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§ Amplifier

§ Voltage summing

§ Voltage substraction

§ Voltage buffer

§ Voltage-controlled current source

§ Current-controlled voltage source

EXAMPLE 15.

Figure 15.3 Noninverting fixed-gain amplifier. Figure 15.4 Circuit for Example 15.2. Calculate the output voltage from the circuit of Fig. 15.4 for an input of 120 &V. Solution The gain of the op-amp circuit is calculated using Eq. (15.2) to be A! 1 % # R R 1 f #! 1 % # 2 2 4 . 0 k k $ $ #! 1 % 100! 101 The output voltage is then Vo! AVi! 101(120 &V)! 12.12 mV

Chapter 15 Op-Amp Applications 4 .3 k" 33 k" 33 k" ! (110.3)(&14.2)(&14.2)! 22.2 ' 10 3 so that Vo! AVi! 22.2 ' 10 3 (80 #V)! 1.78 V Show the connection of an LM124 quad op-amp as a three-stage amplifier with gains of $10, &18, and &27. Use a 270-k" feedback resistor for all three circuits. What output voltage will result for an input of 150 #V? Solution For the gain of $10: A 1! 1 $ % R R 1 f %! $ 10

Calculate the output voltage for the circuit of Fig. 15.9. The inputs are V 1! 50 mV sin(1000 t ) and V 2! 10 mV sin(3000 t ). EXAM Figure 15.8 Summing amplifier.

652 Chapter 15 Op-Amp Applications

15.2 VOLTAGE SUMMING

Another popular use of an op-amp is as a summing amplifier. Figure 15.

connection with the output being the sum of the three inputs, each mul

different gain. The output voltage is

Vo! "

!

R

R

1 f

# V 1 %

R

R

2 f

# V 2 %

R

R

3 f

# V 3

" Figure 15.7 Circuit for Example 15.5 (using LM348).

Calculate the output voltage for the circuit of Fig. 15.9. The inputs are V 1! 50 mV sin(1000 t ) and V 2! 10 mV sin(3000 t ). Figure 15.8 Summing amplifier. Figure 15.9 Circuit for Example 15.6.

Solution

The output voltage is Vo! " !

3 3 3 3 0 k k $ $

V 1 %

3 1 3 0 0 k k $ $

V 2

" ! "(10 V 1 % 33 V 2 )

Vo! " !

R R 3 f

" " # R R 1 f

V 1

$ # R R 2 f

V 2

$ Vo! " "

R R 2 f

V 2 "

R R 3 f

R R 1 f

V 1

(15.4) Determine the output for the circuit of Fig. 15.10 with components Rf! 1 M%, R 1! 100 k%, R 2! 50 k%, and R 3! 500 k%. Solution The output voltage is calculated to be Vo! " "

5 1 0 M k % %

V 2 "

5 1 00 M k % %

1 1 00 M k % %

V 1

! "(20 V 2 " 20 V 1 )!! 20( V 2! V 1 ) The output is seen to be the difference of V 2 and V 1 multiplied by a gain factor of "20. Another connection to provide subtraction of two signals is shown in Fig. 15.11. This connection uses only one op-amp stage to provide subtracting two input signals. Using superposition the output can be shown to be Vo! # R 1 R $ 3 R 3

R 2 R $ 2 R 4

V 1 "

R R 4 2

V 2 (15.5)

15.2 Voltage Summing 653 Vo! " !

3 3 3 3 0 k k $ $

V 1 %

3 1 3 0 0 k k $ $

V 2

" ! "(10 V 1 % 33 V 2 ) ! "[10(50 mV) sin(1000 t ) % 33(10 mV) sin(3000 t )] ! " [0.5 sin(1000 t )! 0.33 sin(3000 t )] Voltage Subtraction Two signals can be subtracted, one from the other, in a number of ways. Figure 15. shows two op-amp stages used to provide subtraction of input signals. The resulting output is given by Figure 15.10 Circuit to subtract two signals.

Vo! " "

M

k

# V 2 "

M

k

M

k

# V 1

! "(20 V 2 " 20 V 1 )!! 20( V 2! V 1 )

The output is seen to be the difference of V 2 and V 1 multiplied by a gain factor of "20. Another connection to provide subtraction of two signals is shown in Fig. 15.11. This connection uses only one op-amp stage to provide subtracting two input signals. Using superposition the output can be shown to be Vo! # R 1

R

3 R 3

R 2

R

2

R 4

# V 1 "

R

R

4 2

# V 2 (15.5)

Determine the output voltage for the circuit of Fig. 15.12. Figure 15.11 Subtraction circuit.

gure 15.13 shows an op-amp connected to provide this buffer amplifier operation. e output voltage is determined by Vo! V 1 (15.6) gure 15.14 shows how an input signal can be provided to two separate outputs. The vantage of this connection is that the load connected across one output has no (or tle) effect on the other output. In effect, the outputs are buffered or isolated from ch other. Figure 15.13 Unity-gain (buffer) amplifier. ing as an ideal circuit with very high input impedance and low output impedance. Figure 15.13 shows an op-amp connected to provide this buffer amplifier operation. The output voltage is determined by Vo! V 1 (15.6) Figure 15.14 shows how an input signal can be provided to two separate outputs. The advantage of this connection is that the load connected across one output has no (or little) effect on the other output. In effect, the outputs are buffered or isolated from each other. Figure 15.13 Unity-gain (buffer) amplifier. Figure 15.14 Use of buffer amplifier to provide output signals.

Chapter 15 Op-Amp Applications Voltage-Controlled Voltage Source An ideal form of a voltage source whose output Vo is controlled by an input voltage V 1 is shown in Fig. 15.16. The output voltage is seen to be dependent on the input voltage (times a scale factor k ). This type of circuit can be built using an op-amp as shown in Fig. 15.17. Two versions of the circuit are shown, one using the inverting input, the other the noninverting input. For the connection of Fig. 15.17a, the output voltage is Vo! "# R

R

1 f

V 1! kV 1 (15.7)

eal voltage- source. Figure 15.17 Practical voltage-controlled voltage source circuits.

Figure 15.20 Ideal cu controlled voltage sourc Figure 15.19 Practical voltage- controlled current source. Figure 15.21 Practical form of current-controlled voltage source. Current-Controlled Voltage Source An ideal form of a voltage source controlled by an input current is shown in Fig. 15.20. The output voltage is dependent on the input current. A practical form of the circuit is built using an op-amp as shown in Fig. 15.21. The output voltage is seen to be Vo! $ I 1 RL! kI 1 (15.10) Current-Controlled Current Source An ideal form of a circuit providing an output current dependent on an input current is shown in Fig. 15.22. In this type of circuit, an output current is provided depen- dent on the input current. A practical form of the circuit is shown in Fig. 15.23. The input current I 1 can be shown to result in the output current Io so that

Io! I 1 " I 2! I 1 "

I 1

R

R

2 1

!

R

R

1 2

"

I 1! kI 1 (15.11)

the circuit of Fig. 15.24a, calculate IL.

the circuit of Fig. 15.24b, calculate Vo.

Figure 15.23 Practical form of current-controlled current source.

o 1 2 1 R 2!^ R 2 "^ 1 1 (a) For the circuit of Fig. 15.24a, calculate IL. (b) For the circuit of Fig. 15.24b, calculate Vo. LE 15.

Solution

(a) For the circuit of Fig. 15.24a, IL! #

V

R

1 1

k

V

$

#! 4 mA Figure 15.24 Circuits for Example 15.10.

2. Calculate the output voltage of the circuit of Fig. 15.49 for input of 150 mV rms. + - 180 kΩ Vo 3.6 kΩ V 1 +12 V 741 −12 V 5 11 10 6 4 + - 750 kΩ Vo 36 kΩ V 1 +9 V 741 −9 V 5 11 10 6 4 Figure 15.48 Problem 1 Figure 15.49 Problem 2 *3. Calculate the output voltage in the circuit of Fig. 15.50. **+

-** Vo 510 kΩ 18 kΩ V 1 20 μV 22 kΩ 680 kΩ 33 kΩ 750 kΩ