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Pulse and Digital Circuits Venkata Rao K., Rama Sudha K. and Manmadha Rao G. Fig.13.3 Output for the given input when time constant is very small 14. A current pulse of amplitude 5 A in Fig.2p.11 is applied to a parallel RC combination shown in Fig.2p.12. Plot to scale the waveforms of the current flowing through capacitor for the cases: (i) t p =0.1RC, (ii) t p = RC, (iii) t p = 5RC Fig.2p.11The given input to the circuit Fig. 2p.12 The given circuit Solution: Till t = t p , using Laplace transforms, the circuit can be drawn as in Fig.14.1. © 2010 Dorling Kindersley India Pvt. Ltd 18
Pulse and Digital Circuits Venkata Rao K., Rama Sudha K. and Manmadha Rao G. Fig.14.1 Circuit in terms of Laplace transforms Applying KCL, we have 5 5RCs 5 IC () s R s 1 RCs 1s 1 R s Cs RC Taking t RC Laplace inverse, the charging current is iC ( t) 5e At t = t p, the current suddenly falls from 5 A to 0. The voltage across the capacitor at t = t p is [ 5 iC ( t p )] R Therefore for t ≥ t p, [5 iC( tp)] R [5 iC( tp)] IC () s 1 1 sR ( ) ( s ) Cs RC Taking Laplaceinverse i ( t) [5 i ( t )] e C C p -t-t ( p ) RC The circuit that represents the discharge of the condenser is presented in Fig.14.2. Case 1: For 0 < t < t i C p ( t) 5e i C decays exponentially, Fig.14.2 Circuit that indicates the discharge of the condenser t RC 0.1RC RC at t t , i ( t ) 5e 4.524 A p C p For t > t p , i C rises exponentially as © 2010 Dorling Kindersley India Pvt. Ltd 19
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