9: Capacitors And Inductors
9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryE1.1 Analysis of Circuits (2017-10110)9: Capacitors and InductorsCapacitors and Inductors: 9 – 1 / 12
Capacitors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryA capacitor is formed from two conducting plates separated by a thininsulating layer.If a current i flows, positive change, q , willaccumulate on the upper plate. To preservecharge neutrality, a balancing negative chargewill be present on the lower plate.E1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 2 / 12
Capacitors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryA capacitor is formed from two conducting plates separated by a thininsulating layer.If a current i flows, positive change, q , willaccumulate on the upper plate. To preservecharge neutrality, a balancing negative chargewill be present on the lower plate.There will be a potential energy difference (or voltage v ) between the platesproportional to q .dv Aǫq where A is the area of the plates, d is their separation and ǫ isthe permittivity of the insulating layer (ǫ0 8.85 pF/m for a vacuum).E1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 2 / 12
Capacitors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryA capacitor is formed from two conducting plates separated by a thininsulating layer.If a current i flows, positive change, q , willaccumulate on the upper plate. To preservecharge neutrality, a balancing negative chargewill be present on the lower plate.There will be a potential energy difference (or voltage v ) between the platesproportional to q .dv Aǫq where A is the area of the plates, d is their separation and ǫ isthe permittivity of the insulating layer (ǫ0 8.85 pF/m for a vacuum).The quantity C Aǫd is the capacitance and is measured in Farads (F),hence q Cv .E1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 2 / 12
Capacitors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryA capacitor is formed from two conducting plates separated by a thininsulating layer.If a current i flows, positive change, q , willaccumulate on the upper plate. To preservecharge neutrality, a balancing negative chargewill be present on the lower plate.There will be a potential energy difference (or voltage v ) between the platesproportional to q .dv Aǫq where A is the area of the plates, d is their separation and ǫ isthe permittivity of the insulating layer (ǫ0 8.85 pF/m for a vacuum).The quantity C Aǫd is the capacitance and is measured in Farads (F),hence q Cv .The current, i, is the rate of charge on the plate, hence thedqcapacitor equation: i dt C dvdt .E1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 2 / 12
Types of Capacitor9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelCapacitor symbol represents the two separatedplates. Capacitor types are distinguished bythe material used as the insulator.Inductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryE1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 3 / 12
Types of Capacitor9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryCapacitor symbol represents the two separatedplates. Capacitor types are distinguished bythe material used as the insulator.Polystyrene: Two sheets of foil separated by athin plastic film and rolled up to save space.Values: 10 pF to 1 nF.E1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 3 / 12
Types of Capacitor9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryCapacitor symbol represents the two separatedplates. Capacitor types are distinguished bythe material used as the insulator.Polystyrene: Two sheets of foil separated by athin plastic film and rolled up to save space.Values: 10 pF to 1 nF.Ceramic: Alternate layers of metal and ceramic(a few µm thick). Values: 1 nF to 1 µF.E1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 3 / 12
Types of Capacitor9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryCapacitor symbol represents the two separatedplates. Capacitor types are distinguished bythe material used as the insulator.Polystyrene: Two sheets of foil separated by athin plastic film and rolled up to save space.Values: 10 pF to 1 nF.Ceramic: Alternate layers of metal and ceramic(a few µm thick). Values: 1 nF to 1 µF.Electrolytic: Two sheets of aluminium foilseparated by paper soaked in conductingelectrolyte. The insulator is a thin oxide layeron one of the foils. Values: 1 µF to 10 mF.E1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 3 / 12
Types of Capacitor9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryCapacitor symbol represents the two separatedplates. Capacitor types are distinguished bythe material used as the insulator.Polystyrene: Two sheets of foil separated by athin plastic film and rolled up to save space.Values: 10 pF to 1 nF.Ceramic: Alternate layers of metal and ceramic(a few µm thick). Values: 1 nF to 1 µF.Electrolytic: Two sheets of aluminium foilseparated by paper soaked in conductingelectrolyte. The insulator is a thin oxide layeron one of the foils. Values: 1 µF to 10 mF.Electrolytic capacitors are polarised: the foil with the oxide layer mustalways be at a positive voltage relative to the other (else explosion).Negative terminal indicated by a curved plate in symbolE1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 3 / 12
Types of Capacitor9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryCapacitor symbol represents the two separatedplates. Capacitor types are distinguished bythe material used as the insulator.Polystyrene: Two sheets of foil separated by athin plastic film and rolled up to save space.Values: 10 pF to 1 nF.Ceramic: Alternate layers of metal and ceramic(a few µm thick). Values: 1 nF to 1 µF.Electrolytic: Two sheets of aluminium foilseparated by paper soaked in conductingelectrolyte. The insulator is a thin oxide layeron one of the foils. Values: 1 µF to 10 mF.Electrolytic capacitors are polarised: the foil with the oxide layer mustalways be at a positive voltage relative to the other (else explosion).Negative terminal indicated by a curved plate in symbol or “-”.E1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 3 / 12
Inductors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors are formed from coils of wire, oftenaround a steel or ferrite core.Inductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryE1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 4 / 12
Inductors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryInductors are formed from coils of wire, oftenaround a steel or ferrite core.µN AThe magnetic flux within the coil is Φ l i where N is the number ofturns, A is the cross-sectional area of the coil and l is the length of the coil(around the toroid).µ is a property of the material that the core is made from and is called itspermeability. For free space (or air): µ0 4π 10 7 1.26 µH/m, forsteel, µ 4000µ0 5 mH/m.E1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 4 / 12
Inductors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryInductors are formed from coils of wire, oftenaround a steel or ferrite core.µN AThe magnetic flux within the coil is Φ l i where N is the number ofturns, A is the cross-sectional area of the coil and l is the length of the coil(around the toroid).µ is a property of the material that the core is made from and is called itspermeability. For free space (or air): µ0 4π 10 7 1.26 µH/m, forsteel, µ 4000µ0 5 mH/m.From Faraday’s law: v N dΦdt E1.1 Analysis of Circuits (2017-10110)µN 2 A dildtdi L dt.Capacitors and Inductors: 9 – 4 / 12
Inductors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryInductors are formed from coils of wire, oftenaround a steel or ferrite core.µN AThe magnetic flux within the coil is Φ l i where N is the number ofturns, A is the cross-sectional area of the coil and l is the length of the coil(around the toroid).µ is a property of the material that the core is made from and is called itspermeability. For free space (or air): µ0 4π 10 7 1.26 µH/m, forsteel, µ 4000µ0 5 mH/m.From Faraday’s law: v N dΦdt µN 2 A dildtWe measure the inductance, L µN 2 A,lE1.1 Analysis of Circuits (2017-10110)di L dt.in Henrys (H).Capacitors and Inductors: 9 – 4 / 12
Passive Components9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelWe can describe all three types of passive component by the relationshipbetween V and I using, in each case, the passive sign convention.Inductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryE1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 5 / 12
Passive Components9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelWe can describe all three types of passive component by the relationshipbetween V and I using, in each case, the passive sign convention.Resistor: v RiInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryE1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 5 / 12
Passive Components9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelWe can describe all three types of passive component by the relationshipbetween V and I using, in each case, the passive sign convention.Resistor: v RiInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummarydiInductor: v L dtE1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 5 / 12
Passive Components9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelWe can describe all three types of passive component by the relationshipbetween V and I using, in each case, the passive sign convention.Resistor: v RiInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummarydiInductor: v L dtCapacitor: i C dvdtE1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 5 / 12
Passive Components9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelWe can describe all three types of passive component by the relationshipbetween V and I using, in each case, the passive sign convention.Resistor: v RiInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummarydiInductor: v L dtCapacitor: i C dvdtNotes: (1) There are no minus signs anywhere whatever you were taught atschool.(2) We use lower case, v , for time-varying voltages.E1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 5 / 12
Series and Parallel Inductors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and Parallelv v1 v2Inductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryE1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 6 / 12
Series and Parallel Inductors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and Paralleldidi L2 dtv v1 v2 L1 dtInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryE1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 6 / 12
Series and Parallel Inductors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and Paralleldidi L2 dtv v1 v2 L1 dtdi (L1 L2 ) dtInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryE1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 6 / 12
Series and Parallel Inductors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitorsdidi L2 dtv v1 v2 L1 dtdi (L1 L2 ) dtSame equation as a single inductor of value L1 L2 Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryE1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 6 / 12
Series and Parallel Inductors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitorsdidi L2 dtv v1 v2 L1 dtdi (L1 L2 ) dtSame equation as a single inductor of value L1 L2 Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy Summarydidt d(i1 i2 )dtE1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 6 / 12
Series and Parallel Inductors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitorsdidi L2 dtv v1 v2 L1 dtdi (L1 L2 ) dtSame equation as a single inductor of value L1 L2 Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy Summarydidt d(i1 i2 )di1 dtdtE1.1 Analysis of Circuits (2017-10110) di2dtCapacitors and Inductors: 9 – 6 / 12
Series and Parallel Inductors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitorsdidi L2 dtv v1 v2 L1 dtdi (L1 L2 ) dtSame equation as a single inductor of value L1 L2 Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy Summarydidt d(i1 i2 )di1di2 dtdt dt v11vL1 L2 v L1 L2E1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 6 / 12
Series and Parallel Inductors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitorsdidi L2 dtv v1 v2 L1 dtdi (L1 L2 ) dtSame equation as a single inductor of value L1 L2 Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy Summarydidt v d(i1 i2 )di1di2 dtdt dt v11vL1 L2 v L1 L21di1 dt1L L1E1.1 Analysis of Circuits (2017-10110)2Capacitors and Inductors: 9 – 6 / 12
Series and Parallel Inductors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitorsdidi L2 dtv v1 v2 L1 dtdi (L1 L2 ) dtSame equation as a single inductor of value L1 L2 Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy Summarydidt v d(i1 i2 )di1di2 dtdt dt v11vL1 L2 v L1 L21di1 dt1L L12Same as a single inductor of valueE1.1 Analysis of Circuits (2017-10110)1L11 L12Capacitors and Inductors: 9 – 6 / 12
Series and Parallel Inductors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitorsdidi L2 dtv v1 v2 L1 dtdi (L1 L2 ) dtSame equation as a single inductor of value L1 L2 Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy Summarydidt v d(i1 i2 )di1di2 dtdt dt v11vL1 L2 v L1 L21di1 dt1L L12Same as a single inductor of valueE1.1 Analysis of Circuits (2017-10110)1L11 L12 L1 L2L1 L2Capacitors and Inductors: 9 – 6 / 12
Series and Parallel Inductors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and ParallelInductors Series and ParallelCapacitorsdidi L2 dtv v1 v2 L1 dtdi (L1 L2 ) dtSame equation as a single inductor of value L1 L2 Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy Summarydidt v d(i1 i2 )di1di2 dtdt dt v11vL1 L2 v L1 L21di1 dt1L L12Same as a single inductor of value1L11 L12 L1 L2L1 L2Inductors combine just like resistors.E1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 6 / 12
Series and Parallel Capacitors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and Paralleli i1 i2Inductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryE1.1 Analysis of Circuits (2017-10110)Capacitors and Inductors: 9 – 7 / 12
Series and Parallel Capacitors9: Capacitors and Inductors Capacitors Types of Capacitor Inductors Passive Components Series and Paralleldvi i1 i2 C1 dvdt C2 dtInductors Series and ParallelCapacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy SummaryE1.1 Analysis of Circuits (2017-10110)Capa
Series and Parallel Inductors Series and Parallel Capacitors Current/Voltage Continuity Average Current/Voltage Buck Converter Power and Energy Summary E1.1 Analysis of Circuits (2017-10110) Capacitors and Inductors: 9 – 2 / 12 A capacitor is formed from File Size: 1MB
Inductors in Series – No Mutual inductance When inductors are connected in series, the total inductance is the sum of the individual inductors' inductances. L T L 1 L 2 L N Example #1 Three inductors of 10mH, 40mH and 50mH are connected together in a series
SMD Inductors Series All specification & dimensions are subject to change,please call your nearest KLS sales represesntative for update information ORDER INFORMATION Product NO.: KLS1 - -2218 SP32 K-R Inductors SMD INDUCTORS Series Electrical code 1.0 220:.μH Tolerance:K 10%,M 20%. KLS18-SP32 SMD
Inductors in series add like resistors in series. Note the total inductance is greater than the individual inductances. Two inductors in parallel: I V I1 L1 I2 L2 Since the inductors are in
AC polymeric film capacitors can be used on both circuits but using AC film capacitors for DC circuits would increase the size and cost of a UPS system. As a result, DC electrolytic capacitors are used in the DC circuit and The difference between service life and AC polymeric film capacitors are used in reliability will be discussed in section 7.
Two inductors in series: Apply Kirchhoff's Laws, Inductors in series add like resistors in series. V V 1 V 2 L 1 dI dt L 2 dI dt L tot dI dt L tot L 1 L 2 L i L2: Resistors and Capacitors The tot
Mutually coupled inductors in series Consider there are two inductors L1 and L2 in series, which are magnetically coupled and have a mutual inductance M. The magnetic field of the two inductors could be aiding or opposing each other, depending on their orientation (fig 6.1). a) b) Fig. 6.1. Mutually cou
Inductors LL and LS have been implemented as bond wire inductors. In this design we have modeled bond wire inductors with an inductance of 1 nH/mm, a series resistance of 0.5 Ω/mm, and we have also accounted for pad capacitances of 100 fF at each bond pad. Bond wire inductors are a
Oracle Marketing API Reference Guide Release 11i Part No. B10587-01 March 2003
