9. Capacitors + Capacitance

• Capacitor


  Stores charge Q
• Capacitor


  • 2 parallel conductive plates separated by an insulating material
  • Dielectric
  • Stores charge
  • No electron flow through dielectric
  • A becomes +ve w.r.t. B
  • Retains charge for a length of time
  • Temporary battery

  
• Capacitance


  Measure of ability to store charge
• Coulomb's Law


  Force between two charged bodies proportional to product of charges and inversely proportional to square of distance
• Energy Storage


  Stored in electric field between opposite charges on plates
• Voltage Rating


  Maximum DC voltage that can be applied without risk of damage
• Dielectric Strength


  • Air 80 V/mil
  • Ceramic 1000 V/mil
  • Mica 1500 V/mil
  • Glass 2000 V/mil
• Temperature Coefficient


  Change in capacitance with temperature (positive or negative)
• Leakage


  No dielectric is perfect - always some conduction, charge leaks away
• Capacitor Physical Characteristics


  • Capacitance proportional to plate area
  • Capacitance inversely proportional to plate separation
  • Capacitance proportional to dielectric constant

  
• Types of Capacitors


  • Mica
  • Ceramic
  • Tubular Plastic Film
  • Electrolytic
  • Variable

  
• Mica Capacitors


  • Capacitance range 1pF - 0.1uF
  • Voltage range 100 - 2500 VAC
  • Temperature coefficient -20 to +100 ppm/°C

  
• Ceramic Capacitors


  • High dielectric constants (1200 typical)
  • High capacitance in small size

  
• Ceramic Multilayer Capacitors


  • Capacitance range 1pF - 2.2uF
  • Voltage rating up to 6kV
  • Temperature coefficient -2000 to +2105 ppm/°C

  
• Plastic Film Capacitors


  • Capacitance up to 100uF
  • Polycarbonate, parylene, polyester, polystyrene, polypropylene, mylar
• Electrolytic Capacitors


  • Polarised (positive and negative plates)
  • Capacitance up to 200,000uF
  • Low breakdown voltage (max 350V)
  • High leakage

  
• Variable Capacitors


  • Used for frequency selection in radios and TVs
  • Change effective plate area to change capacitance
• Trimmers


  • Fine adjustment of capacitance
  • Ceramic, mica or plastic dielectric
  • Change plate separation to change capacitance
• Varactors


  • Semiconductor device
  • Change capacitance by changing voltage across terminals
• Series Capacitors


  1. Effective plate separation increases, therefore capacitance decreases

  2. Total charge QT = Q1 = Q2 = ... = Qn

  3. 1/CT = 1/C1 + 1/C2 + ... + 1/Cn

  
• Parallel Capacitors


  1. Effective plate area increases, therefore capacitance increases

  2. Separate charging currents

  
• Charging a Capacitor


  • Voltage builds up to supply voltage, opposite in polarity
  • When fully charged, no current flow - capacitor blocks constant DC

  
• Discharging a Capacitor


  • Excess electrons move from one plate to the other
  • Energy stored in capacitor is dissipated in the wire (or resistance)

  
• RC Time Constant


  Rate at which capacitor charges or discharges is determined by time constant τ = RC
• Capacitors in AC Circuits

  • Current leads voltage by 90°
  • Capacitive reactance Xc opposes current flow

  
• Power in Capacitors


  • Instantaneous power p = vi
  • True power Ptrue = 0 for ideal capacitor
  • Reactive power Pr = Vrms Irms = Vrms^2/Xc

  
• Testing Capacitors


  • Failures can be catastrophic or by degradation
  • Analogue ohmmeter can be used to test capacitors