week 15 day 1

Lecture 

Sketching Bode Magnitude plot with one zero  at the origin and 2 simple poles: 

Bode magnitude plot and Bode Phase Plot with one simple zero,  one simple pole and one pole at the origin>

Sketching Bode magnitude plot and Bode Phase Plot with a constant shift :

 Translating a Bode Plot into Transfer Function

Derivation of Half power frequency of RLC circuit in series. Half power frequencies are the 2 frequency that provided half the power dissipated through resistor at resonance frequency Algebraically there are four solutions obtained from our equation, but since half power frequency is always greater than zero( positive) we can eliminate two of the four solutions

 Calculating resonance frequency and half power frequency of RLC circuit with 2-ohm resistor, 1 mH inductor, and 0.4 pF capacitor

Summary 

Bode Plot are a semi-log plot that helps us to predict the behavior of transfer function in relations with frequency by using linear functions to approximate the behavior of poles and zeroes. Resonance Frequency is the frequency where the circuit is purely resistive. Resonance frequency of RLC circuit in series is equal to one over the square root of the product of inductance and capacitance.