EE410 Quiz 9/8/2014 A lumped element circuit has: Z = 4 - 3j ohms Provide the following, using the proper symbols and units (as above): 1. Resistance 2. Admittance (rectangular form) 3. Reactance 4. Susceptance 5. Conductance 6. Impedance (rectangular form) 7. Magnitude of Impedance 8. Phase of Admittance 9. Phase of Impedance 10. Magnitude of Admittance

Impedance/Admittance Review Impedance: Z = R + jX Pure ResistancePure Reactance Admittance: Y = G + jB Pure ConductancePure Susceptance Y=1/Z does NOT imply B = -1/X, or G = 1/R (unless one or the other is zero). X > 0, “Inductive”  L X < 0, “Capacitive” -1/  C B > 0, “Capacitive”  C B < 0, “Inductive” -1/  L

Resonance Series Resonance: Parallel Resonance:

For Parallel Resonance |Y| is minimum (real, = G) at resonance,  =  0 |Y| increases by 3 dB (  = +  /4) when : Similar for Series Resonance

Energy Loss When v c (t) = V max, I l (t) = 0 Stored energy = CV max 2 /2 Power loss in resistor = V max 2 /2R Energy loss per cycle = (2  /   )(V max 2 /2R)

Reactive Components with Parasitic Losses (“unloaded” Q) Series model: Q u = |X C /R s | = 1/  C s R s Parallel model: Q u = B C /G p =  C p R p If Z = 1/Y then