smart lighting filters & the behavior of l and c at low and high frequencies k. a. connor mobile...
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SMART LIGHTING
Filters & The Behavior of L and C at Low and High Frequencies
K. A. ConnorMobile Studio Project
Center for Mobile Hands-On STEM
SMART LIGHTING Engineering Research Center
ECSE Department
Rensselaer Polytechnic Institute
Intro to ECSE Analysis
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K. A. Connor 15 September 2015
Outline
• Open and Short Circuits
• Behaving Like an Open or Short• Inductors at Low and High Frequencies
• Starting Point for Exploration?• Types of Filters
Short Open
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K. A. Connor 15 September 2015
L & C at DC (f = 0)
• Experiment: Use an ohmmeter to measure the resistance of a capacitor and an inductor. • Resistance of capacitor → ∞
• Usually measure as beyond range of meter• With more expensive meter, large R (many MΩ)• Large compared to any other resistance in circuit, so treated
as open circuit
• Resistance of inductor is small but finite, due to resistance of wire used to construct the coil.
• For 1mH or less, usually an Ohm or two. • Usually much smaller than any other resistance in a circuit
so treated as approximately zero (short circuit)
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K. A. Connor 15 September 2015
L, C at Low and High f
• For low frequencies (near zero) we can generally assume that • A capacitor behaves like an open circuit• An inductor behaves like a short circuit
• For high frequencies (to be defined) it is not surprising that we can assume the opposite• A capacitor behaves like a short circuit• An inductor behaves like an open circuit
Why?
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K. A. Connor 15 September 2015
L & C vs f
• Capacitors behave like their impedance is inversely proportional to frequency
• Inductors behave like their impedance is proportional to frequency
fZC
1~
fZL ~Will test these expressions
Consistent with observations
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K. A. Connor 15 September 2015
Transmission Line
• Modeling with R, L, G, C
Simplify
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K. A. Connor 15 September 2015
Chebyshev
Simplify
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K. A. Connor 15 September 2015
Types of Filters