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 9, Problem D9.18P

Design an amplifier system with three inverting op-amps circuits in cascadesuch that the overall closed-loop voltage gain is A v = v O / v I = 300 . Themaximum resistance is limited to 200 k Ω and the minimum resistance islimited to 20 k Ω . In addition, the maximum current in any resistor is to belimited to 60 μ A when v O = 6 V .

Expert Solution & Answer
Check Mark
To determine

The design parameters for an inverting op-amp circuit.

Answer to Problem D9.18P

The value of the resistance R2 is 100kΩ , R3 is 20kΩ , R4 is 120kΩ , R5 is 20kΩ and the value of the resistance R6 is 100kΩ .

Explanation of Solution

Calculation:

The required diagram for the inverting op amp with feedback is shown below.

The required diagram is shown in Figure 1.

  Microelectronics: Circuit Analysis and Design, Chapter 9, Problem D9.18P

The expression for the value of the voltage v11 is given by,

  v11=v21

Substitute 0 for v21 in the above equation.

  v11=0

The expression for the voltage v22 is given by,

  v22=v12

Substitute 0 for v22 in the above equation.

  v12=0

The expression for the value of the voltage v13 is given by.

  v13=v23

Substitute 0 for v23 in the above equation.

  v13=0

The expression for the output voltage of the first op-amp is given by,

  vO1=vI(R2R1)

The expression for the second voltage of the first op amp is given by,

  vO2=vO1(R2R4)

Substitute vI(R2R1) for vO1 in the above equation.

  vO2=vI(R2R1)(R4R3)

The expression for the voltage gain is given by,

  Av=vOvI

Substitute 300 for Av and 6V for vO in the above equation.

  300=6VvIvI=0.02V

Apply KCL at the negative terminal of the right most op-amp.

  v O20R5=0vOR6vO=v O2R6R5vOv O2=R6R5

Substitute vI(R2R1)(R4R3) for vO2 in the above equation.

  vOvI( R 2 R 1 )( R 4 R 3 )=R6R5vOvI=R6R5( R 2 R 1 )( R 4 R 3 )

Substitute Av for vOvI in the above equation.

  Av=R6R5(R2R1)(R4R3)

Substitute 300 for Av in the above equation.

  300=R6R5(R2R1)(R4R3)

The expression for the value of the current R6,min is given by,

  R6,min=vOi6,max

Substitute 60μA for i6,max and 6V for vO in the above equation.

  R6,min=6V60μA=0.1MΩ

The expression for the value off the voltage i5,max is given by,

  i5,max=i6,max

Substitute 60μA for i6,max in the above equation.

  i5,max=60μA

The expression for the value of the current i5,max is given by,

  i5,max=vOR 5,maxR 6,minR5,min

Substitute 60μA for i5,max , 0.1MΩ for R6,min and 6V for vO in the above equation.

  60μA=(6V)R 5,max0.1MΩR5,min

The expression to determine the range of the current is given by,

  |i2|=10|vO1R2|

Substitute 0.02V for vO1 and 0.2MΩ for R2 in the above equation.

  |i2|=10|0.02V0.2MΩ||i2|=1μA<60μA

The expression for the value of the mid stage gain is given by,

  vOvO1=6

Substitute (10)(0.02V) for vO2 in the above equation.

  v O2( 6)( 10)( 0.02V)=6vO=1.2V

The expression for the minimum value of the resistance R3,min is given by,

  R3,min=vO260μA

Substitute (10)(0.02V) for vO2 in the above equation.

  R3,min=( 10)( 0.02V)60μA=3.33kΩ

The maximum value of the resistance R3 to be used is 20kΩ .

The expression for the value of the resistance R4 is given by,

  R4=6R3

Substitute 20kΩ for R3 in the above equation.

  R4=6(20kΩ)120kΩ

The expression for the gain of the voltage gain of right most amplifier is given by,

  vOvO2=5

Substitute (10)(6)(0.02V) for vO2 in the above equation.

  vO=5(10)(6)(0.02V)=6V

The value for the current |i5|max is given by,

  |i5|max=60μA

The expression for the value of the resistance R5,min is given by,

  R5,min=| v O2| i 5 ||max

Substitute 60μA for |i5|max and (10)(6)(0.02V) for vO2 in the above equation.

  R5,min=|( 10)( 6)( 0.02V)| 60μA||=20kΩ

The expression for the maximum value of the resistance R6 is given by,

  R6=5R5

Substitute 20kΩ for R5 in the above equation.

  R6=5(20kΩ)=100kΩ

Conclusion:

Therefore, the value of the resistance R2 is 100kΩ , R3 is 20kΩ , R4 is 120kΩ , R5 is 20kΩ and the value of the resistance R6 is . 100kΩ .

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Chapter 9 Solutions

Microelectronics: Circuit Analysis and Design

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