Derive the equation for the magnitude of the gain. Include a detailed set of steps Begin with the given circuit. Each step should include an explanation (example, circuit analysis theorem, math step). Provide a sketch of the Bode Plot for the magnitude of the gain. Use the two- asymptote representation in addition to other curves and information as needed. Indicate the 3db frequency, the gain in the passband, axis identifiers along with units. For the equation for magnitude of the gain, plug in frequencies 0 Hz and "infinite" Hz (this can be considered several multiples of the 3db frequency). Approximate the magnitude at these 2 frequencies and highlight the frequencies on the Bode Plot.

A system is described by transfer function H(s). The frequency response for such system is shown in Figure 1.2 (attached). Use the frequency response data to perform the following tasks:  (i) Obtain the gain and phase margins. (ii) Design a lead compensator to increase the phase margin to at least 33°. (iii) Design a lag compensator to increase the phase margin to at least 43°.

[3] Let X(e") be DTFT of x[n]. When the magnitude and phase of X(e") are plotted as below, magnitude phase 0.5T 4 -0.5T.. - IT Express DTFT of x[n-1] in terms of X(e), and plot its magnitude and phase.

Problem A For the Circuit Shown: Derive the equation for the magnitude of the gain. Include a detailed set of steps Begin with the given circuit. Each step should include an explanation (example, circuit analysis theorem, math step). O Va Provide a sketch of the Bode Plot for the magnitude of the gain. Use the two- asymptote representation in addition to other curves and information as needed. Indicate the 3db frequency, the gain in the passband, axis identifiers along with units. For the equation for magnitude of the gain, plug in frequencies 0 Hz and "infinite” Hz (this can be considered several multiples of the 3db frequency). Approximate the magnitude at these 2 frequencies and highlight the frequencies on the Bode Plot. R Vb с