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RC Filters B. Furman 02SEP2014. Mechatronics Concept Map System to Control Sensor Signal Conditioning Controller (Hardware & Software) Power Interface.

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Presentation on theme: "RC Filters B. Furman 02SEP2014. Mechatronics Concept Map System to Control Sensor Signal Conditioning Controller (Hardware & Software) Power Interface."— Presentation transcript:

1 RC Filters B. Furman 02SEP2014

2 Mechatronics Concept Map System to Control Sensor Signal Conditioning Controller (Hardware & Software) Power Interface ActuatorUser Interface Power Source BJ Furman 15JAN11 ME 106 ME 154 ME 157 ME 195 ME 120 ME 297A ME 106 ME 120 ME 106 ME 190 ME 187 ME 110 ME 136 ME 154 ME 157 ME 182 ME 189 ME 195 ME 106 ME 120 ME 106 INTEGRATION

3 How to Handle Noisy Signals? Inset from: http://cache.national.com/ds/LM/LM35.pdf Filter!

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

5 Previously A time varying function Why? A sinusoidal function, which can also be thought of as rotating vector

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

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

8 Generalized Voltage Divider What is V o in terms of V i, Z 1, and Z 2 ? ViVi + Z2Z2 Z1Z1 VoVo

9 RC Filters - 1 Frequency dependent voltage divider  Impedance of a resistor, R  Impedance of a capacitor, Z C R ViVi + C VoVo

10 RC Filters - 2 Transfer function  Complex number Magnitude  (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 R ViVi C VoVo

11 RC Filters - 3 Behavior  How does the magnitude and angle of the transfer function change with frequency? Ex. R=10k, C=1uF R ViVi C VoVo Filter ?

12 Bode Plots (the frequency response of the filter) Magnitude vs. frequency Phase angle vs. frequency

13 Mechatronics Concept Map System to Control Sensor Signal Conditioning Controller (Hardware & Software) Power Interface ActuatorUser Interface Power Source BJ Furman 26JAN06 ME 106 ME 154 ME 157 ME 195 ME 120 ME 297A ME 106 ME 120 ME 106 ME 190 ME 187 ME 110 ME 136 ME 154 ME 157 ME 182 ME 189 ME 195 ME 106 ME 120 ME 106 INTEGRATION

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