Draw a functional block diagram showing the transfer

Question

Part 1

A low pass filter has the following specifications:

F_p=2.4MHz L_p=3dB
F_s=6MHz    L_s=40dB

1. Determine the required order of a Butterworth filter that meets the above specifications.

2. Design a Butterworth passive filter (75Ω termination) that meets the specifications using the filter prototype design table given in your online notes. In your design, you must show the following:the low pass prototype circuit, prototype component values and the actual filter component values.

Part 2

1. Draw a functional block diagram showing the transfer function of the circuit of a phase locked loop (PLL) and label the input and the output of each component.

2. Derive the closed loop transfer function T(s) and the error transfer function E(s) of the PLL using the functional block diagram developed in the question above.

3. Assuming the filter in your PLL is a 1^st order low pass filter having a system natural frequency, ω_n = 4rad/s and damping factor ζ = 0.5, determine the frequency at which the PLL reaches its maximum response.