+_+_ +_+_ a voltage divider circuit produces an output voltage, v 0 that is proportional to the...
TRANSCRIPT
inV
oV
+
_
+
_
1R
2R
A voltage divider circuit produces an output voltage, V0 that is
proportional to the input voltage, Vin. The input voltage is
supplied by a voltage source. The constant of proportionality is called the gain of the voltage divider.
21
20
RR
R
V
Vg
in
inV
+
_
1R
2R
3R
4R
1_0V
2_0V
3_0V
By suitably calculating the values of resistances a compound voltage divider circuit can be designed.
inV
oV
+
_
+
_
1R
2R
Knob
Potentiometer is a current or voltage dividing equipment. It incorporates a resistor, which has three terminals; two end terminals, and one middle terminal (knob), as shown in the Figure-6.3. The middle terminal is movable. The extreme ends are connected to the external input voltage signal, and the middle terminal along with one of the end terminal is taken as output. The potentiometer can provide different ratios of input to output resistance, causing a proportionate division of input voltage for various positions of the movable knob.
diode
One cycle
time
time
time
Output voltage
Input voltage
hwV _0
fwV _0
(a)
(b)
(c)
R
Diode-1
inV+
-
Diode-2
hwV _0
ground
R
+
-
inV+
-
(d)
(e)
A
B
C
inV+
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D-1
D-2
D-3
D-4
R
(f)
A
B
C
D
E
F
G
H
I
I
Rectification is a process by which an alternating current is transformed or rectified into a direct current (DC).
Half-waverectification
Full-waverectification
(d) Half-wave rectifier circuit; (e) Center-tapped FW rectifier ckt; (f) Bridge type FW rectifier ckt.
AC i/p signal
Rectifier circuitinV+
-
RC
+
-
time
fwV _0
(b)
time
hwV _0
(a)Smoothed signal of the Half-wave rectifier
Smoothed signal of the Full-wave rectifier
Capacitor output
Capacitor output
In many occasions, the pulsating output requires smoothing in order to get a constant DC signal. A steady and constant voltage can be obtained by connecting a capacitor at the output of the rectifier circuit.
zenerV
+
-
R
Zener diodeinput
+
_
Zener diodes, a specially designed diode, are used for stabilizing or regulating the voltage in a circuit. The zener diode is always connected in reverse biased condition and are designed to work at the reverse breakdown voltage known as zener voltage. The voltage across the zener diode is reasonably constant over a wide range of input current variations.
R
clippingV
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inV+
- V-1 V-2
D-1D-2
time
Input signal
Clipped signal
+ ve
- ve
(a)
(b)
A B
CD
V-1
V-2 V-2
V-1
A clipping circuit transmits an arbitrary signal within the limits. The signal above and below the limits are suppressed. For this reason clipping circuits are also referred to as voltage limiters. Diodes can be used in the design of clipping circuits.
oVinV
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R
D
C
Input voltage
time
Output voltage
time
oVinV
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R
D
C
Input voltage
time
Output voltage
time
Range
Range
Range
Range
(a)
(b)
(c)
(d)
(e)
(f)
Clamping circuits are of two types, namely positive clamper or negative clamper.
Input signal
Clamped output(+ve clamping)
Clamped output(-ve clamping)
input Output
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-
+
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inv ovinv
vG 0
input
+
-
inv Output
+
-
ov
inv
vG 0
1G 2G 3G 4G
(a)
(b)
The overall gain of such a multistage amplifier is approximately equal to the product of the individual gains.
nGGGG .....21
+
_
(a) (b)
Input
OutputOutput
Input
+
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Feedback resistanceFeedback resistanceInput resistance Input resistance
The OPAMP boosts the amplitude significantly and the output voltage is proportional to its input voltage. The OPAMP was originally developed for use in realization of mathematical operations such as addition, subtraction, multiplication (amplification), integration, and differentiation in analog computers. For this reason they are called operational amplifiers. Inverting and noninverting configurations are useful in the design of amplifiers, filters, and other signal conditioning applications.
1R
R
V
VA f
s
oinv
1
1R
R
V
VA f
s
ononinv
Inverting Non-inverting
0V
+
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3V
2V
1V R
R
R
R
Ground
(a)
R
R
Inverting terminal
NonInverting terminal
1V
2V
(b)
oV
+
-
inV
oV
R
C
+
-
inV
oV
R
C
+
-
Ground
GroundGround
(c) (d)
_
+
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+
_
+
_
+
)( 3210 VVVV
(a) An adder; (b) Subtractor; (c) Integrator; (d) Differentiator
dtVRC
V in
10
dt
dVRCV in0
120 VVV
inodV _
+
-
+
-
outodV _
-
+
(a) (b)
+
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outocV _
-
+
inocV _
+
-
Open-loop common-mode configurationOpen-loop differential mode configuration
Differential amplifiers are characterized by a factor called the Common Mode Rejection Ratio (CMRR), which is the ratio of the open-loop differential gain , and open-loop common-mode gain , and is expresses in dB.
odA
ocA
oc
od
A
ACMRR 10log20
inod
outodod V
VA
_
_inoc
outococ V
VA
_
_
Gain
Lf
Frequency response curve of a high-pass filter
Frequency
Maximum gain
-3dB
Gain
Uf
Frequency response curve of a low-pass filter
Frequency
Maximum gain
-3dB
(a) (b)
The integrator and differentiator circuits are electronic filters because the circuits filter out some frequency components from the input signal.
(a) Gain versus. frequency response curve of a typical low-pass (integrator) filter;
(b) Gain vs. frequency response curve of a typical high-pass (differentiator) filter
UfLf
Maximum gainPower normalized to zero dB (100% power)
-3dB (50% power)
100% gain
71% hain
(a)
frequency
frequency frequency
UfLf
Maximum gainPower normalized to zero dB (100% power)
-3dB (50% power)
100% gain
71% hain
(b)frequency
UfLf
Maximum gainPower normalized to zero dB (100% power)
-3dB (50% power)
100% gain
71% hain
(c)
UfLf
Maximum gainPower normalized to zero dB (100% power)
-3dB (50% power)
100% gain
71% hain
(d)
Frequency response curve of various filters.
(a) Bandpass filter
(b) Band-reject filter
(c) Narrow-band filter (d) Notch filter
When the filters are designed using only passive elements such as capacitors and inductors, they are referred to as passive filters. A smoothing capacitor at the output of the rectifier circuit can be treated as a low-pass filter (Figure-6.5). Filters that are designed either using a transistor or OPAMP are called active filters.
A typical active bandpass filter using OP-AMP
Input CIRCUIT-1 Isolator CIRCUIT-2 Output
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-
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-
+
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(a)
(b)
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+Input
Output
Circuit-1 Circuit-2
Optoisolator
LED
Photodiode
(c)
Light
An isolator is a circuit that allows signals to be transferred between two circuits or systems, while keeping those circuits or systems electrically isolated from each other. The gain of the isolator or unity amplifier is unity. The isolation can also be achieved by utilizing optical signals. The electrical signal at the
output of the previous circuit is converted to light signal by a LED. Then the light signal is again converted to get back the electrical signal by using a photodiode or phototransistor.
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1V
2V
oV
R R
RR
R
R
R
R
R Ground
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Instrumentation amplifier is a kind of differential amplifier. It uses three OPAMPs. The third OPAMP behaves as an isolator. For high precision and high accuracy applications instrumentation amplifier are used. The configuration the open-loop differential gain is very high and the open-loop common-mode gain is small. It possesses high CMRR.
Excitation voltage
R1
R2
R3 R4+
-
Output
+
-
A
BC
D
Instrumentation Amplifier
+
-
Wheatstone bridge is a four-arm, four-terminal resistance-measuring electronic network. The bridge circuit is an important signal conditioning circuit, that can form the basis of capturing a very small fraction of change in the resistance value. The bridge is very reliable and is considered as a sophisticated and precision signal-conditioning circuit.
COMPARATORInput Output
+
-
+
-Comparator Input
Threshold or reference level
timeComparator Output
time
A typical sensor signal
+V volts
Comparators are employed in applications in which some sort of signal comparison is required. It is a circuit that typically contains a threshold or reference voltage level to which the voltage level of another signal is compared. If the signal to be compared is greater than the reference voltage setting then the comparator circuit provides an output in terms of a pulse or step signal.
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+inV
oV
oV
inV
saturationV
saturationV
oV
inV
saturationV
saturationV
-
+
inV
oV
(a)
(b)
ccV
ccV
ccV
ccV
ccV
ccV
ccV
ccV
The two open-loop OPAMP circuits shown above can be used as comparators. The transition occurs based on whether the reference voltage (Vref = Vin ) is less than zero or greater than 0.
-
+
oV
ccV
ccV
+
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refV
inV+
-
Figure shows a comparator circuit using an OPAMP in non-inverting mode. In the figure a reference source, which is equal to the threshold level, has been connected to the noninverting terminal. The signal to be compared with the reference voltage is applied to the inverting terminal. Whenever the input voltage is greater than the reference voltage the transition occurs, providing an output pulse or step.
Zero Crossing DetectorInput Output
+
-
+
-
ZCD Output
time
ZCD Input
time
time
ZCD Input
time
ZCD Output
Zero crossing detector (ZCD) is a kind of comparator that provides a signal (pulse or step) at the output when the input signal passes the zero level.
Amplitude Amplitude
Amplitude
AmplitudeAmplitude
Amplitude
time
time
time
time
time
time
(a) (b)
(c) (d)
(e) (f)
Signal conditioning circuits include waveform generators. Within automation and control, various types of oscillatory waveforms are required. The types of oscillatory waves are sinusoidal, triangular, impulsive, square- wave, saw-
tooth, staircase, and so on. Oscillators are electronic circuits that generate a oscillatory output voltage that repeats regularly at constant intervals.
Amplifier
Feedback circuit
A
B
All oscillator circuits are positive feedback systems.
Voltage divider
4R3R
2R
1R
2C
1C
Ground
oV
Lead-lag circuit
_
+
Depending upon the circuit configuration, different types of oscillators exist. They include the Wien-Bridge oscillator, phase-shift oscillator, Colpitts oscillator, Clapp oscillator, Hartley oscillator, and most versatile Crystal oscillators. Figure illustrates an OPAMP-based Wien-Bridge oscillator.
The lead-lag circuit provides a positive feedback.
RRR 34
CCC 21
RCfosc 2
1
If
then
3R
2R
1R
C
_
+
oV1V
saturationV
saturationV
oV
time
time
1V
lV
uV
Voltage across capacitor C
An OPAMP-based square-wave oscillator. The voltage across the capacitor is triangular in nature. If , then the frequency of oscillation is,
1V 23 86.0 RR
CRfosc
12
1
3R
2R
1R
CGround
_
+_
+
Ground
Comparator Integrator
oV
1V
saturationV
saturationV
1V
time
time
oV
lV
uV
The OPAMP-based triangular wave oscillator is shown in the figure. It uses two OPAMPs. The first OPAMP is a comparator and the second is an integrator. The voltage at the output of the first OPAMP is square-wave in nature. The integrator integrates the square-wave, producing a triangular wave.
3
2
14
1
R
R
CRfosc
Symbol
XTAL
R
L
C
0C
For getting stable and accurate oscillatory signal output, a piezoelectric quartz crystal is often used. The property of the quartz crystal is that when a changing mechanical stress is applied to the crystal, an oscillatory voltage is developed, whose frequency is the same as that of the mechanical stress vibrations. The highest vibration occurs at the natural frequency of the crystal. The frequency depends on dimensions, type of cut, thickness, temperature, etc.
There are many ways to design oscillator circuits. A basic oscillator circuit is available in IC form. NE555 or LM555, which are called timers that have the building blocks in one package. 555 IC are highly stable devices for generating relatively accurate oscillations.
-
+
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+
R
R
R
Threshold
Control
Trigger
6
5
2
Comparator-1
Comparator-2
Flip-flop
Reset4
Output3
7Discharge
ccV
Ground
ccV3/2
ccV3/1
Transistor
1
(active low)
The internal basic building blocks of 555.
7
6
2
C
F01.0
aR
bR
3
5
1
Output
oV
555
)(tVc
ccV
A typical configuration of 555 by the use of external components for the generation of rectangular waves is shown in Figure. This type of configuration is called the free-running mode because the triggering signal is captivated from the timer. That is the trigger signal is generated from the 555 itself. The free-running mode of operation of 555 is called the astable mode. The time it stays high and the time it stays low are determined by the values of the external components.
CRRTf
CRRTTT
CRT
CRRT
ba
ba
b
ba
)2(
44.11
)2(693.0
693.0
)(693.0
21
2
1
ccV3/2ccV
ccV3/1
uV
time
time1T 2T
Output
Voltage waveforms across the output pin
Voltage waveforms across the capacitor
7
6
C
F01.0
aR
bR
3
5
1
Output
oV
555
)(tVc
ccV
2
Trigger signal
A monostable multivibrator circuit, on the other hand, has an output that stays in a given state (either low or high) until a separate signal triggers the timer. The trigger signals are provided externally. The monostable mode requires only two external components, and C. Time period is determined by
aR
CRT a1.1
+
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inV
oscV+ -
+
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D-1
D-2D-3
D-4
Ch
A
B
inV
outV
oscV
time
time
time
C D
1R
2R
Output+
- Vout
E
Sample and hold circuits (S/H) are very important in the context of analog to digital (AD) conversion of the signal. An S/H circuit is one that samples the analog signal at a particular instant and retains the value for a specified time for subseq-uent use.
Analog signal
Sampler Quantiser Binary Converter
Digital signal
Sample and hold
Analog signal
Quantised signalQuantisation level-15
Quantisation level-1
54321 SSSSS
54321 QQQQQ
Sampled signal
time
time
time
Amplitude
1110
0110
0110
1001
0110
5
4
3
2
1
Q
Q
Q
Q
Q
(a)
(b)
(c)
(d) Quanisation level-0
The analog to digital conversion (ADC) is achieved through three sub processes such as,
•Sampling•Quntisation•Coding
MultiplierPulsed signal
Analog signal in time domain
time
time
time
Analog signal in frequency domain
Multiplied signal in the frequency domain
sf sf2
USB-1 USB-2LSB-2LSB-1Signal
Multiplied signal in the frequency domain
sf sf2
USB-1 USB-2LSB-2LSB-1Signal
Multiplied signal in the frequency domain
sf sf2
USB-1 USB-2LSB-2LSB-1Signal
Ms ffCase :1
Mf frequency
frequency
frequency
frequency
Ms ffCase :2
Ms ffCase :2
Overlapping
Not overlapping
(b)
(a)
(c)
(d)
(e)
(f)
(g)
(h)
1
One of the important parameters of an ADC is the sampling frequency. There is a strict relationship between the sampling freq. and the signal freq. as far as exact recovery of the analog signal from the sampled signal is concerned. This relationship appears as the sampling theorem and states that "the sampling rate should be at least twice that of the highest frequency of the analog signal."
outV
dV
R 2R 4R 8R
16R32R
64R
128R
7
6
5
4
3
2
1
0
D
D
D
D
D
D
D
D0S
1S
2S
3S4S
5S
7S6S
fR
Ground
Data bits
0I 2I 3I 4I 5I 6I 7I2I-
+
Mainly two techniques are employed as far as Digital to Aanalog Conversion is concerned; binary resister-based and R-2R ladder-based D/A converters, respectively.
Binary resister-basedDAC
7
6
5
4
3
2
1
0
D
D
D
D
D
D
D
D
Data bits
0S 1S 2S 3S 4S 5S 7S6S
0I2I3I4I5I6I7I 2I
2R 2R 2R 2R 2R 2R 2R 2R 2R
Output
outI
256 mA R-2R ladder-based D/A converters
R
VI
R
VI
R
VI
R
VI
R
VI
R
VI
R
VI
R
VI
dddd
dddd
7654
3210
;2
;4
;8
16;
32;
64;
128
Digital to Analog Converter (D/A)
Counter
Input analog signal
Comparator
+
_
01234567 DDDDDDDD
00000000
00010000
00100000
00110000
01000000
01010000
01100000
01110000
10000000
10010000
10100000
10110000
11000000
11010000
11100000
11110000
00000001
00010001
00100001
00110001
01000001
01010001
01100001
01110001
10000001
Initial point
Counter output
Analog signal
Digital Equivalent
Only 24 levels out of 128 levels have been shown
Initial catching
Circuit diagram of a counter based A/D converter. There are three blocks; a comparator circuit that gives an output, i.e., a pulse when the inverting terminal exceeds the input analog signal, D/A converter converts digital signal to analog signal. The counter counts from zero to upward. The counter
based technique inherits initial catching problem.
Digital to Analog Converter (D/A)
Successive Approximation Register
Input analog signal
Comparator
+
_
01234567 DDDDDDDD
Buffer
MSB
LSB
pulse at the output, if the input signal is greater than the signal at the inverting terminal. The output is fed to a register, called buffer. The buffer is connected to another register called Successive Approximation Register (SAR). The output of the SAR is the digital equivalent of the analog input. The last block, as before is a digital to analog converter, whose input is from SAR and the output is connected to the inverting terminal of the comparator.
Successive approximation technique overcomes the initial catching problem. There are four blocks. The comparator, that produces a
N S
0
+_
Scale
Coil
Pointer
Input terminal
polepole
Galvanometer is an instrument that detects the presence, direction, and strength of an electrical current in a conductor. They operate on fundamental magnetic law that an electric current flowing through a wire in the presence of a magnetic field produces a force in the wire. Four basic components are integrated in order to observe the phenomenon, i.e., the flow of current. The components are a magnetic field, a coil, a pointer, and display.
Galvanometer Galvanometer
Ammeter Voltmeter
Ammeter connection
Ammeter
Circuit element
Voltmeter connection
Voltmeter
A B A
B
GalvanometerGalvanometer Galvanometer
Ammeter Voltmeter
Ammeter connection
AmmeterAmmeter
Circuit element
Voltmeter connection
Voltmeter
A B A
B
(a) (b)
(c) (d)
The galvanometer is used to measure small currents. To measure higher values some potentiometer type circuits are connected as heavy currents could damage the galvanometer. When the galvanometer is converted to measure the current it is called ammeter and when it is converted to measure the voltage it is called voltmeter.
(-) Cathode
+ + +
Intensity control grid
Focusing grid
Accelerating grid
Pair of Horizontal plates
Pair of vertical plates
Florescence screen
Electron beam
Cathode Ray Tube
The Cathode Ray Oscilloscope (CRO) is an equipment commonly used to measure and display signal parameters such as amplitude, frequency, and phase. A wide range of both AC and DC levels can be measured and displayed. The CROs are versatile, reliable, stable and can be handled easily. For these reasons, it is being used in many laboratories, research centers, and industrial sectors. CRT (Cathode Ray Tube) constitutes the main part of the CRO.
Cathode Ray Tube
Vertical plates
.Y=deflection
DC signal
.O
y2
Y=deflection
Vertical plates
DC signal inreverse direction
Wrt above
Peak deflection
Vertical plates
Sinusoidal signal
Vertical plates
.Y=deflection
DC signal
.Y=deflection
Vertical plates
Y=deflectionY=deflection
Vertical plates
DC signal inreverse direction
Wrt above
Peak deflection
Vertical plates
Sinusoidal signal
y1
O
y2
y1
HorizontalAxis
VerticalAxis The signal whose
parameters are to be measured and displayed is fed to the vertical plates. a linear saw-tooth signal called sweep signal is fed to the horizontal deflection plates for complete visualization. The frequency informa-tion of the signal can also be obtained.
Linear
Amplitude
Time
Sudden fall
A linear saw-tooth signal called sweep signal is applied across the horizontal deflection plates. Application of one cycle of the sweep signal, to the horizontal plates, causes the beam to be deflected across the screen. When the sweep signal suddenly falls to zero, the beam flies back to its initial position. Application of second cycle causes the beam to start deflecting in the horizontal direction again. However, because of the nature of the fluorescent screen and the other additional electronic circuitry, the fly-back part of the return trace of the beam cannot be seen. The sweep signal repeats, drawing the beam horizontally again and again in order to provide an illusion that the fluorescent point is not moving.
Vertical Amplifier
Trigger Generator
HorizontalAmplifier
Horizontal plate
Vertical plate
Screen
Sweep Generator
Input signal whose parameter is to be measuredA schematic block diagram of a typical CRO has been shown. The signal to be displayed is amplified by the vertical amplifier and applied to the vertical deflection plates of the CRT.
A portion of the signal in the vertical amplifier is applied to the trigger generator in order to provide triggering signal to the sweep generator. This pulse turns on the sweep generator, initiating the saw-tooth waveform. The saw-tooth wave is amplified by the horizontal amplifier and applied to the horizontal deflection plates.