Question

Prelab Consider the circuits (systems) in Figure 1 2000 1k2 Vo Vi 10pF 2H (b) 2002 Figure We want to understand what these systems do, and how they are expected to behave. Because they are "physical systems" they are causal. For each of the circuits: 1. Use the integration-in-time-domain properties of the Laplace transfom to derive the impedance of the capacitors and inductors. Since both capacitors and inductors are causal systems, what are the regions of convergence of their Laplace transforms? 2. Derive the transfer function (from input voltage to output voltage, in Laplace representation) of each system. Compute its pole(s) and zero(s), and the region of convergence 3. Letsjw. Substitute and compute the magnitude of the transfer function and verify analytically your intuition about how each system reacts to low frequency components ( 0 of the input signal, and to very high frequency components (). Can you substitute jw for s? Explain why this is possible or not. What is the effect of resistors on a passive circuit's poles? 4. If the input is a unit step function u(t), what are the main features you will expect to see in the output? Justify by formally deriving the time-domain response of cach system to a unit step (you will use a partial fraction expansion, and the inverse Laplace transform for each fraction term).

Answer 1