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Archive for October 20th, 2018

Squidwrench Electronics Workshop Session 6: Capacitors

Capacitors as charge-storage devices with An introduction to Function Generators & Oscilloscopes

Capacitor show-and-tell

Capacitor show-n-tell

Capacitor show-n-tell

Things to remember

  • The green one over on the left is the 1 farad cap my EE prof said I’d never see: “It would be as big as a house”
  • The small disk in front of it is a 600 mF (milli, not micro) polyacene “battery” rated at 3.3 V
  • Air-variable and wax-dielectric caps = ghosts from the past
  • Reverse-biased diodes act as capacitors, due to charge separation
  • Silver-mica caps are pretty things to behold
  • Voltage rating vs size vs dielectric, a cap charged to 10 kV will get your attention

Warmup exercise: Measure the caps with a variety of meters, noting they do not reach 1 farad. General patter, Q&A, introducing equations as needed.

I will resolutely squash all discussion of capacitors as analog / small signal circuit elements.

Cap construction

  • C = εA/d with ε = dielectric permittivity = ε0 × εR
  • ε0 = vacuum permittivity = 8.84 × 10-12 F/m
  • εR = relative permittivity, air = 1.0006
  • dielectrics: wax vs paper vs plastics vs whatever
  • ignoring dissipation factor for now
  • caution on dielectric absorption
  • electrolytic caps vs capacitor plague
  • brave / daring / foolish: aluminum foil with chair mat dielectric (εR ≈ 3)

Useful equations

  • C = Q/V and (nonlinearly) C = Δq/ΔV
  • thus Q = C × V, Δq = C × Δv = Δc × V
  • by definition, i = Δq/Δt, so i = C × Δv/Δt
  • “displacement current” vs “actual current”
  • stored energy = 1/2 × C × V²

Quick demo

  • charge 1 F cap to 3.7 V at 20 mA from constant current power supply
  • estimate charge time
  • plot V vs T
  • disconnect power supply, connect white LED, observe light output for the next few hours

Capacitor applications in charge-storage mode

  • Constant current → voltage ramp (scope horizontal)
  • Large cap = no-corrosion (kinda sorta) small-ish battery
  • Change plate d → microphone (need V)
  • Trapped charge in dielectric → Electret mic (no V, but need amp)
  • Change C (varactor) → parametric low noise amplifier (narrowband)

Parallel caps

  • C = C1 + C2
  • expanded plate area “A”
  • capacitor paradox vs reality: never switch paralleled caps!

Series caps

  • 1/C = 1/C1 + 1/C2
  • increased separation “d”, sorta kinda
  • floating voltage on center plates = Bad Idea

Now for some hands-on lab action

Connect function generator to resistor voltage divider

Resistor voltage divider - oscilloscope connections

Resistor voltage divider – oscilloscope connections

  • calculate total resistance and series current
  • calculate expected voltages from current
  • show input & output waveforms on scope
  • overview of oscilloscope controls / operations

Replace lower R with C, then measure V across cap

RC Circuit - integrator

RC Circuit – integrator

  • series circuit: fn gen → R → C (C to common)
  • scope exponential waveform across C
  • not constant current → not linear voltage ramp
  • except near start, where it’s pretty close
  • e^-t/τ and (1 – exp(-t/τ))
  • time constant τ = RC (megohm × microfarad = ohm × farad = second)
  • show 3τ = 5% and 5τ < 1%
  • integration (for t << τ)
Tek 2215A oscilloscope - cap as integrator

Tek 2215A oscilloscope – cap as integrator

Flip R and C, measure V across resistor

RC Circuit - differentiator

RC Circuit – differentiator

  • series circuit: fn gen → C → R (R to common)
  • scope exponential waveform across R  ∝ current through cap (!)
  • same time constant as above
  • differentiation (for t << τ)
Tek 2215A oscilloscope - cap as differentiator

Tek 2215A oscilloscope – cap as differentiator

If time permits, set up a transistor switch

NPN switch - Cap charge-discharge

NPN switch – Cap charge-discharge

  • display voltage across cap
  • measure time constants
  • calculate actual capacitance

Other topics to explore

  • measure 1 F cap time constant, being careful about resistor power
  • different function generator waveforms vs RC circuits
  • scope triggering
  • analog vs digital scope vs frequency

All of which should keep us busy for the better part of a day …

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