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A REPORT ON
ANALOG ASSIGNMENT ON TEXASINSTRUMENTATION KIT
In partial fulfillment of the course:
Analog Electronics EEE F 341
Submitted by:
NITISH MITTAL 2011B3A3373P
HRISHIKESH MUKTE 2011B3A3385P
NANDURI PRABHAKAR
NARASIMHA
2011B1A3742P
Lab Instructors: Priya Gupta,Jitendra
Lab Section No: 2
Assignment Question:
Group No: 1
Assignment 2 - Group A
Instructor-in-Charge: Prof. V.K.CHAUBEY
BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI
RAJASTHAN, 333031APRIL, 2015
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EXPERIMENT NO. 1: SECOND ORDER MFB BANDPASS FILTER
AIM
Design a second order MFB Band pass filter with a mid frequency of Fm = 1 KHz, a Quality
factor of Q=1, and a Gain of -2.
CIRCUIT DIAGRAM
To Implement the second order MFB Band pass filter the following circuit design was used.
Fig. 1 - Circuit Diagram for second order MFB Band pass filter
PRINCIPLE
The multiple feedback filters use one op-amp for a two-pole section, injecting signal into the
inverting input of the op-amp, usually with the non-inverting input grounded. This limits the
swing of the common mode input voltage and provides better distortion for larger signal
swings. Gain depends on resistor ratios, so pass-band gain is dependent on the accuracy of
the resistors chosen. It is not possible to build multiple feedback filters with zeros. Multiple
feedback topologies are generally preferred because of better sensitivity to component
variations and better high-frequency behavior and are used in filters to have high quality
factor and require high gain.
TRANSFER FUNCTION:-
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MATHEMATICAL FORMULAE:
OBSERVATIONS & CALCULATIONS
Theoretical values of R 2 and R 1 are calculated as 3.2k Ω and 795.77Ω, and C=0.1uF. R 3 is
calculated as an infinitely large value and thus open circuit.
In TI kit for R 1 3.2k (series of 2.2k and 1k) and 1k are put in parallel. For R 2 2.2k and 1k are
put in series.
Frequency(in KHz) Vin(in mV) Vout (in mV) Gain(V/V)
0.08 100 16 0.160.213 100 41.8 0.418
0.305 100 65.6 0.656
0.404 100 80 0.8
0.495 100 102 1.02
0.592 100 126 1.26
0.708 100 151 1.51
0.81 100 179 1.79
0.915 100 195 1.95
1.031 100 202 2.02
1.13 100 204 2.04
1.201 100 208 2.08
1.307 100 193 1.93
1.411 100 184 1.84
1.5 100 176 1.76
1.628 100 161 1.61
1.747 100 150 1.5
1.908 100 132 1.32
2.117 100 115 1.15
2.341 100 103 1.03
2.52 100 94 0.94
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2.6 100 90.5 0.905
2.714 100 87.6 0.876
3 100 76.7 0.767
3.214 100 72.9 0.729
3.528 100 64.5 0.645
3.7 100 60.4 0.604
4.2 100 53.7 0.537
4.524 100 51.2 0.512
5.153 100 43.8 0.438
6.192 100 36.7 0.367
6.571 100 33.9 0.339
6.98 100 32 0.32
7.55 100 29.9 0.299
9.122 100 24 0.24
10.2 100 21.2 0.21220 100 11.3 0.113
Gain at Fm = -2.02
Lower cut off frequency = 670 Hz.
Upper cut off frequency = 1.8 kHz
Observed Bandwidth = 1.130 kHz.
Theoretical bandwidth = 994.7 Hz
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TI CIRCUITRY
WAVEFORMS
The phase response and bode plot of the transfer function can be seen below.
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Ideal Wave Forms
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WAVEFORMS FROM DSO
Various waveforms of input output were observed on DSO
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CONCLUSION
After conducting the experiment, the gain and center frequency of for second order MFB
Band pass filter are found to be almost equal to their theoretical values. Gain for the passstage was around -2 and the center frequency came out to be 1 kHz. The bandwidth was
found to be 1.130 kHz, in close proximity to the theoretical value of 0.994 kHz.
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EXPERIMENT NO. 2: 4-bit R-2R ladder DAC using op-amp
AIM
Design a 4-bit R-2R ladder DAC using op-amp. Measure the analog output voltage for digital
input word. Calculate maximum linearity error and accuracy.
CIRCUIT DIAGRAM
Fig. 4 - Circuit Diagram for a 4-bit R-2R ladder DAC using op-amp.
PRINCIPLE
The circuit uses only two resistor values. Each switch has its own binary bit of the digital
input word, which controls it. The switch is connected to Vr when the binary bit is 1 and
connected to ground when the binary bit is 0.
The Thevenin of the circuit is computed. The Thevenin on both sides of the circuit gives the
current flowing in the opamp and thus the opamp output voltage can be computed.
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Accuracy is a comparison of the actual output of a DAC with the expected output. It is
expressed as a percentage of a full-scale, or maximum, output voltage. Accuracy is a measure
of what voltage is expected at the output vs. what actually appears.
A linear error is a deviation from the ideal straight-line output of a DAC. A special case is an
offset error, which is the amount of output voltage when the input bits are all zeros.
Advantages
– Only two resistor values
– Does not need as precision resistors as Binary weighted DACs
– Cheap and Easy to manufacture
Disadvantages
– Slower conversion rate
The values will be observed using a multimeter.
MATHEMATICAL FORMULAE:
From the circuit, the output voltage is:
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OBSERVATIONS & CALCULATIONS:
Choosing the value of Vref = 5V, R = 1 k Ω, 2R = 2.2 k Ω, Rf = 2.2 k Ω.
Decimal Binary
Word
Voutput(in
Volts)(observed)
Voutput (in
Volts)(theoretical)
Accuracy (in %)
(Vexpected-Vactual)/Vexpected*100
Linearity (Deviation)
Vobs-Vtheory
0 0000 0 0 0
1 0001 -0.6958 -0.625 -11.328 -0.0708
2 0010 -1.3308 -1.25 -6.464 -0.0808
3 0011 -2.001 -1.875 -6.72 -0.126
4 0100 -2.53 -2.5 -1.2 -0.03
5 0101 -3.2 -3.125 -2.4 -0.075
6 0110 -3.841 -3.75 -2.427 -0.091
7 0111 -4.524 -4.375 -3.4057 -0.149
8 1000 -4.864 -5 2.72 0.1369 1001 -5.54 -5.625 1.511 0.085
10 1010 -6.175 -6.25 1.2 0.075
11 1011 -6.857 -6.875 0.262 0.018
12 1100 -7.384 -7.5 1.547 0.116
13 1101 -8.063 -8.125 0.763 0.062
14 1110 -8.637 -8.75 1.29 0.113
15 1111 -8.684 -9.375 7.371 0.691
V0= -2.2k[b3/2.2k + b2/4.4k + b3/8.8k + b0/19.6k]* Vref
V0= 5[b3 + b2/2 + b1/4 + b0/8]
Analog Output Voltage vs. Digital Input Graph
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
0 1 1 0
1 1
1 0 0
1 0 1
1 1 0
1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
Vout Analog vs Digital Word
Voutputanalog(observed)
Vout(Theoretical)
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Linearity vs. digital output
Accuracy vs. digital output
CONCLUSION
Thus, the R-2R ladder can be used to obtain binary weighted voltages or currents using only a
single-sized resistor (the resistors of size 2R can be made of two resistors of size R, to
improve matching properties.) As a result, this R-2R approach gives better accuracy. Further,
the resistors can be lower in value, giving high speed operation.
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.50.6
0.7
0.8
0 1 1 0
1 1
1 0 0
1 0 1
1 1 0
1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
Linearity
Linearity
-15
-10
-5
0
5
10
1 1 0
1 1
1 0 0
1 0 1
1 1 0
1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
Accuracy
Accuracy
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EXPERIMENT NO. 3:Aastable multivibrator (Triangular wave generator)
AIM
Design an astable multivibrator (Triangular wave generator), for a frequency of 1 KHz.
CIRCUIT DIAGRAM
The Circuit Diagram for an astable multivibrator (Triangular wave generator), used for
framing the circuit during the experimentation phase is shown below.
Circuit Diagram of an astable multivibrator (Triangular wave generator)
PRINCIPLE
The astable multivibrator has no stable states. Let us assume that the output is at +Vsat at the
instant of switching on the power supplies. The capacitor C will start charging towards +Vsat
through R and the voltage across the capacitor which is also the input to the inverting
terminal will start rising exponentially towards +Vsat with a time constant RC. The momentthe capacitor voltage reaches Vut, the inverting input voltage will exceed the non-inverting
terminal voltage and the output Vo will be switched to – Vsat. The capacitor will start
discharging and its voltage will decrease exponentially towards – Vsat. This new state will
continue till Vlt. At this instant, the output will again be switched back to +Vsat and the cycle
will repeat. There are two quasi-stable states and the circuit oscillates between +Vsat and -
Vsat producing a square waveform at the output. The time period is determined by the time
constant of the RC network and the value of the threshold voltages.
The simplest method of forming a triangular waveform generator is to integrate the square
waveform. Thus, by connecting an integrator to a square waveform generator, a triangularwaveform can be generated.
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The frequency of the square and the triangular waveforms are identical. R3C1 is chosen equal
to T and R4 resistor shunts the capacitor to obtain a stable triangular waveform.
MATHEMATICAL FORMULAE
Frequency of triangular waveform, is given as:
F =2
41
CALCULATIONS
Calculating we get theoretical values of R 2 = 4k, R=10k and R 1=1k and C=0.1F. These values
give a frequency of 1k Hz theoretically. Or using a capacitance of 1uF gives R 2=4k, R=10k
and R 1=100 ohms.
So adjusting these values in the TI kit the desired frequency of 1k is obtained using R 2=3k,
R=10k and R 1=1k. The capacitance is kept at 1uF. R 3 and R 4 = 1k to keep gain as unity. The
appropriate triangular waveform cannot be obtained at C= 0.1uF.
R1 = 1k R2 = 3k R = 10k
R3 = 1k R4 = 1k
C = 1uF
TI KIT CIRCUITRY
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WAVEFORMS
Square waveform obtained at output of 1st amplifier (F=1.020Hz)
The square waveform showing Max and Min and Peak to Peak values.
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Required Triangular Waveform Obtained at Output with required frequency (f=1.020Hz)
Triangular Waveform - max, min and peak to peak values.
Amplitude of output waveform = 3.64V (pk to pk)
CONCLUSION
A simple astable multivibrator was designed with certain values of R and C and triangularwaveform observed.
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READINGS FOR THE EXPERIMENTS (Verified by the lab assistants)
Readings for the second order MFB band Pass Filter
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Readings for 4 bits R-2R ladder DAC using op-amp
Readings for Astable Multivibrator (triangular wave generator
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References
1) Laboratory Experiments and PSPICE Simulations in Analog Electronics, Maheshwari
L.K., Anand M.M.S., Prentice Hall of India, 2006
2) Analog Electronics, LK Maheshwari and MMS Anand, PHL Learning Private Limited
Delhi, 2013