Operational Amplifiers – Part II solution

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Description

1 Objectives

The purpose of the lab is to study some of the advanced opamp configurations commonly found in practical appli- cations. The circuits studied will include the summing amplifier, the differential amplifier and the instrumentation amplifier.

2 Introduction

2.1 Summing Amplifier

An inverting amplifier can be modified to accommodate multiple input signals as shown in Fig. 1. Since the circuit is linear, the output voltage can easily be found by applying the superposition principle: the output voltage is a weighted sum of the two input signals. The weighting factor is determined by applying one of the input signals while the other is grounded and analyzing the resulting circuit. Since the circuit is linear, the analysis is repeated for the other input, and the final result is the addition of both signals. The advantage of this approach is that we can easily recognize the effect of each signal on the circuit’s performance, and the overall output can be obtained in most of the cases by inspection. For the circuit in Fig. 1, the output voltage can be found as

Vo = −

R3

R1

V + R3

i 1 R2

Vi 2

(1)

R3

Figure 1: Summing amplifier circuit

The summing amplifier can be extended to have any number of input signals. Consider a two-bit digital signal applied to the inputs of the circuit in Fig. 1, resulting in an analog voltage at the output that is determined by the binary input. A more general configuration based on this circuit can be used to build digital-to-analog converters (DAC).

2.2 Differential Amplifier

The differential amplifier is designed to amplify the difference of the two inputs. The simplest configuration is shown in Fig. 2. If the resistor values are chosen such that R2 /R1 = R4 /R3 , then the output of the amplifier is given by:

V = R2

o R1

(Vi 2 − Vi 1 ) (2)

R2

+5V R1

2 7 1

V+ N1 6

N2 Vo

V−

3 4 5

Vi1

Vi2

R3 R4

5V

Figure2:Differentialamplifiercircuit

c Department of Electrical and Computer Engineering, Texas A&M University

This expression shows that the circuit amplifies the difference between the two input signals Vi 2 − Vi 1 and rejects the common mode input signals (Vo = 0 if Vi 1 = Vi 2 ). Therefore, the differential amplifier can be used in a very noisy environment to reject common noise that appears at both inputs. When the same signal is applied to both inputs, the voltage gain is defined as common-mode gain (ACM ), which is zero for an ideal differential amplifier. The common-mode rejection ratio is defined as,

CMRR =

ADM (Differential-mode gain)

ACM (Common-mode gain)

(3)

Substituting ACM = 0 to the above expression, CMRR for an ideal differential amplifier becomes infinite. In practice, resistors have a tolerance of typically 5%, and the common-mode gain will not be zero, resulting in finite CMRR .

2.3 Instrumentation Amplifier

The instrumentation amplifier is a differential amplifier that has high input impedance and the capability of gain adjustment through the variation of a single resistor. A typical instrumentation amplifier is shown in Fig. 3.

+5V

3 7

1 R R

V+ N1 6

V−

2 4 5 R

5V

+5V

2 7 1

Rgain

V+ N1 6

N2 Vo

V−

3 4 5

+5V

5V

2 7 1 R

V+ N1 6

N2

V−

3 4 5 R R

Vi2

5V

Figure 3: Typical instrumentation amplifier circuit

The voltage drop across Rgain is equal equal to the voltage difference of the two input signals. Therefore, the current through Rgain caused by the voltage drop must flow through the two R resistors above and below Rgain . The output voltage can be calculated as

Vo =

2R

1 +

Rgain

(Vi 2 − Vi 1 ) (4)

Though this configuration looks cumbersome to build a differential amplifier, the circuit has several properties that make it very attractive. It presents high input impedance at both terminals because the inputs connect into non-inverting terminals. Also a single resistor Rgain can be used to adjust the voltage gain.

3 Calculations

1. For the summing amplifier in Fig. 1, find R1 and R2 to have Vo = −(Vi 1 + 2Vi 2 ), if R3 = 15k Ω.

2. For the differential amplifier in Fig. 2, find R1 to have Vo = Vi 2 − Vi 1 , if R2 = R3 = R4 = 10k Ω.

3. For the instrumentation amplifier in Fig. 3, find R to have Vo = 3(Vi 2 − Vi 1 ), if Rgain = 1k Ω.

4. For each circuit, find Vo if Vi 1 = 0.2 sin(2π1000t ) and Vi 2 = 0.3V .

4 Simulations

For all simulations, provide screenshots showing the schematics and the plots with the simulated values prop- erly labeled.

1. Draw the schematics for the circuits in Figs. 1, 2, and 3 with the calculated component values using the UA741 opamp model.

2. Apply the inputs Vi 1 = 0.2 sin(2π1000t ) and Vi 2 = 0.3V , and obtain the time-domain waveforms for the input and output voltages using transient simulation. Confirm that the circuits operate as designed.

5 Measurements

For all measurements, provide screenshots showing the plots with the measured values properly labeled.

5.1 Summing Amplifier

1. Build the circuit in Fig. 1 with the simulated component values.

2. Apply the inputs Vi 1 = 0.2 sin(2π1000t ) and Vi 2 = 0.3V , and obtain the time-domain waveforms for the input and the output voltages using the scope to confirm that the circuit is a summing amplifier.

3. Raise the DC input voltage Vi 2 until clipping at the output is observed.

5.2 Differential Amplifier

1. Build the circuit in Fig. 2 with the simulated component values.

2. Apply the inputs Vi 1 = 0.2 sin(2π1000t ) and Vi 2 = 0.3V , and obtain the time-domain waveforms for the input and the output voltages using the scope to confirm that the circuit is a differential amplifier.

3. Apply Vi 1 = 0.2 sin(2π1000t ) and connect Vi 2 to ground. Measure ADM = Vo /Vi .

4. Apply Vi 1 = Vi 2 = 0.2 sin(2π1000t ). Measure ACM = Vo /Vi .

5. Calculate the common-mode rejection ratio (CMRR).

5.3 Instrumentation Amplifier

1. Build the circuit in Fig. 3 with the simulated component values.

2. Apply the inputs Vi 1 = 0.2 sin(2π1000t ) and Vi 2 = 0.3V , and obtain the time-domain waveforms for the input and the output voltages using the scope to confirm that the circuit is a instrumentation amplifier.

6 Report

1. Include calculations, schematics, simulation plots, and measurement plots.

2. Prepare a table showing calculated, simulated and measured results.

3. Compare the results and comment on the differences.

7 Demonstration

1. Build the circuits in Figs. 2 and 3 on your breadboard and bring it to your lab session.

2. Your name and UIN must be written on the side of your breadboard.

3. Submit your report to your TA at the beginning of your lab session.

4. For the differential amplifier in Fig. 2:

• Show the time-domain waveforms with Vi 1 = 0.2 sin(2π1000t ) and Vi 2 = 0.3V .

• Measure Adm with Vi 1 = 0.2 sin(2π1000t ) and Vi 2 = 0.

• Measure Acm with Vi 1 = Vi 2 = 0.2 sin(2π1000t ).

• Calculate CMRR

5. For the instrumentation amplifier in Fig. 3:

• Show the time-domain waveforms with Vi 1 = 0.2 sin(2π1000t ) and Vi 2 = 0.3V .