Electronics
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Rectfier waveforms
Half wave rectified
 Vrms = Vp / 2
 Vdc = Vav = Vp / π
Full wave rectified
 Vdc = Vav = 2Vp/π
 Vrms = Vp/√2
3 phase full wave
 Vdc = Vav = Vp(3√3/π) = 1.65Vp

RMS voltage
(all symmetrical around zero volts except pulse)
sine wave Vp/√2
square wave Vp
triangle wave Vp/√3
Sawtooth wave Vp/√3
Pulse train Vp√D
  where D is duty cycle, percent time spent high
To add a DC offset(Vd) to a waveform
  Vrms = √(Va² + Vd²) where Va is the RMS of the
  waveform.

Junction Transistor Amplifier
Common Emitter (β = HFE)
  input Resistance Rb = 25β/Ie (Ie in ma)
    This is paralleled by the bias resistors
  Voltage gain Av = RʟIe/25 (Ie in ma, Rʟ in Ω)
  Output resistance is Rʟ
Common Emitter with emitter resistor
    This allows you to set the gain by omission
    of the bypass cap on all or part of Re.
    input Resistance Rb = REβ + 25β/Ie (Ie in ma)
    This is paralleled by the bias resistors
  Voltage gain Vg = RL / (RE+Re)
  Output resistance is Rʟ
  Re = 25 mV / IE
Common Collector (emitter follower)
  input Resistance is Reβ
    This is paralleled by the bias resistors
  Voltage gain Av = approx 1
  Output resistance is the source R/β
     where source R is the output R of the previous
     stage in parallel with Re
Common Base
  input Resistance Rb = 25/Ie (Ie in ma)
  Output resistance is R∟
  Current gain = 1

Opamp: feedback gain with finite gain
G₀ is gain with infinite gain opamp, with finite gain A
G = G₀A/(A+1+G₀)