Plotting Impedance Complex Impedance Admittance Y 1Z YGj

Plotting Impedance Complex Impedance Admittance , Y = 1/Z Y=G+j. B Conductance, G = 1/R Susceptance, B = 1/X |Y| = G 2 + B 2 / Y = Arc. Tan(B/G) = Arc. Tan(-X/R) |Z| = 1/|Y| / Z = 1// Y = -/ Y • • Resistance (R) along positive x-axis (right). Inductive reactance (XL) along positive yaxis (up). Capacitive reactance (XC) along negative yaxis (down). Negative x-axis (left) not used. Tips 1. ELI the ICE man lives in SARL PARC a) Inductive Circuits: Voltage leads current (phase angle is positive) Time Constants b) Capacitive Circuits: Voltage lags current (phase angle is negative) For RC Ckt, τ = R x C c) SARL: Series Above Resonance appears Inductive For RL Ckt, τ = L/R d) PARC: Parallel Above Resonance appears Capacitive RC and RL Time Constants 2. If reactance & resistance have same magnitude, phase angle = ± 45° a) If reactance is less than resistance, phase angle is less than ± 45° Charging Discharging b) If reactance is greater than resistance, phase angle is greater than ± 45° % of Time 3. If the reactance = 0, phase angle = 0. Circuit is purely resistive. , voltage & Applied Starting Constants current in phase. Voltage 4. For series circuits, add impedances. Inductive & Capacitive Reactance in 1 63. 20% 36. 80% series cancel. 2 86. 50% 13. 50% 5. For parallel circuits, add admittances. 3 95. 00% 6. When taking the reciprocal of an angle, flip the sign 4 98. 20% 1. 80% 7. 1/j = -j 5 99. 30% 0. 70% 8. In parallel circuits, the resultant impedance is smaller than the resistance or reactance. Quality Factor Power Equations • For Series Resonant Circuits: • Apparent Power (v-a) P = I x E Q = X/R Where: X = Capacitive or • Real Power (watts) P = I x E x cos(θ) Inductive • Power Factor (PF) = Real Pwr/Apparent Pwr = cos(θ) reactance at resonance Resonant Freq, Band Width R = Series resistance • Resonant Frequency (f. R) = 1 / (2π √LC ) • For Parallel Resonant Circuits, • Half-power bandwidth (BW) = f 2 -f 1 = Δf = f 0 / Q = f. R / Q where a large value of R is in parallel with C & L Q = R/X Where: X = Capacitive or Powdered Iron Cores Inductive reactance at • N = 100 x √L / AL Units Conversion resonance • L = Inductance in μH 9 1, 000, 000 giga G 10 R = Resistance • AL = Inductance Index in μH/(100 turns). 6 1, 000 mega Q = X/R M for a 10 small R in series with L sin (0°) = 0 cos (0°) = 1 • N = Number of Turns 3 Ferrite Cores sin (30°) = 0. 5 sin (45°) = 0. 707 sin (60°) = 0. 866 sin (90°) = 1 • N = 1000 x √L / AL • L = Inductance in m. H • AL = Inductance Index in m. H/(1000 turns) • N = Number of Turns cos (30°) = 0. 866 cos (45°) = 0. 707 cos (60°) = 0. 5 cos (90°) = 0 kilo basic unit milli micro pico K m μ p 10 1, 000 1 10 -3 10 -6 10 -12 0. 001 0. 000000000001