Microelectronics: Circuit Analysis and Design
Microelectronics: Circuit Analysis and Design
4th Edition
ISBN: 9780073380643
Author: Donald A. Neamen
Publisher: McGraw-Hill Companies, The
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Chapter 12, Problem 12.9TYU
To determine

To show: The variation in magnitude of the input resistance Rif as the feedback resistance varies.

To explain: The influence of Rif on RF .

Expert Solution & Answer
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Answer to Problem 12.9TYU

The influence of RF on Rif is determined by the relation RF(1RC12||RB2)+(Aifgm2(RC2+RLRC2))(1RC||RB2||rπ2)gm1+[(RFRs||RB1||rπ1||RF)(1RC1||RB2)] and the plot for the variation in the input resistance when the feedback resistance is varied between 5kΩ and 50kΩ is shown in Figure 6.

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  Microelectronics: Circuit Analysis and Design, Chapter 12, Problem 12.9TYU , additional homework tip  1

Figure 1

Feedback resistor value is varied between 5kΩ and 50kΩ

Calculation:

Mark the nodes and redraw the circuit.

The given diagram is shown in Figure 2

  Microelectronics: Circuit Analysis and Design, Chapter 12, Problem 12.9TYU , additional homework tip  2

Figure 2

Mark the values and draw the PSpice circuit for the above circuit.

The required circuit is shown in Figure 3

  Microelectronics: Circuit Analysis and Design, Chapter 12, Problem 12.9TYU , additional homework tip  3

Figure 3

The snip for the drop box of the internal parameters of the transistor is shown in Figure 4

  Microelectronics: Circuit Analysis and Design, Chapter 12, Problem 12.9TYU , additional homework tip  4

Figure 4

The simulation settings to estimate the magnitude of the current gain as the value of RF is varied between 5kΩ and 50kΩ is shown in Figure 5

  Microelectronics: Circuit Analysis and Design, Chapter 12, Problem 12.9TYU , additional homework tip  5

Figure 5

Then left click on the trace option then select add trace and type “ABS(V(vi)l(li))” then command in the trace magnitude of the resistance Rif as the feedback resistance varies between 5kΩ and 50kΩ , the required relation is shown in Figure 6

  Microelectronics: Circuit Analysis and Design, Chapter 12, Problem 12.9TYU , additional homework tip  6

Figure 6

By KCL the expression for the current Ii is given by,

  Ii=Vπ1Rs||RB1||rπ1+Vπ1Ve2RFVe2=Vπ1(RFRs||RB1||rπ1||RF)IiRF

The expression for the node voltage is given by,

  VC1=Vπ2+Ve2

Apply KCL at node VC1 .

  gm1Vπ1+VC1RC1||RB2+Vπ2rπ2=0gm1Vπ1+Vπ2+Ve2RC1||RB2+Vπ2rπ2=0gm1Vπ1+Vπ2(1RC1||RB2||rπ2)+Ve2RC12||RB2=0

Substitute Vπ1(RFRs||RB1||rπ1||RF)IiRF for Ve2 in the above equation.

  gm1Vπ1+Vπ2(1RC1||RB2||rπ2)+1RC12||RB2[Vπ1(RFRs||RB1||rπ1||RF)IiRF]=0Vπ1=IiRF(1RC12||RB2)Vπ2(1RC||RB2||rπ2)gm1+[(RFRs||RB1||rπ1||RF)(1RC1||RB2)] …… (1)

Consider A=RFRs||RB1||rπ1||RF , B=1RE2+1RF , C=1RC1||RB2 and D=1RC1||RB2||rπ2 in the above equation. So the equation is,

  Vπ1=IiRFCVπ2Dgm1+[AC]

The expression for the output current is given by,

  IO=(gm2Vπ2)(RC2RC2+RL)Vπ2=IOgm2(RC2+RLRC2)

Substitute IOgm2(RC2+RLRC2) for Vπ2 in equation (1).

  Vπ1=IiRF(1RC12||RB2)(IOgm2(RC2+RLRC2))(1RC||RB2||rπ2)gm1+[(RFRs||RB1||rπ1||RF)(1RC1||RB2)]

Substitute AifIi for IO in the above equation.

   V π1 = I i R F ( 1 R C12 || R B2 )+( A if I i g m2 ( R C2 + R L R C2 ) )( 1 R C || R B2 || r π2 ) g m1 +[ ( R F R s || R B1 || r π1 || R F )( 1 R C1 || R B2 ) ]

   V π1 I i = R F ( 1 R C12 || R B2 )+( A if g m2 ( R C2 + R L R C2 ) )( 1 R C || R B2 || r π2 ) g m1 +[ ( R F R s || R B1 || r π1 || R F )( 1 R C1 || R B2 ) ]

   R if = R F ( 1 R C12 || R B2 )+( A if g m2 ( R C2 + R L R C2 ) )( 1 R C || R B2 || r π2 ) g m1 +[ ( R F R s || R B1 || r π1 || R F )( 1 R C1 || R B2 ) ]

Conclusion:

Therefore, the influence of RF on Rif is determined by the relation RF(1RC12||RB2)+(Aifgm2(RC2+RLRC2))(1RC||RB2||rπ2)gm1+[(RFRs||RB1||rπ1||RF)(1RC1||RB2)] and the plot for the variation in the input resistance when the feedback resistance is varied between 5kΩ and 50kΩ is shown in Figure 6

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Chapter 12 Solutions

Microelectronics: Circuit Analysis and Design

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Current feedback amplifiers - Overview and compensation techniques; Author: Texas Instruments;https://www.youtube.com/watch?v=2WZotqHiaq8;License: Standard Youtube License