The New Hotness

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

Capacitor show-and-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 × ε_R
• ε₀ = vacuum permittivity = 8.84 × 10^-12 F/m
• ε_R = 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 (ε_R ≈ 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

• 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

• 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)

Flip R and C, measure V across resistor

• 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)

If time permits, set up a transistor switch

• 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 …