1. RC Filters
B. Furman
09FEB2016

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

3. How to Handle Noisy Signals?
Filter!
Inset from:

4. Impedance of a Capacitor
Derive the impedance of a capacitor
Physics for a capacitor C
V(t)
A time varying function
Differentiate both sides
Explain the concept of ‘impedance’ (in terms that a 6th grader could understand). Opposition to the flow of current.
Impedance can be described as the relationship of voltage to current. For a resistor, its impedance is its resistance, R, since V/I = R.
More charge, more voltage (pressure). Flash lamp driver.
The impedance – the ratio of voltage to current
What is s?

5. What is s? Previously Why? A time varying function
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)
(imaginary axis) j b
is of the form: q a
Real axis
Magnitude =
Direction =

7. Sinusoidal Function
Visualize the connection between the vector and the sinusoidal function of time
Suppose the real component is plotted as a function of time

8. Generalized Voltage Divider
What is Vo in terms of Vi, Z1, and Z2? Vi + Z2 Z1 Vo

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

10. RC Filters - 2 Transfer function Complex number MagnitudeVi C Vo
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

11. How does this come about?

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

13. Bode Plots (the frequency response of the filter)
Using a spreadsheet
Magnitude vs. frequency
Phase angle vs. frequency
Hendrik Bode, Researcher at Bell Labs.

14. Bode Plots – Matlab/Octave Style

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