# Chapter V across the resistor divided by

### Chapter V across the resistor divided by

Chapter 2: Principles of electronic communication systems ? Key words: • Electrical and electronics • Wires and cables • Analogue electronics • Digital electronics • Information, message and data • Analogue information • Digital information 2 Introduction to electronic communication systems 2. 1 Basic electronic components, symbols and circuits Components of an electronic ( or electrical) circuit Any electrical circuit consists if three (3) basic parts Energy source – converts non-electric energy into energy. Examples are batteries and generators. Output device – uses electric energy to do work. Examples are motor, lamp, or display.

Connection – allows electric current to flow. Examples are wire and cable. pic Figure 2.

1: Basic electric circuits. The basic electronic communication circuit composed of electronic (or electrical) components are: A voltage source Resistors, Capacitors, and Inductors While the basic parameters of any electronic communication circuits are: Voltage (in Volts) Current (in Ampere), and Power (in Watts) Figure 2. 2: The schematic diagram Resonant RLC circuit: Three components, R, C, and L connected to an AC voltage source: an ideal inductance, and ideal capacitance, and an ideal resistance in (a) Series-parallel and (b) Parallel.

Resister:A resistor is a two-terminal electronic component designed to oppose an electric current by producing a voltage drop between its terminals in proportion to the current, that is, in accordance with Ohm’s law: V = IR. The resistance R is equal to the voltage drop V across the resistor divided by the current I through the resistor. Figure 2. 3: R resister. Potentiometer: A potentiometer is a three-terminal resistor Figure 2.

4: Potentiometer. Variable resistor: Figure 2. 5: Variable resistor. Capacitor: A capacitor is an electrical/electronic device that can store energy in the electric field between a pair of conductors (called “plates”).Figure 2. 6: Capacitor. Inductor: An inductor is a passive electrical component with significant inductance.

pic Figure 2. 7: Inductor. Switch: A switch is a mechanical device used to connect and disconnect an electric circuit Figure 2. 8: Switches(s).

Two or more switches in parallel form a logical OR; the circuit carries current if at least one switch is ‘on’. See OR gate. Transformer A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled electrical conductors pic Figure 2. 9: Transformer.

Fuse:In electronics and electrical engineering a fuse (short for fusible link) is a type of over-current protection device. Figure 2. 10: Fuse.

Electric current Electric current is the flow (movement) of electric charge. The SI unit of electric current is the ampere. Electric current is measured using an ammeter.

The electric charge may be either electrons or ions. The nature of the electric current is basically the same for either type. Ohm’s law Ohm’s law applies to electrical circuits; it states that the current through a conductor between two points is directly proportional to the potential difference (i. . voltage drop or voltage) across the two points, and inversely proportional to the resistance between them. The mathematical equation that describes this relationship is: pic where I is the current, measured in amperes V is the potential difference measured in volts R is the resistance measured in ohms Conventional current Figure 2.

11: (a) A voltage source, V, drives an electric current, I, through resistor, R, the three quantities obeying Ohm’s law: I = V/R. (b) Diagram showing conventional current notation. Electric charge moves from the positive side of the power source to the negative.Series circuits Series circuits are sometimes called current-coupled or daisy chain-coupled. The current that flows in a series circuit will flow through every component in the circuit. Therefore, all of the components in a series connection carry the same current. Figure 2.

12: A configuration of series circuits, R, L and C. Parallel circuit If two or more components are connected in parallel they have the same potential difference (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities.Hence, the same voltage is applicable to all circuit components connected in parallel.

. Figure 2. 13: A configuration of parallel circuits, R.

Find total current The total current I is the sum of the currents through the individual components, in accordance with Kirchhoff’s circuit laws. The current in each individual resistor is found by Ohm’s law. pic Factoring out the voltage gives To find the total current in a component with resistance Ri, use Ohm’s law again: Find total Resistance To find the total resistance of all components, add the reciprocals of the resistances Ri of each component and take the reciprocal of the sum: pic Capacitors: Capacitors follow the same law using the reciprocals.

The total capacitance of capacitors in parallel is equal to the sum of their individual capacitances: Figure 2. 14: A configuration of parallel circuits, C. Find total capacitance pic Voltage: Electrical tension (or voltage after its SI unit, the volt) is the difference of electrical potential between two points of an electrical or electronic circuit, expressed in volts. 1 It is the measurement of the potential for an electric field to cause an electric current in an electrical conductor.

Depending on the difference of electrical potential it is called extra low voltage, low voltage, high voltage or extra high voltage. Specifically, voltage is equal to energy per unit charge. 2 pic Figure 2. 15: International safety symbol “Caution, risk of electric shock” (ISO 3864), colloquially known as High voltage. DC circuits: pic pic where V = potential difference (volts), I = current intensity (amps), R = resistance (ohms), P = power (watts).

AC circuits pic pic pic where V=voltage, I=current, R=resistance, P=true power, Z=impedance, ? =phasor angle between I and VTotal voltage in series and parallel circuits Voltage sources and drops in series: pic Voltage sources and drops in parallel: pic Where pic is the nth voltage source or drop Voltage drops Across a resistor (Resistor R): pic Across a capacitor (Capacitor C): pic Across an inductor (Inductor L): pic where V=voltage, I=current, R=resistance, X=reactance. Direct current (DC) Direct current (DC) is the unidirectional flow of electric charge. Direct current is produced by such sources as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type.Direct current may flow in a conductor such as a wire, but can also be through semiconductors, insulators, or even through a vacuum as in electron or ion beams. In direct current, the electric charges flow in a constant direction, distinguishing it from alternating current (AC). A term formerly used for direct current was Galvanic current. Figure 2.

16: Types of direct current. Direct current may be obtained from an alternating current supply by use of a current-switching arrangement called a rectifier, which contains electronic elements (usually) or electromechanical elements (historically) that allow current to flow only in one direction.Direct current may be made into alternating current with an inverter or a motor-generator set. The first commercial electric power transmission (developed by Thomas Edison in the late nineteenth century) used direct current. Because of the advantage of alternating current over direct current in transforming and transmission, electric power distribution today is nearly all alternating current. For applications requiring direct current, such as third rail power systems, alternating current is distributed to a substation, which utilizes a rectifier to convert the power to direct current.

See War of Currents.Direct current is used to charge batteries, and in nearly all electronic systems as the power supply. Very large quantities of direct-current power are used in production of aluminum and other electrochemical processes. Direct current is used for some railway propulsion, especially in urban areas. High voltage direct current is used to transmit large amounts of power from remote generation sites or to interconnect alternating current power grids. pic Figure 2.

17: This symbol is found on many electronic devices that either require or produce direct current. Applications of DC: ElectromagnetismElectric current produces a magnetic field. The magnetic field can be visualized as a pattern of circular field lines surrounding the wire. Electric current can be directly measured with a galvanometer, but this method involves breaking the circuit, which is sometimes inconvenient. Current can also be measured without breaking the circuit by detecting the magnetic field associated with the current. Devices used for this include Hall effect sensors, current clamps, current transformers, and Rogowski coils. Figure 2.

18: According to Ampere’s law, an electric current produces a magnetic field. Measuring instrumentsInstruments for measuring potential differences include the voltmeter, the potentiometer (measurement device), and the oscilloscope. The voltmeter works by measuring the current through a fixed resistor, which, according to Ohm’s Law, is proportional to the potential difference across the resistor. The potentiometer works by balancing the unknown voltage against a known voltage in a bridge circuit. The cathode-ray oscilloscope works by amplifying the potential difference and using it to deflect an electron beam from a straight path, so that the deflection of the beam is proportional to the potential differenceFigure 2. 19: A multi-meter set to measure voltage, current or resistance.

Degree A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of plane angle, representing 1? 360 of a full rotation; one degree is equivalent to ? /180 radians pic Figure 2. 20: Degree Radian The radian is a unit of plane angle, equal to 180/? degrees, or about 57. 2958 degrees. It is the standard unit of angular measurement in all areas of mathematics beyond the elementary level. Angular frequencyIn physics (specifically mechanics and electrical engineering), angular frequency ? (also referred to by the terms angular speed, radial frequency, circular frequency, and radian frequency) is a scalar measure of rotation rate.

Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity. The term angular frequency vector picis sometimes used as a synonym for the vector quantity angular velocity . In SI units, angular frequency is measured in radians per second, with dimensions s? 1 since radians are dimensionless. One revolution is equal to 2? adians, hence pic Where ? is the angular frequency or angular speed (measured in radians per second), T is the period (measured in seconds), f is the frequency (measured in hertz), v is the tangential velocity of a point about the axis of rotation (measured in metres per second), r is the radius of rotation (measured in metres). pic Figure 2.

21: Angular frequency is a measure of how fast an object is rotating 2. 2 Periodic, aperiodic and transient signals Signals and waveforms are central to any communication system. A signal is defined as ‘any sign, gesture, token, etc. that carry a communicate information’. The word ‘signal’, as applied to electronic communications, therefore implies an electrical quantity (e. g. voltage) possessing some characteristic (e.

g. amplitude) which varies unpredictably. A waveform is defined as ‘the shape of a wave or oscillation obtained by plotting the value of some changing quantity against time’. In electronic communications the term waveform implies an electrical quantity which varies periodically and therefore predictably. Strictly this precludes a waveform from conveying information.However, a waveform can be adapted to convey information by varying one or more of its parameters in sympathy with a signal. Such waveforms are called carriers and typically consist of a sinusoid or pulse train modulated in: • Amplitude • Phase, or • Frequency Fluctuating voltages and currents can be alternatively classified as either: Periodic, or Aperiodic Periodic signal A periodic signal, if shifted by an appropriate time interval, is unchanged.

Aperiodic signal An aperiodic signal does not possess shifting by an appropriate time interval. In this context the term periodic signal is clearly synonymous with waveform.In this section our principal concern is with periodic signals and one type of aperiodic signal, i. e. transients.

Transient signal A transient signal is one which has a well defined location in time. This does not necessarily mean it must be zero outside a certain time interval but it does imply that the signal at least tends to zero as time tends to ± ?. The one-sided decaying exponential function is an example of a transient signal which has a well defined start and tends to zero as t > ?. If a signal’s parameters (amplitude, shape and phase in the case of a period signal.Amplitude, shape and location in the case of a transient signal) are known, then the signal is said to be deterministic.

This means that, in the absence of noise, any future value of the signal can be determined precisely. Signals which are not deterministic must be described using probability theory. Figure 2. 6 shows alternating-current (AC) or sinusoidal wave form v(t).

By convention sinusoids is express by the cosine function. The parameters of sinusoidal wave are:: Ais the amplitude (the peak value) ?ois radian frequency ?is phase angle To is repetition period o is the cyclical frequency (i. e. the reciprocal of period To) pic Figure 2. 22: A sinusoidal waveform. Electronic communications signals can be analogue or digital. 2.

3 Sinusoids, cissoids and phasors 2. 3. 1 Examples of the transmitting signals Example-1: Periodic Signals A periodic signal is defined as one which has the property: pic(1) In above equation, n is any integer and T is the repetition period (or simply period) of the signal. Figure 2. 7, shows an example of a periodic signal. pic Figure 2. 23: An example of a periodic signal.

pic Figure 2. 4: An example of generation of sinusoids by projection of a radius onto perpendicular planes. Figure 2. 25: An example of circular trigonometric functions plotted against phase: (a) cosine, and (b) sine, function of phase angle. Figure 2. 26: An example of circular trigonometric functions plotted against time (a) cosine and (b) sine, function of time.

Figure 2. 27: (a) Rotating vector or cisoid, (b) Sketch of cisoid with time progressing perpendicular to the complex plane. Figure 2.

28: (a) Synthesis of real sinusoid wave from two counter-rotating, conjugate, cissoids, (b) Phasor corresponding to pic,Figure 2. 3 show a communication system with input and output information notations, transmitters’ and receivers’ basic components, transmission medium and noise factor. pic Figure 2. 31: Parameters of communication systems. Transmitter A transmitter is an electronic device which, usually with the aid of an antenna, propagates an electromagnetic signal such as radio, television, or other telecommunications.

Receiver A receiver is an electronic device which, usually with the aid of an antenna, receive electromagnetic signals such as radio, television, or other telecommunications. Figure 2. shows a functional diagram of the basic elements of a digital communication system. The source output may be either an analogue signal, such as an audio or video signal, or a digital signal. In a digital communication system, the messages produced by the source are converted into a sequence of binary digits. The process of efficiently converting the output of either an analogue or digital source into a sequence of binary digits is called source encoding or data compression. The sequence of binary digits from the source encoder, which we call the information sequence, is passed to the channel encoder.

The purpose of the channel encoder is to introduce, in a controlled manner, some redundancy in the binary information sequence that can be used at the receiver to overcome the effects of noise and interference encountered in the transmission of the signal. pic Figure 2. 32: Basic elements of a digital communication system. A typical communication system carries: • Information • Messages, and • Signals Clearly, the concept of information is central to any communication. While, the message, is defined as the physical manifestation of information as produced by the source.Whatever form the message takes, the goal of a communication system is to reproduce at the destination an acceptable replica of the source message.

There are many kinds of information sources, including machines as well as people, and messages appear in various forms. Nonetheless, we can identify two distinct message categories, analogue and digital. This distinction, in turn, determines the criterion for successful communication. Signal In the fields of electronic communications , a signal is any time-varying quantity.Components (or parameters) of an electronic signal pic Figure 2.

33: A sinusoidal voltage. where: 1 = Amplitude (peak), 2 = Peak-to-peak, 3 = RMS, 4 = Wave period Analogue signal An analogue or analogue signal is any continuous signal for which the time varying feature (variable) of the signal is a representation of some other time varying quantity, i. e. analogous to another time varying signal. It differs from a digital signal in that small fluctuations in the signal are meaningful. pic Figure 2.

34: An example of analogue signal. Analogue messageAn analogue message is a physical quantity that varies with time, usually in a smooth and continuous fashion. Examples of analogue messages are the acoustic pressure produced when you speak, the angular position of an aircraft gyro, or the light intensity at some point in a television image.

Since the information resides in a time-varying waveform, an analogue communication system should deliver this waveform with a specified degree of fidelity. Discrete signal A discrete signal or discrete-time signal is a time series, perhaps a signal that has been sampled from a continuous-time signal.Unlike a continuous-time signal, a discrete-time signal is not a function of a continuous-time argument, but is a sequence of quantities; that is, a function over a domain of discrete integers.

Each value in the sequence is called a sample. When a discrete-time signal is a sequence corresponding to uniformly spaced times, it has an associated sampling rate; the sampling rate is not apparent in the data sequence, so may be associated as a separate data item. Digital signals Digital signals are digital representations of discrete-time signals, which are often derived from analog signals.

A digital signal is a discrete-time signal that takes on only a discrete set of values. It typically derives from a discrete signal that has been quantized. Common practical digital signals are represented as 8-bit (256 levels), 16-bit (65,536 levels), 32-bit (4. 3 billion levels), and so on, though any number of quantization levels is possible, not just powers of two. Figure 2. 35: (a) Discrete sampled signal, (b) Digitised (quantised) digital signal, (c) Digital signal.

Practical digital signal The term digital signal is used to refer to more than one concept.It can refer to discrete-time signals that have a discrete number of levels, for example a sampled and quantified analogue signal, or to the continuous-time waveform signals in a digital system, representing a bit-stream. In the first case, a signal that is generated by means of a digital modulation method is considered as converted to an analogue signal, while it is considered as a digital signal in the second case. Figure 2. 5 shows a digital signal. pic Figure 2. 36: Digital signal: 1) Low level, 2) High level, 3) Rising edge, and 4) Falling edge, (Also a digital waveform).

Digital message A digital message is an ordered sequence of symbols selected from a finite set of discrete elements. Examples of digital messages are: the Letters printed on this page a listing of hourly temperature readings, or the keys you press on a computer keyboard Since the information resides in discrete symbols, a digital communication system should deliver these symbols with a specified degree of accuracy in a specified amount of time. Whether analogue or digital, few message sources are inherently electrical. Consequently, most communication systems have input and output transducers.Continuous wave A continuous wave or continuous waveform (CW) is an electromagnetic wave of constant amplitude and frequency; and in mathematical analysis, of infinite duration. Continuous wave is also the name given to an early method of radio transmission, in which a carrier wave is switched on and off. Information is carried in the varying duration of the on and off periods of the signal.

In radio transmission, CW waves are also known as “undamped waves”, to distinguish this method from damped wave transmission. WaveformWaveform means the shape and form of a signal such as a wave moving in a solid, liquid or gaseous medium. In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form.

In these cases, the term ‘waveform’ refers to the shape of a graph of the varying quantity against time or distance. An instrument called an oscilloscope can be used to pictorially represent the wave as a repeating image on a CRT or LCD screen. By extension of the above, the term ‘waveform’ is now also sometimes used to describe the shape of the graph of any varying quantity against time. pic Figure 2.

37: Sine, square, triangle, and sawtooth waveforms. Class work-: Tutorial – 1 2. 4. 2 Base-band signal and bandwidth Base-band signal For base-band signals (i.

e. signals with significant spectral components all the way down to their fundamental frequency. Figure 2. 38: (a) Spectrum of a base-band signal, amplitude as a function of frequency, where B is bandwidth, (b) A graph of a band-pass filter’s gain magnitude, illustrating the concept of -3 dB (or half-power) bandwidth, at a gain of 0. 707.The frequency axis of this symbolic diagram can be linear or logarithmically scaled. . Bandwidth Bandwidth, B, is the difference between the upper and lower cut-off frequencies of a communication channel or a signal spectrum, and is typically measured in hertz. In case of a base-band channel or signal, the bandwidth is equal to its upper cut-off frequency. Bandwidth in hertz is a central concept in many fields, including electronics, information theory, radio communications, signal processing, and spectroscopy. Bandwidth (Explanation) 