Pulse and Digital Circuits course file

Syllabus copy

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

II Year B.Tech. ECE -II Sem T P C 4+1* 0 4

Pulse and Digital Circuits (PDC)

UNIT I

LINEAR WAVE SHAPING

High pass and low pass RC circuits and their response for sinusoidal, step, pulse, square and ramp inputs. High pass RC network as differentiator, Low pass RC network as an integrator, Attenuators and its application as a CRO probe, RL and RLC circuits and their response for step input, Ringing circuit.

UNIT II

NON-LINEAR WAVE SHAPING

Diode clippers, Transistor clippers, clipping at two independent levels, Comparators, Applications of Voltage Comparators, Clamping operation, Clamping circuit taking Source and Diode resistance into account, Clamping circuit theorem, Practical clamping circuits, Effect of diode characteristics on clamping Voltage, Synchronized Clamping.

UNITIII

SWITCHING CHARACTERISTICS OF DEVICES

Diode as a switch, Piecewise linear diode characteristics, Diode Switching times, Transistor as a Switch, Break down voltages, Transistor in saturation, Temperature variation of saturation parameters, Transistor-switching times, Silicon Controlled switch circuits.

SAMPLING GATES

Basic operating principles of sampling gates, Unidirectional and Bi-directional sampling gates, Four Diode Sampling Gate, Reduction of pedestal in Gate Circuits, Six Diode Gate, Applications of sampling gates.

UNIT IV

MULTIVIBRATORS

Analysis and Design of Bistable, Monostable, Astable Multivibrators and Schmitt trigger using transistors.

TIME BASE GENERATORS

General features of a time base signal, methods of generating time base waveform, Miller and Bootstrap time base generators – Basic Principles, Transistor Miller Time Base Generator, Transistor Bootstrap Time Base Generator, Current Time Base Generators, Methods of Linearity improvement.

UNIT V

SYNCHRONIZATION AND FREQUENCY DIVISION

Pulse Synchronization of Relaxation Devices, Frequency division in Sweep Circuit, Stability of Relaxation devices, Astable Relaxation circuits, Monost Transistors able relaxation circuits, Synchronization of a sweep circuit with symmetrical signals, Sine wave frequency division with a sweep circuit, A Sinusoidal Divider using Regeneration and Modulation

REALIZATION OF LOGIC GATES USING DIODES & TRANSISTORS

AND, OR and NOT gates using Diodes and Transistors, DCTL, RTL, DTL, TTL and CML Logic Families and its Comparison.

TEXT BOOKS

Millman’s Pulse, Digital and Switching Waveforms - J. Millman, H. Taub and Mothiki S Prakash Rao, 2nd ed. 2008, TMH

Solid State Pulse circuits - David A. Bell, , 4th Edn.., 2002 . PHI

REFERENCES

Pulse and Digital Circuits –A. Anand Kumar, 205, PHI.

Fundamentals of Pulse and digital Circuits – Ronald J Tocci, 3 ed., 2008

Pulse and digital Circuits – Motheki S Prakash Rao, 2006, TMH.

Wave Generation and Shaping - L. Strauss.

** Course objectives and Outcomes**

COURSE OBJECTIVES:

The main objectives of this course are:

CO 1: Understand the applications of diode as Integrator, differentiator, clippers, clamper circuits.

CO 2: Learn various switching devices such as diode, transistor, SCR.

CO 3: Difference between logic gates and sampling gates.

CO 4: Design Multivibrators for various applications, synchronization techniques and sweep circuits.

CO 5: Realize logic gates using diodes and transistors.

COURSE OUTCOMES:

At the end of the course, the student will be able to:

CO1: Understand the applications of diode as Integrator, differentiator, clippers, clamper circuits.

CO2: Learn various switching devices such as diode, transistor, SCR.

CO3: Difference between logic gates and sampling gates

CO4: Design Multivibrators for various applications, synchronization techniques and sweep circuits

CO5: Realize logic gates using diodes and transistors.

** Brief notes on the importance of the course and how it fits into the curriculum**

This is the basic course for electronic engineers to understand the behavior of active and passive devices and circuit configurations used for the generation and processing of pulse, digital and switching waveforms. These non-sinusoidal signals find extensive application in fields such as computers, control systems, counting and timing systems, data-processing systems, digital instrumentation ,pulse communication, radar, telemetry, television and in many areas of experimental research. By studying this course students can understand better the courses in their future semesters such as control systems, IC Applications and Microprocessor and Microcontrollers.

** Prerequisites if any**

The following subject’s knowledge is required for understanding the PDC course.

1.Electronic Devices and Circuits 2.Electric Circuits 3. STLD.

** Instructional Learning Outcomes**

Instructional objectives and learning outcomes

Instructional Unit-wise objectives

To study and analyze linear wave shaping circuits such as R-C and R-L-C transient circuits .

To study and analyze non-linear wave shaping circuits such as clippers, clampers and comparators.

To study the switching characteristics of diode, transistor and SCR.

To study the operating principles of various sampling gates.

To design and analyze various multivibrators using transistors.

To design and analyze time base generators

To design and analyze various sweep circuits.

To discuss and realize logic gates using diodes and transistors

**Instructional objectives**

Unit 1: Linear Wave Shaping

To study about linear wave shaping circuits and Non-linear wave shaping circuits for different input signals.

To describe the application of a low pass circuit as an integrator.

To understand the principles of working of uncompensated and compensated attenuators and the operation of the attenuator circuit in CRO probe.

To derive the response of high pass RC, RL and RLC circuits to different types of inputs like Sinusoidal, pulse, step, square, ramp and exponential inputs.

To describe the application of high pass circuit as Differentiator.

To understand the operation of the ringing circuit.

Unit 2: Non-linear Wave Shaping

To study the principle of operation of various series and shunt clipping circuits

To study about diode comparators and double differentiators as amplitude comparators and it’s applications .

To study the principle of operation of various clamping circuits and verify the clamping circuit theorem.

To derive the necessary relations to plot steady state output.

To describe the effect of diode characteristics on the clamping voltage.

To describe synchronized clamping.

Unit 3: Switching characteristics of Devices:

To study the principle of operation of diodes and transistors as switches.

To study the effect of inter-electrode capacitances on switching times.

To study the switching times of devices and derive the necessary relations.

To study the temperature dependence of the transistor on various parameters.

To understand the use of transistor switch as latch.

To realize the use of transistor switches with inductive and capacitive loads.

To study the principle of operation of switching circuits using SCS.

To understand the working of unidirectional and bidirectional sampling gates and their variations

To understand the working of sampling gates using Diodes (two, four and six) and transistors.

To realize the applications of sampling gates in sampling scope

To derive a choppers stabilized amplifier using sampling gates

Unit 4: Multivibratos

To study the principle of operation of the multivibrators.

To study the applications of multivibrators.

To realize the need for a commutating condenser in a monostable multivibrator and bistable multivibrator.

To study the principle of operation of Time base generators

To study the features of the Time base signal.

To study the principle of operation of Miller Time base

To study the principle of operation of Bootstrap Time base generator

To study the principle of operation of UJT saw tooth generator.

To study the principle of operation of time base generators using Op-Amps.

Unit 5: Synchronization and frequency division

To study the operation of synchronization and frequency division circuits..

To describe the methods of achieving frequency synchronization and division in other relaxation circuits like astable and monostable multivibratos

To realize the circuit that eliminates jitter in a relaxation divider

To understand the principle of operation of the circuits that achieve frequency synchronization and division using symmetric circuits

Realization of logic gates using Diodes and Transistors

To understand the principle of operation of basic logic gates like AND, OR and NOT gates

To implement these gates using Diodes and Transistors

To understand the various logic families like DCTL, RTL, DTL, TTL and CML and their comparison

To implement simple Boolean functions using different logic families.

**Student Learning Outcomes**

Unit 1: Linear Wave Shaping

After completing this unit, the students are able to

Design linear wave shaping circuits using linear elements like R C and L.

Derive the expressions and plot the response of low pass RC circuits to different types of inputs namely sinusoidal, step, pulse, square-wave, exponential and ramp.

Describe the application of a low pass circuit as an integrator.

Understand the principles of working of uncompensated and compensated attenuators and the operation of the attenuator circuit in CRO probe.

Derive the response of high pass RC and RL circuits to different types of inputs like Sinusoidal, pulse, step, square, ramp and exponential inputs.

Describe the application of high pass circuit as Differentiator.

Understand the operation of the ringing circuit.

Find the response of RL and RLC circuits to step input.

Unit 2: Non-linear Wave Shaping

After completing this unit, the students are able to

Design various series and shunt clipping circuits and their combinations.

Understand the principle of operation of two level emitter coupled transistor clippers and noise clippers

Describe simple diode comparators and double differentiators as amplitude comparators.

Explain the applications of comparators.

Design various clamping circuits and verify the clamping circuit theorem.

Derive the necessary relations to plot steady state output.

Describe the effect of diode characteristics on the clamping voltage.

Describe synchronized clamping.

State and derive the clamping circuit theorem

Unit 3: Switching characteristics of Devices and sampling gates

After completing this unit, the students are able to

Use diodes and transistors as switches.

Describe the effect of inter-electrode capacitances on switching times.

Describe the switching times of devices and derive the necessary relations.

Describe the temperature dependence of the transistor on various parameters.

Understand the use of transistor switch as latch.

Realize the use of transistor switches with inductive and capacitive loads.

Design switching circuits using SCS.

Understand the working of unidirectional and bidirectional sampling gates and their variations

Design sampling gates using Diodes (two, four and six) and transistors.

Describe the output by adjusting the levels of the control signal

Realize the applications of sampling gates in sampling scope

Derive a choppers stabilized amplifier using sampling gates

Unit 4: Multivibratos & Time Base Generators

After completing this unit, the students are able to

Explain the principle of operation of the multivibrators.

Analyze and design Bistable, Monostable and Astable multivibrators and able to calculate and frequency / pulse width of the generated signal.

Plot the waveforms at various points in the circuit.

Describe the emitter coupled astable multivibrators

Use an astable multivibrator for applications such as voltage to frequency converter and frequency modulator

Understand the working of emitter coupled monostable multivibrator

Realize the need for a commutating condenser in a monostable multivibrator and bistable multivibrator.

Realize the application of a monostable multivibrator as a voltage to time converter

Analyze fixed bias and self bias bistable multivibrators

Analyze and design emitter coupled bistable multivibrator, also called Schmitt trigger

Describe the applications of bistable multivibrator circuits.

Able to design different types of Time base generators

Explain the features of the Time base signal.

Design Miller Time base Generator and explain the principle of operation.

Design Bootstrap Time base generator and explain the principle of operation.

Design UJT saw tooth generator.

Design current Time base generator.

Design time base generators using Op-Amps.

Unit 5: Synchronization and frequency division & Realization of logic gates using Diodes and Transistors

After completing this unit, the students are able to

Understand the principle of frequency synchronization using exponential methods like UJT relaxation oscillator circuit.

Describe the methods of achieving frequency synchronization and division in other relaxation circuits like astable and monostable multivibratos

Realize the circuit that eliminates jitter in a relaxation divider

Understand the principle of operation of the circuits that achieve frequency synchronization and division using symmetric circuits

Understand the principle of operation of basic logic gates like AND, OR and NOT gates

Implement these gates using Diodes and Transistors

Understand the various logic families like DCTL, RTL, DTL, TTL and CML and their comparison

Able to implement simple Boolean functions using different logic famili**es.**

** Detailed notes**

UNIT- I

1. INTRODUCTION

Linear network: Circuit designed with linear elements Resistors, Capacitor and Inductors is called linear network.

Linear elements :Resistor ,capacitors and inductors are called linear elements because the current passing to the elements is proportional to the applied voltage, there is a linear relation between current and voltage.

When a sinusoidal signal applied to linear network the output also sinusoidal in nature but a non-sinusoidal signal response is different.

When devices such as diodes, bipolar junction transistors (BJTs) and field-effect transistors (FETs) are used in amplifiers, oscillators, rectifiers and other such applications, these devices are used either as linear or nonlinear circuit elements, for which they have to be used in a limited range of the transfer characteristic (defines the relation between the input and the output). If the operation goes beyond the linear region of the transfer characteristic, unwanted frequencies called harmonics—integer multiples of the fundamental frequency—appear in the output of the circuit. However, when the signal swing is large, as in power amplifiers, the output is invariably distorted. This distortion can be minimized using a push–pull configuration as this arrangement eliminates even harmonics. To analyze a given circuit comprising such devices, it is possible to replace the device by its equivalent circuit. To simplify the analysis, it is necessary, at times, to piece-wise linearize the transfer characteristic so that the behavior of the device can be predicted in that limited region of operation.

These devices—diodes, transistors, FETs and so on—can also be used as switches in switching applications by driving the device into the OFF state in one case and by driving the device into the ON state in the other case. However, the inter-electrode capacitances limit the switching speed. Operational amplifiers and negative resistance devices also find applications in pulse and switching circuits. This chapter presents a brief overview of the fundamentals to facilitate comprehension of the principles of pulse and switching circuits.

1.2 CURRENT AND VOLTAGE SOURCES

Normally either ac or dc sources are used as current and voltage sources. A source can be either a voltage source (Thévenin source) or a current source (Norton source). An ideal voltage source should have zero internal resistance so that when current is drawn from the source, there is no voltage drop across the internal resistance of the source and the entire source voltage is available at its output terminals. Similarly, in a current source, no appreciable amount of current should flow through the internal resistance of the generator and the entire source current should flow through the load. For this, the internal resistance of the current source should ideally be infinity.

Figure 1.1(a) shows a practical voltage or Thévenin source and Fig. 1.1(b) a current or Norton source. It is possible to convert a Thévenin source into a Norton source and vice versa. To convert the Thévenin source [represented in Fig. 1.1(a)] into a Norton source [see Fig. 1.1(b)], we calculate the current (I) in the circuit using the relation I = V/Rs, where RS is the internal resistance in shunt with the current source I. Similarly, to convert the Norton source into a Thévenin source as shown in Fig. 1.1(a), we calculate the voltage (V) across RS as V = IRS, where RS is its internal resistance in series with the source V. Consider the single-loop network using a voltage source, as shown in Fig. 1.2. From Fig. 1.2:

FIGURE 1.1(a) Thévenin or voltage source

FIGURE 1.1(b) Norton or current source

The single-loop network shown in Fig. 1.2 is analyzed using Ohm’s law. In this circuit, R1 andR2 comprise a potential divider. So, Eq. (1.1) is used to calculate VR2 directly instead of first calculating the current and then the voltage.

However, to analyze a network that has more than one loop, i.e., calculate the current in a given loop or voltage across the given branch, two basic network theorems—Kirchoff’s voltage law and Kirchoff’s current law—are used.

FIGURE 1.2 A single-loop network

Linear systems are those that satisfy both homogeneity and additivity.

(i) Homogeneity: Let x be the input to a linear system and y the corresponding output, as shown in Fig. 2.1. If the input is doubled (2x), then the output is also doubled (2y). In general, a system is said to exhibit homogeneity if, for the input nx to the system, the corresponding output is ny (where n is an integer). Thus, a linear system enables us to predict the output.

FIGURE 2.1 A linear system

(ii) Additivity: For two input signals x1 and x2 applied to a linear system, let y1 and y2 be the corresponding output signals. Further, if (x1 + x2) is the input to the linear system and (y1+ y2) the corresponding output, it means that the measured response will just be the sum of its responses to each of the inputs presented separately. This property is called additivity. Homogeneity and additivity, taken together, comprise the principle of superposition.

(iii) Shift invariance: Let an input x be applied to a linear system at time t1. If the same input is applied at a different time instant t2, the two outputs should be the same except for the corresponding shift in time. A linear system that exhibits this property is called a shift-invariant linear system. All linear systems are not necessarily shift invariant.

A circuit employing linear circuit components, namely, R, L and C can be termed a linear circuit. When a sinusoidal signal is applied to either RC or RL circuits, the shape of the signal is preserved at the output, with a change in only the amplitude and the phase. However, when a non-sinusoidal signal is transmitted through a linear network, the form of the output signal is altered. The process by which the shape of a non-sinusoidal signal passed through a linear network is altered is called linear waveshaping. We study the response of high-pass RC andRL circuits to different types of inputs in the following sections.

2.2 HIGH-PASS CIRCUITS

Figures 2.2(a) and 2.2(b) represent high-pass RC and RL circuits, respectively.

FIGURE 2.2(a) A high-pass RC circuit

Consider the high-pass RC circuit shown in Fig. 2.2(a). The capacitor offers a low reactance (XC = 1/jωC) as the frequency increases; hence, the output is large. Consequently, high-frequency signals are passed to the output with negligible attenuation whereas, at low frequencies, due to the large reactance offered by the condenser, the output signal is small. Similarly, in the circuit shown in Fig. 2.2(b), the inductive reactance XL (= jωL) increases with frequency, leading to a large output. At low frequencies, the reactance of the inductor XLbecomes small; hence, the output is small. Therefore, the circuits in Figs. 2.2(a) and (b) are called high-pass circuits. In the case of L, XL is directly proportional to frequency; and in the case of C, XC is inversely proportional to frequency. C and L may therefore be called inverse circuit elements. Thus, in the high-pass circuit of Fig. 2.2(a), C appears as a series element; and in the high-pass circuit of Fig. 2.2(b), L appears as a shunt element. The time constant τ is given by: τ = RC = L/R.

FIGURE 2.2(b) A high-pass RL circuit

What will be the response if different types of inputs such as sinusoidal, step, pulse, square wave, exponential and ramp are applied to a high-pass circuit?

LOW PASS RC CIRCUITS

A low-pass circuit is one which gives an appreciable output for low frequencies and zero or negligible output for high frequencies. In this chapter, we essentially consider low-pass RCand RL circuits and their responses to different types of inputs. Also, we study attenuators that reduce the magnitude of the signal to the desired level. Attenuators which give an output that is independent of frequency are studied. One application of such a circuit is as a CRO probe. Further, the response of the RLC circuit to step input is considered and its output under various conditions such as under-damped, critically damped and over-damped conditions is presented. The application of an RLC circuit as a ringing circuit is also considered.

3.2 LOW-PASS CIRCUITS

Low-pass circuits derive their name from the fact that the output of these circuits is larger for lower frequencies and vice-versa. Figures 3.1(a) and (b) represent a low-pass RC circuit and a low-pass RL circuit, respectively.

In the RC circuit, shown in Fig. 3.1(a), at low frequencies, the reactance of C is large and decreases with increasing frequency. Hence, the output is smaller for higher frequencies and vice-versa. Similarly, in the RL circuit shown in Fig. 3.1(b), the inductive reactance is small for low frequencies and hence, the output is large at low frequencies. As the frequency increases, the inductive reactance increases; hence, the output decreases. Therefore, these circuits are called low-pass circuits. Let us consider the response of these low-pass circuits to different types of inputs.

FIGURE 3.1(a) A low-pass RC circuit; and (b) a low-pass RL circuit

3.2.1 The Response of a Low-pass RC Circuit to Sinusoidal Input

For the circuit given in Fig. 3.1(a), if a sinusoidal signal is applied as the input, the output vo is given by the relation:

where, ω2 = 1/CR = 1/τ. From Eq. (3.1), the phase shift θ the signal undergoes is given as:

θ = tan−1(ω/ω2) = tan−1(τ/T)

Figure 3.2(a) shows a typical frequency vs. gain characteristic. Hence, f2 is the upper half-power frequency. At ω = ω2,

Figure 3.2(b) shows the variation of gain with frequency for different values of τ. As is evident from the figure, the half-power frequency, f2, increases with the decreasing values of τ, the time constant. The sinusoidal signal undergoes a change only in the amplitude but its shape remains preserved.

Figure 3.2(c) shows the variation of θ as a function of frequency. As (τ/T) becomes large, θapproaches 90°. This characteristic can be appreciated when we talk about an integrator later.

Non-sinusoidal Waveforms

Any waveform whose shape is different from that of sinusoidal wave is called a non-sinusoidal waveform. For example pulse square, symmetrical square triangular and saw-tooth are non- sinusoidal waves. When one quantity is dependent upon some other variable quantity varies with respect to others. In case of electronic circuits function usually means that current or voltage varies with respect to time. All these waveform are the function voltage or current with respect to time such as step, ramp and exponential are explained as under:

Step Function:

A step function shown in Fig. 1(a), makes an instantaneous jump from one steady value to

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another steady value. A step means an instantaneous change in level.

In such a case, voltage maintains zero value for all times t < 0 and maintains the value V for all times t > 0 is called a step voltage.

Ramp Function:

A ramp function shown in Figure 1(b) isone that voltage increases or decreases linearly with time. Slope of the function is constant. In such a case, voltage is zero for t < 0 and increases linearly with time for t > 0.it is linear change in function with respect to time called a ramp.

Exponential Function:

An exponential function is a function of voltage that increases or decreases exponentially with time. In such a case, voltage is zero for t < 0 and increases nonlinearly with time t called an exponential voltage. The terms used for exponential are ex and e-x. Exponential quantity gap is known as an exponential curve.

Different Types of Waveforms

Let us now discus the pulse square, symmetrical square, Triangular and saw-tooth waveforms.

Pulse waveform

Figure 2(a) shows the waveform of an ideal pulse. The pulse amplitude is V and the pulse duration is tp. It is evident from Fig. 2(b) and (c) that the pulse may be considered as the sum of the step voltage +V, whose discontinuity occur at t = 0 and a step voltage —V, whose discontinuity occurs at t = tp. The pulse waveform find extensive use is almost every field of electronics such as communication, computer, defense equipment, etc.

2 LI NEAR WAVE SHAPI NG & DI FFERENT TYPES O F WAVEFO RM S

Square waveform

A waveform which maintains itself at one constant voltage level V1 for a time T1 and at another constant level V2 for time T2 and is repetitive with a period T = T1 + T2 as shown in Fig. 2 (a) is called a square waveform. The square waveform is used in digital electronic circuits, radars and as synchronizing pulses in television.

Symmetrical square waveform

A square waveform for which T1 = T2 = T/2 as shown in Fig. 3(b) is called a square waveform. It may be noted that because of the symmetry, the voltage levels V1 and V2 are equal and

opposite V1 = —V2. The symmetrical square waveform is very useful in digital electronic circuits.

T triangular waveform

A waveform which increase linearly with time to a voltage level V for a time T/2 and then decreases linearly to its original level for a time T/2 and is repetitive with a period T as shown in Fig. 4(a) is called triangular waveform. It may be noted from this figure, that a triangular wave may be considered as the sum of ramp voltage, which increases at a rate of 2V/T for a time T/2 and the ramp voltage which decreases at a rate of —2V/T for the remaining time T/2. The triangular waveform is used in scanning circuits, where a uniform left-to-right scan is required as

In computer displays. These are also used in timing circuit for electronics applications.

Saw tooth waveform

A waveform increases linearly with time to a voltage level V for a time T and then changes abruptly to its original level and is repetitive as shown in Fig. 4(b) is called saw tooth waveform. It is also called sweep waveform or time-base waveform. The saw tooth waveform is used in the scanning circuit of cathode ray oscilloscopes and televisions.

Differences between Low-pass and High-pass circuit showing circuit diagrams.

Low-Pass Circuit

High-Pass Circuits

(i) In a low pass circuit is taken across the capacitor.

(ii) It passes low frequency signals and blocks the high frequency signals.

(iii)

(iv) Current through the circuit is given as:

(v) Output voltage is given as

(vi) Magnitude of amplitude is given by:

Where = cut off frequency.

(vii) Phase angle:

(viii) Frequency response curve:

(ix) At very high frequencies the capacitive reactance become very small so 0/p becomes equal to i/p.

(x) R-C circuits with time constant larger than time period of the input signal are used as by-pass capacitors.

(xi) It is used is generation of triangular and ramp waveforms.

(i) In high pass RC data, the O/P voltage is taken across the resistance.

(ii) It blocks P attenuates low frequencies, but allows high frequency signals to pass through it.

(iii)

(iv) Current through the circuit is given as:

(v) Output voltage is given as:

(vi) Magnitude amplitude is given by:

where = frequency at which = R.

(vii) Phase angle:

(viii) Frequency response curve:

(ix) With the increase in frequency the reactance of the capacitor decreases and therefore, the output will be zero and gain increase.

(x) R-C circuits with RC >> T is employed in R-C coupling of amplifiers where distortion and differentiation of waveform is to be avoided.

(xi) R-C circuits with RC << T is employed generate pipes for triggering electronic circuit such as flip-flop multivibrators.

**Related Links**

Pulse and Digital Circuits course file