SMART LIGHTING Filters & The Behavior of L and C at Low and High Frequencies K. A. Connor Mobile Studio Project Center for Mobile Hands-On STEM SMART LIGHTING Engineering Research Center ECSE Department Rensselaer Polytechnic Institute Intro to ECSE Analysis

K. A. Connor15 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

K. A. Connor15 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)

K. A. Connor15 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?

K. A. Connor15 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 Will test these expressions Consistent with observations

K. A. Connor15 September 2015 Transmission Line Modeling with R, L, G, C Simplify

K. A. Connor15 September 2015 Chebyshev Simplify

K. A. Connor15 September 2015 Types of Filters