Quantum Noise Units

The Boltzmann Constant

$$ k_B = 1.380649 \times 10^{-23} \frac{\textrm{J}}{K} $$ $$ \frac{\textrm{J}}{\textrm{K}}\left(\frac{1/\textrm{s}}{1/\textrm{s}}\right) = \frac{\textrm{J/s}}{\textrm{K}\cdot \textrm{Hz}} = \frac{\textrm{W}}{\textrm{Hz}\cdot \textrm{K}} $$ $$ k_B = 1.380649 \times 10^{-23} \frac{\textrm{W}}{\textrm{Hz}\cdot \textrm{K}} $$ $$ 1 \frac{\textrm{W}}{\textrm{Hz}\cdot \textrm{K}} \times $$ $$ \left(\frac{10^{9}\textrm{ Hz}}{1 \textrm{ GHz}}\right)\left(\frac{1 \textrm{ fW}}{10^{-15}\textrm{ W}}\right)\left(\frac{1 \textrm{ K}}{1000 \textrm{ mK}}\right) $$ $$ = 10^{21} \frac{\textrm{fW}}{\textrm{GHz} \cdot \textrm{mK}} $$ $$ k_B = 0.01380649 \frac{\textrm{fW}}{\textrm{GHz} \cdot \textrm{mK}} $$ $$ k_B = 13.80649 \frac{\textrm{fW}}{\textrm{GHz} \cdot \textrm{K}} $$

The Planck Constant

$$ h = 6.62607015 \times 10^{-34} \textrm{J} \cdot \textrm{s} $$ $$ \textrm{J} \cdot \textrm{s } \left(\frac{1/\textrm{s}}{1/\textrm{s}}\right) = \frac{\textrm{W}}{\textrm{Hz}^2} $$ $$ 1 \frac{\textrm{W}}{\textrm{Hz}^2} \times $$ $$ \left(\frac{10^{9}\textrm{ Hz}}{1 \textrm{ GHz}}\right)^2\left(\frac{1 \textrm{ fW}}{10^{-15}\textrm{ W}}\right) $$ $$ = 10^{33} \frac{\textrm{fW}}{\textrm{GHz}^2} $$ $$ h = 0.662607015 \frac{\textrm{fW}}{\textrm{GHz}^2} $$

The Elementary Charge

$$ e = 1.602176634 \times 10^{-19} \textrm{ C} $$ $$ 1 \textrm{ W} = 1 \textrm{ A}^2 \cdot \Omega $$ $$ 1 \textrm{ C} = 1 \textrm{ A} \cdot \textrm{s} = 1 \frac{\textrm{A}}{\textrm{Hz}} $$ $$ 1 \frac{\textrm{A}}{\textrm{Hz}}\left(\frac{\textrm{A} \cdot \Omega}{\textrm{A} \cdot \Omega}\right) = 1 \frac{\textrm{W}}{\textrm{A} \cdot \Omega \cdot \textrm{Hz}} $$ $$ 1 \frac{\textrm{W}}{\textrm{A} \cdot \Omega \cdot \textrm{Hz}} \left(\frac{10^{9}\textrm{ Hz}}{1 \textrm{ GHz}}\right) \left(\frac{1 \textrm{ fW}}{10^{-15}\textrm{ W}}\right) \left(\frac{1 \textrm{ A}}{10^{3}\textrm{ mA}}\right) $$ $$ = 10^{21} \frac{\textrm{fW}}{\textrm{GHz} \cdot \textrm{mA} \cdot\Omega} $$ $$ e = 160.2176634 \frac{\textrm{fW}}{\textrm{GHz} \cdot \textrm{mA} \cdot\Omega} $$ $$ e = 160.2176634 \frac{\textrm{fW}}{\textrm{GHz} \cdot \textrm{mV}} $$

Thermal Noise