RC Filters B Furman 09 FEB 2016 Mechatronics

RC Filters B. Furman 09 FEB 2016

Mechatronics Concept Map Power Source User Interface ME 106 ME 120 Controller ME 106 (Hardware & Software) Power Interface Signal Conditioning INTEGRATION ME 106 ME 154 ME 157 ME 195 ME 106 ME 190 ME 187 ME 106 ME 120 Actuator Sensor System to Control ME 110 ME 182 ME 136 ME 189 ME 154 ME 195 ME 157 ME 120 ME 297 A BJ Furman 15 JAN 11

How to Handle Noisy Signals? Filter! Inset from: http: //cache. national. com/ds/LM/LM 35. pdf

Impedance of a Capacitor n Derive the impedance of a capacitor Physics for a capacitor V(t) C A time varying function Differentiate both sides The impedance – the ratio of voltage to current What is s?

What is s? n Previously A time varying function n Why? A sinusoidal function, which can also be thought of as rotating vector

Complex Numbers and Vectors n Think of a complex number as a vector ¨ Vectors have: Magnitude (length) n Direction (angle) n (imaginary axis) j b is of the form: Magnitude = Direction = q a Real axis

Sinusoidal Function n Visualize the connection between the vector and the sinusoidal function of time n Suppose the real component is plotted as a function of time http: //upload. wikimedia. org/wikipedia/commons/8/89/Unfasor. gif

Generalized Voltage Divider n What is Vo in terms of Vi, Z 1, and Z 2? Z 1 + Vi Z 2 Vo

RC Filters - 1 n Frequency dependent voltage divider ¨ Impedance of a resistor, R ¨ Impedance of a capacitor, ZC R + Vi C Vo

RC Filters - 2 n Vi R C Vo Transfer function ¨ Complex n Magnitude ¨ n number (Magnitude of numerator)/(Magnitude of denominator) Angle (“phase angle”) ¨ ¨ (angle of num) – (angle of denom) How much the output is out of time synchronization with input

How does this come about?

RC Filters - 3 n Vi R C Vo Behavior ¨ How does the magnitude and angle of the transfer function change with frequency? n Ex. R=10 k, C=1 u. F Filter ?

Bode Plots Using a spreadsheet (the frequency response of the filter) Magnitude vs. frequency Phase angle vs. frequency

Bode Plots – Matlab/Octave Style

Mechatronics Concept Map Power Source User Interface ME 106 ME 120 Controller ME 106 (Hardware & Software) Power Interface Signal Conditioning INTEGRATION ME 106 ME 154 ME 157 ME 195 ME 106 ME 190 ME 187 ME 106 ME 120 Actuator Sensor System to Control ME 110 ME 182 ME 136 ME 189 ME 154 ME 195 ME 157 ME 120 ME 297 A BJ Furman 26 JAN 06