Useful Information: RF
----------------------


SMITH CHART

Series C : follow circles anticlockwise
Series L : follow circles clockwise
Shunt C  : reflect point around a vertical line through 1.0,
           follow circles anticlockwise,
           reflect back
Shunt L  : as for Shunt C but rotate clockwise


--------------------------------------------------------------------------------
RETURN LOSS & VSWR

RL = 20*log(|L|)

                                     R-Z0
  where L = reflection coefficient = ----
                                     R+Z0

       1+10^-(RL/20)
VSWR = -------------
       1-10^-(RL/20)


--------------------------------------------------------------------------------
TRANSMISSION LINE CHARACTERISTIC IMPEDANCE

Z0 = SQR(L/C)

  where L = inductance per unit length
  where C = capacitance per unit length


TRANSMISSION LINE IMPEDANCE

Looking into line open circuited at far end:

Zin = Z0/tan(a)

  where a = electrical length as an angle


--------------------------------------------------------------------------------
TRANSMISSION LINE VELOCITY

v = 1/SQR(L*C)

  where v = velocity (metres / sec)
  where L = inductance per metre
  where C = capacitance per metre

v = c/SQR(er)

  where c  = velocity of light in vacuum
  where er = (effective) dielectric constant


--------------------------------------------------------------------------------
COAXIAL CABLE IMPEDANCE

Circular outer:

Z0 = 138/SQR(e)*log(D/d)

  where e = dielectric constant (epsilon r)
        d = outside dia. of inner
        D = inside dia. of outer

Square outer:

Z0 = 138/SQR(e)*log(k*D/d)

  where k = 1+0.078705*tanh((D/d -1)^0.466)*3.38)
        D = inside width of square


--------------------------------------------------------------------------------
COAXIAL CABLE LOSS

a2 = a1 * SQR(f2/f1)

   where a1, a2 are attenuation (in dB/unit length) at frequencies f1, f2


--------------------------------------------------------------------------------
WILKINSON SPLITTER

        <--1/4 wave-->
          -----------+---- -3dB
         /           |
0dB ----<            R =2*Zio           impedance of quarter wave lines = SQR(2)*Zio
         \           |
          -----------+---- -3dB

useful bandwidth approx 2:1


--------------------------------------------------------------------------------
PHASE NOISE OF AN OSCILLATOR

                    [        w0^2    ]   [     wc ]   F*k*T0
phase noise = 0.5 * [ 1 + ---------- ] * [ 1 + -- ] * ------
                    [     4*wm^2*Q^2 ]   [     wm ]     Ps

where wm = frequency offset
      w0 = oscillation frequency
      wc = flicker cutoff frequency
      Q  = loaded Q
      F  = noise figure (large signal)
      k  = Boltzman constant
      T0 = noise temperature
      Ps = output power

ref. A Simple Model of Feedback Oscillator Noise Spectrum
D. Leeson, IEEE Letters Feb 1996


--------------------------------------------------------------------------------
INDUCTANCE OF A STRAIGHT WIRE

L = 0.2*l*(ln(l/d)+0.5)

where d = wire dia (mm)
      l = length (mm)