Problem 1 [45 pts]: The network function for a circuit is T(s) = s+100 (1.a) [10 pts] Find the DC gain, infinite frequency gain in the unit of dB, and cut off frequency we in the unit of Rad/sec. (1.b) [20 pts] Sketch the Bode Diagrams for both the magnitude and phase responses. Please label the plots properly. Calculate the gain at @ = we, and @ = 0.5wig. Identify the type of filter. (1.c) [15 pts] Design an active RC circuit (R, C, and OP-AMP) to realize this transfer function, pick C = laF. Draw the designed circuit structure. (1.d) [5 pts]: what is the error in dB between true magnitude responses and straight-line approximation at the above two frequencies in (1.b)? Show your work