Capacitors and capacitance

dielectric

insulatory material between two capacitor plates

voltage between plates

proportional to q (charge): v = (d/Ae) d

DC current

cannot flow through capacitor as there is an insulator between the two terminals

AC current

can flow through a capacitor as voltage across a capacitor is proportional to the charge on it. AC must correspond to alternating charge.

• this gives the impression that an alternating current flows through capacitor

mechanical analogy of AC current through capacitor

• Air (charge) cannot pass through a window in spite of the pressure difference (voltage potential)

• However, alternating pressure can make the window vibrate, producing air movement

capacitor in parallel

voltage V is applied across two capacitors

Q = Q1 + Q2 —> C = C1+C2

capacitor in series

Q1 = Q2 = Q3, V = V1 + V2, 1/C = 1/C1+1/C2…

Exponential signal

RISE: signal reaches 63% at one time constant (tau), and 95% at 3 tau

FALL: signal reaches 37% at one time constant and 5% at 3 tau

capacitor and exponential

as capacitor charges…

• V(t), charging voltage, increases

• V_R (voltage across resistor) decreases

• I (t), charging current, decreases

• results in exponential behaviout of I and V(t)

RC circuit and time constant

• Charging current determined by R and voltage across it

• Increasing R increases time taken to charge C

• Increasing C increaes time taken to charge C as it can store more charge

• Time required to charge to a particular voltage determined by CR

• this is the time constant

step responses of an RC circuit

V(t) = Vs(1-e^(-t/RC))

Discharging capacitor in RC circuit

• at t = 0, V(t) = Vs

• via KVL first order differentials: V(t) = V2e^(-t/RC)

DC blocking

• capacitor used to block DC voltage from passing to a part of the circuit

Capacitor filtering effect

• circuits have different effects on the input signal at different frequencies

• higher frequencies pass through capacitor with little to no reduction

signal gain (Vout/Vin)

Vout/Vin

plot for filtering effect of Capacitor

• if signal gain is plotted (Vout/Vin) against frequency, lower the gain and stronger suppression

• 0 frequency = -infinite gain (dB)

• circuit can then block a DC signal

• Logarithmic scale for both axes:

voltage gain

A = modulus of Vout/Vin (modulus of signal gain)

of lower than 1 (Vin is greater), this is the attenuation

decibels

unit of voltage gain

voltage gain log

20log10(vout/vin)

power gain (dB)

G = 10log (Pin/Pout)

why do we provide voltage and power gain ratios in log form

higher dynamic range

• hearing and seeing sensitivity is logarithmic not linear

polystyrene capacitoy

• two sheets of foil rolled up to save space with thin plastic film

ceramic capacitor

alternating layers of metal and ceramic

electrolytic capacitor

two sheets of aluminium foil separated by paper soaked in conducting electrolyte. The insulator is a thin oxide layer on one of the foils

• polarised (oxide layer side must always be at positive voltage relative to other side)

• negative side indicated by curved symbol

current/voltage continuity

• voltage across capacitor never changes instantaneosly

• it tries to keep its voltage constant

• i = C dv/dt