Answer Happy

For problems 1-3, given a transfer function G(s) sketch the magnitude and phase characteristics in the logarithmic scale (i.e. Bode-plots) of the system using the following rules-of-thumb: i. "Normalize" the G(s) by extracting poles/zeros, substituting s-jw and writing the TF using DC-gain KO and time-constants ii. Arrange break-points (poles, zeros or wn for complex-conjugate poles) in ascending order Based on the term Ko (jw) Fk, determine: a. initial slope of the magnitude-response asymptote for low frequencies as Fk 20 dB/dec (e.g. flat for k=0, -20 dB/Dec for one pole at s=0 etc.) b. "anchor" point through which the magnitude-response asymptote passes for w=1 (i. e. 20 log10 Ko) C. initial value of the phase-response asymptote for low frequencies as Fk 90⁰ Start going from w=0 towards ∞ iv. V. For each break-point that corresponds to a real pole/zero you encounter, adjust: magnitude-response asymptote slope by- m 20 dB/Dec for a pole and + m20 dB/Dec for a zero (m= multiplicity/order of pole/zero at the breakpoint) a. b. phase-response asymptote by - m90° for a single pole and + m 90° for a single zero (m= multiplicity/order of pole/zero at the breakpoint) vi. For each break-point wn that corresponds to a complex-conjugate set of poles/zeros, adjust: a. magnitude-response asymptote slope by -m40 dB/Dec for a set of cc poles and +m40 dB/Dec for a set of cc zeros (m= multiplicity/order of cc poles/zeros at the breakpoint) b. phase-response asymptote by - m180⁰ for a set of cc poles and + m180⁰ for a set of cc zeros (m= multiplicity/order of cc poles/zeros at the breakpoint) vii. For <√2/2 (or 0.7) be aware of a resonant "bump" or a "dip" of approximately Mr = ( i.e. Mr = 20 log₁0 dB). Draw the approximate magnitude and phase responses by fitting a curve along the asymptotes
Problem 3 G(s) = 4000 (s² +16s+400)