$. Then plot the readings on a graph, taking $I</em>C$ along y-axis and $V_{CE}$ along x-axis.
• The collector current $I<em>C$ varies with $V</em>{CE}$ for $V<em>{CE}$ between 0 and 1V only. After this, collector current becomes almost constant and independent of $V</em>{CE}$.
• This value of $V<em>{CE}$ upto which collector current $I</em>C$ changes with $V<em>{CE}$ is called the knee voltage ($V</em>{knee}$). The transistors are always operated in the region above knee voltage.
• Above knee voltage, $I<em>C$ is almost constant. However, a small increase in $I</em>C$ with increasing $V_{CE}$ is caused by the collector depletion layer getting wider and capturing a few more majority carriers before electron-hole combinations occur in the base area.
• For any value of $V<em>{CE}$ above knee voltage, the collector current $I</em>C$ is approximately equal to $\beta \times I_B$.

Output resistance

• It is the ratio of change in collector-emitter voltage ($\Delta V<em>{CE}$) to the change in collector current ($\Delta I</em>C$) at constant $I_B$.
• Output resistance, $r<em>o = \frac{\Delta V</em>{CE}}{\Delta I<em>C}$ at constant $I</em>B$
• The output characteristics of CB circuit are horizontal, they have noticeable slope for the CE circuit.
• The output resistance of a CE circuit is less than that of CB circuit, with a value of the order of 50 k$\Omega$.

Common Collector Connection

• In this circuit arrangement, input is applied between base and collector while output is taken between the emitter and collector.
• Here, collector of the transistor is common to both input and output circuits and hence the name common collector connection.

Current Amplification Factor $\gamma$

• In common collector circuit, input current is the base current $I<em>B$ and output current is the emitter current $I</em>E$.
• The ratio of change in emitter current ($\Delta I<em>E$) to the change in base current ($\Delta I</em>B$) is known as current amplification factor in common collector (CC) arrangement.
• $\gamma = \frac{\Delta I<em>E}{\Delta I</em>B}$
• This circuit provides about the same current gain as the common emitter circuit as $\Delta I<em>E \approx \Delta I</em>C$.
• Its voltage gain is always less than 1.

Relation between $\gamma$ and $\alpha$

• $\gamma = \frac{\Delta I<em>E}{\Delta I</em>B}$
• $\alpha = \frac{\Delta I<em>C}{\Delta I</em>E}$
• $I<em>E = I</em>B + I_C$
• $\Delta I<em>E = \Delta I</em>B + \Delta I_C$
• $\Delta I<em>B = \Delta I</em>E – \Delta I_C$
• $\gamma = \frac{\Delta I<em>E}{\Delta I</em>E – \Delta I_C}$
• $\gamma = \frac{1}{1 - \alpha}$

Expression for collector current

• $I<em>C = \alpha I</em>E + I_{CBO}$
• $I<em>E = I</em>B + I<em>C = I</em>B + (\alpha I<em>E + I</em>{CBO})$
• $I<em>E (1 – \alpha) = I</em>B + I_{CBO}$
• $I<em>E = \frac{I</em>B}{1 - \alpha} + \frac{I_{CBO}}{1 - \alpha}$
• $I<em>C \approx I</em>E = (\beta + 1) I<em>B + (\beta + 1) I</em>{CBO}$

Applications

• The common collector circuit has very high input resistance (about 750 k$\Omega$) and very low output resistance (about 25 $\Omega$).
• Due to this reason, the voltage gain provided by this circuit is always less than 1. Therefore, this circuit arrangement is seldom used for amplification.
• Due to relatively high input resistance and low output resistance, this circuit is primarily used for impedance matching i.e. for driving a low impedance load from a high impedance source.

Comparison of Transistor Connections

• CB Circuit: The input resistance ($r<em>i$) of CB circuit is low because $I</em>E$ is high. The output resistance ($r_o$) is high because of reverse voltage at the collector. It has no current gain ($\alpha$ < 1) but voltage gain can be high. The CB circuit is seldom used. The only advantage of CB circuit is that it provides good stability against increase in temperature.
• CE Circuit: The input resistance ($r<em>i$) of a CE circuit is high because of small $I</em>B$. Therefore, $r<em>i$ for a CE circuit is much higher than that of CB circuit. The output resistance ($r</em>o$) of CE circuit is smaller than that of CB circuit. The current gain of CE circuit is large because $I<em>C$ is much larger than $I</em>B$. The voltage gain of CE circuit is larger than that of CB circuit. The CE circuit is generally used because it has the best combination of voltage gain and current gain. The disadvantage of CE circuit is that the leakage current is amplified in the circuit, but bias stabilisation methods can be used.
• CC Circuit: The input resistance ($r<em>i$) and output resistance ($r</em>o$) of CC circuit are respectively high and low as compared to other circuits. There is no voltage gain ($A_v$ < 1) in a CC circuit. This circuit is often used for impedance matching.

Commonly Used Transistor Connection

• Out of the three transistor connections, the common emitter circuit is the most efficient. It is used in about 90 to 95 per cent of all transistor applications.
• The main reasons for the widespread use of this circuit arrangement are :
  • High current gain: In a common emitter connection, $I<em>C$ is the output current and $I</em>B$ is the input current. In this circuit arrangement, collector current is given by: $I<em>C = \beta I</em>B + I<em>{CEO}$. As the value of $\beta$ is very large, therefore, the output current $I</em>C$ is much more than the input current $I_B$. Hence, the current gain in CE arrangement is very high. It may range from 20 to 500.
  • High voltage and power gain: Due to high current gain, the common emitter circuit has the highest voltage and power gain of three transistor connections. This is the major reason for using the transistor in this circuit arrangement.
  • Moderate output to input impedance ratio: In a common emitter circuit, the ratio of output impedance to input impedance is small (about 50). This makes this circuit arrangement an ideal one for coupling between various transistor stages. However, in other connections, the ratio of output impedance to input impedance is very large and hence coupling becomes highly inefficient due to gross mismatching.