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Lumped Element Circuit Parameters: Resistance, Admittance, Reactance, Susceptance, Conductance

Calculate and understand various properties of a lumped element circuit with given impedance values. Explore resistance, admittance in rectangular form, reactance, susceptance, conductance, impedance in rectangular form, magnitude of impedance, phase of admittance and impedance, and magnitude of admittance. Review impedance and admittance concepts including pure resistance, pure reactance, pure conductance, and pure susceptance.

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Lumped Element Circuit Parameters: Resistance, Admittance, Reactance, Susceptance, Conductance

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  1. EE410 Quiz9/8/2014 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

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

  3. Resonance Series Resonance: Parallel Resonance:

  4. For Parallel Resonance |Y| is minimum (real, = G) at resonance, w = w0 |Y| increases by 3 dB (Q = +p/4) when : Similar for Series Resonance

  5. Energy Loss When vc(t) = Vmax , Il(t) = 0 Stored energy = CVmax2/2 Power loss in resistor = Vmax2/2R Energy loss per cycle = (2p/w0)(Vmax2/2R)

  6. Reactive Components with Parasitic Losses (“unloaded” Q) If Z = 1/Y then Series model: Qu = |XC/Rs| = 1/wCs Rs Parallel model: Qu = BC/Gp = wCpRp

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