Please read Chapter 14, Sections 14.1-14.3 on low-pass and high-pass filters. We covered most of this material in Lab 1 and it may be helpful for answering item 6 below. In Chapter 14, don't worry about the transfer function H(s). The complex frequency response, H(jw), is defined as the ratio of the output phasor to the input phasor.

Please begin reading Chapter 10 on sinusoidal steady-state power for the weeks of Jan. 26 and Feb. 2.

Chapter 9: Problems 42, 50, 60, and 66.

Draw a circuit with a sinusoidal voltage source v_s(t) = 1 cos( w t) (V), a resistor (R), and a capacitor (C) in series. Specify the output voltage v_o(t) so that the circuit will be a high-pass filter in the sinusoidal steady state as the radian frequency w of the source is varied.

• Find the expression for the complex frequency response H( jw ), which is defined as the ratio of the output phasor to the input phasor.
• Find the expression for the magnitude of the frequency response, |H( jw )|.
• Make a rough sketch of the amplitude gain |H( jw )| versus w.
• Make a rough sketch of the phase response, /_ H( jw ) versus w.
• Find an expression for the cutoff frequency w_c as a function of R and C. Indicate the location of w_c on your sketch in the previous item. The cutoff frequency is the value at which the magnitude of the frequency response equals 1/sqrt(2) times the maximum value.
• Specify values for R and C that will produce a cutoff frequency of 1000 Hz.
  (Note that w_c is in radians/sec, so you need to convert to Hz!)