What is transient in AC circuit? and why it is Necessary??

 ✱WHAT IS TRANSIENT?

➝"Transient is occurs due to the sudden change in the supply voltage or change in  energy stored by memory element (Inductor or capacitor) is called as a transient". 

➝The time taken by memory element to comes from one steady state value to another steady state value is referred as a Transient time or response of an ac Circuit.

• Electrical Network or Circuit is mainly consisting of three elements, which are ;

1. RESISTANCE (R)
2. INDUCTOR (L)
3. CAPACITOR (C)

• Out of this three elements Inductor (L) and Capacitor (C) are memory elements because it stored energy proportional to the 1/2 L×I^2 and 1/2 C×V^2 respectively, but Resistor (R) is memory less element because it doesn't stored any energy in it.
• Now we are studying standard discharging and normal discharging equation.

❋STANDARD DISCHARGING EQUATION:-

                              y0 (t) = y0 e^-t/τ .........(1)

Where; τ= Time constant

Assuming various value of time constant 0, τ, 2τ, 3τ, .........∞

     y (t=0) = y0 × e^-0  = y0

     

        y (t=τ)  = y0 × e^-1  =0.367 y0

        

        y (t=2τ)  = y0 × e^-2  =0.135 y0

         

          y (t=∞)  = y0 × e^-∞  =0

Fig (a) STANDARD DISCHARGING CURVE.

➝As shown in the above figure behaviour of standard discharging.

❋NORMAL DISCHARGING EQUATION:-

                 y(t) = K + y0 × e^-t/τ ...........(2)

   Assuming various value of time constant 0, τ, 2τ, 3τ, .........∞           

       y(t=0) = K + y0 × e^-0  = K +y0 

      y(t=τ) = K + y0 × e^-1  = K +0.368y0 

      y(t=∞) = K + y0 × e^-∞  = K

Fig (b) NORMAL DISCHARGING CURVE.

• Please remember in Network Theory "t = 5τ" is called as a SETTLING TIME.
• "SETTLING TIME IS DEFINED AS A TIME AT WHICH RESPONSE OF THE NETWORK IS COMES TO STEADY STATE REGION IS CALLED AS A SETTLING TIME OF NETWORK".

• From the above discussion we conclude that Ideally the memory element (Inductor or capacitor) is DISCHARGED TO ZERO but Practically it doesn't discharge to Zero (few amount of energy is stored in it).

    ....................Thank you 🙂..........

        

What is Two port and One port Networks???

• ONE PORT NETWORK:-

➝ A Network is considered as a rectangular box with Two input terminal are called as a ONE PORT OR SINGLE PORT NETWORK.

Fig(a) ONE PORT NETWORK

• TWO PORT NETWORK:-

➝A Network is considered as a rectangular box with Two input terminal and Two output terminal are called as a Two port Networks or Four terminal Network.

Fig(b) TWO PORT NETWORK

• 
  DIFFERENT PARAMETERS OF TWO PORT NETWORK:-

1. IMPEDANCE OR OPEN CIRCUIT "Z" PARAMETER.
2. "Y" - PARAMETER OR SHORT CIRCUIT PARAMETERS.
3. "H" - PARAMETERS OR HYBRID PARAMETERS.
4. TRANSMISSION PARAMETERS OR ABCD PARAMETERS.

❋ OPEN CIRCUIT "Z" PARAMETER:-

Fig(c) Z PARAMETER

⇨Consider the above Network in this two port network each input voltage V1 and output voltage V2 is expressed in terms of input current I1 and Output Current I2 respectively.

⇨According to ohm's law........

                           V = R×I 

   But here,.  R = Z so,

                          [V] = [Z]×[I] ................(1)

⇨In matrix form..........

                                                     ..................(2)

⇨From the figure of two port network we can write down the equation of V1&V2 which is exactly Same as KVL equation..........

                   V1 = Z11×I1 + Z12×I2 ..............(3)

                   V2 = Z21×I1 + Z22×I2 ..............(4)

➝ASSUMING OUTPUT PORT IS OPEN CIRCUITED (I2=0):-

    Put I2= 0 in Equation Number (3)&(4)......

                    V1= Z11×I1 

                ∴ Z11 = V1/I1|I2=0 ......................(5)

  And.         V2 = Z21×I1 

                ∴ Z21 = V2/I1|I2=0 ......................(6)

➝ASSUMING INPUT PORT IS OPEN CIRCUITED (I1=0) :-

   Now put I2=0 in Equation Number (3)&(4)......

                     V1 = Z12×I2 

                  ∴ Z12 = V1/I2|I1=0 ....................(7)

                    V2 = Z22×I2 

                     V2 = Z22×I2

                  ∴ Z22 = V2/I2|I1=0 ................,...(8)

Where ;

• Z11&Z22 = DRIVING IMPEDANCE OF INPUT AND OUTPUT RESPECTIVELY.
• Z12&Z21 = TRANSFER IMPEDANCE OF INPUT AND OUTPUT RESPECTIVELY. 

✱EQUIVALENT MODEL OF"Z" PARAMETER:-

Fig(d) EQUIVALENT MODEL OF Z PARAMETER

   .....................Thank you 🙂👍...................

                    

                   

Why SILICON material is mostly preferred for manufacturing POWER ELECTRONICS COMPONENTS??

• First we will see what is power electronics?

➝ " Power Electronics is the branch of electronics that deals with controls and conversion of large power"

➝In power electronics special power electronics components like IGBT (INSULATED GATE BIPOLAR JUNCTION TRANSISTOR), SCR ( SILICON CONTROLLED RECTIFIER), GTO (GATE TURN OFF THYRISTOR), MOSFET( METAL OXIDE SEMICONDUCTOR FIELD EFFECT TRANSISTOR), ETC. Are used for various purposes like VARIABLE FREQUENCY DRIVE (VFD), AUTOMATIC VOLTAGE CONTROLLED (AVC), AUTOMATIC SPEED CONTROL OF INDUCTION MACHINES, etc.

• ADVANTAGES OF POWER ELECTRONICS:-

⇨It has high efficiency.

⇨Reliable and flexible operations.

⇨It is possible to make fully automatic system.

⇨Less maintenance is required.

• DISADVANTAGES OF POWER ELECTRONICS:-

⇨Power Electronics devices produced harmonics in the system and due to harmonics disturbance are produced in the system.

⇨Power Electronics devices are costly.

❇️WHY SILICON MATERIAL IS MOSTLY PREFERRED FOR MAKING POWER ELECTRONICS COMPONENTS?

• SOME IMPORTANT POINTS:-

1. Band :- Band is defined as the collection of energy.
2. Conduction Band:-  It is the band which is partially filled with electrons or empty.
3. Valance Band :- It is the band which is fully filled with free electrons at 0° absolute temperature.
4. Energy Gap : It shows amount of energy which is required to moves free electrons from valance Band to conduction band.
5. Conductivity :- Conductivity is the ability of the material to pass charge or free electrons through it.

• Energy gap diagram of GERMANIUM and SILICON material;

Fig(a) ENERGY GAP OF GERMANIUM AND SILICON.

                            Eg = 1/ σ ...................(1)

 Where :- 

                  Eg = Energy gap 

                   σ  =  Conductivity of material

 

       From figure ;

             σGe = 1/.73

                      = 1.369 ................(2)

               σSi =  1/ 1.1

                      = .909 .................(3)

So we know that 

                             σGe > σSi

From this calculation we understand that conductivity of GERMANIUM IS GREATER THAN the conductivity of SILICON.

✲BUT DUE TO THE FOLLOWING REASONS SILICON MATERIAL IS MOSTLY PREFERRED:- 

Fig (b) COMPARISON BETWEEN GERMANIUM AND SILICON

• After studying this above TABLE we conclude that SILICON MATERIAL IS MOSTLY PREFERRED FOR MAKING POWER ELECTRONICS COMPONENTS.

       ...............Thank you 🙂👍...............

What is RESONANCE in series RLC circuit????

• RESONANCE:-

➝ " It is the phenomenon at which the effect of Inductive reactance (XL) and Capacitive reactance (XC) are compensated to each other in RLC circuit is called as a RESONANCE".

➝At the time of resonance circuit is behaves as a pure resistive circuits and at the time of resonance power factor of the circuit is UNITY.

❋RESONANCE IN SERIES RLC CIRCUIT:-

Fig(a) SERIES RLC CIRCUIT

⇨The Impedance Z of series RLC circuit is given as;

                 Z = R + jwL + j 1/WC

            ∴.  Z = R + wL - j/wc ................(1)

Magnitude

 |Z| = √R^2 + j( wL - 1/WC)^2 ...........(2)

➝ Current in RLC resonance circuit is;

                  I = V/Z amp. ..........(3)

          I = V/ √R^2 + j(wL - 1/WC)^2 ㄥ tan-1 (wL - 1/WC)/R   ...................(4)

• AT THE TIME OF RESONANCE XL = XC ;

                 XL = XC

              W0L = 1/ W0C 

               W0^2 = 1/ LC

          ∴ W0  = 1/ √LC rad/ Sec ...........(5)

• Frequency at the time of resonance ;

                     

                   W0 = 1/ √LC rad/ sec ....... ..(6)

                    

                   F0 = 1/ 2π√LC Hertz (Hz) .......(7)

❋ PROPERTY OF SERIES RLC RESONANCE CIRCUIT:-

⇾At the time of resonance the applied voltage is in phase with resultant current, it means the power factor is unity (COSΦ = 0).

⇾At the time of resonance the effects of XL &XC are compensated to each other, therefore the behaviour of the network is purely RESISTIVE.

⇾At the time of resonance the Current I = V/R amp. And it's value is maximum because total impedance of the circuit at the time of resonance is only "R" so I is maximum according to ohms law.

⇾At the time of resonance the Impedance Z is minimum.

           .................... Thank you 🙂................

What are the property of INCIDENCE matrix? Why we used it in Network analysis?

• INCIDENCE MATRIX:-

➝ "Incidence matrix is the mathematical representation of node current and voltage in various branches of the network".

➝Incidence matrix is used to describe the Nature of Incoming and Outgoing branches across any nodes in the Network.

➝Order of Incidence matrix is;

                 [A]n×B.    

           Where; n = Numbers of node

                          B = Number of branches 

• HOW TO MAKE INCIDENCE MATRIX OF GRAPH:-

Fig(a) GRAPH OF NETWORK

• Before making Incidence matrix of any graph following points are keep in mind.

⇨ +1 = If Direction of current is Away from node.
⇨ -1  = If Direction of current is Towards the node.

⇨ 0   =  If note Incidence 

• Now select any one node and check direction of current in all branches of the network corresponding to this particular node.
• Suppose we consider Node "A" please observed in fig (a) direction of current in branch 1 is towards the node so it is -1, and direction of current in branch 2 & 6 is away from the node so it is +1 and finally branch 3,4&5 are not Incidence so it is 0.
• All this steps are perform by taking one by one nodes.
• Finally we get Incidence matrix as shown in below figure.

Fig(b) INCIDENCE MATRIX OF GIVEN GRAPH 

✱PROPERTY OF INCIDENCE MATRIX:-

➝ Summation of all the columns of Incidence matrix is equal to ZERO.

➝ If the network ha Number of nodes is equal to numbers of branches (n = B) then the resultant Incidence matrix is a SQUARE MATRIX.

➝ The determinants of square matrix is always ZERO.

" INCIDENCE MATRIX IS USED TO FIND THE POSSIBLE TREES OF ANY NETWORKS WITHOUT DROWNING IT".

        .................THANK YOU 🙂.................

Concept of NETWORK TOPOLOGY.

• First we will discussed some important definition and then we will learn how to make GRAPH from any given NETWORKS.

❇️ IMPORTANT DEFINITIONS RELATED TO NETWORK TOPOLOGY;

1. GRAPH :- When all elements in the Network like Inductor, capacitor, Resistance etc. Are replaced by simple single line with small circle at both the ends then this type of configuration is called as a GRAPH.
2. NODE OR VERTICES :- Node is defined as the intersection of two or more branches at one common point is called as a NODE OR VERTICES.
3. BRANCH :- Branch of network is defined as a line which represents one Network element or combination of elements connected between two common point.
4. DEGREE OF NODE :- Degree of node is defined as the number of incoming branches across any node.
5. COMPLETE GRAPH :- A graph in which only one line segment is connected between any node pair is referred as a COMPLETE GRAPH.
6. NON CONNECTED GRAPH OR UN CONNECTED GRAPH :- A graph in which any node is isolated ( means no any branch is connected between this node) is known as a Non connected or un connected graph.
7. ORIENTED GRAPH :- A graph in which direction of current is indicated in all the branches then it's called as a ORIENTED GRAPH.
8. NON ORIENTED GRAPH :- A graph in which the direction of current is not indicated then it's know as a NON ORIENTED GRAPH.

❋Now we take one example and learn how to draw GRAPH of any random given NETWORKS.

Fig(a) ANY RANDOM ELECTRICAL NETWORK

➡️ STEPS TO MAKE GRAPH FROM ANY NETWORK :-

⇾Fisrt identify numbers of nodes in the given network and mark it as 1,2,3.... Or a,b,c.... Or p,q,r......etc.

⇾After identify nodes represent each node as circle in paper (number of node = number of circle).

⇾Now replaced all the network element like Inductor, capacitor, resistance etc with simple one line.

⇾Replaced all independent voltage sources with short circuit and all independent current sources are open circuit.

⇾Finally connect all this line segment with their respective nodes.

⇾Graph of network is ready but it is non oriented graph if we like to make oriented graph then assign direction of current in all the branches with respect to given source in the Network.

Fig(b) GRAPH OF THE GIVEN NETWORK.

• For any complete graph if we know number of nodes then we easily calculates number of branches of network.

           

  For any complete graph number of branches ;.        

                      B = n×(n - 1)/ 2............(1)

Where ; n = Numbers of nodes

        ................... Thank you 🙂....................

Why transformer doesn't work on DC supply???

• Before understanding this concept first we need to know working principle of transformer.

Fig (a) Working principle of transformer

• Working principle of transformer:-

➝ Transformer is works on the principle of MUTUAL INDUCTION.

➝ According to principle of MUTUAL INDUCTION, if time varying current (AC CURRENT) is given to the primary winding of transformer then it produces the time varying flux and due to this time varying flux EMF is induced in the primary winding, we already discussed in the previous article some amount of this primary winding flux is linked with secondary winding also, so EMF is induced in seconady Winding due to rate of change of current in the primary winding.

• Consider the equation of induced voltage in inductor or Coil;

Induced voltage V = -N di/dt ................(1)

                Where; - (minus) sign is due to LENZ LAW

                                 di/dt = Rate of change of current

❇️ CASE NUMBER :-1 INPUT IS AC

Fig (b) Input Sine wave

⇨According to Faraday's law we know that voltage is induced in the coil if and only there is relative motion between Conductor and Magnetic field.

⇨Suppose if we connect Sinusoidal input supply with primary of transformer then it produces time varying flux so EMF is induced in the primary winding and we know that supply is Sinusoidal EMF is also induced in the secondary winding due to rate of change of flux in the primary.

⇨So if we connect AC SUPPLY to the primary winding of transformer then transformer is satisfactory work with ac supply.

❇️CASE NUMBER :-2 INPUT IS DC

Fig (c) Input DC supply

⇨Suppose if we connect DC supply with primary winding of transformer, then it produces CONSTANT FLUX, Because DC is constant source it's value remain constant.

⇨Due to DC rate of change of flux will be Zero, so induced voltage in the primary winding will be ZERO.

                V = -N di/dt 

HERE di/dt = zero so V=0 means short circuit

• PLEASE OBSERVED VOLTAGE ZERO MEANS SHORT CIRCUIT, SO RESULT IS THAT THERE IS AN EXCESSIVE LARGE CURRENT IS FLOW THROUGH THE PRIMARY OF TRANSFORMER, DUE TO THIS LARGE CURRENT PRIMARY OF TRANSFORMER IS DAMAGED AFTER FEW TIME.
• So, from above discussion we conclude that TRANSFORMER DOESN'T WORK ON DC SUPPLY.

            ....................... Thank you 🙂.....................