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

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

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)

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?

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

K. A. Connor 15 September 2015

Transmission Line

• Modeling with R, L, G, C

Simplify

K. A. Connor 15 September 2015

Chebyshev

Simplify

K. A. Connor 15 September 2015

Types of Filters