Transients analysis and Its derivations

Transients and its types and Important differential derivations

1. Haseeb Memon 18EL-batch a [email protected]

2. Transient Introduction of Transient. Type of Transient. Importance of Differential Equation in Transient. Transient in RL circuit (DC). Short circuit current, Time constant.

3. What are Transients? Introduction Transients are the surges or spikes in electric currents and voltages which are transmitted through power or data lines. Electrical transients are momentary bursts of energy induced upon power, data, or communication lines. They are characterized by extremely high voltages that drive tremendous amounts of current into an electrical circuit for a few millionths, up to a few thousandths, of a second. A stage in which variations are created is called transient stage .

4. Transient Analogy(for understanding) Its analogy can be compared with bucket of water in which water is in its normal state but when a water is touched it create some waveforms or disturbances (which are similar to transient)and after sometime disturbances will end and then water will be in its normal steady state as it was before.

5. Presence of Transient Its Important to note that The  transient  part will  not present  in the response of an electrical circuit or network, if it contains only resistances. Because  resistor  is having the ability to adjust any amount of voltage and current . The  transient part occurs  in the response of an electrical circuit or network due to the presence of energy storing elements such as  inductor and capacitor . Because they can’t change the energy stored in those elements instantly.

6. Types of Transient Types Of Transient On the basis of Energy storing devices. Single-energy Transient: These transients are those in which only one form of energy, either electromagnetic or electrostatic is involved as in R-L and R-C circuits. Double Energy Transient: These transients are those in which both electromagnetic or electrostatic is involved as in R-L-C circuits.

7. Initiation Transients : These are produced when a circuit, which is originally dead, is energized. Subsidence Transients : These are produced when an energized circuit is rapidly de-energized and reaches an eventual steady-stage of zero current or voltage, as in the case of short-circuiting an R-L or R-C circuit suddenly. Transition Transients : These are due to sudden but energetic changes from one steady state to another . Classification of Transient

8. Complex Transients : These are produced in a circuit which is simultaneously subjected to two transients due to two independent disturbances or when the disturbing force producing the transients is itself variable. Relaxation Transients : In these transients, the transition occurs cyclically towards states, which when reached, become unstable themselves.

9. Order of Transient Some of the important differential equations, used in the treatment of single and double energy transients, are given below. We will consider both first-order and second-order differential equations. First Order Equations Second Order Equations

10. First Order Differential Equation Any circuit with a single energy storage element , an number of sources , and an arbitrary number of resistors is a circuit of first order. RL or RC circuit are example of First order transient.

11. Second Order Differential Equation Any circuit with a single capacitor, a single inductor, an arbitrary number of sources, and an arbitrary number of resistors is a circuit of second order. RLC circuit is an example of Second order transient equation.

12. A First-Order RC Circuit One capacitor and one resistor in series The source and resistor may be equivalent to a circuit with many resistors and sources Lect12 EEE 202 13 R C v s ( t ) + – v c ( t ) + – v r ( t ) + –

13. A First-Order RL Circuit One inductor and one resistor in parallel The current source and resistor may be equivalent to a circuit with many resistors and sources Lect12 EEE 202 14 v ( t ) i s ( t ) R L + –

14. A Second Order RLC Circuit The source and resistor may be equivalent to a circuit with many resistors and sources As seen In the circuit below capacitor, Inductor are involved. Lect12 EEE 202 15 v s ( t ) R C i ( t ) L + –

15. Importance Of Differential Equation in Transients

16. Importance Differential Equation is used to analyze and study the response of circuit when subjected to transient. Every voltage and current is the solution to a differential equation.

17. The Differential Equation Every voltage and current is the solution to a differential equation In a circuit of order n , these differential equations have order n The number and configuration of the energy storage elements determines the order of the circuit n  number of energy storage elements Lect12 EEE 202 18

18. The Differential Equation Equations are linear, constant coefficient: The variable x ( t ) could be voltage or current The coefficients a n through a depend on the component values of circuit elements The function f ( t ) depends on the circuit elements and on the sources in the circuit Lect12 EEE 202 19

19. Transients in RL Circuit(DC)

20. Transients in RL Circuit(DC) A  LR Series Circuit  consists basically of an inductor of inductance, L connected in series with a resistor of resistance, R. The resistance “R” is the DC resistive value of the wire turns or loops that goes into making up the inductors coil. Consider the LR series circuit below.

21. The current, i begins to flow through the circuit but does not rise rapidly to its maximum value of Imax as determined by the ratio of V / R (Ohms Law). This limiting factor is due to the presence of the self induced emf within the inductor as a result of the growth of magnetic flux, (Lenz’s Law).

22. Kirchhoff’s voltage law (KVL) gives us:

23. Time Constant The Time constant is time Required for transient to decrease to zero. The time required for the current flowing in the LR series circuit to reach its maximum steady state value is equivalent to about  5 time constants  or 5τ.

24. T H E E N D Thank you!