A series RC circuit is connected to a voltage source v_i(t), and the output is the voltage across the capacitor, v_o(t).

(a) Find the transfer function H(s) = V_o(s)/V_i(s) of this filter when the resistor is R=10 kΩ­, and the capacitor C = 1μF.

(b) To normalize this circuit we let R_n = R/k_m, C_n = C(k_mk_f) where k_m is a magnitude scale and k_f is a frequency scale. Choose values of kmand k_f so that the resistor and the capacitor are unity.

(c) Find the normalized transfer function T(S) of the filter with R_n = 1 and C_n = 1. Calculate the magnitude response of the normalized and of the not normalized filters, plot them together in the same figure and have two frequency scales—the actual and the normalized one. What do you notice? Explain.