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February 2011

Master of Science in Telecom Technology (MScTT) Semester 1

ME0005 Basic Principles of network 4 Credits

(Book ID: B0024)

Assignment Set 1 (60 Marks)

Each question carries Ten marks. 610 = 60

1. State and Explain Kirchhoffs Voltage and Current Law.

Kirchhoff's current law (KCL)

The current entering any junction is equal to the current leaving that junction. i1 + i4 = i2+ i3

This law is also called Kirchhoff's point rule, Kirchhoff's junction rule (or nodalrule), and Kirchhoff's first rule.

The principle of conservation ofelectric charge implies that:

At any node (junction) in an electrical circuit, the sum ofcurrents flowing intothat node is equal to the sum of currents flowing out of that node.

orThe algebraic sum of currents in a network of conductors meeting at a point iszero. (Assuming that current entering the junction is taken as positive andcurrent leaving the junction is taken as negative).

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Recalling that current is a signed (positive or negative) quantity reflecting directiontowards or away from a node, this principle can be stated as:

n is the total number of branches with currents flowing towards or away from the node.

This formula is also valid forcomplex currents:

The law is based on the conservation of charge whereby the charge (measured in

coulombs) is the product of the current (in amperes) and the time (which is measuredin seconds).

Kirchhoff's voltage law (KVL)

The sum of all the voltages around the loop is equal to zero. v1 + v2 + v3 + v4 = 0

This law is also called Kirchhoff's second law, Kirchhoff's loop (or mesh) rule, andKirchhoff's second rule.

The principle of conservation of energy implies that

The directed sum of the electrical potential differences (voltage) around any

closed circuit is zero.orMore simply, the sum of the emfs in any closed loop is equivalent to the sum ofthe potential drops in that loop.or

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The algebraic sum of the products of the resistances of the conductors and thecurrents in them in a closed loop is equal to the total emfavailable in that loop.

Similarly to KCL, it can be stated as:

Here, n is the total number of voltages measured. The voltages may also be complex:

2. State and prove Thevenines Theorem.

In circuit theory, Thvenin's theorem for linear electrical networks states that any

combination of voltage sources, current sources, and resistors with two terminals is

electrically equivalent to a single voltage source Vand a single series resistorR. For

single frequency AC systems the theorem can also be applied to general impedances,

not just resistors.

Calculating the Thvenin equivalent

To calculate the equivalent circuit, the resistance and voltage are needed, so twoequations are required. These two equations are usually obtained by using thefollowing steps, but any conditions placed on the terminals of the circuit should alsowork:

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1. Calculate the output voltage, VAB, when in open circuit condition (no loadresistormeaning infinite resistance). This is VTh.

2. Calculate the output current, IAB, when the output terminals are short circuited(load resistance is 0). RTh equals VTh divided by this IAB.

The equivalent circuit is a voltage source with voltage VTh in series with aresistance RTh.

Step 2 could also be thought of as:

2a. Now replace voltage sources with short circuits and current sources withopen circuits.2b. Replace the load circuit with an imaginary ohmmeterand measure the totalresistance, R, "looking back" into the circuit. This is RTh.

The Thvenin-equivalent voltage is the voltage at the output terminals of the original

circuit. When calculating a Thvenin-equivalent voltage, the voltage dividerprinciple isoften useful, by declaring one terminal to be Vout and the other terminal to be at theground point.

The Thvenin-equivalent resistance is the resistance measured across points A and B"looking back" into the circuit. It is important to first replace all voltage- and current-sources with their internal resistances. For an ideal voltage source, this means replacethe voltage source with a short circuit. For an ideal current source, this means replacethe current source with an open circuit. Resistance can then be calculated across theterminals using the formulae forseries and parallel circuits. This method is valid onlyfor circuits with independent sources. If there are dependent sources in the circuit,

another method must be used such as connecting a test source across A and B andcalculating the voltage across or current through the test source.

PROOF OF THEVENINS THEOREM

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The circuit in above can be used to prove Thevenins theorem. Equation (1) in thediagaram expresses an external voltage VY connected to the load terminals, as afunction of current IY and some constants. It is valid to do so, since we are dealing witha linear circuit. Let us some that the internal independent sources remain fixed. Then,as the external voltage VY is varied, current IY will vary, and the variation IY with VY is

accounted for by provision of a coefficient , named as k1 in equation (1). It can be seenthat k1 reflects resistance of the circuit as seen by external voltage source VY.Coefficient k2 reflects the contribution to terminal voltage by internal sources andcomponents of the circuit. It is valid to do so, since we are dealing with a linear circuit,and a linear circuit obeys the principle of superposition. Each independent internalsource within the circuit contributes its part to terminal voltage and constant k2 is thealgebraic sum of contributions of internal sources. Adjust external voltage source suchthat current IY becomes zero. As shown by equation (2), the coefficient k2 is Theveninsvoltage. To determine Thevenins resistance, set external source voltage to zero. If theinternal sources are such as to yield positive Thevenins voltage, current IY will benegative and coefficient k1 is Thevenins resistance, as shown by equation (3). This

concludes the proof of Thevenins theorem

3. What is a filter? Design a Constant K band Pass filter

Electronic filters are electronic circuits which perform signal processing functions,

specifically to remove unwanted frequency components from the signal, to enhance

wanted ones, or both

Constant k filters, also k-type filters, are a type ofelectronic filterdesigned using the

image method. They are the original and simplest filters produced by this methodology

and consist of a ladder network of identical sections ofpassive components.

Constant k low-pass filter half section. Here inductance L is equal Ck2

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Constant k band-pass filter half section.L1 = C2k2 and L2 = C1k2

Image impedance ZiTof a constant k prototype low-pass filter is plotted vs. frequency. The impedance is purely resistive (real) below c, and purely reactive (imaginary)above c.

The building block of constant k filters is the half-section "L" network,

composed of a series impedanceZ, and a shunt admittanceY. The "k" in "constant k"is the value given by,

Thus, kwill have units of impedance, that is, ohms. It is readily apparent that in orderforkto be constant, Ymust be the dual impedance ofZ. A physical interpretation of k

can be given by observing that kis the limiting value ofZi as the size of the section (interms of values of its components, such as inductances, capacitances, etc.)approaches zero, while keeping kat its initial value. Thus, kis the characteristicimpedance, Z0, of the transmission line that would be formed by these infinitesimallysmall sections. It is also the image impedance of the section at resonance, in the caseof band-pass filters, or at = 0 in the case of low-pass filters. For example, thepictured low-pass half-section has

.

Elements L and Ccan be made arbitrarily small while retaining the same value ofk. Zand Yhowever, are both approaching zero, and from the formulae (below) for imageimpedances,

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Image impedance

The image impedances of the section are given by

and

Provided that the filter does not contain any resistive elements, the image impedancein the pass band of the filter is purely real and in the stop band it is purely imaginary.For example, for the pictured low-pass half-section,[9]

The transition occurs at a cut-off frequency given by

Below this frequency, the image impedance is real,

Above the cut-off frequency the image impedance is imaginary,

Transmission parameters

The transfer function of a constant k prototype low-pass filter for a single half-sectionshowing attenuation in nepers and phase change in radians.See also: Image impedance#Transfer function

The transmission parameters for a general constant k half-section are given by [10]

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and for a chain ofn half-sections

For the low-pass L-shape section, below the cut-off frequency, the transmission

parameters are given by[8]

That is, the transmission is lossless in the pass-band with only the phase of the signalchanging. Above the cut-off frequency, the transmission parameters are:[8]

Prototype transformations

The presented plots of image impedance, attenuation and phase change correspondto a low-pass prototype filtersection. The prototype has a cut-off frequency ofc = 1rad/s and a nominal impedance k= 1 . This is produced by a filter half-section withinductance L = 1 henry and capacitance C= 1 farad. This prototype can be impedancescaled and frequency scaled to the desired values. The low-pass prototype can alsobe transformed into high-pass, band-pass or band-stop types by application of suitablefrequency transformations.

4. Derive the expression for characteristic impedance of Band pass filter

There are two topologies that are used for these filters, namely the Pi and the Tconfigurations. Rather than having a single element in each leg of the filter as in thecase of the low pass and high pass filters, the band pass filter has a resonant circuit ineach leg. These resonant circuits are either series or parallel tuned LC circuits.

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LC Pi and T section band pass filters

The equations below provide the values for the capacitors and resistors for a constant-k filter. As the filter is a band pass filter there are two cut off frequencies. One at thelow edge of the pass band and the toher at the top edge of the pass band.

L1 = Zo / (pi (f2 - f1)) Henries

L2 = Zo (f2 - f1) / (4 pi f2 f1) Henries

C1 = (f2 - f1) / (4 pi f2 f1 Zo) Farads

C2 = 1 / (pi Zo (f2 - f1)) Farads

Zo = l / (pi*C2*(f2-f1))

Zo = characteristic impedance in ohmsC1 and C2 = Capacitance in FaradsL1 and L2 = Inductance in Henriesf1 and f2 = Cut off frequencies in Hertz

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5. Explain Symmetrical T-attenuator.

The T-pad is a specific type ofattenuatorcircuit in

electronics whereby the topology of the circuit is formed in the shape of the letter "T".

Attenuators are used in electronics to reduce the level of a signal. They are alsoreferred to as pads due to their effect of padding down a signal by analogy withacoustics. Attenuators have a flat frequency response attenuating all frequenciesequally in the band they are intended to operate. The attenuator has the opposite task

of an amplifier. The topology of an attenuator circuit will usually follow one of thesimple filter sections. However, there is no need for more complex circuitry, as there iswith filters, due to the simplicity of the frequency response required.

Circuits are required to be balanced or unbalanced depending on the geometry of thetransmission lines they are to be used with. Forradio frequency applications, theformat is often unbalanced, such as coaxial. For audio and telecommunications,balanced circuits are usually required, such as with the twisted pairformat. The T-padis intrinsically an unbalanced circuit. However, it can be converted to a balanced circuitby placing half the series resistances in the return path. Such a circuit is called an H-section, or else an I-section because the circuit is formed in the shape of a serifed

letter "I".An attenuator is a form of a two-port network with a generator connected to one portand a load connected to the other. In all of the circuits given below it is assumed thatthe generator and load impedances are purely resistive (though not necessarily equal)and that the attenuator circuit is required to perfectly match to these. The symbolsused for these impedances are;

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the impedance of the generatorthe impedance of the load

Popular values of impedance are 600 in telecommucations and audio, 75 for videoand dipole antennae, 50 forRF

The voltage transfer function,A, is,

While the inverse of this is the loss, L, of the attenuator,

The value of attenuation is normally marked on the attenuator as its loss, LdB, indecibels (dB). The relationship with L is;

Popular values of attenuator are 3dB, 6dB, 10dB, 20dB and 40dB.

However, it is often more convenient to express the loss in nepers,

where is the attenuation in nepers

6. Explain First order Low pass Active filter

Active Filters contain active components such as operational amplifiers or transistorswithin their design. They draw their power from an external power source and use it toboost or amplify the output signal. Operational amplifiers can also be used to shape oralter the frequency response of the circuit by producing a more selective outputresponse by making the output bandwidth of the filter more narrower or even wider.

The most common and easily understood active filter is the Active Low Pass Filter.Its principle of operation and frequency response is exactly the same as RC low passfilter, the only difference being it uses an op-amp for amplification and gain control.The simplest form of a low pass active filter is to connect an inverting or non-invertingamplifierto the basic RC low pass filter as shown.

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First-order Low Pass Butterworth Filter

This 1st-Order low pass Butterworth type filter, consists simply of a passive RC filterconnected to the input of a non-inverting operational amplifier. The frequencyresponse of the circuit will be the same as that of the passive RC filter, except that theamplitude of the output signal is increased by the passband voltage gain of theamplifier and for a non-inverting amplifier this given as: 1 + R2/R1.

For a non-inverting amplifier circuit, the magnitude of the voltage gain for the filter isgiven as a function of the feedback resistor (R2) divided by its corresponding inputresistor (R1) value and is given as:

Voltage Gain for a First-order Low Pass Filter

Where: AF = the Passband Gain of the filter, (1 + R2/R1) = the Frequency of the Input Signal in Hertz, (Hz)

c = the Cut-off Frequency in Hertz, (Hz)

When dealing with filter circuits the magnitude of the pass band gain of the circuit isgenerally expressedin Decibels ordB as a function of the voltage gain

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August 2010

Master of Science in Telecom Technology (MScTT) Semester 1

ME0005 Basic Principles of network 4 Credits

(Book ID: B0024)

Assignment Set 2 (60 Marks)

Each question carries Ten marks. 610 = 60

1. What are the basic parameters of Transmission Lines? Explain them

Z and Y are the impedance and admittance per unit length

Z = R + jL and Y = G + jC, where

R is the series resistance per unit length ?z, /m

L is the series inductance per unit length ?z, H/mG is the shunt conductance per unit length ?z, S/m

C is the shunt capacitance per unit length ?z, F/m

The equations for V and I are

dV/dz = ZI anddI/dz = YV, simultaneous solution of which yields

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d2V/dz2= ZYV andd2I/dz2 = ZYI; z here represents distance along the transmission line.

The solution of these equations is in the form of waves in the +z and -z direction, which for

sinusoidal excitation take the form

V(z) = V+et-jz + V-et+jz) and I(z) = I+e(t-jz)+ I+e(t+jz)

To distinguish it from the free-space wavelength nomenclature or o, the wavelength on a

waveguide or coaxial transmission line is often referred to as theguide wavelength g.

For a single wave solution in one direction, the ratio V(z)/I(z) is the same everywhere on theline, and is defined as the characteristic impedance Zo, which for a lossless line is a real

number

where the minus sign reflects the fact that the magnetic field, and hence the current, of the

negative-going propagation is reversed compared to that of a positive-going wave. If both

waves exist, the instantaneous voltage or current as function of location is the sum of voltagesor

currents of both waves. The characteristic impedance Zo is the ratio of voltage to current of

either wave independently, but not necessarily their sum.

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2. Which are the secondary Parameters of Transmission Line?

The propagation constant, symbol , for a given system is defined by the ratio of theamplitude at the source of the wave to the amplitude at some distancex, such that,

Since the propagation constant is a complex quantity we can write:

where

, the real part, is called the attenuation constant, the imaginary part, is called the phase constant

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That does indeed represent phase can be seen from Euler's formula;

which is a sinusoid which varies in phase as varies but does not vary in amplitudebecause;

The reason for the use of base e is also now made clear. The imaginary phaseconstant, i, can be added directly to the attenuation constant, , to form a singlecomplex number that can be handled in one mathematical operation provided they areto the same base. Angles measured in radians require base e, so the attenuation islikewise in base e.

For a copper transmission line, the propagation constant can be calculated from theprimary line coefficients by means of the relationship;

where;

, the series impedance of the line per metre and,, the shunt admittance of the line per metre.

Attenuation constant

In telecommunications, the term attenuation constant, also called attenuationparameterorcoefficient, is the attenuation of an electromagnetic wave propagatingthrough a medium per unit distance from the source. It is the real part of thepropagation constant and is measured in nepers per metre. A neper is approximately8.7dB. Attenuation constant can be defined by the amplitude ratio;

The propagation constant per unit length is defined as the natural logarithmic of ratioof the sending end current or voltage to the receiving end current or voltage.

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Copper lines

The attenuation constant for copper (or any other conductor) lines can be calculatedfrom the primary line coefficients as shown above. For a line meeting the distortionlesscondition, with a conductance G in the insulator, the attenuation constant is given by;

however, a real line is unlikely to meet this condition without the addition of loadingcoils and, furthermore, there are some frequency dependant effects operating on theprimary "constants" which cause a frequency dependence of the loss. There are twomain components to these losses, the metal loss and the dielectric loss.

The loss of most transmission lines are dominated by the metal loss, which causes afrequency dependency due to finite conductivity of metals, and the skin effect inside aconductor. The skin effect causes R along the conductor to be approximatelydependent on frequency according to;

Losses in the dielectric depend on the loss tangent (tan) of the material, whichdepends inversely on the wavelength of the signal and is directly proportional to thefrequency.

Phase constant

In electromagnetic theory, the phase constant, also called phase change constant,parameterorcoefficient is the imaginary component of the propagation constant fora plane wave. It represents the change in phase per metre along the path travelled bythe wave at any instant and is equal to the angular wavenumberof the wave. It isrepresented by the symbol and is measured in units of radians per metre.

From the definition of angular wavenumber;

This quantity is often (strictly speaking incorrectly) abbreviated to wavenumber.Properly, wavenumber is given by,

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which differs from angular wavenumber only by a constant multiple of 2, in the sameway that angular frequency differs from frequency.

For a transmission line, the Heaviside condition of the telegrapher's equation tells usthat the wavenumber must be proportional to frequency for the transmission of thewave to be undistorted in the time domain. This includes, but is not limited to, the idealcase of a lossless line. The reason for this condition can be seen by considering that auseful signal is composed of many different wavelengths in the frequency domain. Forthere to be no distortion of the waveform, all these waves must travel at the samevelocity so that they arrive at the far end of the line at the same time as a group. Sincewave phase velocity is given by;

it is proved that is required to be proportional to . In terms of primary coefficients ofthe line, this yields from the telegrapher's equation for a distortionless line thecondition;

However, practical lines can only be expected to approximately meet this conditionover a limited frequency band.

3. Discuss Standing Wave Ratio.

In telecommunications, standing wave ratio (SWR) is the ratio of the amplitude of apartial standing wave at an antinode (maximum) to the amplitude at an adjacent node(minimum), in an electrical transmission line.

The SWR is usually defined as a voltage ratio called the VSWR, forvoltage standingwave ratio. For example, the VSWR value 1.2:1 denotes a maximum standing waveamplitude that is 1.2 times greater than the minimum standing wave value. It is alsopossible to define the SWR in terms ofcurrent, resulting in the ISWR, which has thesame numerical value. Thepower standing wave ratio (PSWR) is defined as thesquare of the VSWR.

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The voltage component of a standing wave in a uniform transmission line consists ofthe forward wave (with amplitude Vf) superimposed on the reflected wave (withamplitude Vr).

Reflections occur as a result of discontinuities, such as an imperfection in an otherwiseuniform transmission line, or when a transmission line is terminated with other than itscharacteristic impedance. The reflection coefficient is defined thus:

is a complex numberthat describes both the magnitude and the phase shift of thereflection. The simplest cases, when the imaginary part of is zero, are:

= 1: maximum negative reflection, when the line is short-circuited,

= 0: no reflection, when the line is perfectly matched, = + 1: maximum positive reflection, when the line is open-circuited.

For the calculation of VSWR, only the magnitude of , denoted by , is of interest.Therefore, we define

= | | .

At some points along the line the two waves interfere constructively, and the resultingamplitude Vmax is the sum of their amplitudes:

At other points, the waves interfere destructively, and the resulting amplitude Vmin isthe difference between their amplitudes:

The voltage standing wave ratio is then equal to:

As , the magnitude of , always falls in the range [0,1], the VSWR is always +1.

The SWR can also be defined as the ratio of the maximum amplitude of the electricfield strength to its minimum amplitude, i.e. Emax / Emin.

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4. Explain the working of simple telephone Communication.

A simple Telephone system.

Schematic of a telephone installation.

A traditional landline telephone system, also known as "plain old

telephone service" (POTS), commonly handles both signaling and audio informationon the same twisted pair(C) of insulated wires: the telephone line. The signalingequipment consists of a bell, beeper, light or other device (A7) to alert the user toincoming calls, and number buttons or a rotary dial (A4) to enter a telephone numberfor outgoing calls. Although originally designed for voice communication, the systemhas been adapted for data communication such asTelex, Fax,broadband, and dial-upInternet communication. Most of the expense of wire-lines are the wires, so sendingboth received and sent voices on one pair of wires reduces the expense of wire-lineservice. A twisted pair line rejects electromagnetic interference (EMI) and crosstalkbetter than a single wire or an untwisted pair. The microphone and speaker signals do

not interfere on the twisted pair because a hybrid coil (A3) subtracts the microphone'ssignal from the signal sent to the local speaker. The junction box (B) arrests lightning(B2) and adjusts the line's resistance (B1) to maximize the signal power for the line'slength. Telephones have similar adjustments for inside line lengths (A8). The wire'svoltages are negative compared to earth, to reduce galvanic corrosion. Negativevoltage attracts positive metal ions toward the wires.

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The telephone consists of an alerting device, usually a ringer (A7), that remainsconnected to the phone line whenever the phone is "on hook", and other componentswhich are connected when the phone is "off hook". The off-hook components include atransmitter (microphone,A2), a receiver (speaker,A1) and other circuits for dialing,filtering (A3), and amplification.

A calling party wishing to speak to another party will pick up the telephone's handset,operating a "switchhook" (A4), which powers the telephone by connecting thetransmitter (microphone), receiver (speaker) and related audio components to the line.The off-hook circuitry has a low resistance (less than 300 ohms) which causes directcurrent (DC) to flow from the telephone exchange (D) through the line (C). Theexchange detects this current, attaches a digit receiver circuit to the line, and sends adial tone to indicate readiness. On a modern push-button telephone, the caller thenpresses the number keys to send the telephone number of the called party. The keyscontrol a tone generator circuit that makes DTMF tones that the exchange receives. Arotary-dial telephone uses pulse dialing, sending electrical pulses, that the exchange

can count to get the telephone number. (Most exchanges are still equipped to handlepulse dialing.) If the called party's line is not in use, the exchange sends an intermittentringing signal (about 90 volts alternating current (AC) in North America and UK and 60volts in Germany) to alert the called party to an incoming call. If the called party's lineis in use, the exchange sends a busy signal to the calling party. However, if the calledparty's line is in use but has call waiting installed, the exchange sends an intermittentaudible tone to the called party to indicate an incoming call.

The phone's ringer (A7) is connected to the line through a capacitor (A6), a devicewhich blocks direct current but permits alternating current. So, the phone draws nocurrent when it is on hook, but exchange circuitry (D2) can send an AC voltage down

the line to ring for an incoming call. (When there is no exchange, telephones oftenhave hand-cranked magnetos to make the ringing voltage.) When a landline phone isinactive or "on hook", the circuitry at the telephone exchange (D1) detects the absenceof direct current and therefore "knows" that the phone is on hook with only the alertingdevice electrically connected to the line. When a party initiates a call to this line, theexchange sends the ringing signal. When the called party picks up the handset, theyactuate a double-circuit switchhook (D2) which simultaneously disconnects the alertingdevice and connects the audio circuitry to the line. This, in turn, draws direct currentthrough the line, confirming that the called phone is now active. The exchange circuitryturns off the ring signal, and both phones are now active and connected through theexchange. The parties may now converse as long as both phones remain off hook.

When a party "hangs up", placing the handset back on the cradle or hook, directcurrent ceases in that line, signaling the exchange to disconnect the call.

Calls to parties beyond the local exchange are carried over "trunk" lines whichestablish connections between exchanges. In modern telephone networks, fiber-optic

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cable and digital technology are often employed in such connections. Satellitetechnology may be used for communication over very long distances.

5. With neat block diagram explain elements of a switching system.

The purpose of a telecommunication switching system is to provide the means to passinformation from any terminal device to any other terminal device selected by theoriginator.Telecommunication system can be divided into four main parts. They are1. End system or Instruments2. Transmission system3. Switching system4. Signaling.End Systems or Instruments. The end system or instruments are a transmitter orreceiver that are responsible for sending information or decoding or inverting receivedinformation or message into an intelligible message. End systems in the telelphone

networkhave evolved from analog telephones to digital handsets and cellular phones.However, endlessarrays of other devices are being attached to telephone lines, including computerterminals

used for data transmission.

Transmission System. Signals generated by the end system or the instrumentsshouldbe transported to the destination by some means. The transmission on links conveys

theinformation and control signals between the terminals and switching centers. Atransmissionlink can be characterized by its bandwidth, link attenuation and the propagation delay.Tomaintain signal quality, the signal must be regenerated after a certain distance.In general a communication path between two distinct points can be setup beconnectinga number of transmission lines in tandem. The transmission links include two-wirelines, coaxialcables microwave radio, optical fibers and satellites. Functionally, the communicationchannels between switching system are referred to as trunks. Fig. 1.4 shows thevarious possible

transmission media.

Switching System. The switching centers receives the control signals, messages orconversations and forwards to the required destination, after necessary modification(link

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amplifications) if necessary. A switching system is a collection of switching elementsarrangedand controlled in such a way as to setup a communication path between any twodistant points.A switching center of a telephone network comprising a switching network and its

control andsupport equipment is called a central office.In computer communication, the switching technique used is known as packetswitchingor message switch (store and forward switching). In telephone network the switchingmethodused is called circuit switching. Some practical switching system are step-by-step,cross barredrelay system, digital swtiching systems, electronic switching system etc.Signalling Systems. A signalling system in a data communication networksexchanges

signalling information effectively between subscribers. The signalling systems areessentialbuilding blocks in providing the ultimate objective of a worldwide automatic telephoneservicesstandardized. Signalling provides the interface between different national systems.Theintroduction of signalling system was the big step in improving the PSTN.The consultative committe on international telegraphy and telephony (CCITT) based inGeneva, recommended seven formats related to signalling. The first five formatsrelated to Inbandsignalling and the last two in the category of common channel signalling. In In-band

signalling, voice information and signalling information travel on common paths, whereas in

common channel signalling, they travel on separate paths.

6. With neat diagram explain three stage Networks.

The blocking probability and the number of switching elements can be reduced

significantly by adopting a 3 stage structure in place of 2-stage networks.The

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general NxN 3-stage structure in place of 2-stage networks. The general NxN 3-

stahe blocking network is shown in figure. The N inlets and N outlets are divided

into r blocks of p inlets and p outlets each respectively. The network is realized by

using switching matrices of size pxs in stage 1,r x r in stage 2, and s x p in stage

3.Here any arbitrary inlet in the first stage has s alternative paths to reach any

arbitrary outlet in the third stage.The total number of swithing elements is given by

S=rps+sr2+spr=2Ns+sr2=s(2N+r2)

If we use square matrices in the first and third stage, we have p=s=N/r

And S=(2N2 /r)+Nr and

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Smin=2N2N

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