A way to gain insight into the behaviour of different discretization rules is to look at
the distortion in magnitude and phase angle introduced by the rule on the representation
of a simple first-order system, such as an inductance, as a function of frequency.
1. With the rules listed below find the frequency-domain equivalent-circuit of the
discretized L. Express this equivalent circuit in terms of an Re (equivalent resistance) and an Le (equivalent inductance). Find the simplest representation:
Should Re and Le be in series or in parallel?
(a) Trapezoidal (class notes)
(b) Backward Euler (class notes)
(c) Forward Euler (derive)
(d) Gear’s second order (derive)
2. Plot the magnitude and phase distortion of the discretizations in 1) for fpu = 0 →
3. Comment on the expected numerical stability based on the equivalent circuit