Introduction to Electric Circuits

186 Transient analysis Response of the RC circuit to a pulse input voltage Let the pulse of amplitude V and width T (>5~') sh ...

8.3 Circuits containing resistance and capacitance 187 accordance with Equation (8.19). The output voltage waveform is then as s ...

188 Transient analysis Example 8.8 The integrator circuit shown in Fig. 8.20 has R = 10 kf~ and C = 0.01 txF. Sketch the wavefor ...

8.3 Circuits containing resistance and capacitance 189 The RC differentiator circuit v( B i c .~ r I I I^0 V o = M R o Figure 8. ...

190 Transient analysis so that Vc + VR- 0. The voltage across the resistor will therefore have to change immediately to -Vc at t ...

8.3 Circuits containing resistance and capacitance 191 change but the voltage across the resistor can and it changes immediately ...

192 Transient analysis 8.4 THE LAPLACE TRANSFORM It is a common technique to transform problems to a different form in order to ...

8.4 The Laplace transform 193 The inverse transform is written f(t) = L-~[F(s)] (8.24) F(s) is often written as f which is read ...

194 Transient analysis These transform pairs, together with a few other commonly encountered ones, are given in Table 8.1. Table ...

8.4 The Laplace transform 195 Capacitance If the current is given by i(t) then the voltage across the plates will be given by Vc ...

196 Transient analysis Transforming to the time domain from the s-domain From the transform circuit of Fig. 8.32 we have that V/ ...

8.4 The Laplace transform 197 Equating the coefficients of s 1 we have that I=A+B Equating the coefficients of s o we have that ...

198 Transient analysis Let (R/Ll/ [s + (R/Ell : [A/sl + + (R/L)}I Then R/L- A[s + (R/L)] + Bs so that (R//L)s ~ (A + B)s + (AR// ...

8.4 The Laplace transform 199 1~ Cs /// (= 1/0.1s). The transform circuit thus takes the form shown in Fig. 8.36. From this circ ...

200 Transient analysis Solution Figure 8.37 V:,kV( R C ? HI -Os~ Th~ R C Th2 ) L The circuit is shown in Fig. 8.37 and it should ...

8.5 Self-assessment test 201 Completing the square of the denominator we have i(s) = (500/L)/[{s + (R/2L)} 2 + {(1/CL) - (R/2L)2 ...

202 Transient analysis 5 Define a step voltage. 6 Give the symbol for and the unit of time constant. 7 Give an expression for th ...

8.6 Problems 203 2 The armature of a relay operates on a 200 V supply and is actuated when the current through its coil is 240 m ...

204 Transient analysis (b) a single pulse of amplitude 20 V and width 5 ms; (c) a train of pulses of amplitude 20 V, width 5 ms ...

9 Two-port networks 9.1 INTRODUCTION Figure 9.1 +o I1^1 2-port network I2 r I2 o+ o- A two-port network has four terminals as sh ...