Filters & The Behavior of L and C at Low and High Frequencies

1. 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

2. Outline • Open and Short Circuits • Behaving Like an Open or Short • Inductors at Low and High Frequencies • Starting Point for Exploration? • Types of Filters Open Short

3. 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)

4. 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?

5. L & C vs f • Capacitors behave like their impedance is inversely proportional to frequency • Inductors behave like their impedance is proportional to frequency Consistent with observations Will test these expressions

6. Transmission Line • Modeling with R, L, G, C Simplify

7. Chebyshev Simplify

8. Types of Filters