LINEAR INTEGRATED CIRCUITS UNIT 2 FILTERS AND DESIGN

LIC FILTERS

1. UNIT – II Op-Amp, IC-555 & IC 565 Applications: Introduction to Active Filters, Characteristics of Band pass, Band reject and All Pass Filters, Analysis of 1st order LPF & HPF Butterworth Filters, waveform Generators – Triangular, Saw tooth, Square wave, IC555 Timer – Functional Diagram, Monostable and Astable Operations, Applications, IC565 PLL – Block Schematic, Description of Individual Blocks, Applications.

2. Introduction Filters are circuits that are capable of passing signals within a band of frequencies while rejecting or blocking signals of frequencies outside this band . This property of filters is also called “frequency selectivity”. Filter can be passive or active filter. Passive filters : The circuits built using RC, RL, or RLC circuits. Active filters : The circuits that employ one or more op-amps in the design an addition to resistors and capacitors

3. Passive filters Passive filters use resistors, capacitors, and inductors (RLC networks). To minimize distortion in the filter characteristic, it is desirable to use inductors with high quality factors P ractical inductors includes a series resistance.   They are particularly non-ideal They are bulky and expensive

4. Active filters overcome these drawbacks and are realized using resistors, capacitors, and active devices (usually op-amps) which can all be integrated:  Active filters replace inductors using op-amp based equivalent circuits.

5. Active filters can be designed to provide required gain  no attenuation . Advantages of Active Filters over Passive Filters No loading problem , because of high input resistance and low output resistance of op-amp. Cost effective solution as a wide variety of economical op-amps

6. Disadvantages Active RC filters also have some disadvantages: limited bandwidth of active devices limits the highest attainable frequency (passive RLC filters can be used up to 500 MHz) require power supplies (unlike passive filters) increased sensitivity to variations in circuit parameters caused by environmental changes compared to passive filters For many applications, particularly in voice and data communications , the economic and performance advantages of active RC filters far outweigh their disadvantages.

7. Applications Active filters are mainly used in communication and signal processing circuits. They are also employed in a wide range of applications such as entertainment, medical electronics , etc.

8. Active Filters 1. Low-pass filters High-pass filters Band-pass filters Band-reject filters Each of these filters can be built by using op-amp as the active element combined with RC, RL or RLC circuit as the passive elements. There are 4 basic categories of active filters:

9. Ideal Filters Stopband Passband Passband P a s sb a nd S t opb a nd Lowpass Filter Highpass Filter Bandstop Filter Stopband Passband Stopband Bandpass Filter M(  ) Passband Stopband M(  )      c  c  c 1  c 1  c 2  c 2

10. Analog Filter Responses H ( f ) f H ( f ) f f c Ideal “brick wall” filter f c Practical filter

11. Actual response V o A low-pass filter is a filter that passes frequencies from 0Hz to critical frequency, f c and significantly attenuates all other frequencies. Ideal response Ideally , the response drops abruptly at the critical frequency, f c roll-off rate Low-Pass Filter Response

12. Stopband is the range of frequencies that have the most attenuation. Critical frequency , f c , (also called the cutoff frequency ) defines the end of the passband and normally specified at the point where the response drops – 3 dB (70.7%) from the passband response. Passband of a filter is the range of frequencies that are allowed to pass through the filter with minimum attenuation (usually defined as less than -3 dB of attenuation). Transition region shows the area where the fall-off occurs. roll-off rate

13. At low frequencies, X C is very high and the capacitor circuit can be considered as open circuit. Under this condition, V o = V in or A V = 1 (unity). At very high frequencies, X C is very low and the V o is small as compared with V in . Hence the gain falls and drops off gradually as the frequency is increased.

14. The bandwidth of an ideal low-pass filter is equal to f c : The critical frequency of a low-pass RC filter occurs when X C = R and can be calculated using the formula below:

15. A high-pass filter is a filter that significantly attenuates or rejects all frequencies below f c and passes all frequencies above f c . The passband of a high-pass filter is all frequencies above the critical frequency . V o Actual response Ideal response Ideally , the response rises abruptly at the critical frequency, f L High-Pass Filter Response

16. The critical frequency of a high-pass RC filter occurs when X C = R and can be calculated using the formula below:

17. A band-pass filter passes all signals lying within a band between a lower-frequency limit and upper-frequency limit and essentially rejects all other frequencies that are outside this specified band. Band-Pass Filter Response Actual response Ideal response

18. The bandwidth (BW) is defined as the difference between the upper critical frequency (f c2 ) and the lower critical frequency (f c1 ) .

19. The frequency about which the pass band is centered is called the center frequency , f o and defined as the geometric mean of the critical frequencies.

20. The quality factor (Q) of a band-pass filter is the ratio of the center frequency to the bandwidth. The quality factor (Q) can also be expressed in terms of the damping factor (DF) of the filter as : The higher value of Q, the narrower the bandwidth and the better the selectivity for a given value of f o . (Q>10) as a narrow-band or (Q<10) as a wide-band

21. Narrow Band Pass Filter A narrow band pass filter employing multiple feedback is depicted. This filter employs only one op-amp, as shown in the figure. In comparison to all the filters discussed so far, this filter has some unique features that are given below. It has two feedback paths, and this is the reason that it is called a multiple-feedback filter. The op-amp is used in the inverting mode.

22. Wide Band pass Filter A wide bandpass filter can be formed by simply cascading high-pass and low-pass sections To form a ± 20 db / decade bandpass filter, a first-order high-pass and a first-order low-pass sections are cascaded; It means that, the order of the bandpass filter is governed by the order of the high-pass and low-pass filters it consists of.

23. Band-Stop Filter Response Band-stop filter is a filter which its operation is opposite to that of the band-pass filter because the frequencies within the bandwidth are rejected , and the frequencies above f c1 and f c2 are passed . Actual response For the band-stop filter, the bandwidth is a band of frequencies between the 3 dB points, just as in the case of the band-pass filter response. Ideal response

24. Band Reject Filter Types of Band Reject Filter Circuit, 1. Narrow band reject filter 2. Wide band reject filter Narrow band reject filter : The narrow band reject filter is also called the notch filter. Because of its higher Q which is greater than 10, the bandwidth of the narrow band reject filter is much smaller than that of the wide band reject filter. The band reject filter is also called a band stop or band elimination filter because it eliminates a certain band of frequencies.

25. Wide band Reject Filter Wide band reject filter using a low pass filter, a high pass filter and a summing amplifier. For a proper band reject response, the low cutoff frequency f L of the high pass filter must be larger than the high cutoff frequency f H of the low pass filter.

26. Animation A "Group" of waves passing through a Typical Band-Pass Filter

27. All Pass Filter All Pass Filter Design is one that passes all frequency components of the input signal without attenuation. Any ordinary wire can be used to perform this char­acteristic but the most important factor in an all pass filter is that it provides predictable phase shifts for different frequencies of the input signal.

28. SUMMARY The bandwidth of a low-pass filter is the same as the upper critical frequency. The bandwidth of a high-pass filter extends from the lower critical frequency up to the inherent limits of the circuit. The band-pass passes frequencies between the lower critical frequency and the upper critical frequency . A band-stop filter rejects frequencies within the upper critical frequency and upper critical frequency. All Pass Filter Design is one that passes all frequency components of the input signal without attenuation.

29. Frequency Response of filters Ideal Practical Filters are often described in terms of poles and zeros A pole is a peak produced in the output spectrum A zero is a valley (not really zero )

30. Order of the Filter

31. First Order Low-Pass Butterworth Filter Butterworth filter is a type of filter whose frequency response is flat over the pass band region. Low-pass filter (LPF) provides a constant output from DC up to a cutoff frequency f (H) and rejects all signals above that frequency. The first order low pass butter worth filter is realized by R-C circuit used along with an op-amp, used in the non inverting configuration .

32. First Order Low-Pass Butterworth Filter

33. Because of simplicity, Butterworth filters are considered. In 1 st . order LPF which is also known as one pole LPF. Butterworth filter and it’s frequency response are shown above. RC values decide the cut-off frequency of the filter. Resistors R 1 & R F will decide it’s gain in pass band. As the OP-AMP is used in the non-inverting configuration, the closed loop gain of the filter is given by 1 R VF A  1  R F

34. 1 V  in V           (1) C R  jX jX C 1 2  fC C X     (2)   1   2  fC  V in    j   1  1  jV in 2  f RC  j    R  j  2  fC  V  j V in 1  2  fRC V in  1  j 2  fRC  EXPRESSION FOR THE GAIN OF THE FILTER: Reactance of the capacitor is , Equation (1) becomes Voltage across the capacitor V 1 =

35. f = frequency of the input signal    H    V V in V in R F  V  A  V    1  1  V F 1 R  1  j 2  f RC f A VF 1  j   f Output of the filter is,

36. The operation of the low-pass filter can be verified from the gain magnitude equation, (7-2a): At very low frequencies, that is, f < f H , At f = f H , f < f H ,

37. DESIGN PROCEDURE: Step1: Choose the cut-off frequency f H Step2: Select a value of ‘C’ ≤ 1 µF (Approximately between .001 & 0.1µF) Step3: Calculate the value of R using Step4: Select resistors R 1 & R 2 depending on the desired pass band gain. (Try different gains) = 2. So R F =R 1

38. Frequency Scaling Once the filter is designed, sometimes, it is necessary to change the value of cut-off frequency f H . The method used to change the original cut-off frequency f H to a new cut-off frequency f H1 is called as frequency scaling. To achieve such a frequency scaling, the standard value capacitor C is selected first. The required cut-off frequency can be achieved by calculating corresponding value of resistance R. Thus , the resistance R is generally a potentiometer with which required cut-off frequency fH can be adjusted and changed later on if required.

39. For a first order Butterworth LPF, calculate the cut –off frequency if R=10K  & C=0.001µF.Also calculate the pass band voltage gain if R 1 =10K  R F =100K   15.915 KHz H f  1 2   10  10 3  0.001  10  6 1 2  RC  1+100K/10K =11 Design a 1 st order LPF for the following specification Pass band voltage gain = 2. Cut off frequency, f C = 10KHz. A VF = 2; Let R F = 10K  R F /R 1 =1 Let C = 0.001µF 1 2   10  10 3  0.001  10  6 2  f C & R   1 1 2  RC f  H H R=1 5 .9K 

40. Determine the gain of the first order low pass filter if the phase angle is 59.77 o  and the pass band gain is 7. Explanation: Given the phase angle, φ =- tan -1 (f/ f H ) => f/ f H =- φ tan( φ) = - tan(59.77 o ) => f/ f H = -1.716. Substituting the above value in gain of the filter, |(V O /V in )| = A F /√ (1+(f/ f H ) 2 ) =7/√[1+(-1.716) 2 )] =7/1.986 =>|(V O /V in )|=3.5.

41. 1 st ORDER HPF A high pass filter is a circuit that attenuates all the signals below a specified cut off frequency denoted as f L . Thus, a high pass filter performs the opposite function to that of low pass filter. First Order High Pass Butterworth Filter circuit can be obtained by interchanging frequency determining resistances and capacitors in low pass filter circuit

42. Circuit diagram & frequency response are shown above. Again RC components decide the cut off frequency of the HPF where as R F & R 1 decide the closed loop gain. 1 st ORDER HPF: f L is shown for HPF

43. V R C W h e r e X  in C 1 2  fC R  jX 1 Voltage V  in in V j V  R R  2  fC 1 1 V   R  R  j 2  fC  R  1  j 2  fRC j 2  fC in  f   L  V j  f    f l   f  1  j  in f L V F 1 V f 1  j f A L  V F     jf  Output voltage = V  A . V     L   f  1  j   f  L  V F    f  jf  A V V in EXPRESSION FOR THE GAIN: Gain = Magnitude=

44. Compute the pass band gain and high cut-off frequency for the first order high pass filter. Explanation: The pass band gain of the filter, A F  =1+(R F /R 1 ) =>A F =1+(10kΩ/10kΩ)=2. The high cut-off frequency of the filter, f H =1/2πRC =1/(2π×20kΩ×0.01µF) =1/1.256×10 -3  =796.18Hz.

45. Wave form Generators Three types: Square Wave Generator Triangular Wave Generator Saw tooth Wave Generator

46. Square Wave Generator

47. Contd.. The Square Wave Generator Using Op amp means the astable multivibrator circuit using op-amp, which generates the square wave of required frequency It looks like a comparator with hysteresis (Schmitt trigger), except that the input voltage is replaced by a capacitor. The circuit has a time dependent elements such as resistance and capacitor to set the frequency of oscillation.

48. Triangular Waveform Generator The output of integrator is a Triangular Wave Generator Using Op amp if its input is a square wave. This means that a Triangular Wave Generator Using Op amp can be formed by simply connecting an integrator to the square wave generator as shown in the Fig.

49. In practical circuits, resistance R4 is connected across C to avoid the saturation problem at low frequencies as in the case of practical integrator as shown in the Fig.

50. Triangular Waveform Generator using lesser components

51. Amplitude and Frequency Calculation The frequency and amplitude of the Triangular Wave Generator Using Op amp wave can be determined as follows : When comparator output is at + Vsat , the effective voltage at point P is given by When effective voltage at P becomes equal to zero, we can write above equation

52. Similarly, when comparator output is at – Vsat , we can write, The peak to peak amplitude of the triangular wave can be given as The time taken by the output to swing from – Vramp to + Vramp (or from + Vramp to – Vramp ) is equal to half the time period T/2. Refer Fig. This time can be calculated from the integrator output equation as follows :

53. Substituting value of Vo( pp ) we get, Triangular Wave Generator Using Op amp

54. Saw Tooth Waveform Generator A sawtooth waveform is used in pulse width modulation circuits and time-base generators. A potentiometer is used when the wiper moves toward negative voltage(-V); then the rise time becomes more than the fall time. When the wiper moves towards positive voltage(+V), then the rise time becomes less than the fall time.

55. Applications: The sawtooth waveform is most common waveform used to create sounds with subtractive virtual and analog music synthesizers. Therefore, it is used in music. The sawtooth is the form of horizontal and vertical deflection signals that are used to generate a raster on monitor screens or CRT based television. The magnetic field suddenly gets collapsed on the wave’s cliff, which causes the resting position of its electron beam as quickly as possible. The magnetic field produced by the deflection yoke drags the electron beam on the wave’s ramp, creating a scan line.

56. 555 TIMER 71

57. IC 555 Timer The 555 Timer is one of the most popular and versatile integrated circuits ever produced! “ Signetics ” Corporation first introduced this device as the SE/NE 555 in early 1970. It is a combination of digital and analog circuits. It is known as the “time machine” as it performs a wide variety of timing tasks. Applications for the 555 Timer include: Ramp and Square wave generator Frequency dividers Voltage-controlled oscillators Pulse generators and LED flashers Malla Reddy College of Engineering and Technology 72

58. 555 timer- Pin Diagram The 555 timer is an 8-Pin D.I.L. Integrated Circuit or ‘chip’ Malla Reddy College of Engineering and Technology 73 Notch Pin 1

59. 555 timer- Pin Description Pin Name Purpose 1 GND Ground, low level (0 V) 2 TRIG OUT rises, and interval starts, when this input falls below 1/3 V CC . 3 OUT This output is driven to approximately 1.7V below + V CC or GND. 4 RESET A timing interval may be reset by driving this input to GND, but the timing does not begin again until RESET rises above approximately 0.7 volts. Overrides TRIG which overrides THR. 5 CTRL "Control" access to the internal voltage divider (by default, 2/3 V CC ). 6 THR The interval ends when the voltage at THR is greater than at CTRL. 7 DIS Open collector output; may discharge a capacitor between intervals. In phase with output. 8 V +, V CC Positive supply voltage is usually between 3 and 15 V. 74

60. 555 Timer Description: Contains 25 transistors, 2 diodes and 16 resistors Maximum operating voltage 16V Maximum output current 200mA If you input certain signals they will be processed / controlled in a certain manner and will produce a known output. INPUT PROCESS OUTPUT Best treated as a single component with required input and output 75

61. Block Diagram of 555 Timer S R Q Q Malla Reddy College of Engineering and Technology 76 Threshold Control Voltage Trigger Discharge V ref + R S Q Q Truth Table Fig: Functional Diagram of 555 Timer

62. Inside the 555 Timer Operation: The voltage divider has three equal 5K resistors. It divides the input voltage (V cc ) into three equal parts. The two comparators are op-amps that compare the voltages at their inputs and saturate depending upon which is greater. The Threshold Comparator saturates when the voltage at the Threshold pin (pin 6) is greater than (2/3) V cc . The Trigger Comparator saturates when the voltage at the Trigger pin (pin 2) is less than (1/3) V cc 77

63. Inside the 555 Timer The flip-flop is a bi-stable device. It generates two values, a “high” value equal to V cc and a “low” value equal to 0V. When the Threshold comparator saturates, the flip flop is Reset (R) and it outputs a low signal at pin 3. When the Trigger comparator saturates, the flip flop is Set (S) and it outputs a high signal at pin 3. The transistor is being used as a switch, it connects pin 7 (discharge) to ground when it is closed. When Q is low, Q bar is high. This closes the transistor switch and attaches pin 7 to ground. When Q is high, Q bar is low. This open the switch and pin 7 is no longer grounded 78

64. Features of IC 555 Timer The Features of IC 555 Timer are: 1 . The 555 is a monolithic timer device which can be used to produce accurate and highly stable time delays or oscillation. It can be used to produce time delays ranging from few microseconds to several hours. 2 . It has two basic operating modes: monostable and astable . 3 . It is available in three packages: 8-pin metal can, 8-pin mini DIP or a 14-pin. A 14-pin package is IC 556 which consists of two 555 times. Malla Reddy College of Engineering and Technology 79

65. Contd … 4. The NE 555( signetics ) can operate with a supply voltage in the range of 4.5v to 18v and output currents of 200mA. 5 . It has a very high temperature stability, as it is designed to operate in the temperature range of -55⁰c to 125 o c. 6 . Its output is compatible with TTL, CMOS and Op-Amp circuits. Malla Reddy College of Engineering and Technology 80

66. Uses of 555 timer What the 555 timer is used for: To switch on or off an output after a certain time delay i.e. Games timer, Childs mobile, Exercise timer. To continually switch on and off an output i.e. warning lights, Bicycle indicators . As a pulse generator i.e. To provide a series of clock pulses for a counter. 81

67. Schematic Diagram of 555 Timer 82

68. 555 Timer operating modes 555 has three operating modes : 1. Monostable Multivibrator 2. Astable Multivibrator 3. Bistable Multivibratior 83

69. 555 Timer operating modes The 555 has three operating modes : 1. Monostable Multivibrator 2.Astable Multivibrator 3. Bistable Multivibratior 84

70. 555 Timer as Monostable Multivibrator Description: In the standby state, FF holds transistor Q 1 ON, thus clamping the external timing capacitor C to ground. The output remains at ground potential. i.e. Low. As the trigger passes through V CC /3, the FF is set, i.e. Q bar=0, then the transistor Q 1 OFF and the short circuit across the timing capacitor C is released. As Q bar is low , output goes HIGH. 85

71. 555 Timer as Monostable Multivibrator Fig (a): Timer in Monostable Operation with Functional Diagram Fig (b): Output wave Form of Monostable 86

72. Monostable Multivibrator- Description Voltage across it rises exponentially through R towards V cc with a time constant RC. After Time Period T, the capacitor voltage is just greater than 2V cc /3 and the upper comparator resets the FF, i.e. R=1, S=0. This makes Q bar =1, C rapidly to ground potential. The voltage across the capacitor as given by, at If –ve going reset pulse terminal (pin 4) is applied, then transistor Q 2 -> OFF, Q 1 -> ON & the external timing capacitor C is immediately discharged. 87

73. Behavior of the Monostable Multivibrator The monostable multivibrator is constructed by adding an external capacitor and resistor to a 555 timer. The circuit generates a single pulse of desired duration when it receives a trigger signal, hence it is also called a one-shot. The time constant of the resistor-capacitor combination determines the length of the pulse. 88

74. Uses of the Monostable Multivibrator Used to generate a clean pulse of the correct height and duration for a digital system Used to turn circuits or external components on or off for a specific length of time. Used to generate delays. Can be cascaded to create a variety of sequential timing pulses. These pulses can allow you to time and sequence a number of related operations. 89

75. Monostable Multivibrator 90 Problem: In the monostable multivibrator of fig, R=100k Ω and the time delay T=100ms. Calculate the value of C ? Solution: T=1.1RC

76. Applications in Monostable Mode Missing Pulse Detector. Linear Ramp Generator. Frequency Divider. Pulse Width Modulation. 91

77. 1.Missing Pulse Detector Fig (a) : A missing Pulse Detector Monostable Circuit Fig (b) : Output of Missing Pulse Detector 92

78. Missing Pulse Detector- Description When input trigger is Low, emitter-base diode of Q is forwarded biased capacitor is clamped to 0.7v(of diode), output of timer is HIGH width of T o/p of timer > trigger pulse width. T=1.1RC select R & C such that T > trigger pulse. Output will be high during successive coming of input trigger pulse. If one of the input trigger pulse missing trigger i/p is HIGH, Q is cut off, timer acts as normal monostable state. It can be used for speed control and measurement. 93

79. 2.Linear Ramp Generator at pin 2 > V cc /3 Capacitor voltage at pin 6 94

80. 3.Frequency Divider Fig: Diagram of Frequency Divider Description: A continuously triggered monostable circuit when triggered by a square wave generator can be used as a frequency divider, if the timing interval is adjusted to be longer than the period of the triggering square wave input signal. The monostable multivibrator will be triggered by the first negative going edge of the square wave input but the output will remain HIGH(because of greater timing interval) for next negative going edge of the input square wave as shown fig. 95

81. 4.Pulse Width Modulation Fig a: Pulse Width Modulation Fig b: PWM Wave Forms 96

82. Pulse Width Modulation- Description The charging time of capacitor is entirely depend upon 2V cc /3. When capacitor voltage just reaches about 2V cc /3 output of the timer is coming from HIGH to Low level. We can control this charging time of the capacitor by adding continuously varying signal at the pin-5 of the 555 timer which is denoted as control voltage point. Now each time the capacitor voltage is compared control voltage according to the o/p pulse width change. So o/p pulse width is changing according to the signal applied to control voltage point. So the output is pulse width modulated form. 97

83. Pulse Width Modulation Practical Representation Fig: PWM & Wave forms 98

84. Astable Multivibrator Astable multivibrator is simply an oscillator. The astable multivibrator generates a continuous stream of rectangular off-on pulses that switch between two voltage levels. The frequency of the pulses and their duty cycle are dependent upon the RC network values. The capacitor C charges through the series resistors R A and R B with a time constant (R A + R B ) C. The capacitor discharges through R B with a time constant of R B C

85. Astable Multivibrator 100 1 – Ground 5 – FM Input (Tie to gnd via bypass cap) 2 – Trigger 6 – Threshold 3 – Output 7 – Discharge 4 – Reset (Set HIGH for normal operation) 8 – Voltage Supply (+5 to +15 V) Fig (a): Diagram of Astable Multvibrator

86. Astable Multivibrator 101 Fig (b): Functional Diagram of Astable Multivibrator using 555 Timer A 1 A 2 V 1 V 2 V T V C V o V A R 2 R 1 R 3 A 1 A 2 Q 1

87. Astable Multivibrator- Description 102 Connect external timing capacitor between trigger point (pin 2) and Ground. Split external timing resistor R into R A & R B , and connect their junction to discharge terminal (pin 7). Remove trigger input, monostable is converted to Astable multivibrator. This circuit has no stable state. The circuits changes its state alternately. Hence the operation is also called free running oscillator.

88. 103 Resistive voltage divider (equal resistors) sets threshold voltages for comparators V 1 = V TH = 2/3 V CC V 2 = V TL = 1/3 V CC Two Voltage Comparators For A 1 , if V + > V TH then R =HIGH For A 2 , if V - < V TL then S = HIGH RS FF If S = HIGH, then FF is SET, = LOW, Q 1 OFF, V OUT = HIGH If R = HIGH, then FF is RESET, = HIGH, Q 1 ON, V OUT = LOW Transistor Q 1 is used as a Switch Astable 555 Timer Block Diagram Contents

89. 104 Operation of a 555 Astable V CC V C (t) R A R B Assume initially that the capacitor is discharged. For A 1 , V + = V C = 0V and for A 2 , V - = V C = 0V, so R=LOW, S=HIGH, = LOW , Q1 OFF, V OUT = V CC Now as the capacitor charges through R A & R B , eventually V C > V TL so R=LOW & S=LOW. FF does not change state.

90. 105 Operation of a 555 Astable Continued…… V C (t) R B Q1 Once V C  V TH R=HIGH, S=LOW, = HIGH ,Q1 ON, V OUT = 0 Capacitor is now discharging through R B and Q 1 to ground. Meanwhile at FF, R=LOW & S=LOW since V C < V TH .

91. 106 Operation of a 555 Astable Continued….. Once V C < V TL R=LOW, S=HIGH, = LOW , Q1 OFF, V OUT = V CC Capacitor is now charging through R A & R B again. V CC V C (t) R A R B

92. Timing Diagram of a 555 Astable 107 V C (t) V TH V TL V OUT (t) T L T H t = 0 t = 0' t t 1 2 3

93. Astable Multivibrator- Analysis 108 Contd… . The capacitor voltage for a low pass RC circuit subjected to a step input of V cc volts is given by, The time t 1 taken by the circuit to change from 0 to 2V cc /3 is, The time t 2 to charge from 0 to v cc /3 is So the time to change from V cc /3 to 2V cc /3 is , So, for the given circuit, The output is low while the capacitor discharges from 2V cc /3 to V cc /3 and the voltage across the capacitor is given by, …… Charging time

94. Astable Multivibrator- Analysis 109 After solving, we get, t=0.69RC For the given circuit , Both R A and R B are in the charge path, but only R B is in the discharge path. The total time period, Frequency , Duty Cycle, …… Discharging time …….1.45 is Error Constant

95. Behavior of the Astable Multivibrator The astable multivibrator is simply an oscillator. The astable multivibrator generates a continuous stream of rectangular off-on pulses that switch between two voltage levels. The frequency of the pulses and their duty cycle are dependent upon the RC network values. The capacitor C charges through the series resistors R A and R B with a time constant (R A + R B )C. The capacitor discharges through R B with a time constant of R B C 110

96. Uses of the Astable Multivibrator Flashing LED’s Pulse Width Modulation Pulse Position Modulation Periodic Timers Uses include LED s, pulse generation, logic clocks, security alarms and so on. 111

97. Applications in Astable Mode 112 Square Generator FSK Generator Pulse Position Modulator

98. 1.Square Generator 113 To avoid excessive discharge current through Q 1 when R 1 =0 connect a diode across R 2 , place a variable R in place of R 1 . Charging path R 1 & D; Discharging path R 2 & pin 7. 10µF C 1 3 Fig: Square Wave Generator

99. 2. FSK Generator 114 Description: In digital data communication, binary code is transmitted by shifting a carrier frequency between two preset frequencies. This type of transmission is called Frequency Shift Keying (FSK) technique. Fig: FSK Generator Contd…..

100. FSK Generator 115 The frequency of the output wave form given by, When input digital is LOW, Q 1 is ON then R 3 parallel R 1 A 555 timer is astable mode can be used to generate FSK signal. When input digital data is HIGH, T 1 is OFF & 555 timer works as normal astable multivibrator.

101. 2. Pulse Position Modulator 116 Fig (a): Pulse position Modulator Fig (b): Output Wave Form of PPM Description: The pulse position modulator can be constructed by applying a modulating signal to pin 5 of a 555 timer connected for astable operation. The output pulse position varies with the modulating signal, since the threshold voltage and hence the time delay is varied. The output waveform that the frequency is varying leading to pulse position modulation.

102. Astable Multivibrator 117 Problem: In the astable multivibrator of fig, RA=2.2K Ω , RB=3.9K Ω and C=0.1µF. Determine the positive pulse width t H , negative pulse width t Low , and free-running frequency f o . Solution: Duty Cycle ,

103. Comparison of Multivibrator Circuits 118 Monostable Multivibrator Astable Multivibrator 1. It has only one stable state 1. There is no stable state. 2. Trigger is required for the operation to change the state. 2. Trigger is not required to change the state hence called free running. 3. Two comparators R and C are necessary with IC 555 to obtain the circuit. 3. Three components R A , R B and C are necessary with IC 555 to obtain the circuit. 4. The pulse width is given by T=1.1RC Seconds 4. The frequency is given by, 5. The frequency of operation is controlled by frequency of trigger pulses applied. 5. The frequency of operation is controlled by R A , R B & C. 6. The applications are timer, frequency divider, pulse width modulation etc… 6. The applications are square wave generator , flasher, voltage controlled oscillator, FSK Generator etc..

104.  Find the charging and discharging time of 0.5µF capacitor. Explanation: The time required to charge the capacitor is tHigh =0.69(RA+RB)C =0.69(10kΩ+5kΩ)x0.5µF =5ms. The time required to discharge the capacitor is tLow =0.69xRC =0.69x5kΩx0.5µF=2ms.

105. Astable multivibrator operating at 150Hz has a discharge time of 2.5m. Find the duty cycle of the circuit. Explanation: Given f=150Hz.Therefore,T=1/f =1/150 =6.67ms. ∴ Duty cycle, D%=( t Low /T) x 100% = (2.5ms/6.67ms)x100% = 37.5%.

106. Determine the frequency and duty cycle of a rectangular wave generator. Explanation: Frequency=1.45/(R A +R B )C . Where R A =100 Ω+50Ω=150Ω, R B =100 Ω+20Ω=120Ω. =>∴ f=1.45/((150+120)x0.1µF) = 53703Hz = 53.7kHz. Duty cycle, D% = [R B /(R A +R B )] x 100% = 120 Ω/(150Ω +120Ω) x 100% = 0.55×100% = 55%.

107. PHASE-LOCKED LOOPS 122 PLL

108. PHASE-LOCKED LOOPS- Introduction 123 The phase-locked loop is a negative feedback system in which the frequency of an internal oscillator (vco) is matched to the frequency of an external waveform with some Pre-defined phase difference. V d (t) PHASE COMPARATOR (PC) LOW PASS FILTER (LPF) VCO AMPLIFIER (A) V i (t ) V o (t) V p (t) (EXTERNAL R & C DETERMINES VCO FREQUENCY) Contd…..

109. PHASE-LOCKED LOOPS 124 Contd….. The phase comparator (phase detector) can be as simple as an exclusive-or gate (digital signals) or is a mixer (non-linear device - frequency multiplier) for analog signals. T he phase comparator generates an output voltage V p (t) (relates to the phase difference between external signal V i (t) and vco output V o (t) ). If the two frequencies are the same (with a pre-defined phase difference ) then V p (t ) = 0. If the two frequencies are not equal ( with various phase differences), then V p (t) = 0 and with frequency components about twice the input frequency. Phase Comparator:

110. PHASE-LOCKED LOOPS 125 Contd….. T he low pass filter removes these high frequency components and V d (t) is a variable dc voltage which is a function of the phase difference. Voltage Controlled Oscillator: The vco has a free-running frequency, f o , approximately equal to the input frequency. the vco frequency varies as a function of V d (t) The feedback loop tries to adjust the vco frequency so that: V i (t ) FREQUENCY = V o (t ) FREQUENCY THE VCO IS SYNCHRONIZED, OR LOCKED TO V i (t) Low pass filter:

111. PLL LOCK RANGE 126 Lock range is defined as the range of frequencies in the vicinity of the vco’s Natural frequency (free-running frequency) for which the pll can maintain lock with the input signal. The lock range is also called the tracking Range. The lock range is a function of the transfer functions of the pc, amplifier, and vco. Hold-in range: The hold-in range is equal to half the lock range The lowest frequency that the pll will track is called the lower lock limit. The highest frequency that the pll will track is called the upper lock limit Contd….. Lock range:

112. PLL LOCK RANGE 127

113. PLL CAPTURE RANGE 128 Contd…. Capture range is defined as the band of frequencies in the vicinity of f o where the pll can establish or acquire lock with an input range (also called the acquisition range). Capture range is a function of the BW of the lpf ( lpf BW capture range). Capture range is between 1.1 and 1.7 times the natural frequency of the vco . The pull-in range: The pull-in range is equal to half the capture range The lowest frequency that the pll can lock onto is called the lower capture limit CAPTURE RANGE:

114. PLL CAPTURE RANGE The highest frequency that the pll can lock onto is called the upper capture limit 129

115. 130 PLL LOCK/CAPTURE RANGE LOCK RANGE > CAPTURE RANGE

116. PLL- Basic Components 131 Phase detector: Transfer function: K Φ [ V/radians]. Implemented as: four quad multiplier, XOR gate , state machine . Voltage controlled oscillator (VCO ): Frequency is the first derivative of phase. Transfer function: K VCO /s [radians/(V•s )] Low pass filter: Removes high frequency components coming from the phase detector. Determines loop order and loop dynamics.

117. PLL OPERATION- Putting All Together 132 OPEN-LOOP GAIN:

118. PLL OPERATION 133 K d K f K a K o HOLD-IN RANGE

119. PLL 565 Pin Configuration 134

120. PLL- Example 135 Problem: f n = 200 kHz, f i = 210 kHz, K d = 0.2 V/rad, K f = 1, K a = 5 , K o = 20 kHz/V PLL OPEN-LOOP GAIN: VCO FREQUENCY CHANGE for LOCK: PLL OUTPUT VOLTAGE: Solution: Contd…..

121. PLL-Example 136 STATIC PHASE ERROR: HOLD-IN RANGE: LOCK RANGE: PHASE DETECTOR OUTPUT VOLTAGE :

122. Salient Features of 565 PLL 1. Operating frequency range =0.01Hz to 500KHz 2. Operating voltage range = ±6v to ± 12v 3. Input level required for tracking: 10mv rms min to 3v peak to peak max 4. Input impedance = 10k Ω typically. 5. Output sink current : 1mA typically. 6. Output source current: 10mA typically 7. Drift in VCO Centre frequency: 300 PPM/ ⁰c 8. Drift in VCO Centre frequency with supply voltage: 1.5 percent/V max 9. Triangle wave amplitude: 2.4 V pp at ± 6v supply voltage. 10. Square wave amplitude: 5.4 V pp at ± 6v supply voltage. 11. Bandwidth adjustment range: < ± 1 to ± 60% 137

123. PLL APPLICATIONS 138 Analog and digital modulation Frequency shift keying ( fsk ) decoders Am modulation / demodulation Fm modulation / demodulation Frequency synthesis Frequency generation

124. PLL APPLICATIONS 139 1.FM Demodulator: 2.FM Modulator:

125. Voltage Controlled Oscillator (VCO) 140 A voltage controlled oscillator is an oscillator circuit in which the frequency of oscillations can be controlled by an externally applied voltage

126. VCO Operation 141

127. VCO Analysis 142 Contd…..

128. VCO Analysis 143

129. Features of VCO 144

130. Applications of VCO 145 The various applications of VCO are: 1. Frequency Modulation. 2. Signal Generation (Triangular or Square Wave) 3. Function Generation. 4. Frequency Shift Keying i.e. FSK demodulator. 5. In frequency multipliers. 6. Tone Generation.

131. VCO 146 Contd….

132. VCO 147

133. Thank You 148