107_33 - 1 Electrical Engineering Technology EET 107...

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Unformatted text preview: 1 Electrical Engineering Technology EET 107 Introduction to Circuit Analysis # 33 Professor Robert Herrick Purdue University © EET 107 - 33 Introduction to Circuit Analysis 2 Electrical Engineering Technology Capacitance, Capacitive Reactance & Series – Parallel Capacitance Purdue University © EET 107 - 33 Introduction to Circuit Analysis 3 Overview u Capacitance and Capacitors u Capacitive Reactance u Series and Parallel Capacitance Purdue University © EET 107 - 33 Introduction to Circuit Analysis 4 Capacitance Effect Two conductors separated by an insulator ! separated wires Purdue University © insulation conductor plates EET 107 - 33 wire with insulation laying on chasis Introduction to Circuit Analysis 5 Capacitor Device insulation conductor plates Conductor plates separated by an insulator with lead wire connected to the conductors. Purdue University © EET 107 - 33 Introduction to Circuit Analysis 6 Capacitor Device conductor plates Conductor plates are formed by plates or conducting foil. Purdue University © EET 107 - 33 Introduction to Circuit Analysis 7 Capacitor Device insulation Dielectric Insulation could be air, glass, mica, or other insulation material. Purdue University © EET 107 - 33 Introduction to Circuit Analysis 8 Charged Capacitor Q+ Q− ++++++++ electric field -------- Electric Field Electric flux between two charges. Purdue University © EET 107 - 33 Introduction to Circuit Analysis 9 Capacitor Symbol C “C” represents capacitance Purdue University © EET 107 - 33 Introduction to Circuit Analysis 10 Capacitance C ++++++++ -------- Units Unit symbol Purdue University © Farads F EET 107 - 33 Introduction to Circuit Analysis 11 Capacitance C Q + ++++++++ -------- V C = Q/V capacitance = charge / voltage 1F = 1C / 1V Purdue University © EET 107 - 33 Introduction to Circuit Analysis 12 Capacitance A capacitor storing 20C of charge creates a 5V drop, find its capacitance. C + ++++++++ 20C -------- 5V - C = Q / V = 20 C / 5 V = 4 F Purdue University © EET 107 - 33 Introduction to Circuit Analysis 13 Capacitance A 10F capacitor has a 5V drop. How much charge is stored? Q = CV = Purdue University © 10F + ++++++++ Q -------- 5V - 10 F × 5 V = 50 C EET 107 - 33 Introduction to Circuit Analysis 14 Electric Field Electric Flux Lines ++++++++ electric field or Flux -------- Flux Density Flux per unit area Purdue University © EET 107 - 33 Introduction to Circuit Analysis 15 Electric Field + ++++++++ electric field d V - -------- Electric Field Strength E = V/d Purdue University © volts per meter EET 107 - 33 Introduction to Circuit Analysis 16 Electric Field + ++++++++ electric field d -------- V - If electric field strength too high, insulation breaks down and conducts ! Purdue University © EET 107 - 33 Introduction to Circuit Analysis 17 Electric Storm ++ + ++ + + + + −− − − − − − − − − − −− −− −−−− − − −− ++++++++++++++++ Earth (b) Earth-cloud electric field Purdue University © EET 107 - 33 (c) Electrifying experience Introduction to Circuit Analysis 18 Insulator ++++++++ vacuum Dielectric Constant Vacuum is reference -------- εo = 8.85 x10-12 F/m Purdue University © EET 107 - 33 Introduction to Circuit Analysis 19 Relative Dielectric Constant εr ε = εr εo ++++++++ insulator -------- Air Mica Purdue University © εr = 1.0006 εr = 5.0 EET 107 - 33 Introduction to Circuit Analysis 20 Relative Dielectric Constant Increases C ++++++++ insulator -------- C = εr Co Mica C = 5 Co Purdue University © EET 107 - 33 Introduction to Circuit Analysis 21 Capacitance ++++++++ insulator -------- C=εA/d ε = εr εo A = area of plate d = distance between plates Purdue University © EET 107 - 33 Introduction to Circuit Analysis 22 Capacitance ++++++++ insulator -------- C=εA/d εé then C é A é then C é d é then C ê Purdue University © EET 107 - 33 Introduction to Circuit Analysis 23 Dielectric Charge Effect ++++++++ ----------insulator ++++++++ -------- Purdue University © Induced Charge Varying charge produces induced current. EET 107 - 33 Introduction to Circuit Analysis 24 Capacitor Types Many types of capacitors, for example: Mica, Ceramic, Mylar, Polystyerene, Polycarbonate, Teflon, Glass, Porcelain, Tantalum, Electrolytic, Oil, Vacuum Purdue University © EET 107 - 33 Introduction to Circuit Analysis 25 Capacitor Types Each type has its unique characteristics in terms of size, frequency response, voltage levels, and so forth. Purdue University © EET 107 - 33 Introduction to Circuit Analysis 26 100uF 50WVDC Electrolytic Capacitor - Electrolytic or polarized capacitor Polarity Sensitive ! Reverse polarity: EXPLODE !?! Required +− DC Polarity Exceed POW Working VDC EXPLODE !?! Purdue University © EET 107 - 33 Introduction to Circuit Analysis 27 Capacitor - Key Characteristics • Stores charge C • Stores voltage V=Q/C • Resists change in voltage • Retains voltage • Returns charge like E supply Purdue University © EET 107 - 33 Introduction to Circuit Analysis 28 Capacitor - Key Characteristics i + v • i = C dv/dt • i = C ∆v/ ∆t • C − v must vary to create induced i Purdue University © EET 107 - 33 Introduction to Circuit Analysis 29 Overview u Capacitance and capacitors u Capacitive Reactance u Series and Parallel Capacitance Purdue University © EET 107 - 33 Introduction to Circuit Analysis 30 Reactance – Opposition to AC Current 1 XC = 2π f C c XC = capacitive reactance f = frequency (ohms) (Hz) C = capacitance (F) Purdue University © EET 107 - 33 Introduction to Circuit Analysis 31 Reactance - example c C = 1 µF f = 2 kHz sine wave 1 1 XC = = = 80Ω 2π f C 2π • 2kHz • 1µF Purdue University © EET 107 - 33 Introduction to Circuit Analysis 32 RC Sine Wave Response: 1 µF Capacitor 1 XC = 2π f C f (Hz) 1 10 100 1k 10 k 100 k 1M Purdue University © Xc(Ω) 159 k 15.9 k 1.59 k 159 15.9 1.59 0.16 EET 107 - 33 HIGH Xc ac open LOW Xc ac short Introduction to Circuit Analysis Reactance - low frequency f = 0Hz c 33 DC 1 1 XC = = = ∞Ω 2π f C 2π • 0 Hz • C Capacitor appears as open to DC steady state Purdue University © EET 107 - 33 Introduction to Circuit Analysis 34 Reactance - high frequency c f = ∞Hz Very high frequency or sudden DC change 1 1 XC = = = 0Ω 2π fc 2π • ∞Hz • C Capacitor appears as a short to high frequencies or a sudden change in signal Purdue University © EET 107 - 33 Introduction to Circuit Analysis 35 Quick Look Frequency Effects C Sine wave f + esupply(t) + vC(t) − R + vR(t) − open Low f + esupply(t) short R Purdue University © + vR(t) − High f EET 107 - 33 + esupply(t) 0V R + vR(t) − Introduction to Circuit Analysis 36 Overview u Capacitance and Capacitors u Capacitive Reactance u Series and Parallel Capacitance Purdue University © EET 107 - 33 Introduction to Circuit Analysis 37 Series Capacitors Total Reactance XC1 c1 XC2 c2 XCT XCT = XC1 + XC2 + XC3 Purdue University © EET 107 - 33 c3 XC3 Introduction to Circuit Analysis 38 Series Capacitors X CT = X C1 + X C 2 + X C 3 substitute 1 1 1 1 = + + 2πfCT 2πfC1 2πfC 2 2πfC3 1 1 1 1 =+ + CT C1 C2 C3 Purdue University © EET 107 - 33 Introduction to Circuit Analysis 39 Series Capacitors Total Capacitance c1 CT c2 1 1 1 1 =+ + CT C1 C2 C3 c3 Capacitance in series adds like resistance in parallel Purdue University © EET 107 - 33 Introduction to Circuit Analysis 40 Example - total series capacitance 1 1 1 1 =+ + CT C1 C2 C3 6F c1 3F CT c2 1 1 1 1 =+ + CT 6F 3F 2F c3 2F CT = 1 F Purdue University © EET 107 - 33 Introduction to Circuit Analysis 41 Example - pair reduction 6 F c1 6F series with 3F = 2F 3F c2 2F in series with 2F = 1F c3 2 F CT = 1 F Purdue University © EET 107 - 33 Introduction to Circuit Analysis 42 Capacitance R è 1/C correspondence RT = R1 + R2 + R3 series resistance 1/CT = 1/C1 + 1/C2 + 1/C3 series capacitance Purdue University © EET 107 - 33 Introduction to Circuit Analysis 43 Parallel Capacitors Total Reactance XCT C2 XC2 C1 XC1 C3 XC3 1 1 1 1 = + + X CT X C1 X C 2 X C 3 Purdue University © EET 107 - 33 Introduction to Circuit Analysis 44 Parallel Capacitors 1 1 1 1 = + + X CT X C1 X C 2 X C 3 substitute 1 1 1 1 = + + 1 / 2πfCT 1 / 2πfC1 1 / 2πfC 2 1 / 2πfC3 CT = C1 + C2 + C3 Purdue University © EET 107 - 33 Introduction to Circuit Analysis 45 Parallel Capacitors Total Capacitance CT C1 C2 C3 CT = C1 + C2 + C3 Capacitance in parallel adds like resistance in series Purdue University © EET 107 - 33 Introduction to Circuit Analysis 46 Parallel Capacitors CT 2u C1 3u C2 CT = 2 µF + 3 µF + 6 µF = 11 Purdue University © EET 107 - 33 6u C3 µF Introduction to Circuit Analysis 47 Overview u Capacitance and Capacitors u Capacitive Reactance u Series and Parallel Capacitance Purdue University © EET 107 - 33 Introduction to Circuit Analysis ...
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