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ME 2134E Lab Report

Linear Circuits

LIN SHAODUN A0066078X

Lab Group 2B

Date 27th Sept 2011

1

TABLE OF CONTENTS

OBJECTIVES 2

EXPERIMENT PROCEDURE AND RESULT 3

RESULTS 4

DISCUSSION 7

CONLCUSION 9

2

OBJECTIVES

The objectives of the experiments are as follow:

To understand the properties of an ideal operational amplifier.

To understand the limitations of a practical operational amplifier.

To be familiar with the typical applications of an operational amplifier.

EXPERIMENT PROCEDURE AND LAB RESULT

1. Inverting Amplifier

a) Connect the circuit of KHz and compare it with the predicted value.

b) Figure 1, using both the positive and negative power supplies.

c) Adjust the sine wave generator on the E&L CADET II Ruggedized Electronic Circuit

Trainer to give an output of 1 at 1 KHz.

d) Monitor and with the dual channel oscilloscope. Measure the voltage gain of the

operational amplifier at 1 KHz and compare it with the predicted value.

Figure 1

Table 1: Actual gain vs. Predicted Gain for inverting Amplifier

1.00V 98.0k

9.531V 9.82 k

Voltage gain 9.531 Predicted Gain 9.98

2. Frequency response of Amplifier

Measure the frequency response of the amplifier by noting the voltage gain at the frequencies

indicated below: At the “half power cut-off frequency”, the gain drops to of the gain

at 1 KHz, determine this frequency.

3

Table 2: Frequency response of Amplifier

Frequency (kHz) 0.01 0.1 1 10 20 30 40 50 60 100

Gain = / 9.53 9.53 9.53 9.53 9.22 8.59 7.03 5.78 5.00 3.28

of the gain at 1 KHz , by linear interpolation, we

have:

Half power cut-off frequency

3. Input Bias Current

a) Remove the sine wave generator and short the input to ground. Measure the DC

output voltage with the voltmeter.

b) Ground the non-inverting, input with a 10 kΩ resistor instead of the straight wire.

Measure the DC output voltage again.

Table 3: Effect of input bias current balancing resistance

No Bias Current balancing

resistance

With 10 kΩ Bias Current

balancing resistance

Output Voltage 8.8mV 3.0mV

4. Non-inverting Amplifier

Connect the circuit shown in Figure 2, measure the gain of the amplifier at 1 KHz by

monitoring and on the oscilloscope.

0

1

2

3

4

5

6

7

8

9

10

10 100 1000 10000 100000

Ga

in

Frequncy (Hz)

Frequency Response of Amplifier

6.739

42.3 kHz

4

Figure 2

Table 4: Actual gain vs. Predicted Gain for inverting Amplifier

1.00V 98.0k

10.31 9.82 k

Voltage gain 10.31 Predicted Gain 10.98

5. Comparator Circuit

Connect the comparator circuit shown in Figure 3, determine its transfer characteristics

(relationship between and ).

Figure 3

Table 5: Input vs. Output

-14.75 -12 -10 -8 -6 -4 -3 -2.8 -2.6 -2.5 -2.3 -2 -0.5 1.5 3.5 14.86

5.17 5.12 5.08 5.00 4.85 4.53 4.12 3.9 3.45 -0.24 -0.29 -0.31 -0.34 -0.37 -0.37 -0.39

5

In this experiment, the switches from “High” to “Low” when

6. Digital to Analog Converter

Connect the Digital-to-Analog converter in Figure 4, verify the circuit using the switches

available on the test system.

Figure 4

Table 6: Digital to Analog Converter

In the experiment, S6 is the MSB and S8 is the LSB.

-1

0

1

2

3

4

5

6

-15.0 -12.5 -10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0 12.5 15.0

Ou

tpu

t (V

)

Input (V)

Transfer Characteristics

BINARY BIT 000 001 010 011 100 101 110 111

THEORETICAL(V) 0 -0.625 -1.25 -1.875 -2.5 -3.125 -3.75 -4.375

EXPERIMENTAL(V) -0.0092 -0.626 -1.251 -1.869 -2.490 -3.107 -3.732 -4.34

6

From above chart, we can see the analog output matches with theoretical value very well.

(k=0.9911 and R2=1)

DISCUSSION

1. Experiment 1: Actual Gain vs. Theoretical Gain

The gain obtained from experiment result is quite closed to the predicted value. The minor

difference (~5%) is caused by the following factors:

a) We use ideal Op Amp assumption when calculate the close loop gain, but the

characteristic of Op Amp (741) used in the experiment is not ideal:

Parameters Idealized Op Amp Actual Op Amp (741)

Open Loop Gain, Avo ~200,000

Input impedance, Zin ~2.0M

Output impedance, Zout 0 ~40

Input Current. Iin 0 ~10nA

Bandwidth, BW 1.5MHz

Offset Voltage, Vi 0 1V (in Experiment)

b) During experiment, the input voltage is not stable, it has approx. 2% fluctuation

(1.000~1.023V).

c) The measurement equipment like oscilloscope also contributes system errors when

read the output pk-pk value.

2. Experiment 2 : Frequency Response of Amplifier

This experiment shows that the actual Op Amp has a limited bandwidth, at higher frequency

(>20 KHz) the close-loop gain is lower than at lower frequency condition. The frequency

y = 0.9911x - 0.0099

R² = 1.0000

-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

-5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0

Exp

erim

enta

l (V

)

Theoretical (V)

Digital to Analog Converter

7

response analysis of the circuit illustrated that there is a tradeoff between gain and

bandwidth. This trade off must be recognized when designing with op amps.

From the frequency response chart, it’s able to find out the half power cut-off frequency,

which is the frequency where the close-loop gain is 70.7% or -3dB of the maximum gain.

3. Experiment 3 : Input Bias Current Error

Under ideal conditions, the output voltage should be zero when the input is connected to

ground. However, this is not true for real life Op Amp.

Consider the inverting amplifier circuit shown below:

If the input voltage is zero, there should be zero current coming into the inverting input of the

op-amp. However, there is a small bias current, I1, which goes through Rf. This current

creates a voltage at the output equal to I1Rf. This is the error voltage. The same voltage will

be seen at the output of a non-inverting amplifier. If we look at the voltage follower circuit

shown below, it is easy to see that the output error voltage is –I1Rs.

In a non-inverting amplifier we add a resistor Rc. The compensating resistor value equals the

parallel combination of Ri and Rf. The input creates a voltage drop across Rc that offsets the

voltage across the combination or Ri and Rf. Thus, the output is reduced. The same is done

for the inverting amplifier.

8

In the experiment, when an input bias current compensating resistor (10K) is added to the

non-inverting pin, the output voltage is decreased from 8.8mV to 3.0mV, which proves the

effectiveness of compensating resistor.

4. Experiment 4: Non Inverting Amplifier

The gain obtained from experiment result is quite closed to the predicted value. The minor

difference (~5%) is caused by the same reasons explained in Experiment 1.

5. Experiment 5: Comparator Circuit

This experiment examines the principle behind the comparator circuit, which compares input

value Vi against the reference voltage Vref and determines the operation of the op-amp

(either on or off) due to the Zener diode’s properties (forward or reversed bias). The actual

cut-off value of the input voltage is not equal to the reference voltage (2.5V instead of 3.0V),

possibly caused by the forward offset voltage.

6. Experiment 6: Digital to Analog converter

From the experiment result, we can see the analog output match with theoretical calculation

very well.

CONCLUSION

In conclusion, with this experiment I have better understanding about the application of

Operational Amplifier; it can be used as an inverting amplifier, non-inverting amplifier,

comparator and a digital-to-analog converter. I also have better understanding about the

limitations of Operational Amplifier, such as limited band width and input bias current error.