Capacitors

Capacitors store separated electric charges, and therefore energy. The "capacitance" of a capacitor is stated in terms of the amount of charge (Q) stored at a given voltage drop (across the capacitor):

C = Q / V.

The unit of capacitance is the "Farad", which is equal to a C / V. Itis a very large unit; typical capacitances are measured in microfaradsor picofarads. The canonical capacitor consists of a dielectric substance sandwiched between two parallel conducting plates. It has capacitance

C = e A / d,

Capacitor Types (Floyd, pp. 474-477)

• Capacitors are often classified by the materials used for the dielectric (the insulator between the capacitor's plates).
• Some types are air, paper, plastic film, mica, ceramic, electrolyte, and tantalum.
• Each type has its own advantages and disadvantages; see pages 474-478 of the textbook for discussion of the various types.
• Often you can tell a capacitor's type by the appearance of the package. For example, ceramic capacitors typically look like this:
  Here's a typical plastic-film capacitor:
  Here's how electrolytic capacitors usually look:

• Unit of Capacitance (Floyd, p. 468)

  • Capacitance is abbreviated C.
  • The unit of capacitance is the farad, abbreviated F.
  • Typical capacitors found in electronic equipment are in the microfarad (μF) or picofarad (pF) range. Recall that micro- means 10^-6 and that pico- means 10^-12.
  • You'll also remember that nano- means 10^-9. But for some reason, the nanofarad has traditionally not been used, even in cases where that might make the most sense.
    • For example, if a capacitance is equal to 1×10^-9 F (or 0.000000001 farads), you might think that you'd write that as 1 nF. But in fact, most people would write this as either 1000 pF or 0.001 μF. This is strange and confusing, but you just have to get used to it.
  • In recent years, however, it's becoming more common to see nanofarads (nF) used.
    • For instance, the capacitance meters that the EET department bought 10 or 15 years ago displayed all capacitance values in either μF or pF. But the capacitance meters that we've bought in the past 5 years display capacitance values in μF, nF, or pF.

    • Capacitors in Series (Floyd, pp. 480-481)

      
      
      • Suppose you have two or more capacitors connected in series, as in the picture above. To find their total capacitance, use the reciprocal formula:

         C_T = 1 ÷ (1÷C₁ + 1÷C₂ +  ... + 1÷C_n)

      • This equation has the same form as the equation you've learned for finding the total resistance of resistors connected in parallel. So we see that capacitors in series combine like resistors in parallel.

      Stray Capacitance

      • Stray capacitance exists between any two conductors that are separated by an insulator, such as two wires separated by air. This means that a circuit may contain some capacitance even if there's no capacitor in the circuit.
      • Stray capacitance is usually small (a few pF), and you can usually ignore it, but it can have undesirable effects in high-frequency AC circuits.

      Capacitors in Parallel (Floyd, pp. 484-485)

      
      
      • Suppose you have two or more capacitors connected in parallel, as in the picture above. To find their total capacitance, simply add the individual capacitances:

        C_T = C₁ + C₂ +  ... + C_n

      • So we see that capacitors in parallel combine like resistors in series.

      Don't Connect Capacitors Directly Across a Voltage Source

      • In general you should not connect a capacitor (or combination of capacitors) directly across a voltage source, since the resulting surge of current could damage the capacitor or the voltage source:
        
      • Instead, you should always have a resistance in series with the capacitor(s), to limit the amount of current that flows.

      
      

Low Pass Filter / Integrator

High Pass Filter / Differentiator

Notes: