Class Physics English Volume

V o F C L (b) Figure . (a) Block diagram of an oscillator (b) Tank circuit iii) Feedback network The circuit used to feed a portion of the output back to the input is called the feedback network. If the portion of the output fed to the input is in phase with the input, then the magnitude of the input signal increases. This process is called positive feedback which is necessary for sustained oscillations.

Working The tank circuit generates electrical oscillations and acts as the AC input source to the transistor amplifier. Amplifier amplifies frequency as shown in Figure . (a). Non- sinusoidal oscillators generate complex, non-sinusoidal waveforms like square- wave, triangular-wave and sawtooth-wave as shown in Figure .

(b), (c), (d). t (d) t (a) t (b) t (C) Figure . (a) Sinusoidal waveform (b) Square waveform (c) Triangular waveform (d)Sawtooth waveform Sinusoidal oscillations are of two types: Damped and undamped. If the amplitude of the electrical oscillations decreases with time due to energy loss, it is called damped oscillations as shown in Figure .

(a). On the other hand, the amplitude of the electrical oscillations remains constant with time in undamped oscillations as shown in Figure . (b). t (a) t (b) Figure .

(a) Damped oscillations (b) Undamped oscillations Transistor oscillator An oscillator circuit consists of three components. They are i) tank circuit ii) amplifier and iii) feedback network. The block diagram is shown in Figure . (a).

Unit electronics and Communication · to generate audio tones · to generate clock signal in digital circuits · as sweep circuits in TV sets and CRO EXAMPLE . Calculate the range of the variable capacitor that is to be used in a tuned-collector oscillator which has a fixed inductance of μH. The frequency band is from kHz to kHz. Solution Resonant frequency, LC π On simplifying, we get C f L π i) When frequency = kHz, C = = pF ii) When frequency = kHz, C = = pF Therefore, the capacitor range is from to pF.

DIGITAL ELECTRONICS Digital Electronics is the branch of electronics which deals with digital signals. It is increasingly used in numerous applications ranging from high end processor circuits to miniature circuits for signal processing, communication etc. Digital signals are preferred over analog signals due to their better performance, accuracy, speed, flexibility and immunity to noise. .

the input AC signal. In practical oscillator circuits, there is loss of some energy in inductor coils and capacitors due to electrical resistance. A small amount of energy is used up in overcoming these losses during every cycle of charging and discharging of the capacitor. Due to this, the amplitude of the oscillations decreases gradually.

Hence, the tank circuit produces damped electrical oscillations. In order to produce undamped oscillations, a positive feedback is provided from output to input by feedback network. This compensates energy loss in tank circuit. The frequency of oscillations is determined by the values of L and C and is given by LC π ( .

) Barkhausen conditions for sustained oscillations The following conditions called Barkhausen conditions should be satisfied for sustained oscillations in the oscillator. · There should be positive feedback. · The loop phase shift must be or integral multiples of 2π. · The loop gain must be unity.

That is, A β = . Here, A is the voltage gain of the amplifier, b is the feedback ratio (the fraction of the output that is fed back to the input). There are different types of oscillator circuits based on the different types of tank circuits. Examples: Hartley oscillator, Colpitts oscillator, Phase shift oscillator and Crystal oscillator.

Applications of oscillators Transistor oscillators are used · to generate periodic sinusoidal or non sinusoidal wave forms · to generate RF carriers Unit electronics and Communication . . Logic gates A logic gate is an electronic circuit whose function is based on digital signals. They are binary in nature.

The logic gates are considered as the basic building blocks of most of the digital systems. They have one output with one or more inputs. There are three types of basic logic gates: AND, OR, and NOT. The other logic gates are Ex-OR, NAND, and NOR.

They can be constructed from the basic logic gates. Digital electronics deals with logical operations. The variables are called logical variables. The operators like logical addition (+) and logical multiplication ( .

) are called logical operators. When the logical operators (+, .) operate on logical variables (A, B), they give logical constant (Y). The equation that represents this operation is called logical statement. For example, Logical operator: + Logical variable: A, B Logical constant: Y Logical statement: Y = A + B The possible combinations of inputs and the corresponding output are given in the form of a table called truth table.

The circuits which perform the basic logical operations such as logical addition, multiplication and inversion are discussed below. AND gate Circuit symbol The circuit symbol of a two input AND gate is shown in Figure . (a). A and B are inputs and Y is the output.

It is a logic gate and hence A , B , and Y can have the value of either or . . . Analog and Digital Signals There are different types of signals used in Electronics.

They are (i) Analog signals and (ii) Digital signals. An analog signal is a continuously varying voltage or current with respect to time. Such signals are employed in rectifying circuits and transistor amplifier circuits. Digital signals are signals which contain only discrete values of voltages.

Digital signals need two states: switch ON and OFF. ON is considered as one state and OFF is considered as the other state. It can also be defined as high (ON) or low (OFF) state, closed (ON) or open (OFF). These high and low states are defined using binary numbers or in Boolean Algebra.

The state represents the terms: circuit on, high voltage, a closed switch. Similarly a state represents circuit off, low voltage or an open switch. Positive and Negative Logic In digital systems, there exists two voltage levels: 5V (high) and 0V (low). In a positive logic system; a binary stands for 5V and stands for 0V while in negative logic system, stands for 0V and stands for 5V as shown in Figure .

. (a) (b) +5v 0v Postive logic +5v 0v Negative logic Figure . (a) Positive logic (b) Negative logic Unit electronics and Communication Boolean equation: Y It performs logical addition and is different from arithmetic addition. Logic operation The output of OR gate is high (logic state) when either of the inputs or both are high.

The truth table of OR gate is shown in Figure . (b). NOT gate Circuit symbol The circuit symbol of NOT gate is shown in Figure . (a).

A is the input and Y is the output. Y NOT (a) Inputs Output Y= A (b) Figure . (a) NOT gate (b) Truth table Boolean equation: Y Logic operation The output is the complement of the input. It is represented with an overbar.

It is also called as inverter. The truth table infers that the output Y is when input A is and vice versa. The truth table of NOT is shown in Figure . (b).

NAND gate Circuit symbol The circuit symbol of NAND gate is shown in Figure . (a). A and B are inputs and Y is the output. Y AND (a) Inputs Output Y=A.B (b) Figure .

(a) Two input AND gate (b) Truth table Boolean equation: Y A B It performs logical multiplication and is different from arithmetic multiplication. Logic operation The output of AND gate is high only when all the inputs are high. In the rest of the cases, the output is low. It is represented in the truth table (Figure .

(b)). OR gate Circuit Symbol The circuit symbol of a two input OR gate is shown in Figure . (a). A and B are inputs and Y is the output.

Y OR (a) (b) Figure . (a) Two input OR gate (b) Truth table Inputs Output Y= A+B Unit electronics and Communication Y NOR Y NOT OR Z (a) Inputs Output (OR) Output (NOR) Z = A+B Y = A+B (b) Figure . (a) NOR gate (b) Truth table Ex-OR gate Circuit symbol The circuit symbol of Ex-OR gate is shown in Figure . (a).

A and B are inputs and Y is the output. The Ex-OR operation is denoted as ⊕ . Boolean equation Y A B A B Y ⊕ Logic operation The output is high only when either of the two inputs is high. In the case of an Ex-OR gate with more than two inputs, the output will be high when odd number of inputs are high.

The truth table of Ex-OR gate is shown in Figure . (b). Y (a) Inputs Output (Ex-OR) Y ⊕ (b) Figure . (a) Ex-OR gate (b) Truth table Y NAND Y AND NOT Z (a) Inputs Output (AND) Output (NAND) Z = A.B Y = A.B (b) Figure .

(a)Two input NAND gate (b) Truth table Boolean equation: Y A B Logic operation The output Y equals the complement of AND operation. The circuit is an AND gate followed by a NOT gate. Therefore, it is summarized as NAND. The output is at logic zero only when all the inputs are high.

The rest of the cases, the output is high (Logic state). The truth table of NAND gate is shown in Figure . (b). NOR gate Circuit symbol The circuit symbol of NOR gate is shown in Figure .

(a). A and B are inputs and Y is the output. Boolean equation: Y Logic operation The output Y equals the complement of OR operation ( A OR B ). The circuit is an OR gate followed by a NOT gate and is summarized as NOR.

The output is high when all the inputs are low. The output is low for all other combinations of inputs. The truth table of NOR gate is shown in Figure . (b).

Unit electronics and Communication BOOLEAN ALGEBRA Boolean Algebra is basically a choice between two options (i) yes or no (ii) high or low. These two options in Boolean algebra are represented by binary numbers or . It is a concept that relates logic and mathematics which is a century old, made up by George Boole in . Later the importance of Boolean algebra was realized in the design of computer circuits.

Today we are in a digital world and most of the comforts that we experience is due to digitization with the foundation based on Boolean algebra. The concept of high ( ) and low ( ) is not a new one. In fact, it was applied in telephone switching circuits by Shannon in . Laws of Boolean Algebra The NOT, OR and AND operations discussed in section .

. are the Boolean operations. The results of these operations can be summarised as: Complement law Y Y = = Y = = The complement law can be realised as . NAND and NOR gates are known as universal gates because any other logic gate can be made from NAND or NOR gates.

Note EXAMPLE . What is the output Y in the following circuit, when all the three inputs A , B , and C are first and then ? X C Y P Q Solution C X = A . B Y X C EXAMPLE .

In the combination of the following gates, write the Boolean equation for output Y in terms of inputs A and B . Y Solution The output at the st AND gate: AB The output at the nd AND gate: AB The output at the OR gate: Y A B A B Unit electronics and Communication The above laws are used to simplify complicated expressions and to simplify the logic circuitry. DE MORGAN’S THEOREM . .

De Morgan’s First Theorem Statement The first theorem states that the complement of the sum of two logical inputs is equal to the product of its complements. Proof The Boolean equation for NOR gate is Y The Boolean equation for a bubbled AND gate is Y A B Both cases generate same outputs for same inputs. It can be verified using the following truth table. A+B A+B A .

B From the above truth table, we can conclude A A B Thus De Morgan’s first theorem is proved. Hence, a NOR gate is equal to a bubbled AND gate. The corresponding logic circuit diagram is shown in Figure . .

. OR laws Y = A+B Y = + = Y = + = Y = + = Y = + = The OR laws can be realised as st law A + = A nd law A + = rd law A + A = A th law A + A = AND laws Y = A.B Y = . = Y = . = Y = .

= Y = . = The AND laws can be realised as st law A . = nd law A . = A rd law A .

A = A th law A . A = The Boolean operations obey the following laws. Commutative laws A + B = B + A A . B = B .

A Associative laws A + (B + C) = (A + B) + C A . (B . C) = (A .B) . C Distributive laws A( B + C) = AB + AC A + BC = (A + B) (A + C) Unit electronics and Communication EXAMPLE .

Prove the Boolean identity AC + ABC = AC and give its circuit description. Solution Step : AC ( + B ) = AC . [OR law- ] Step : AC . = AC [AND law – ] Therefore, AC + ABC = AC Thus the Boolean identity is proved.

Circuit description: C C AC C Y=AC Y=AC + ABC ABC . . Integrated Chips An integrated circuit is also referred as an IC or a chip or a microchip (Figure . ).

It consists of thousands to millions of transistors, resistors, capacitors, etc. integrated on a small flat piece of semiconductor material that is normally silicon . Integrated circuits (ICs) are the keystone of modern electronics. With the advancement in technology and the emergence of Very Large Scale Integration (VLSI) era it is possible to fit more and more transistors on chips of same piece.

ICs have two main advantages over ordinary circuits: cost and performance. The size, speed, and capacity of chips have progressed enormously with the advancement in technology. Computers, mobile phones, and other digital home appliances are now made possible by the Y Y Figure . NOR gate equals bubbled AND gate .

. De Morgan’s Second Theorem Statement The second theorem states that the complement of the product of two inputs is equal to the sum of its complements. Proof The Boolean equation for NAND gate is Y A B . .

The Boolean equation for bubbled OR gate is Y A and B are the inputs and Y is the output. The above two equations produces the same output for the same inputs. It can be verified by using the truth table A.B A.B A + B From the above truth table we can conclude A B Thus De Morgan’s second theorem is proved. Hence, a NAND gate is equal to a bubbled OR gate.

The corresponding logic circuit diagram is shown in Figure . Y Y Figure . NAND gate equals bubbled OR gate Unit electronics and Communication small size and low cost of ICs. ICs can function as an amplifier, oscillator, timer, microprocessor and computer memory.

These extremely small ICs can perform calculations and store data using either digital or analog technology. Digital ICs use logic gates, which work only with values of ones and zeros. A low signal sent to a component on a digital IC will result in a value of , while a high signal creates a value of . Digital ICs usually find their applications in computers, networking equipment, and most consumer electronics.

Analog ICs or linear ICs work with continuous values. This means a component on a linear IC can take any value and output another value. Linear ICs are typically used in audio and radio frequency amplification. Figure .

Circuits with integrated chips . COMMUNICATION SYSTEMS Introduction Communication is the process of exchanging information by speaking, writing or using some other medium . Communication has existed since the dawn of life in this world. Growth in science and technology removed the locational disadvantage effectively.

Information can be exchanged from one person to another anywhere on this Earth. Right from the researches done in communication by great scientists like J.C. Bose, G. Marconi and Alexander Graham Bell, communication has witnessed development by leaps and bounds.

The communication industry is one of the largest in size and is the oldest since communication through telegraph ( ), telephone ( ), and Radio ( ) started centuries back. The intensive research in the mid- and late nineteenth century has led to the development of long-distance transmission in the shortest possible time. However, the th century witnessed a leap over the development of communication, meeting the demands of speed and secured transfer of data. This section provides a glimpse of the basic concepts of electronic communication, some important communication systems and their applications.

. MODULATION The transmission of information through short distances does not require Unit electronics and Communication phase of the carrier signal remain constant. Amplitude modulation is used in radio and TV broadcasting. The signal shown in Figure .

(a) is the baseband signal that carries information. Figure . (b) shows the high-frequency carrier signal and Figure . (c) gives amplitude modulated signal.

We can see that amplitude of the carrier wave is modified in proportion to the amplitude of the baseband signal. Amplitude Modulated Signal e s Es e c e m Minimum Amplitude Maximum Amplitude Envelope of Modulated Signal Time Time Baseband Signal Carrier Signal (a) (b) (c) Time Ec Em Figure . Amplitude Modulation (a) Baseband signal (b) Carrier signal (c) Modulated signal Advantages of AM i) Easy transmission and reception ii) Lesser bandwidth requirements iii) Low cost Limitations of AM i) Noise level is high ii) Low efficiency iii) Small operating range complicated techniques. The energy of the information signal is sufficient enough to be sent directly.