capacitors and inductors

• Equivalent Series Resistance (ESR)

  Resistance in series with the capacitor that cannot be measured with an ohmmeter
• ESR


  • Can be neglected for many types, but can be a problem for electrolytic capacitors
  • Describes the sources of resistance of a capacitor (resistance of leads, contact connections between leads and plates, ac losses in the dielectric)
• Dielectric Absorption


  Residual charge from remaining polarized atoms, causing residual voltage after discharge, may require a shorting resistor for complete discharge
• Temperature Coefficient


  How capacitance changes with temperature (positive, negative, or zero)
• Types of Capacitors


  • Fixed
  • Electrolytic
  • Surface Mount
  • Variable
  • Supercapacitors
• Electrolytic capacitors

  • Large capacitance at low cost, have a shelf life, polarized
• Surface Mount Capacitors


  • Soldered directly onto printed circuit boards, extremely small for high packing density
• Fixed Capacitors


  • Ceramic - permittivity varies widely, values change little with temperature, voltage, or aging
  • Plastic film
  • Mica - low cost, low leakage, good stability
• Variable Capacitors

  Capacitor whose capacitance can be adjusted within a certain range (trimmer or padder capacitor to make fine adjustments), used for tuning a radio
• Supercapacitors

  • Devices with enormous capacitance values (beyond hundreds of farads, a.k.a ultracapacitors), used in power sources, gps systems, PDAs, medical equipment, security systems, voltage rating only few volts
• Standard Capacitor Values


  • 0.1, 0.22, 0.47 microfarad
  • 0.1, 0.22, 0.47 picofarad
• Capacitors in Parallel


  Total charge is sum of all charges, Q = CV, all voltages are equal
• Capacitors in Series


  Same charge appears on all capacitors, sum of individual voltages, Ct = C1 + C2 + C3
• Voltage across the capacitor does not change instantaneously, voltage begins at zero then gradually climbs to full voltage
• Capacitor Charging


  Electrons move from one plate to another, current lasts only until the capacitor is charged, large initial spike to zero
• Capacitor Energy Storage


  Capacitor does not dissipate power, stored energy when power is transferred to a capacitor, ½ CV^2
• Capacitor Failures and Troubleshooting: Reason - excessive voltage, current, temp, or aging. Test with an ohmmeter (good capacitor = read low, then gradually increase to infinity, short capacitor = stay low meter resistance, leaky capacitor = lower than normal reading, open capacitor = stays at infinity)
• Inductors


  Common form is a coil of wire, used in radio tuning circuits, fluorescent lights, power systems protection circuitry
• Electromagnetic Induction


  Voltage is induced when a magnet moves through a coil of wire, when a conductor moves through a magnetic field, change in current in one coil can induce a voltage in a second coil, change in current in a coil can induce a voltage in that coil
• Induced Voltage and Induction

  If constant current, no voltage induced, if current increased, inductor develops voltage to oppose increase, if current decreased, voltage formed to oppose decrease
• Counter-electromotive force (counter EMF, CEMF, back EMF)


  Electromotive force manifesting as a voltage that opposes the change in current which induced it
• Iron-Core Inductors


  • Flux almost entirely confined to their cores, flux lines pass through the windings, flux linkage as product of flux times number of turns, induced voltage equal to rate of change of NΦ
• Air-Core Inductors


  • All flux lines do not pass through all of the windings, flux directly proportional to current, induced voltage directly proportional to rate of change of current
• Self-Inductance


  Voltage induced in a coil proportional to rate of change of current, proportionality constant is L, units are Henrys (H), inductance of 1 Henry if voltage of 1 volt created by current changing at 1 amp/second, V = L di/dt
• Inductors in Series


  Total inductance is sum of individual inductances
• Inductors in Parallel


  Reciprocal of total inductance is sum of reciprocals of individual inductances
• Core Types


  • Iron cores used for audio/power supply, large inductance but high power losses at high frequencies, ferrite cores used for high-frequency applications
• Variable Inductors


  Inductance may be varied by changing coil spacing or moving a core in/out, used in tuning circuits
• Equivalent Series Resistance (ESR)

  Resistance in series with the capacitor
• Stray Capacitance & Inductance
• Equivalent Series Resistance (ESR)

  • Requires specialized instruments for measurement (cannot be measured with an ohmmeter)
  • Can be a problem for electrolytic capacitors
  • Describes the sources of resistance of a capacitor (resistance of leads, contact connections between leads and plates, ac losses in the dielectric)
• Inductance and Steady State DC
• Dielectric Absorption


  Residual charge from the remaining polarized atoms, causes residual voltage after discharge, may require a shorting resistor for complete discharge
• Energy Stored by an Inductance


  Energy flows into inductor and is stored in its magnetic field, when field collapses energy returns to circuit, no power dissipation so no power loss
• Temperature Coefficient


  How capacitance changes with temperature (positive, negative, or zero)
• Types of Capacitors


  • Fixed, Identified by their dielectrics (ceramic, plastic, mica, aluminum, tantalum oxide), electrolytic, surface mount, variable, supercapacitors
• Troubleshooting Inductors
• Key Points to Remember
• Electrolytic capacitors


  • Large capacitance at low cost, have a shelf life, polarized
• Surface Mount Capacitors


  • Soldered directly onto printed circuit boards, extremely small: High packing density