Match List I with List II:

List I

(Bias Configuration of BJT)

List II

(Stability factor equation)

(A) Fixed Bias Configuration (I) S(VBE) = \(- \frac{-\beta/R_E}{\beta+R_{TH}/R_E}\)
(B) Emitter Bias Configuration (II) S(VBE) = −β/RE
(C) Voltage Divider Configuration (III) S(VBE) = \(- \frac{-\beta/R_C}{\beta+R_B/R_C}\)
(D) Feedback Bias Configuration (IV) S(VBE) = \(- \frac{-\beta/R_E}{\beta+R_B/R_E}\)


Choose the correct answer from the options given below :

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UGC NET Paper 2: Electronic Science 29 Oct 2022 Shift 1
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  1. (A) - (II), (B) - (I), (C) - (IV), (D) - (III)
  2. (A) - (II), (B) - (III), (C) - (IV), (D) - (I)
  3. (A) - (II), (B) - (IV), (C) - (I), (D) - (III)
  4. (A) - (IV), (B) - (II), (C) - (I), (D) - (III)

Answer (Detailed Solution Below)

Option 3 : (A) - (II), (B) - (IV), (C) - (I), (D) - (III)
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Detailed Solution

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Concept:

Stability factor due to base-emitter voltage VBE: The rate of change of collector current IC w.r.t. base-emitter voltage at constant β and ICO is called stability factor due to base-emitter voltage 

\(S(V_{BE}) = \frac{\partial I_C}{\partial V_{BE}}\)

 

Solution:

Biasing Configuration Biasing Circuit Stability Factor w.r.t VBE
Fixed Bias F1 Madhuri Engineering 23.02.2023 D12

\(I_C = β I_B = β \left(\frac{V_{CC}-V_{BE}}{R_B}\right)\)

\(S(V_{BE}) = \frac{\partial I_C}{\partial V_{BE}} = -\frac{β}{R_E}\)

Emitter Bias F1 Madhuri Engineering 23.02.2023 D13

Assuming IE = β IB,

 

\(V_{CC} - I_BR_B-V_{BE} - β I_BR_E=0\)

\(I_C = β I_B = β\left(\frac{V_{CC}-V_{BE}}{R_B+β R_E}\right) \)

\(S(V_{BE}) = \frac{\partial I_C}{\partial V_{BE}} = -\frac{β}{R_B+β R_E}= -\frac{β/R_E}{β + R_B/R_E}\)

Voltage Divider F1 Madhuri Engineering 23.02.2023 D14

Assuming IE = β IB,

\(V_{TH}-I_BR_{TH}-V_{BE}-β I_BR_E=0\)

\(I_C = β I_B = β\left(\frac{V_{TH}-V_{BE}}{R_{TH}+β R_E}\right)\)

\(S(V_{BE}) = \frac{\partial I_C}{\partial V_{BE}} = -\frac{β}{R_{TH}+β R_E}= -\frac{β/R_E}{β + R_{TH}/R_E}\)

Feedback Bias F1 Madhuri Engineering 23.02.2023 D15

\(V_{CC}-β I_BR_C-I_BR_B-V_{BE}=0\)

\(I_C = β I_B = β\left(\frac{V_{TH}-V_{BE}}{R_{B}+β R_C}\right)\)

\(S(V_{BE}) = \frac{\partial I_C}{\partial V_{BE}} = -\frac{β}{R_B+β R_C}= -\frac{β/R_C}{β + R_B/R_C}\)

 

 

Hence, the correct answer is (A) - (II), (B) - (IV), (C) - (I), (D) - (III)

Additional Information

Stability factor due to leakage current ICO: The rate of change of collector current IC w.r.t. base-emitter voltage at constant β and VBE is called stability factor due to leakage current 

\(S(I_{CO}) = \frac{\partial I_C}{\partial I_{CO}} = \frac{1+β}{1-β \left(\frac{\partial I_B}{\partial I_C}\right)}\)

Stability factor due to β : The rate of change of collector current IC w.r.t. base-emitter voltage at constant ICO and VBE is called stability factor due to β. 

\(S(\beta) = \frac{\partial I_C}{\partial \beta}\)

 

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