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ME2134E Linear Circuit lab report NUS
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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.