Time domain response in rc & rl circuits
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The document summarizes time domain responses in RC and RL circuits. It describes that transients are the time-varying currents and voltages resulting from sudden changes in sources. RC circuits with a single energy storage element are first-order circuits that can be used for filtering. The time constant for an RC circuit is RC and for an RL circuit is L/R. It represents the time required for an exponential to decay to 36.7% of its initial value. The document also discusses determining the initial conditions for transient analysis based on inductor current and capacitor voltage remaining constant during circuit changes.
Time domain response in rc & rl circuits
- 1. Time domain response in RC & RL circuits By: Jenish Thumar -130870111038 Dharit Unadkat -130870111039 Shivam Rai -130870111029 Guided by: Prof. Dipti Patel Ec 3rd 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 dt dq ti =)( dt dv c 2 2 1 cvcvdvpdtwEnergy stored A capacitor is an energy storage device memory device. )(=)+( tvtv Cc
- 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 + - Cvs(t) + - vc(t) + - vr(t)
- 5. Basic RL and RC Circuits First-Order RC Circuits )1( t C eEv /tc e E dt dv 0 0 t c t c dt dv EE dt dv RCTime Constant R 5 1 C 2 K E 0s 1ms 2ms 3ms 4ms V(2) 0V 5V 10V SEL>> RC R=2k C=0.1 F
- 6. Basic RL and RC Circuits First-Order RC Circuits Switch to 2 R 1 C 2 K E RC t c Aev Initial condition Evv CC )0()0( 0 Riv cc 0 dt dv RCv c c // tRCt c EeEev /t c e R E i • Transient Response of RC Circuits c c dv i C dt
- 7. Series RL Circuit dt tdi Ltv tiRtv L L LR )( *)( )(*)( sL L VtiR dt di L )(* L V ti L R dt di s L L )()( 0)()( 0,For t tvtvV LRs
- 8. dt tdv Cti tiRtv C R )( *)( )(*)( sc c Vtv dt dv CR )(* sc c V CR tv CRdt dv ) * 1 ()() * 1 ( 0)()( tvtvV cRs Series RC Circuit
- 9. )() 1 ( )( Ktx dt tdx General First Order Differential Equation Solution of First Order Differential Equation determinedbetoconstantsareB,A, 0for tBeA(t) t* x responsenaturalthecalledisBe responseforcedthecalledisA t*
- 10. Basic RL and RC Circuits First-Order RC Circuits RCTime Constant R 5 IS 1 C 2 K E R=2k C=0.1 F Time 0s 1.0ms 2.0ms 3.0ms 4.0ms V(2) 0V 5V 10V SEL>> t RC t C EeEetv )( E dt dv t C 0 0 t C dt dv E
- 11. Basic RL and RC Circuits First-Order RL Circuits Ideal Linear Inductor i(t) + - v(t) The rest of the circuit L dt di LiivP )( 2 1 )( 2 tLiLidipdttwL 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) 0 . 0t t dt di
- 13. Basic RL and RC Circuits First-Order RL Circuits Switch to 2 t L R Aei dt L R i di iR dt di L 0 Initial condition R E It 0,0 /t t L R e R E e R E i Transient Response of RL Circuits R 1 L 2 K E 0 0 0 0 0 : 0 : 1 ln i t t I i t t I t t i I i t R di dt i L R i t L t L R I ti 0 )( ln t L R eIti 0)(
- 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) 00 i R E iL R E i 0 0i 00 v Ev Ev 0 0v RL / RL / RC RC 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