The post Design issues of Data Link Layer appeared first on ece4uplp.
]]>The study of design principles of Data Link Layer deals with the algorithms for achieving reliable, efficient communication between ‘2’ adjacent machines at DLL.
adjacent means those two machines are connected by a wire— a coaxial cable, telephone line (or) pointto point wireless channel.
The essential property of a channel –wire like— means sending the bits in the same order as they are sent .
Let us suppose we have a system A and machine B and these two are connected by a wire and assume that there is no means of any software in any machine then the picture seems to be as follows
as A just puts the bits on the wire and B just takes off the bits.
i.e, they have only a finite data rate and there is a nonzero propagation delay between the time a bit is sent and the time it is received and the communication devices makes errors occasionally.
these are the limitations that have been taken care for the efficiency of the data transfer.
The protocols used for communications must take all these factors into consideration.
i.e design issues and also the nature of errors , their causes and how they can be detected and corrected are all taken care in DLL.
Design issues of DLL:
The DLL has specific functions to carryout those are
i.e, DLL takes the packets coming from N/W layer and are encapsulated into frames for Transmission.
each frame contains a frame header and a trailer and a payload field for holding the packet.
the heart of DLL does the frame formation.
Services provided to the N/W Layer:
The function of DLL is to provide services to N/W layer
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]]>The post Optical Communication System appeared first on ece4uplp.
]]>An Optical fiber transmission link comprises the elements shown in the given figure.
The key sections are
Additional components include optical connectors, splicers, couplers (or) beam splitters and repeaters.
Cable:
optical fiber is one of the most important elements in an optical fiber link. The cable may contain copper wires for powering repeaters which are needed for periodically amplifying and reshaping the signal in long distance communication.
The cable generally contains several cylindrical hairthin glass fibers, each of which is an independent communication channel.
Similar to copper cables, the installation of optical fiber cables can be either aerial, in ducts, under sea (or) buried directly in the ground.
As a result of installation and (or) manufacturing limitations, individual cable lengths will range from several hundred meters to several kilo meters for long distance applications.
The real size and cable weight determines the actual length of a single cable section.
Cable in ducts— shorter length
Aerial/ buried applications—– longer lengths.
The complete longdistance transmission line is formed by splicing (or) connecting together these cable sections.
In optical fibers attenuation is a function of wave length .
In early stages of technology, optical fibers were used in
First window: (800nm900nm) wave length.
Later on optical fibers are used in the longwave length region.
Longwave length region (11001600) nm
Second windowcentered around 1300nm.
Third window centered around 1550nm.
Transmitter:
Once the fiber cable is installed a light source (which is dynamically compatible with the fiber cores) is used to launch power into the fiber.
The electric i/p signal is either analog (or) digital form the Transmitter circuit converts this electric signal to an optical signal.
Optical source is a squarelaw device. In (800900) nm region the light source is made up of
Ga Al As and in long distance region (1100nm1600nm) In Ga AsP is the alloy used.
after an optical signal (light) has been launched into the fiber, it will be attenuated and distorted with increasing distance because of scattering, absorption and dispersion mechanisms in the wave guide.
Receiver:
The attenuated and distorted , modulated optical power emerging from the fiber end will be detected by photo diode (or) photo detector.
Photo detector converts optical power into electrical signal (it also uses a squarelaw).
photo detectors are PIN diodes, Avalanche photo diodes and the type of material it is made up of is In Ga As.
further the electrical signal will be amplified and restored.
therefore the design of the receiver is more complex than that of transmitter.
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]]>The post Colpitt’s Oscillator appeared first on ece4uplp.
]]>It consists of a singlestage inverting amplifier and an LC phase shift Network.
The two capacitors and provides potential divider used for providing . is the feedback element and which provides positive feedback required for sustained Oscillations.
The amplifier circuit is a selfBias Circuit with , and parallel combination of with .
is applied through a resistor (or) RFC choke some times. This RFC choke offers very high impedance to high frequency currents.
value has chosen in such a way that it offers high impedance. Two coupling Capacitors and are used to block d.c currents, that means they do not permit d.c currents into tank circuit.
These capacitors and provides a path from Collector to Base through LC Network.
when is switched on , a transient current is produced in the tank circuit an consequently damped oscillations are setup in the circuit.
The oscillatory current in the tank circuit produces a.c voltages across and . If terminal 1 is more positive w.r. to 2 , then voltages across and are opposite thus providing a phase shift of between 1 and 2.
as the transistor is operating in CE mode , it provides a phase shift of .
Therefore the over all phase shift provided by the circuit results which is an essential condition for developing oscillations.
If the feedback is adjusted so that the loop gain then then the circuit acts as an Oscillator.
The frequency of oscillation depends on the tank circuit and is varied by gang (or) group tuning of and means .
working:
The capacitors and are charged by and are discharged through the coil setting up of oscillations with frequency
.
these oscillations across are applied to the BaseEmitter junction and the amplified version of output is collected across Collector (the frequency of amplifier output is same as that of input of the amplifier) .
This amplified energy is given back to tank circuit to compensate losses.
therefore un damped oscillations results in the circuit.
Derivation for frequency of oscillations:
chose for sustained oscillations.
Analysis(Qualitative):
if , and are pure reactive elements such that , and .
from the general condition for an Oscillator
.
find the real and imaginary parts,
equating imaginary part to zero , since .
.
after simplification
.
by substituting results .
substituting the value of in the real part gives . this is the condition for sustained oscillations.
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]]>The post Brewster’s angle appeared first on ece4uplp.
]]>.
As .
.
by squaring on both sides
By using Snell’s law .
using the above equation substituting this in EQN (I).
.
.
after simplification .
as and .
..
by simplification .
here is called as Brewster’s angle.
Let us assume two mediums are lossless dielectrics and are nonmagnetic then
.
.
.
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]]>The post OSI reference model appeared first on ece4uplp.
]]>This is also known as ISOOSI model(International Standards OrganizationOpen System Interconnection model)
and is used to connect open systems(open they are ready for communication)
The OSI model has 7 layers. These layers are formed by considering the following things
Now the model looks like this
Physical layer:
Physical layer is connected with
At physical layer the data rate, synchronization of bits, line configuration(pointtopoint,Broadcasting) and the topology used and Transmission mode( simplex/duplex) are specified.
Data Link Layer:
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]]>The post Link state Routing(dynamic) appeared first on ece4uplp.
]]>The two problems in Distance Vector Routing are
for these reasons it was replaced by new algorithm known as Link State Routing algorithm (LSR) algorithm.
the main idea of LSR is as follows(for a Router)
Step 1: Discover it’s neighbors and learn their N/W addresses.
Step 2:Measure the delay (or) cost to each of it’s neighbors.
Step 3: Construct a packet with the information a Router has learned.
Step 4: Send this packet to all the Routers.
Step 5:Compute the shortest path to every other Router.
for example,
S 1:Learning about the neighbors
first of all, when a Router is booted to learn about it’s neighbors it will send a packet called ‘HELLO’ on each pointto point line.
the Router on the other hand is expected to send back a reply saying who it is?
when two (or) more Routers are connected by a LAN, the situation is more complicated and the Routers are named uniquely to avoid any conflicts.
In the LAN A, C and F are connected to LAN, when a distance Router hears that 3 Routers are all connected to F, it is essential to know whether all 3 means same F (or) not?
To avoid this we can treat LAN as an additional node N as below
N in the above figure is an artificial node, the path from A to C is represented as ANC.
S2: each Router in LSR requires to know an estimate of delay to each of it’s neighbors.
one way to measure delay send an ECHO packet and get reply immediately and then calculate the roundtripdelay t/2 .
for better results perform this same no.of times and use the average.
while measuring delay one question that arises is to consider the load (or) not? If load is considered, the round trip timer must be started when ECHO packet is queued.
when load is ignored the timer shouted be started when the ECHO packet reaches the front queue.
when a Router has a choice between 2 lines with the same Band width one of which is loaded all the time and the other one is not loaded at all.
Then Router will chose the time with less load as the shortest path, this will result in better performance.
Consider a Sub net which is divided into 2 parts X and Y an is connected by 2 lines CF and EI.
Suppose the line CF is heavily loaded with long delays(including Queuing delay) after the new Routing tables have been installed most of the traffic will now go on EI.
Consequently in the nest update CF will appear as best path. Routing Tables may oscillate wildly causing some potential problems.
One solution to this is to divide the load equally among the lines but that may disturb the concept of best path.
S3: Building link state Packets
Once the transformation needed for the exchange has been collected the next step is for each Router is to build a link state packet.
link state packet consists of information regarding to sender , sequence no, Age, neighbors delays.
for example consider the Sub net
These link state packets have to build periodically and also when a Router going down etc.
S4: Distributing the Link State Packets
The net thing is to distribute the Ls packets reliably. in order to distribute the packets we may use flooding , to make flooding more efficient we use sequence numbers to packets.
The main problem is with sequence no’s repetition of Seq.nos one solution is to use a 32 bit Seq.no. which may take 137 years to repeat the same no.
If a Router crashes the sequence no becomes a zero then there is a possibility a Router may discards it.
To avoid all the above problems we use a parameter called Age whenever Age=0 the Router discards a packet .
after distribution process we use refinements to this distribution process(flooding).
whenever a packet arrives it first placed in a holding area later on another packet arrives the 2 Seq.nos are compared , if they are equal the duplicate is discarded.
The figure shows the buffer space at Router B
Suppose a packet is coming from source A with Seq.no 21 and Age as 60
we may expect an Acknowledgement from C and F but not from A.
Computing the new Routes for a Router :
after constructing the LS packets to all the Routers
we may use Dijkstra’s algorithm to construct the shortest path to all the destinations and this can be updated from time to time.
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]]>The post Distance Vector Routing(dynamic) appeared first on ece4uplp.
]]>dynamic algorithms may consider the current traffic (or) load on the Network.
Two types of dynamic routing algorithms are there
Distance Vector Routing operates by the following way
each Router maintains a table (gives the information about distance to other routers) and updates these routing tables by exchanging information with it’s neighbors.
It is also known as BellmanFord (or) Ford Fulkerson algorithm.
DVR is used in ARPANET and also as RIP.
In DVR each Router will maintain a Routing Table regarding to each Router in the subnet and the estimate of the time (or) distance to the destination.
one can use different design metrics like no.of hops, time delay in (milli Seconds), no.of packets Queued etc.
Here time delay is used as a metric.
Therefore a Router knows a delay to each of it’s neighbors and once every T milli Seconds these delays get updated by exchanging information with it’s neighboring Routers.
Consider a subnet with Routers A,B,…..L . Now choose a Router J with immediate neighbors (directly connected to J) are A, I, H and K.
Now the estimated delay of J to A, I, H & K are 8, 10, 12 & 6 milli Seconds respectively.
Suppose J wants to calculate a new route from J to G this is possible by finding the delay from J to G using the neighbors to J.
i.e, J to G delay (through A) = J to A delay +A to G delay = 8+18=26 mSec.
J to G delay (through I) = J to I delay +I to G delay = 10+31=41 mSec.
J to G delay (through H) = J to H delay +H to G delay = 12+6=18 mSec.
J to G delay (through K) = J to K delay +K to G delay = 6+31=37 mSec.
The best among the 4 possibilities is through H with less delay 18 mSec and makes as entry in it’s Routing table.
In this way Router J computes all possible delays to each router and updates it in it’s Routing table.
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]]>The post Shortest Path Routing (static) appeared first on ece4uplp.
]]>This algorithm just finds the shortest path between them on the graph.
There exists many design metrics to choose to get the shortest path are no.of hops, queue length,transmission delay etc.
for example if we choose no.of hops as metric, the paths ABC, ABE have equal no of hops means that those are equally long but ABC is much larger than ABE.
The labels on the above graph (2,2,7) are computed as a function of the distance, Band width, average traffic, cost etc.
one of the algorithm used for computing the shortest path between 2 nodes is Dijkstra’s algorithm.
it is as follows, Initially all nodes are labeled with infinite distance.
Let us consider the figure as shown below
to find the shortest path from A to D.
step 1: choose the source node as A and mark it as permanent node.
step 2: find the adjacent nodes to A those are B and G then choose the node with the smallest label as the permanent node.
Now this node B becomes the new working node.
step 3: Now start at B and repeat the same procedure
by following above procedure two paths are available ABEGHD with a distance of 11 from A and ABEFHD with a distance of 10 from A.
so the second path is chosen as a shortest path.
therefore the final shortest path is ABEFHD with nodes A,B,E,F,H and D as permanent nodes.
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]]>The post Broadcast Routing(dynamic) appeared first on ece4uplp.
]]>i.e, sending a packet to all destinations simultaneously is called Broadcasting.
Different methods of Broadcasting:
so this is least desirable one.
In this technique each packet contains a list of destinations (or) a bit map for those destinations.
when a packet arrives at a router, the router checks all the output lines it requires. The router generates a new copy of the packet for each output line after sufficient number of hops each packet will carry only one destination.
i.e, multi destination routing is like separately addressed packets (to B,C,D,E & D) must follow the same route one of them pays full fare and rest are free.
A spanning tree is a subset of subnet that includes all the routers but contains no loops.
if each router knows which of it’s lines belong to spinning tree then it broadcasts packet to all the lines except the one it arrived on.
This is efficient method in terms of Band width usage but problem is to maintain the knowledge of all the nodes of spanning tree at a routes.
Consider a subnet and it’s sink tree for router I as root node and how reverse path algorithm works in figure (C)
on the first hop I sends packets to F, H, J & N. on the second hop eight packets are generated among them 5 are given to preferred paths indicated as circles (A,D,G,O,M)
of the 6 packets generated in third hop only 3 are given to preferred paths (C,E & K) the others are duplicates.
in the fourth hop to B and L after this broadcasting terminates.
advantages of reverse path forwarding:
The principle is : if a packet arrives on a line if it is preferred one to reach source it gets forwarded.
if it arrives on a line that is not preferred one that packet is discarded as a duplicate.
ex:
when a packet arrives at ‘L’ the preferred paths are N and P so it forward the packets to both N and P and if a packet arrives at ‘K’ , there the preferred path is M and N is not preferred so it forwards packet to M and discards to N.
This is reverse path forwarding.
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]]>The post Asynchronous Transfer Model(ATM) appeared first on ece4uplp.
]]>Asynchronous Transfer Model is another important connection oriented Network.
Why we call it asynchronous is most of the transmission in telephone systems is synchronous (closed tied to a clock) but ATM is not such type.
ATM was designed in 1990’s, it was the cell ray protocol designed by the ATM forum and was adopted by ITUT.
Design goals:
The problems associated with existing networks:
The design goals come into picture for ATM, since there exists some problems that are associated with the existing systems.
Frame Networks:
Before ATM we have data communications at DLL are based on frame switching and frame networks .
i.e, different protocols use frames of varying size (frame has data and header). If header size is more than that of actual data there is a burden so some protocols have enlarged the size of data unit relative to the header.
if there is no data in such cases there is a wastage , so there is to provide variable frame sizes to the users.
Mixed N/w Traffic:
If there exists variable frame sizes
suppose we have two networks generating frames of variable sizes that is N/W 1 is connected to line 1 and the frame is X. N/W 2is connected to line 2 and of having 3 frames of equal sizes A,B,C are connected to a TDM.
If X has arrived a bit earlier than A,B,C (having more priority than X) on the output line . The frames has to wait for a time to move on to the output line, this causes delay for line 2 N/W.
i.e, Audio and video frames are small so mixing them with conventional data traffic often creates unacceptable delays and makes shared frame links unusable for audio and video information.
but we need to send all kinds of traffic over the same links.
Cell Networks:
so a solution to frame internet working is by adopting a concept called cell networking.
In a cell N/W we use a small data unit of fixed size called cell so all types of data are loaded into identical cells and are multiplexed with other cells and are routed through the cell N/W.
because each cell is small and of same size the problems associated with multiplexing different sized frames are avoided.
Asynchronous TDM:
ATM uses asynchronous TDM hence the name Asynchronous Transfer Model.
i.e, it multiplexes data coming from different channels. it also uses fixed size slots called cells.
ATM Mux’rs fill a slot with a cell from any input channel that has a cell and slot is empty if there is no cell.
ATM architecture:
ATM was going to solve all the world’s networking and telecommunications problems by merging voice, data, cable TV, telex,telegraph…… and everything else into a single integrated system that could do everything for everyone.
i.e, ATM was much successful than OSI and is now widely used in telephone system for moving IP packets.
ATM is a cellswitched N/W the user access devices are connected through a userto N/W interface (UNI) to the switches inside the N/W. The switches are connected through N/WtoN/W interface (NNI) as shown in the following figure
Virtual Connection:
two end points is accomplished through transmission paths (TP’s), Virtual Paths (VP’s) and Virtual Circuits (VC’s)
ATM Virtual Circuits:
Since ATM N/w’s are connectionoriented, sending data requires a connection , first sending a packet to setup the connection.
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]]>The post Parallel Polarization appeared first on ece4uplp.
]]>Parallel polarization means field lies in the XZplane (y=0) that is the plane of incidence, the figure illustrates the case of parallel polarization
then the incident and reflected fields is given by
now the reflected wave is
since
let’s find out then by using the equation , .
and the transmitted fields in the second medium is
where .
Transmission coefficient:
as and also that the tangential components of and are continuous at the boundary z=0.
, since
(1)+(2) implies
.
Reflection coefficient:
from EQN (1)
after simplification
.
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]]>The post Surface impedance appeared first on ece4uplp.
]]>The surface impedance may be defined as the ratio of the tangential component of the electric field at the surface of the conductor to the current density (linear) which flows due to this electric field.
given as (or) .
is the Electric field strength parallel to and at the surface of the conductor.
and is the total linear current density which flows due to .
The represents the total conduction per meter width flowing in this sheet.
Let us consider a conductor of the type plate, is placed at the surface y=0 and the current distribution in the ydirection is given by
Assume that the depth of penetration () is very much less compared with the thickness of the conductor.
from ohm’s law
.
then .
(or) .
we know that
for good conductors .
then
.
therefore the surface impedance of a plane good conductor which is very much thicker than the skin depth is equal to the characteristic impedance of the conductor.
This impedance is also known s input impedance of the conductor when viewed as transmission line conducting energy into the interior of metal.
when the thickness of the plane conductor is not greater compared to the depth of penetration , reflection of wave occurs at the back surface of the conductor.
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]]>The post oblique incidence appeared first on ece4uplp.
]]>Now consider the situation that is more general case that is the oblique incidence.
In this case the EM wave (incident wave) not strikes normally the boundary. i.e, the incident wave is not propagating along any standard axes (like x,y and z).
Therefore EM wave is moving in a random direction then the general form is
it is also in the form .
then is called the wave number vector (or) the propagation vector.
and is called the position vector (from origin to any point on the plane of incidence) , then the magnitude of is related to according to the dispersion.
.
.
.
.
i. and are mutually orthogonal.
ii. and lie on the plane .
then the field corresponding to field is .
Now choose oblique incidence of a uniform plane wave at a plane boundary.
the plane defined by the propagation vector and a unit normal vector to the boundary is called the plane of incidence.
the angle between and is the angle of incidence.
both the incident and reflected waves are in medium 1 while the transmitted wave is in medium 2 .
Now,
.
the wave propagates
(1) indicates that all waves are propagating with same frequency. (2) and (3) shows that the tangential components of propagation vectors be continuous.
implies since .
implies .
now velocity .
then from Snell’s law , where and are the refractive indices of the two media.
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]]>The post Poynting theorem appeared first on ece4uplp.
]]>Poynting theorem is used to get an expression for propagation of energy in a medium.
It gives the relation between energy stored in a timevarying magnetic field and the energy stored in timevarying electric field and the instantaneous power flow out of a given region.
EM waves propagates through space from source to destination. In order to find out power in a uniform plane wave it is necessary to develop a power theorem for the EM field known as poynting theorem.
The direction of power flow is perpendicular to and in the direction of plane containing and .
i.e, it gives the direction of propagation .
Watts/m^{2} (or) VA/m^{2}.
Proof:
from Maxwell’s equations
the above equation has units of the form current density Amp/m^{2}. When it gets multiplied by V/m. The total units will have of the form power per unit volume.
Amp/m^{2} , Volts/m.
Amp. Volt/m^{3} Watts/m^{3} Power/volume.
by using the vector identity
then
.
from the equation of Maxwell’s
by using the vector identity
if
from EQN(I) ,
by integrating the above equation by over a volume
by converting the volume integral to surface integral
.
the above equation gives the statement of Poynting theorem.
Poynting theorem:
It states that the net power flowing out of a given volume is equal to the time rate of decrease in the energy stored with in that volume V and the ohmic losses.
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]]>The post Lag compensator appeared first on ece4uplp.
]]>A Lag compensator has a Transfer function of the form
, where and
PoleZero Plot of Lag compensator:
i.e, the pole is located to the right of the zero.
Realization of Lag compensator as Electrical Network:
The lag compensator can be realized by an electrical Network.
Assume impedance of source is zero and output load impedance to be infinite .
The transfer function is
after simplification
after comparing the above equation with the transfer function of lag compensator has a zero at and has a pole at .
from the pole and .
therefore the transfer function has a zero at and a pole at .
.
the values of the three parameters , and C are determined from the two compensator parameters and .
using the EQN(II)
, .
there is an additional degree of freedom in the choice of the values of the network components which is used to set the impedance level of the N/w.
the gain is
D.C gain at is which is greater than 1.
Let the zerofrequency gain as unity, then the Transfer function is .
Frequencyresponse of Lag compensator:
Note:“lag” refers to the property that the compensator adds positive phase to the system over some appropriate frequency range.
, let .
the frequency response of lag compensator is
at .
has a slope +20 dB/decade with corner frequency .
slope is 20 dB/decade with corner frequency .
to find at which frequency the phase is minimum , differentiate w.r to and equate it to zero.
implies , which is invalid because .
.
, at this lead compensator has minimum phase given by
implies .
.
at , .
Choice of :
Any phase lag at the gain cross over frequency of the compensated system is undesirable.
To prevent the effects of lag compensator , the corner frequency of the lag compensator must be located substantially lower than the of compensated system.
In the high frequency range , the lag compensator has an attenuation of dB, which is used to obtain required phase margin.
The addition of a lag compensator results in an improvement in the ratio of control signal to noise in the loop.
high frequency noise signals are attenuated by a factor , while lowfrequency control signals under go unit amplification (0 dB gain).
atypical value of .
Procedure for bodeplot of a lead compensator:
Step 1: Sketch the Bodeplot of the uncompensated system with the gain k. Set the value of k according to the steadystate error requirement.
Measure the gain cross over frequency and the phase margin of uncompensated system.
Step 2: find at which phase angle of uncompensated system is
+ given Phase Margin+ .
is a good assumption for phaselag contribution.
Step 3: find gain of the uncompensated system at and equate it to 20 log () and then find .
Step 4: choose the upper corner frequency of the compensator to one octave to one decade below and find value.
Step 5: Calculate phase lag of compensator at , if it is less than go to next step.
Step 6: Draw the Bode plot of compensated system to meet the desired specifications.
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]]>The post Lead Compensator appeared first on ece4uplp.
]]>A Lead compensator has a Transfer function of the form
, where and
Polezero plot of Lead compensator:
i.e, the pole is located to the left of the zero.
Realization of Lead compensator as an Electrical Network:
The lead compensator can be realized by an electrical Network.
Assume impedance of source is zero and output load impedance to be infinite .
The transfer function is
after simplification
by comparing this equation with the transfer function of lead compensator has a zero at and the pole is .
from the pole and .
therefore the transfer function has a zero at and a pole at .
.
the values of the three parameters , and C are determined from the two compensator parameters and .
using the EQN(II)
, .
there is an additional degree of freedom in the choice of the values of the network components which is used to set the impedance level of the N/w.
the gain is
D.C gain at is which is less than 1.
attenuation is used to determine the steady state performance.
while using a lead N/w , it is important to increase the loop gain by an amount of .
A lead compensator is visualized as a combination of a N/w and an amplifier.
Note:“lead” refers to the property that the compensator adds positive phase to the system over some appropriate frequency range.
Frequencyresponse of a lead compensator:
, let .
the frequency response of lead compensator is
to find at which frequency the phase is maximum , differentiate w.r to and equate it to zero.
implies , which is invalid because .
.
, at this lead compensator has maximum phase given by
implies .
.
at , .
when there is a need for phase leads of more than , two cascaded lead networks are used where each N/w provides half of the required phase.
for phase leads more than , decreases sharply and if single N/w is used will be too low.
Choice of :
In choosing parameters of compensator depends on and C . The value may be anything but for there is a constraint. It depends on inherent noise in Control systems.
from the lead N/w , it’s been observed that the high frequency noise is amplified by while low frequencies by unity.
more (or) less should not be less than 0.07.
Procedure for bodeplot of a lead compensator:
Step 1: Sketch the Bodeplot of the uncompensated system with the gain k. Set the value of k according to the steadystate error requirement.
Measure the gain cross over frequency and the phase margin of uncompensated system.
Step 2: using the relation
Additional phase lead required = specified phase margin Phase Margin of uncompensated system.
is a margin of safety required by the fact that the gain cross over frequency will increase due to compensation.
for example : is a good assumption for 40 dB/decade.
(or) 60 dB/decade.
Step 3: Set the maximum phase of the lead compensator Additional phase lead required and compute .
Step 4: Find the frequency at which the uncompensated system has a gain of dB, which gives the new gain cross over frequency.
with as the gain cross over frequency the system has a phase margin of .
where as with as the gain cross over frequency the system has a phase margin of .
Step 5: Now . find the value of and the transfer function of lead compensator .
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]]>The post Introduction to Root Locus appeared first on ece4uplp.
]]>while in the analysis of a given system, the very first investigation that needs to be made is whether the system is stable or not?
However, the determination of stability of a system is necessary but not sufficient.
A stable system with low damping is also unwanted.
a design problem in which the designer is required to achieve the desired performance for a system by adjusting the location of its close loop poles in the Splane by varying one (or) more system parameters.
The Routh’s criterion obviously does not help much in such problems.
for determining the location of closedloop poles one may resort to the classical techniques of factoring the characteristic equation and determining it’s roots.
when the degree is higher (or) repeated calculations are required as a system parameter is varied for adjustments.
a simple technique, known as the root locus technique, for finding the roots of the ch.eqn introduced by W.R.Evans.
This technique provides a graphical method of plotting the locus of the roots in the Splane as a given system parameter is varied from complete range of values (may be from zero to infinity).
The roots corresponding to a particular value of the system parameter can then be located on the locus (or) value of the parameter for a desired root location can be determined from the locus.
Root Locus:
ch. equation is
let
To find the whether the roots are on the Root locus (or) not
They have to satisfy ‘2’ criteria known as
Magnitude criterion:
the magnitude criterion states that will be a point on root locus, if for that value of s
i.e,
Angle criterion:
where q=0,1,2……….
if is odd multiple of , a point s on the root locus, if is odd multiple of at of , then that point is on the root locus.
Root Locus definition:
The locus of roots of the Ch. eqn in the Splane by the variation of system parameters (generally gain k) from to is known as Root locus.
It is a graphical method
to Inverse Root Locus
to Direct Root Locus
generally Root Locus means Direct Root Locus.
m= no .of zeros
n= no.of poles
from magnitude criterion
The open loop gain k corresponding to a point on Root Locus can be calculated
product of length of vectors from open loop poles to the point /product of length of vectors from open loop zeros to the point .
from the Angle criterion,
i.e,( sum of angles of vectors from Open Loop zeros to point )(sum of angles of vectors from Open Loop poles to point)
where q=0,1,2………
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]]>The post Inductance of a Coaxial cable, Solenoid & Toroid appeared first on ece4uplp.
]]>Consider a coaxial cable with inner conductor having radius a and outer conductor of radius b and the current is flowing in the cable along zaxis in which the cable is placed such that the axis of rotation of the cable coincides with zaxis.
the length of the coaxial cable be d meters.
we know that the between the region is
and since
as , here the flux linkage
where Total flux coming out of the surface
Since the magnetic flux will be radial plane extending from to and to .
Henries.
Inductance of a Solenoid:
Consider a Solenoid of N turns and let the current flowing inside it is ‘I’ Amperes. The length of the solenoid is ‘l’ meters and ‘A’ is its cross sectional area.
– Total flux coming out of solenoid.
flux linkage
, from the definition
As B is the Magnetic flux density given
from EQN(I) ,
because
The field strength H of a solenoid is
EQN (II) becomes
from the inductance definition
Henries.
Inductance of a Toroid:
Consider a toroidal ring with Nturns and carrying current I.
let the radius of the toroid be ‘R’ and the total flux emerging be
then flux linkage
the magnetic flux density inside a toroid is given by
where A is the cross sectional area of the toroid then
Henries.
if the toroid has a height ‘h’ , inner radius and outer radius then its Inductance is Henries.
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]]>The post Classification (or) topologies of feedback Amplifiers appeared first on ece4uplp.
]]>The first part represents the type of sampling at the output .
and the second part represents the type of Mixing at the input
For any Amplifier circuit we require
Classification of feedback Amplifiers is also known as feedback Topologies.
VoltageSeries feedback Connection:
at i/p side connection is Series and at o/p side connection used is Shunt since o/p is collected is voltage.
Series connection increases i/p impedance and Voltage at the o/p indicates a decrease in o/p impedance.
i.e, and .
CurrentSeries feedback Connection:
Series connection increases i/p impedance and Current at the o/p indicates an increase in o/p impedance.
i.e, and .
VoltageShunt feedback Connection:
In this connection, both i/p and o/p impedance decreases .
i.e, and .
CurrentShunt feedback Connection:
Shunt connection decreases i/p impedance and Current at the o/p indicates an increase in o/p impedance.
i.e, and .
Effect of negative feedback on different topologies:
Type of f/b 
Voltage gain

Band Width with f/b  i/p impedance 
o/p impedance 
VoltageSeries  decreases  increases  increases  decreases 
CurrentSeries  decreases  increases  increases  increases 
VoltageShunt  decreases  increases  decreases  decreases 
CurrentShunt  decreases  increases  decreases  increases 
Similarly negative feedback decreases noise and harmonic distortion for all the four topologies.
Note: for any of the characteristics in the above table, increase ‘s shown by multiplying the original value with and decrease ‘s shown by dividing with .
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]]>The post continuity equation appeared first on ece4uplp.
]]>consider a closed surface S with a current density , then the total current I crossing the surface S is given by the volume V
The current coming out of the closed surface is
since the direction of current is in the direction of positive charges, positive charges also move out of the surface because of the current I.
According to principle of conversation of charge, there must be decrease of an equal amount of positive charge inside the closed surface.
therefore the time rate of decrease of charge with in a given volume must be equal to the net outward current flow through the closed surface of the volume.
By Divergence theorem
implies
for a constant surface the derivative becomes the partial derivative
this is for the whole volume.
for a differential volume
, which is called as continuity of current equation (or) Point form (or) differential form of the continuity equation.
This equation is derived based on the principle of conservation charge states that there can be no accumulation of charge at any point.
for steady (dc) currents
from . The total charge leaving a volume is the same as total charge entering it. Kirchhoff’s law follows this equation.
This continuity equation states that the current (or) the charge per second, diverging from a small volume per unit volume is equal to the time rate of decrease of charge per unit volume at every point.
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]]>The post Effect of negative feedback on Band width of an Amplifier appeared first on ece4uplp.
]]>Proof: Consider an amplifier with gain ‘A’
Now the frequency response of the amplifier is as shown in the figure. Frequency response curve means gain (dB) Vs frequency (Hz)
the frequency response of an amplifier consists of three regions
Gain in low frequency region is given as,
open loop gain,
– frequency,
– lower cut off frequency, where Gain in constant region is .
Gain in Highfrequency region is .
In lowfrequency region:
since open loop gain in lowfrequency region is and gain with feedback is
From EQN(I) after substituting in the above equation
Now by dividing the whole expression with
, where and
for example lower cutoff frequency implies is decreasing with negative feedback.
In Highfrequency region:
Gain with out feed back in High frequency region is
Now Gain with negative feed back is
Substituting in the above equation
Now by dividing the whole expression with
, where and
for example lower cutoff frequency implies is increasing with negative feedback.
In Midfrequency region:
Gain with out feed back is
and the gain with negative feed back is
With out feedback  With feedback 
lower cutoff frequency is  lower cutoff frequency , increases 
upper cutoff frequency is  upper cutoff frequency is 
BW =  increases 
Thus negative feedback decreases lower cutoff frequency and increases upper cutoff frequency.
Over all gain decreases with negative feedback and Band Width increases.
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]]>The post Full Wave Rectifier appeared first on ece4uplp.
]]>FWR converts a.c voltage into pulsating DC in twohalf cycles of the applied input signal.
Here we use a Transformer, whose secondary winding has been split equally into two half waves with a common center tapped connection ‘c’.
This configuration results in each diode conducting in turn when it’s anode terminal is positive with respect to Center point ‘c’ of the Transformer.
Working of Full Wave Rectifier:
During positive half cycle of applied i/p signal
i.e, Diode is Forward Biased and is Reverse Biased , under this condition the equivalent circuit is as shown below
, when there is no diode resistance.
Similarly the conditions of diodes will be reversed for the negative half cycle of i/p signal.
i.e, Diode is Reverse Biased and is Forward Biased , under this condition the equivalent circuit is and output voltage is .
the i/p and o/p wave forms are as shown below
FWR is advantageous compared to HWR in terms of its efficiency and ripple factor.
Ripple Factor ():
to find out and of output signal
,
,
,
.
and .
now the ripple factor results to be
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]]>The post Timedomain representation of SSBSC signal appeared first on ece4uplp.
]]>, where is InPhase component of S(t) obtained by
i. Multiplying S(t) with .
ii. and passing the product through a LPF with suitable cutoff frequency.
By finding the Fourier Transform of inphase component
after restricting the signal between
Similarly is the quadrature phase component of s(t), obtained by multiplying S(t) with and by passing the resultant signal through a LPF .
By finding the Fourier Transform of Qphase component
after restricting the signal between
Now Let’s assume S(f) is the required frequency spectrum of SSBSC signal when only USB has been transmitted.
i.e,
from the above figure,
one can obtain , by shifting the signal S(f) towards right by and left by
Now by adding and
from the above figure, results to be
from the frequency spectrum of , the timedomain representation turns out to be
Similarly,
The resultant signals and
from the frequency spectrum of turns out to be
since Signum function is
when expressed in terms of Signum function
By using Hilbert transform of m(t) , the timedomain representation turns out to be
From EQN’s (I) and (II) , the timedomain representation of SSBSC signal results
.
similarly, SSB signal when only LSB has been transmitted
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]]>The post Analog ElectronicCircuits Lab appeared first on ece4uplp.
]]>Expt1iiZener Diode Characteristics
Expt2Full Wave Rectifier with and without filters
Expt3Common Emitter Characteristics
Expt6single stage CE Amplifierfrequency response
Expt8Noninverting Amplifier
Expt9Differentiator and Integrator using opamp
Expt10square and triangular wave generators
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]]>The post Input and Output characteristics of transistor in Common Base Configuration appeared first on ece4uplp.
]]>Input characteristics in Common Base configuration means input voltage Vs input current by keeping output voltage as constant.
i.e, Vs by keeping constant.
Therefore the curve between Emitter current and Emitter to Base voltage for a given value of Collector to Base voltage represents input characteristic.
for a given output voltage , the input circuit acts as a PNjunction diode under Forward Bias.
from the curves there exists a cutin (or) offset (or) threshold voltage below which the emitter current is very small and a substantial amount of Emittercurrent flows after cutin voltage ( 0.7 V for Si and 0.3 V for Ge).
the emitter current increases rapidly with the small increase in . with the low dynamic input resistance of a transistor.
i.e,
This is calculated by measuring the slope of the input characteristic.
i.e, input characteristic determines the input resistance .
The value of varies from point to point on the Nonlinear portion of the characteristic and is about in the linear region.
Output Characteristics:
Output Characteristics are in between output current Vs output voltage with input current as kept constant.
i.e,
i.e, O/p characteristics are in between Vs by keeping as constant.
basically it has 4 regions of operation Active region, saturation region,cutoff region and reachthrough region.
active region:
from the active region of operation is almost independent of
i.e,
when increases, there is very small increase in .
This is because the increase in expands the collectorbase depletion region and shortens the distance between the two depletion regions.
with kept constant the increase in is so small. transistor operates in it’s normal operation mode in this region.
saturation region:
here both junctions are Forward Biased.
Collector current flows even when (left of origin) and this current reaches to zero when is increased negatively.
cutoff region:
the region below the curve ,transistor operates in this region when the two junctions are Reverse Biased.
even though mA. this is because of collector leakage current (or) reversesaturation current (or) .
punch through/reach through region:
is practically independent of over certain transistor operating region of the transistor.
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]]>The post Early effect in Common Base Configuration appeared first on ece4uplp.
]]>In Common Base configuration in the Reverse Bias, As the voltage increases, the spacecharge width between collector and base tends to increase, with the result that the effective width of the base decreases. This dependency of Basewidth on the Collector to emitter voltage is known as the early effect.
The early effect has three consequences:
For higher values of , due to early effect the value of increases, for example changes say from 0.98 to 0.985. Hence there is a very small positive slope in the CB output characteristics and hence the output resistance is not zero.
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]]>The post Hall effect appeared first on ece4uplp.
]]>The figure shows the experimental arrangement to observe Hall effect Now
I Current flowing in the semi conductor (xdirection)
B Applied Magnetic field (zdirection)
E Induced Electric field is along ydirection perpendicular to both I and B.
Now charge carrier electron is moving under the influence of two fields both electric field(E) and Magnetic field(B).
i.e, electron is under the influence of both E and B, E applies some force on electron similarly B.
under equilibrium
, where is the drift velocity
Electric field Intensity due to Hall effect is
is the Hall voltage between plates 1 and 2.
and d is the distance between the two plates.
In an Ntype Semi conductor, the current is due to electrons , plate 1 is negatively charged compared to plate 2.
The current density J related to charge density is
W width of the specimen, d height of the specimen.
From EQN(I) and From EQN(II)
up on multiplying with ‘d’ on both sides
from EQN(III)
, let Hall coefficient
.
Uses of Hall effect (or) Applications of Hall effect:
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]]>The post E due to infinite line charge distribution appeared first on ece4uplp.
]]>Consider a point P at which Electric field intensity has to be determined which is produced by the line charge distribution.
from the figure let the coordinates of P are ( a point on yaxis) and assume is a small differential charge confirmed to a point M as coordinates.
produces a differential field
the position vector and the corresponding unit vector
then the Electric field strength produced by the infinite line charge distribution is
to solve this integral let
as
.
is a function of only, there is no component and is the perpendicular distance from the point P to line charge distribution .
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]]>The post Energy Density in Electrostatic Fields appeared first on ece4uplp.
]]>To determine the Energy present in an assembly of charges (or) group of charges one must first determine the amount of work necessary to assemble them.
It is seen that , when a unit positive charge is moved from infinity to a point in a field, the work is done by the external source and energy is expended.
If the external source is removed then the unit positive charge will be subjected to a force exerted by the field and will be moved in the direction of force.
Thus to hold the charge at a point in an electrostatic field, an external source has to do work , this energy gets stored in the form of Potential Energy when the test charge is hold at a point in a field.
when external source is removed , the Potential Energy gets converted to a Kinetic Energy.
In order to derive the expression for energy stored in electrostatics (i.e, the expression of such a Potential Energy)
Consider an empty space where there is no electric field at all, the Charge is moved from infinity to a point in the space ,let us say the point as , this requires no work to be done to place a charge from infinity to a point in empty space.
i.e, work done = 0 for placing a charge from infinity to a point in empty space.
now another charge has to be placed from infinity to another point . Now there has to do some work to place at because there is an electric field , which is produced by the charge and is required to move against the field of .
Hence the work required to be done is
i.e, .
Work done to position at = .
Now the charge to be moved from infinity to , there are electric fields due to and , Hence total work done is due to potential at due to charge at and Potential at due to charge at .
Work done to position at = .
Similarly , to place a charge at in a field created by (n1) charges is ,work done to position at
Total Work done
The total work done is nothing but the Potential energy in the system of charges hence denoted as ,
if charges are placed in reverse order (i.e, first and then and then and finally is placed)
work done to place
work done to place
work done to place
Total work done
EQN (I)+EQN(II) gives
let , and are the resultant Potentials due to all the charges except that charge.
i.e, is the resultant potential due to all the charges except .
Joules.
The above expression represents the Potential Energy stored in the system of n point charges.
simillarly,
Joules
Joules
Joules for different types of charge distributions.
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]]>The post SwitchesCircuit Switching appeared first on ece4uplp.
]]>Circuit Switches (or) Structure of Circuit Switch:
The Switches used in Circuit Switching are called CircuitSwitches
SpaceDivision Switch:
Crossbar Switch:
In this type of Switch we connect n inputs and m outputs using micro switches (Transistors) at each cross point to form a crossbar switch of size n X m.
The number of cross points required = n X m.
As n and m increases, cross points required also increases, for example n=1000 and m=1000 requires n X m= 1000 X 1000 cross points. A crossbar with these many number of cross points is impractical and statics show that 25% of the cross points are in use at any given time.
Multi stage Switch:
The solution to Crossbar Switch is Multi stage switching. Multi stage switching is preferred over crossbar switches to reduce the number of cross points. Here number of crossbar switches are combined in several stages.
Suppose an N X N crossbar Switch can be made into 3 stage Multi bar switch as follows.
The total number of cross points = , so the number of cross points required are less than singlestage crossbar Switch = .
for example k=2 and n=3 and N=9 then a Multistage switch looks like as follows.
The problem in Multistage switching is Blocking during periods of heavy traffic, the idea behind Multi stage switch is to share intermediate crossbars. Blocking means times when one input line can not be connected to an output because there is no path available (all possible switches are occupied). Blocking generally occurs in tele phone systems and this blocking is due to intermediate switches.
Clos criteria gives a condition for a nonblocking Multi stage switch
, and Total no.of Cross points .
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]]>The post GATE problems in EMT appeared first on ece4uplp.
]]>Ans: Given loss less insulator
Cm/Sec
from
from Equations I and II
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]]>The post Solved Example problems in Electro Magnetic Theory appeared first on ece4uplp.
]]>Ans. Given P(1,3,5)
Cylindrical :
Similarly
Spherical :
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]]>The post Phase Locked Loop (PLL) appeared first on ece4uplp.
]]>Let the input to PLL is an FM signal
let
Now the signal at the output of VCO is FM signal (another FM signal, which is different from input FM signal) Since Voltage Controlled Oscillator is an FM generator.
the corresponding phase
It is observed that S(t) and b(t) are out of phase by . Now these signals are applied to a phase detector , which is basically a multiplier
the error signal
on further simplification , the product yields a higher frequency term (Sum) and a lower frequency term (difference)
This product e(t) is given to a loop filter , Since the loop filter is a LPF it allows the difference and term and rejects the higher frequency term.
the over all output of a loop filter is
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]]>The post Frequency domain representation of a Wide Band FM appeared first on ece4uplp.
]]>i.e, Singletone FM signal is
Now by expressing the above signal in terms of Phasor notation ( , None of the terms can be neglected)
Let is the complex envelope of FM signal.
is a periodic function with period . This can be expressed in it’s Complex Fourier Series expansion.
i.e, this approximation is valid over . Now the Fourier Coefficient
let implies
as and
let as order Bessel Function of first kind then .
Continuous Fourier Series expansion of
Now substituting this in the Equation (I)
The Frequency spectrum can be obtained by taking Fourier Transform
n value  wide Band FM signal 
0  
1  
1  
…  …. 
From the above Equation it is clear that
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]]>The post Matched Filter, impulse response h(t) appeared first on ece4uplp.
]]>Transfer Function of Matched Filter:
Transfer Function of Optimum filter is
if input noise is white noise , its Power spectral density (Psd) is .
then H(f) becomes
From the properties of Fourier Transforms , by Conjugate Symmetry property
Equation (I) becomes
From Timeshifting property of Fourier Transforms
From TimeReversal Property
By Shifting the signal by T Seconds in positive direction(time) ,the Fourier Transform is given by
Now the inverse Fourier Transform of the signal from the Equation(II) is
Let the constant is set to 1, then the impulse response of Matched Filter will become .
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]]>The post Mutual Information I(X ; Y) Properties appeared first on ece4uplp.
]]>Mutual Information is given by equation
we know that
Substitute Equation (II) in Equation (I)
The above Equation can be written as
we knew that
This result can be applied to Mutual Information , If and be , Both and are two probability distributions on same alphabet , then Equation (III) becomes
i.e, , Which implies that Mutual Information is always Nonnegative (Positive).
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]]>The post Example Problems in Electro Magnetic Theory Wave propagation appeared first on ece4uplp.
]]>Ans. Given , and
and
Find the Loss tangent
So given medium is a Conductor (Copper)
then
, .
.
.
2. If for a medium in which a wave with a frequency of is propagating . Determine the propagation constant and intrinsic impedance of the medium when
Ans: Given , , and .
Since , the given medium is a lossless Dielectric.
which implies
.
Ω.
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]]>The post Delta modulation and Demodulation appeared first on ece4uplp.
]]>i.e, Delta Modulation (DM) is a Modulation scheme in which an incoming message signal is over sampled (i.e, at a rate much higher than the Nyquist rate ) to purposely increase the correlation between adjacent samples of the signal. Over sampling is done to permit the use of a sample Quantizing strategy for constructing the encoded signal.
Signaling rate and Transmission Band Width are quite large in PCM. DM is used to overcome these problems in PCM .
DM transmits one bit per sample.
The process of approximation in Delta Modulation is as follows:
The difference between the input () and the approximation () is quantized into only two levels corresponding to Positive and negative differences.
i.e, If the approximation () falls below the signal ()at any sampling epoch(the beginning of a period)output signal level is increased by .
On the other hand the approximation () lies above the signal () , output signal level is diminished by provided that the input signal does not change too rapidly from sample to sample.
it is observed that the change in stair case approximation lies with in .
This process can be illustrated in the following figure
Delta Modulated System: The DM system consists of Delta Modulator and Delta Demodulator.
Delta Modulator:
Mathematical equations involved in DM Transmitter are
error signal:
Present sample of the (input) sampled signal:
last sample approximation of stair case signal:
Quantized error signal( output of onebit Quantizer):
if .
and .
encoding has to be done on the after Quantization that is when the output level is increased by from its previous quantized level, bit ‘1’ is transmitted .
similarly when output is diminished by from the previous level a ‘0’ is transmitted.
from the accumulator
where is the Quantization error.
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]]>The post Fourier Series and it’s applications appeared first on ece4uplp.
]]>The alternative representation if a set of complex exponentials are used,
The resulting representations are known as Fourier Series in ContinuousTime [Fourier Transform in the case of NonPeriodic signal]. Here we focus on representation of ContinuousTime and DiscreteTime periodic signals in terms of basic signals as Fourier Series and extend the analysis to the Fourier Transform representation of broad classes of aperiodic, finite energy signals.
These Fourier Series & Fourier Transform representations are most powerful tools used
The development of Fourier series analysis has a long history involving a great many individuals and the investigation of many different physical phenomena.
The concept of using “Trigonometric Sums”, that is sum of harmonically related sines and cosines (or) periodic complex exponentials are used to predict astronomical events.
Similarly, if we consider the vertical deflection of the string at time t and at a distance x along the string then for any fixed instant of time, the normal modes are harmonically related sinusoidal functions of x.
The scientist Fourier’s work, which motivated him physically was the phenomenon of heat propagation and diffusion. So he found that the temperature distribution through a body can be represented by using harmonically related sinusoidal signals.
In addition to this he said that any periodic signal could be represented by such a series.
Fourier obtained a representation for aperiodic (or) nonperiodic signals not as weighted sum of harmonically related sinusoidals but as weighted integrals of Sinusoids that are not harmonically related, which is known as Fourier Integral (or) Fourier Transform.
In mathematics, we use the analysis of Fourier Series and Integrals in
In addition to the original studies of vibration and heat diffusion, there are numerous other problems in science and Engineering in which sinusoidal signals arise naturally, and therefore Fourier Series and Fourier T/F’s plays an important role.
for example, Sine signals arise naturally in describing the motion of the planets and the periodic behavior of the earth’s climate.
A.C current sources generate sinusoidal signals as voltages and currents. As we will see the tools of Fourier analysis enable us to analyze the response of an LTI system such as a circuit to such Sine inputs.
Waves in the ocean consists of the linear combination of sine waves with different spatial periods (or) wave lengths.
Signals transmitted by radio and T.V stations are sinusoidal in nature as well.
The problems of mathematical physics focus on phenomena in Continuous Time, the tools of Fourier analysis for DT signals and systems have their own distinct historical roots and equally rich set of applications.
In particular, DT concepts and methods are fundamental to the discipline of numerical analysis , formulas for the processing of discrete sets of data points to produce numerical approximations for interpolation and differentiation were being investigated.
FFT known as Fast Fourier Transform algorithm was developed, which suited perfectly for efficient digital implementation and it reduced the time required to compute transform by orders of magnitude (which utilizes the DTFS and DTFT practically).
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]]>The post Block Diagram of Digital Communication System/Elements of DCS appeared first on ece4uplp.
]]>Our basic aim is to understand the various modules and sub systems in the system. If we are trying to understand the design and various features of DCS , it is plus imperative that we have to understand how we should design a transmitter and we must understand how to design a very good quality Receiver. Therefore one must know the features of the channel to design a good Transmitter as well as receiver that is the channel and it’s contribution will come repeatedly in digital Communications.
Source: the primary block (or) the starting point of a DCS is an information source, it may be an analog/digital source , for example the signal considered is analog in nature, then the signal generated by the source is some kind of electrical signal which is random in nature. if the signal is a speech signal (not an electrical signal) that has to be converted into electrical signal by means of a Transducer, which can be considered as a part of source itself.
Sampling & Quantization: the secondary block involves the conversion of analog to discrete signal
this involves the following steps
Sampling: it is the process that involves in the conversion of Continuous Amplitude Continuous Time (CACT) signal into Continuous Amplitude Discrete Time (CADT) signal.
Quantization: it is the process that involves in the conversion of Continuous Amplitude Discrete Time (CADT) signal into Discrete Amplitude Discrete Time (DADT) signal.
Source Encoder: An important problem in Digital Communications is the efficient representation of data generated by a Discrete Source, this is accomplished by source encoder.
” The process of representation of incoming data from a Discrete source into a more suitable form required for Transmission is known as source encoding”
Note:The blocks Sampler, Quantizer followed by an Encoder constructs ADC (Analog to Digital Converter).
∴ the output of Source encoder is a Digital Signal, the advantages of Source coding are
Channel encoder:Channel coding is also known as error control coding. Channel coding is a technique which reduces the probability of error by reducing Signal to Noise Ratio at the expense of Transmission Band Width.The device that performs the channel coding is known as Channel encoder.
Channel encoding increases the redundancy of incoming data , this also involves error detection and error correction along with the channel decoder at the receiver.
Spreading Techniques: Spread Spectrum techniques are the methods by which a signal generated with a particular Band Width is deliberately spread in the frequency domain, resulting in a signal with a wider Band width.
There are two types of spreading techniques available
The output of a spreaded signal is very much larger than incoming sequence. Spreading increases the BW required for transmission, which is a disadvantage even though spreading is done for high security of data.
SS techniques are used in Military applications.
Modulator: Spreaded sequence is modulated by using digital modulation schemes like ASK, PSK, FSK etc depending up on the requirement, now the transmitting antenna transmits the modulated data into the channel.
Receiver: Once you understood the process involved in transmitter Block. One should perform reverse operations in the receiver block.
i.e the input of the demodulator is demodulated after that despreaded and then the channel decoder removes the redundancy added by the channel encoder ,the output of channel decoder is then source decoded and is given to Destination.
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]]>The post Why Digital Communication is preferred over Analog Communication? appeared first on ece4uplp.
]]>Communication is the process of establishing Connection (or) link between two points (which are separated by some distance) and transporting information between those two points. The electronic equipment used for communication purpose is called Communication equipment. The equipment when assembled together forms a communication system.
Examples of different types of communications are
Why Digital?
A General Communication system has two devices and a medium (channel) connecting those two devices. This can be understood that a Transmitter and Receiver are separated by a medium called as Communication channel. To transport an informationbearing signal from one point to another point over a communication channel either Analog or digital modulation techniques are used.
Now Coming to the point, Why Digital communication is preferred over analog Communication?
Why are communication systems, military and commercial alike, going digital?
When an ideal binary digital pulse propagating along a Transmission line. The shape of the waveform is affected by two mechanisms
Both of these mechanisms cause the pulse shape to degrade as a function of line length. During the time that the transmitted pulse can still be reliably identified (i.e. before it is degraded to an ambiguous state). The pulse is amplified by a digital amplifier that recovers its original ideal shape. The pulse is thus “reborn” (or) regenerated.
Circuits that perform this function at regular intervals along Transmission system are called “regenerative repeaters’. This is one of the reasons why Digital is preferred over Analog.
3.Digital Circuits Vs Analog Circuits:
Digital Circuits are less subject to distortion and Interference than are analog circuits because binary digital circuits operate in one of two states FULLY ON (or) FULLY OFF to be meaningful, a disturbance must be large enough to change the circuit operating point from one state to another. Such two state operation facilitates signal representation and thus prevents noise and other disturbances from accumulating in transmission.
However, analog signals are not twostate signals, they can take an infinite variety of shapes with analog circuits and even a small disturbance can render the reproduced wave form unacceptably distorted. Once the analog signal is distorted, the distortion cannot be removed by amplification because accumulated noise is irrecoverably bound to analog signals, they cannot be perfectly generated.
4. With digital techniques, extremely low error rates and high signal fidelity is possible through error detection and correction but similar procedures are not available with analog techniques.
5. Digital circuits are more reliable and can be produced at a lower cost than analog circuits also; digital hardware lends itself to more flexible implementation than analog hardware.
Ex: – Microprocessors, Digital switching and large scale Integrated circuits.
6. The combining of Digital signals using Time Division Multiplexing (TDM) is simpler than the combining of analog signals using Frequency Division Multiplexing (FDM).
7. Digital techniques lend themselves naturally to signal processing functions that protect against interference and jamming (or) that provide encryption and privacy and also much data communication is from computer to computer (or) from digital instruments (or) terminal to computer, such digital terminations are normally best served by Digital Communication links.
8. Digital systems tend to be very signalprocessing intensive compared with analog systems.
Apart from pros there exists a con in Digital Communications that is nongraceful degradation when the SNR drops below a certain threshold, the quality of service can change suddenly from very good to very poor. In contrast most analog Communication Systems degrade more gracefully.
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]]>The post Maxwell’s Equations in Point (or Differential form) and Integral form appeared first on ece4uplp.
]]>The 4 Equations above are known as Maxwell’s Equations. Since Maxwell contributed to their development and establishes them as a selfconsistent set. Each differential Equation has its integral part. One form may be derived from the other with the help of Stoke’s theorem (or) Divergence theorem.
A word statement of the field Equations is readily obtained from their mathematical statement in the integral form.
1. .
i.e, The magneto motive force ( is m.m.f)around a closed path is equal to the conduction current plus the time derivative of the electric displacement through any surface bounded by the path.
2. .
The electro motive force ( is e.m.f)around a closed path is equal to the time derivative of the magnetic displacement through any surface bounded by the path.
3. .
The total electric displacement through the surface enclosing a volume is equal to the total charge within the volume.
4. .
The net magnetic flux emerging through any close surface is zero.
the timederivative of electric displacement is called displacement current. The term electric current is then to include both conduction current and displacement current. If the timederivative of electric displacement is called an electric current, similarly is known as magnetic current, e.m.f as electric voltage and m.m.f as magnetic voltage.
the first two Maxwell’s Equations can be stated as
Maxwell’s Equations of staticfields in differential form and integral form are:
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]]>The post Inconsistensy in Ampere’s law (or) Displacement Current density appeared first on ece4uplp.
]]>From Ampere’s Circuital law which is applicable to Steady Magnetic fields
By taking divergence of Ampere’s law the Ampere’s law is not consistent with timevarying fields
,since
the divergence of the curl is identically zero which implies , but from the continuity equation which is not equal to zero, as is an unrealistic limitation(i.e we can not assume as zero) .
to make a compromise between the above two situations we must add an unknown term to Ampere’s Circuital law
i.e,
then by taking the Divergence of the above equation
from Equation(1),Equation(4) becomes
thus
from Maxwell’s first Equation
then Equation (5) becomes
then
This is the equation obtained which does not disagree with the continuity equation. It is also consistent with all other results. This is a second Maxwell’s Equation is timevarying fields so the term has the dimensions of current density Amperes/Squaremeter. Since it results from a timevarying electric flux density ( ) , Maxwell termed it as displacement current density .
up to this point three current densities are there , and .
when the medium is Nonconducting medium
the total displacement current crossing any given surface is expressed by the surface integral
from Ampere’s law
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]]>The post Correlation Receiver(Special case of Optimum Receiver) appeared first on ece4uplp.
]]>from the figure output of the filter after sampling at seconds is
at output becomes
Now by substituting
by substituting the Equation(2) in Equation(1) over the limits
Now by replacing with the above equation becomes
The equation (3) suggests that the Optimum Receiver can be implemented as shown in the figure, this form of the Receiver is called as correlation Receiver. This receiver requires the integration operation be ideal with zero initial conditions. Correlation Receiver performs coherentdetection.
in general Correlation Receiver can be approximated with Integrate and dump filter.
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]]>The post Relation between E and V appeared first on ece4uplp.
]]>i.e,
.
This equation implies that the total work done in moving a charge from A to B and then from B to A is zero.
i.e,
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]]>The post Electric Potential (V) appeared first on ece4uplp.
]]>Assume a test charge at A in an Electric field, let points A and B are located at units from the origin O,from Coulomb’s law the force acting on a test charge is
The work done in moving a point charge along a differential length is is given by
so the total work done in moving a point charge from A to B is
the direction of work done is always opposite to the direction of displacement.
where A is the initial point and B is the final point. Dividing the work done by the charge gives the potential energy per unit charge denoted by ,this is also known as potential difference between the two points A and B.
Thus
if we take B as initial point and A as final point , then
To derive the expression for V in terms of charge Q and distance r , we can use the concept of Electric field intensity produced by a charge Q, which is placed at a distance r
i.e,
from Equation(1)
since
similarly,
where and are the scalar potentials at the points A and B respectively. If A is located at with respect to origin ,with zero potential and B is located at a distance r with respect to origin. then the work done in moving a charge from A (infinity) to B is given by
here
volts.
hence the potential at any point is the potential difference between that point and a chosen point at which the potential is zero. In other words assuming Zero potential at infinity .
The potential at a distance r from a point charge is the work done per unit charge by an external agent in transferring a test charge from infinity to that point.
i.e,
So a point charge located at a point P with position vector then the potential at another point Q with a position vector is
As like superposition principle is applicable to V also that is for n point charges located at points with position vectors
then the potential at is
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]]>The post few problems on Auto correlatioon Function(ACF) and Energy Spectral Density(ESD) appeared first on ece4uplp.
]]>Ans. We know that Auto correlation function forms fourier transform pair with Energy Spectral Density function
the Fourier Transform of
here
the Fourier Transform of x(t) is X(f) and is and the Energy Spectral Density
By finding the inverse Fourier Transform of S(f) gives the Auto Correlation Function
the ACF of the given signal is inverse Fourier Transform of S(f) which is .
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]]>The post Figure of merit of FM appeared first on ece4uplp.
]]>The incoming signal at the front end of the receiver is an FM signal got interfered by Additive noise , since the FM signal has a transmission band width ,the Band Pass filter characteristics are also considered over the band of interest i.e from to .
The output of Band Pass Filter is is passed through a Discriminator for simplicity simple slope detector (discriminator followed by envelope detector) is used, the output of discriminator is this signal is considered over a band of by using a LPF .
The input noise to the BPF is n(t), the resultant output noise is band pass noise
phasor representation of Band pass noise is where and .
are orthogonal, independent and are Gaussian.
– follows a Rayleigh’s distribution and is uniformly distributed over . are separate random processes.
substituting Equations (1), (3) in (2)
where .
now the analysis is being done from it’s phasor diagram/Noise triangle as follows
is the resultant of two phasors and .
since
because .
is the phase of the resultant signal and when this signal is given to a discriminator results an output.
i.e,
i.e,
As
the second term in the Equation where – denotes noise after demodulation.
this can be approximated to , which is a valid approximation. In this approximation is Quadraturephase noise with power spectral density over
the power spectral density of will be obtained from Equation (6) using Fourier transform property
,
elsewhere.
the power spectral density functions are drawn in the following figure
, from Carson’s rule
the band width of v(t) has been restricted by passing it through a LPF.
Now,
.
To calculate Figure of Merit
Calculation of :
output Noise power
The output signal power is calculated from tha is
From Equations(I) and (II)
Calculation of :
input signal power
noise signal power
from Equations (III) and (IV)
Now the Figure of Merit of FM is
to match this with AM tone(singletone) modulation is used i.e, then the signal power and
since for tone(singletone) modulation .
when you compare singletone FM with AM
.
the modulation index will be beneficial in terms of noise cancellation, this is one of the reasons why we prefer WBFM over NBFM.
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]]>The post Capture effect in Frequency Modulation appeared first on ece4uplp.
]]>Let us suppose un Modulated FM carrier
By considering un modulated FM carrier in terms of frequency(by neglecting phase) i.e has been interfered by a near by interference located at a frequency where is a small deviation from .
the nearby inerference is
when the original signal got interfered by this near by interference , the received signal is
Let
now the phase of the signal is
as implies
since ,
As the demodulated signal is the output of a discriminator
, which is the detected at the output of the demodulator.
the detected output at the demodulator is in the absence of message signal i.e, .
i.e, when message signal is not being transmitted at the transmitter but detected some output which is nothing but the interference.
As ‘A’ is higher the interference is less at t=0 the interference is and is a linear function of , when is small interference is less. That is is closer to interference is less in FM.
Advantage of FM : is Noise cancellation property , any interference that comes closer with the carrier signal (in the band of FM) more it will be cancelled. Not only that it overridden by the carrier strength but also exerts more power in the demodulated signal.
This is known as ‘Capture effect’ in FM which is a very good property of FM. Over years it has seen that a near by interference is 35 dB less in AM where as the near by interference in FM is 6 dB less this is a big advantage.
Two more advantages of FM over AM are:
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]]>The post Propagation of plane EM wave in conducting medium (or) lossy dielectrics appeared first on ece4uplp.
]]>where as a lossless dielectric is a perfect dielectric,then wave equations for conductors are also holds good here
i.e,
then
Equation (1) is called helm holtz equation and is called propagation constant.
Since is a complex quantity it can be expressed as
– is attenuation constant measured in Nepers/meter.
is phase constant measured in radians/meter.
by equating real and imaginary parts separately
and
by substituting value in the equation (2)
let
the roots of the above quadratic expression are
similarly,
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]]>