Time domain response in rc & rl circuits

PPT on Time domain response in RC & RL circuits in Circuits & networks

1. Time domain response in RC & RL circuits By: Jenish Thumar -130870111038 Dharit Unadkat -130870111039 Shivam Rai -130870111029 Guided by: Prof. Dipti Patel Ec 3 rd semester

2. Transients The time-varying currents and voltages resulting from the sudden application of sources, usually due to switching, are called transients . By writing circuit equations, we obtain integrodifferential equations.

3. Basic RL and RC Circuits First-Order RC Circuits Used for filtering signal by blocking certain frequencies and passing others. e.g. low-pass filter Any circuit with a single energy storage element, an arbitrary number of sources and an arbitrary number of resistors is a circuit of order 1. Any voltage or current in such a circuit is the solution to a 1st order differential equation. Ideal Linear Capacitor Energy stored A capacitor is an energy storage device memory device.

4. Basic RL and RC Circuits First-Order RC Circuits One capacitor and one resistor The source and resistor may be equivalent to a circuit with many resistors and sources. R + - C vs ( t ) + - vc ( t ) + - vr ( t )

5. Basic RL and RC Circuits First-Order RC Circuits Time Constant RC R=2k C=0.1F

6. Basic RL and RC Circuits First-Order RC Circuits Switch to 2 Initial condition Transient Response of RC Circuits

7. Series RL Circuit

8. Series RC Circuit

9. General First Order Differential Equation Solution of First Order Differential Equation

10. Basic RL and RC Circuits First-Order RC Circuits Time Constant R=2k C=0.1F

11. Basic RL and RC Circuits First-Order RL Circuits Ideal Linear Inductor i(t) + - v(t) The rest of the circuit L Energy stored: One inductor and one resistor The source and resistor may be equivalent to a circuit with many resistors and sources.

12. Basic RL and RC Circuits First-Order RL Circuits Time constant Indicate how fast i ( t ) will drop to zero. It is the amount of time for i ( t ) to drop to zero if it is dropping at the initial rate . t i ( t ) .

13. Basic RL and RC Circuits First-Order RL Circuits Switch to 2 Initial condition Transient Response of RL Circuits

14. Basic RL and RC Circuits     Initial Value （ t = 0 ） Steady Value ( t  ) time constant  RL Circuits Source (0 state) Source-free (0 input) RC Circuits Source (0 state) Source-free (0 input) Summary

15. Basic RL and RC Circuits Summary The Time Constant For an RC circuit,  = RC For an RL circuit,  = L / R -1/  is the initial slope of an exponential with an initial value of 1 Also,  is the amount of time necessary for an exponential to decay to 36.7% of its initial value

16. Basic RL and RC Circuits Summary How to determine initial conditions for a transient circuit. When a sudden change occurs, only two types of quantities will remain the same as before the change. IL ( t ), inductor current Vc ( t ), capacitor voltage Find these two types of the values before the change and use them as the initial conditions of the circuit after change.

17. Thank You