Online proceedings - EDA Publishing Association

24-26 September 2008, Rome, Italyassociated magnitudes R i , i = 1…N. Using these symbols thea(t) unit-step response of the system can be written asTABLE INa(t)= ∑ R i( 1−exp( −t/ τi))(1)τattenuation factor< 0.43 ti=1P>0.9= t P0.632 t P0.395 t P0.1810 t P0.095a=Fig. 2. Synthesis of the short pulse using two step-functionsThe applied dissipation pulse is shown in Fig.2a. Thepulse is normalised to 1 W, its duration is t P . Obviously thispulse is equal to the difference of the two displaced unit-stepfunctions b) and c) shown in the bottom part of the figure.Thus the a*(t) response for the finite pulse can be assembledas the difference of the two responses for the unit-stepfunctions:* ( t)= a(t + tP) − a(t)=NN(2)R 1−exp( −(t + t ) / τ ) − R 1 − exp( −t/ τ )∑i=1i(P i) ∑ i(i)i=1After some rearrangements we haveNa * ( t)= −∑Ri1−exp( −tP/ τi) exp( −t/ τiorwherei=1( ) )N*a * ( t)= ∑ R iexp( −t/ τi)R*iii=1( 1−exp( −t/ τ ))Pi(3)(4)= R(5)We conclude that the attenuation of the R i magnitudes dependson the t P /τ i relation. For the time constantsτ i