1. The problem statement, all variables and given/known data An accelerometer is connected via a length of coaxial cable to an amplifier. The arrangement is modelled by: (a) a Norton generator in parallel with a capacitor (CP) representing the piezoelectric crystal within the accelerometer; (b) a lumped capacitor (CC) representing the coaxial cable; and (c) a load (RL) representing the amplifier. See attached for circuit diagram. The current generated by the accelerometer (iP) is proportional to the rate of displacement of the piezoelectric crystal. Hence iP = K dx/dt. In laplace form iP(s) = KsΔx(s). (1) Derive an expression for the laplace transfer function T(s) = ΔvL(s) / ΔiP(s). (2) Express ΔvL as a function of time (i.e. the transient response of the voltage ΔvL ) when iP is subject to a step change. (3) Using the values given in TABLE A, estimate the time taken for the voltage vL to reach its steady state value if the current iP is subject to a step change of 2 nA. CP=1400 pF CC=250 pF RL=5 MΩ TABLE A 2. Relevant equations 3. The attempt at a solution Q(1). I believe (based on internet research) that after redrawing the circuit with an equivalent single parallel capacitor, C, that the answer is ΔvL(s) / ΔiP(s) = R / 1+sRC However, I’m struggling with the derivation. In time-domain vL = iPR(1-e^-t/CR). But when I inverse laplace transform R / 1+sRC I get 1/C(1-e^-t/CR). I don’t understand how I can replace R with 1/C in the time-domain. Can anyone help? Q(2). vL(t) = iPR(1-e^-t/CR). Q(3). C = CP+CC = 1400*10^-12 + 250*10^-12 = 1.65*10^-9 Time for vL to reach steady state = 5CR = 5*5*10^6*1.65*10^-9 = 41.25*10^-3 s However, if this is correct the magnitude of the step current is irrelevant to the steady state time for vL. Since the problem specifies a step current of 2nA I’m wary of dismissing this variable as irrelevant. Am I missing something? Any help with the above would be greatly appreciated.