Analysis of Bipolar Junction Transistor (BJT)

A Bipolar Junction Transistor (BJT) is a type of transistor that uses both electron and hole charge carriers. BJTs can be used as amplifiers, switches, or in other applications. Understanding the behavior and characteristics of BJTs is crucial for designing and analyzing circuits that incorporate them.

Correct Option Analysis

Option 1: I_E = [ I_C/β ] + βI_B

This option provides an expression involving the emitter current (I_E), collector current (I_C), and base current (I_B), along with the current gain (β) of the BJT.

To derive this expression, let's start with the basic relationships of currents in a BJT:

• The emitter current (IE) is the sum of the base current (IB) and the collector current (IC):
  I_E = I_B + I_C

The current gain (β) of a BJT is defined as the ratio of the collector current (IC) to the base current (IB):
β = I_C / I_B

From this, we can express the base current (IB) in terms of the collector current (IC) and β:
I_B = I_C / β

Substituting this expression for IB into the original equation for IE, we get:
I_E = (I_C / β) + I_C

Thus, the given expression I_E = [ I_C/β ] + βI_B is correct and aligns with the fundamental relationships of currents in a BJT.

Explanation of Other Options

Option 2: Collector current is the sum of emitter current and base current.

This statement is incorrect. The correct relationship is:
I_E = I_B + I_C
Here, the emitter current (I_E) is the sum of the base current (I_B) and the collector current (I_C), not the other way around.

Option 3: If β is the common emitter amplifier current gain, then I_C = βI_E

This statement is incorrect. The current gain β in a common emitter configuration is defined as:
β = I_C / I_B
Therefore, I_C = βI_B, not I_C = βI_E.

Option 4: The current gain in a common-base amplifier is the ratio of collector current to base current.

This statement is incorrect. The current gain in a common base amplifier configuration is denoted by α and is defined as:
α = I_C / I_E
α is typically close to unity and differs from the current gain β in a common emitter configuration.

PNP Transistor Analysis

A PNP transistor consists of a layer of N-type semiconductor sandwiched between two layers of P-type semiconductor. The three terminals are the emitter (P-type), the base (N-type), and the collector (P-type). When discussing the behavior of the transistor, we need to consider the biasing of the emitter junction and the collector junction.

The collector current (I_C) is primarily due to the movement of holes from the emitter to the collector through the base. However, there is also a small component of current due to the minority carriers (electrons in the P-type collector) that contribute to the total collector current. Thus, the collector current is the sum of the majority carrier current (holes) and the minority carrier current (electrons).

Analysis of Other Options

Option 1: In a PNP transistor, current mainly flows due to electrons in the N-type base.

This statement is incorrect. In a PNP transistor, the majority carriers are holes in the P-type regions (emitter and collector). The current in the transistor is primarily due to the movement of holes from the emitter to the collector. While electrons in the N-type base do play a role, they are minority carriers and do not contribute significantly to the overall current flow.

Option 2: The depletion width of the N-type base is smaller than that of the P-type collector.

This statement is incorrect. The depletion region is formed at the junctions between the different types of semiconductor materials. In a PNP transistor, the emitter-base junction is forward biased, leading to a reduced depletion region. The collector-base junction is reverse biased, leading to a wider depletion region. The width of the depletion region depends on the doping levels and the applied voltage, not the type of semiconductor material. Therefore, the depletion width cannot be simply compared based on the type of material.

Option 4: The depletion region of the emitter junction increases as the applied voltage increases.

This statement is incorrect. In a PNP transistor, the emitter junction is forward biased, which means the applied voltage reduces the barrier potential and the depletion region becomes narrower as the voltage increases. This allows more holes to be injected from the emitter into the base. Therefore, the depletion region of the emitter junction decreases with an increase in the forward bias voltage.

Explanation:

For a bipolar junction transistor (BJT) working as an amplifier, it is crucial to understand the correct biasing and connections of the terminals for both PNP and NPN configurations. Let's analyze the given options to identify the incorrect statement.

Correct Option Analysis:

The correct option is:

Option 2: For the collector junction of an NPN transistor, the P-terminal is connected to positive voltage, and the N-terminal is connected to negative voltage.

This option is incorrect because in an NPN transistor, the collector junction is typically reverse-biased when the transistor is operating in the active region (as an amplifier). In reverse bias, the N-terminal (collector) should be connected to a higher voltage (positive voltage), and the P-terminal (base) should be connected to a lower voltage (negative voltage). Therefore, the statement given in Option 2 contradicts this principle.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: For the emitter junction of a PNP transistor, the P-terminal is connected to positive voltage, and the N-terminal is connected to negative voltage.

This statement is correct. In a PNP transistor, the emitter junction is forward-biased when the transistor is in active mode. The P-terminal (emitter) is connected to a higher voltage (positive voltage), and the N-terminal (base) is connected to a lower voltage (negative voltage).

Option 3: For the emitter junction of an NPN transistor, the P-terminal is connected to positive voltage, and the N-terminal is connected to negative voltage.

This statement is correct. In an NPN transistor, the emitter junction is forward-biased when the transistor is in active mode. The P-terminal (base) is connected to a higher voltage (positive voltage), and the N-terminal (emitter) is connected to a lower voltage (negative voltage).

Option 4: For the collector junction of a PNP transistor, the N-terminal is connected to positive voltage, and the P-terminal is connected to negative voltage.

This statement is correct. In a PNP transistor, the collector junction is reverse-biased when the transistor is in active mode. The N-terminal (collector) is connected to a higher voltage (positive voltage), and the P-terminal (base) is connected to a lower voltage (negative voltage).

Conclusion:

Understanding the correct biasing conditions and terminal connections for PNP and NPN transistors is essential for their proper operation as amplifiers. The incorrect option (Option 2) misrepresents the correct biasing of the collector junction in an NPN transistor, leading to incorrect operation. Proper knowledge of these principles ensures the accurate functioning of BJTs in various electronic circuits.

Explanation:

Correct Option Analysis

In a Common Emitter (CE) BJT amplifier, the correct option is:

Option 4: If the magnitude of the output voltage increases, the input current decreases.

To understand why this option is correct, we need to delve into the operating principles of a CE BJT amplifier and the relationship between its input and output parameters.

Common Emitter (CE) Amplifier:

A Common Emitter amplifier is one of the most widely used configurations in transistor amplifiers. In this configuration, the emitter terminal of the Bipolar Junction Transistor (BJT) is common to both the input and output circuits, hence the name "Common Emitter". It is known for providing significant voltage amplification.

Working Principle:

In a CE amplifier, the input signal is applied to the base-emitter junction, and the amplified output signal is taken from the collector-emitter circuit. The transistor operates in the active region where the base-emitter junction is forward-biased and the collector-base junction is reverse-biased.

The relationship between the input and output parameters can be described as follows:

• The input current (IB) is the current flowing into the base of the transistor.
• The output current (IC) is the current flowing through the collector of the transistor.
• The output voltage (VCE) is the voltage across the collector-emitter terminals.

In the active region, the collector current (IC) is primarily controlled by the base current (IB), following the relation:

IC = β × IB

Where β is the current gain of the transistor.

Explanation of Option 4:

Option 4 states that "If the magnitude of the output voltage increases, the input current decreases." This statement is correct and can be explained by the following points:

• In a CE amplifier, when the output voltage (VCE) increases, it implies that the collector-emitter voltage is increasing.
• This increase in VCE means that the collector current (IC) is increasing, as VCE is proportional to the product of IC and the load resistance (RC).
• Since IC is proportional to the base current (IB), an increase in IC would typically result in a decrease in IB because the transistor is operating in the active region where the relationship between IC and IB is governed by the current gain (β).
• Therefore, if the output voltage (VCE) increases, the input current (IB) decreases as the transistor adjusts to maintain the balance between the input and output currents.

Important Information:

Now let's analyze the other options to understand why they are incorrect:

Option 1: The CE amplifier has the lowest input impedance among all the configurations.

This statement is incorrect. The CE amplifier does not have the lowest input impedance among all configurations. In fact, the Common Base (CB) configuration has the lowest input impedance, while the Common Collector (CC) configuration has the highest input impedance. The CE configuration has an intermediate input impedance, which is lower than the CC configuration but higher than the CB configuration.

Option 2: Its input impedance is lower than CB configuration but higher than CC configuration.

This statement is incorrect. As mentioned earlier, the input impedance of the CE configuration is higher than the CB configuration but lower than the CC configuration. Therefore, the statement should be reversed to be accurate.

Option 3: The input characteristics are plotted between the input current (IB) and input voltage (VBE) at a constant IC.

This statement is incorrect. The input characteristics of a CE amplifier are plotted between the input current (IB) and the input voltage (VBE) at a constant collector-emitter voltage (VCE), not at a constant collector current (IC). The input characteristics show the relationship between IB and VBE, reflecting the behavior of the base-emitter junction.

Conclusion:

In summary, the correct option in the context of a Common Emitter (CE) BJT amplifier is Option 4: "If the magnitude of the output voltage increases, the input current decreases." This is due to the relationship between the input and output currents governed by the current gain (β) of the transistor in the active region. The other options are incorrect based on the analysis of input impedance and input characteristics in different transistor configurations.

Explanation:

In the analysis of a common-base (CB) amplifier using a Bipolar Junction Transistor (BJT), it is crucial to understand the fundamental properties and characteristics that define its operation and performance. Here we will delve into the properties of a CB amplifier and identify which statement is false among the given options.

Common-Base (CB) Amplifier Characteristics:

A common-base amplifier configuration is one where the base of the transistor is common to both the input and output circuits. This means the input is applied to the emitter and the output is taken from the collector, with the base typically grounded or at a fixed bias voltage.

Here are some key characteristics of a CB amplifier:

• Input Impedance: The input impedance of a CB amplifier is generally very low because the input is applied at the emitter, which presents a low impedance path.
• Output Impedance: The output impedance is typically high because the output is taken from the collector, which has a high impedance path.
• Voltage Gain: The voltage gain of a CB amplifier can be significant because it is proportional to the load resistance divided by the input resistance.
• Current Gain: The current gain is less than unity (typically it is close to one but slightly less), making it a current buffer.
• Frequency Response: CB amplifiers have a wide frequency response, making them suitable for high-frequency applications.

Analysis of the Given Statements:

Let's analyze each statement in the context of the characteristics of a CB amplifier:

This statement is true. As mentioned earlier, the input impedance of a CB amplifier is low because the emitter presents a low impedance path, and the output impedance is high because the collector presents a high impedance path.

This statement is true. The output characteristics of a CB amplifier are typically represented by a plot of the output current (IC) versus the output voltage (VCB), showing how the output current varies with the output voltage for different levels of input current.

This statement is false. The output impedance of a CB amplifier is higher than that of a common-emitter amplifier. In a common-emitter configuration, the output impedance is lower due to the feedback effect of the emitter resistor, whereas in a CB configuration, there is no such feedback effect, resulting in higher output impedance.

This statement is true. The input characteristics of a CB amplifier are typically represented by a plot of the input current (IE) versus the input voltage (VEB), showing how the input current varies with the input voltage for different levels of output voltage.

1. It has lower input impedance and higher output impedance.
2. The output characteristics is a plot of output current (IC) vs. output voltage (VCB).
3. The output impedance is lower than that of a common-emitter amplifier.
4. The input characteristics is a plot of input current (IE) vs. input voltage (VEB).

Based on the analysis, the correct answer is option 3: "The output impedance is lower than that of a common-emitter amplifier." This statement is false because, in reality, the output impedance of a CB amplifier is higher than that of a common-emitter amplifier.

Important Information:

Understanding the differences between various transistor amplifier configurations (such as common-base, common-emitter, and common-collector) is essential for designing and analyzing electronic circuits. Each configuration has its unique characteristics and applications:

• Common-Emitter (CE) Amplifier: Known for its high voltage gain and moderate input and output impedances. It is widely used in amplifier circuits for its good overall performance.
• Common-Collector (CC) Amplifier: Also known as an emitter follower, it has a high input impedance, low output impedance, and a voltage gain of approximately unity. It is commonly used for impedance matching and buffering applications.
• Common-Base (CB) Amplifier: Characterized by low input impedance, high output impedance, and wide frequency response. It is suitable for high-frequency applications and situations where impedance matching is required.

By understanding these configurations and their properties, engineers can select the appropriate amplifier type for their specific application, ensuring optimal performance and efficiency in electronic circuits.

Concept:

For a transistor, the base current, the emitter current, and the collector current are related as:

IE = IB + IC

where IC = β IB

β = Current gain of the transistor

Typical base-emitter voltages, VBE for both NPN and PNP transistors are as follows:

• If the transistor is made up of a silicon material, the base-emitter voltage VBE will be 0.7 V.
• If the transistor is made up of a germanium material, the base-emitter voltage VBE will be 0.3 V.
   

Application:

From the given figure, Apply KVL

10 - I_B × R_B - V_BE = 0

Let us assume V_BE = 0.7 V

10 - I_B (1 × 10⁶) - 0.7 = 0

I_B = 9.3 μA

We know that,

I_C = β I_B

Where,

I_C  & I_B = collector current and base current

Therefore,

I_C = 100 × 9.3 μA

= 930 μA

= 0.93 mA

≈ 1 mA

Early Effect:

• A large collector base reverse bias is the reason behind the early effect manifested by BJTs.
• As reverse biasing of the collector to base junction increases, the depletion region penetrates more into the base, as the base is lightly doped.
• This reduces the effective base width and hence the concentration gradient in the base increases.
• This reduction in the effective base width causes less recombination of carriers in the base region which results in an increase in collector current. This is known as the Early effect.
• The decrease in base width causes ß to increase and hence collector current increases with collector voltage rather than staying constant.
• The slope introduced by the Early effect is almost linear with IC and the common-emitter characteristics extrapolate to an intersection with the voltage axis VA, called the Early voltage.

This is explained with the help of the following VCE (Reverse voltage) vs IC (Collector current) curve:

Concept:

\(\beta = \frac{\alpha }{{1 - \alpha }}\)

Where β = common-emitter current gain

α = Common base current gain

Calculation:

Common base current gain = α = 0.98

\(\beta = \frac{{0.98}}{{1 - 0.98}} = 49\)

Note: \(\alpha = \frac{{{I_C}}}{{{I_E}}}\) & \(\beta = \frac{{{I_C}}}{{{I_B}}}\)

Where I_C = Collector current

I_E = Emitter current

BJT Amplifier:

• Transistors biasing is done to keep stable DC operating conditions needed for its functioning as an amplifier.
• A properly biased transistor must have it's Q-point (DC operating parameters like IC and VCE) at the center of saturation mode and cut-off mode i.e. active mode.
• In the active mode of transistor operation, the emitter-base junction is forward biased and the collector-base junction is reverse biased.​
• In the cut-off mode of transistor operation, the emitter-base junction is reverse biased and the collector-base junction is reverse biased.​

​

Different modes of BJT operations are:

Concept:

In a common base connection,

I_E = I_B + I_C

And I_C = α I_E + I_CBO

Where α is the current amplification factor

I_E = I_B + α I_E + I_CBO

⇒ I_E (1 – α) = I_B + I_CBO

\( \Rightarrow {I_E} = \frac{1}{{\left( {1 - \alpha } \right)}}\left( {{I_B} + {I_{CBO}}} \right)\)

Calculation:

Given that, I_B = 0.02 mA

Current amplification factor (α) = 0.9

I_CBO = 30 μA = 0.03 mA

The emitter current is,

\({I_E} = \frac{1}{{1 - 0.9}}\left( {0.02 + 0.03} \right) = 0.5\;mA\)

Transistor

A transistor is a three-layer, three-terminal device.

The three layers can be (n-p-n or p-n-p) and the three terminals are the collector, base, and emitter.

Transistor when working in the saturation region acts as a closed switch (ON Button) and in the cut-off region acts as an open switch (OFF Button).

Working modes of transistor

Common Emitter(CE) Configuration:

In CE configuration input is connected between base and emitter while the output is taken between collector and emitter.

\(β = \frac{α }{{1 - α }} = \frac{{{I_C}}}{{{I_B}}} = \frac{{{I_C}}}{{{I_E} - {I_C}}}\)

I_E = I_B + I_C  

I_C = β I_B + I_CEO 

IC = α I_E + ICBO

I_C = α (I_C + I_B) + ICBO

IC (1 - α ) = α I_B + ICBO

\(\Large{I_C=\frac{\alpha I_B}{1-\alpha}+\frac{I_{CBO}}{1-\alpha}}\)

In CE configuration, when I_B = 0 then I_C = I_CEO

\(\Large{I_{CEO} = \frac{I_{CBO}}{1 - α}} \)

Where, α = Current gain

β = Current Amplification Factor

IE, IB, IC = Emitter, Base and Collector current respectively

ICEO = Collector emitter cutoff current

ICBO = Collector base cutoff current

Calculation: 

Given: α = 0.98, ICBO = 5 μA, IB = 95 μA

\(β = \frac{0.98 }{(1 - 0.98)}= \frac{0.98 }{0.02 }= 49\)

\(I_{CEO} = \frac{5 × 10^{-6}}{(1 - 0.98)} = 250\ \mu A\)

I_C = 49 x (95 × 10^-6) + 250 × 10^-6 = 4905 × 10^-6 A

\(I_E=\frac{(4905 - 5) × 10^{-6}}{0.98}=\frac{4900 × 10^{-6}}{0.98}=5\ \ mA\)

Concept:

• Transistor: A transistor has two PN junctions i.e., it is like two diodes. The junction between base and emitter may be called emitter diode. The junction between base and collector may be called collector diode.

• The transistor can act in one of the three states:
• CUT-OFF: EMITTER DIODE AND COLLECTOR DIODE ARE OFF.
• ACTIVE: EMITTER DIODE IS ON AND COLLECTOR DIODE IS OFF.
• SATURATED: EMITTER DIODE AND COLLECTOR DIODE ARE ON.

Note: Please understand that the question is asking about the regions of a biased transistor. Biasing is a set of DC voltages that we apply at the Base-emitter 'or' emitter-collector terminal. There are three possibilities based on this voltage, i.e. Active Region, Cut-off region, and Saturation region.