Temperature Compensation

Rules of thumb - diode

I = I_s\left(e^\frac{qV}{nkT} - 1\right)
I = the net current flowing through the diode.
Is = "dark saturation current", or is the reverse bias saturation current (or scale current) the diode leakage current density in the absence of light. Is approximately doubles for every 10 °C increase in temperature - this temperature effect dominates the one in the exponent and results in the voltage drop with temperature. Is is related to the area of the junction and just how it was made.
V = applied voltage across the terminals of the diode.
q = absolute value of electron charge.
k = Boltzmann's constant.
T = absolute temperature (K).
n = ideality factor, a number between 1 and 2 which typically increases as the current decreases.
V_\text{T} = \frac{k T}{q} \,


Simplified trans-conductance of a Transistor

 G_m = \frac{1}{r_e} \cong \frac{qi_c}{kT}


 r_e \cong \frac{kT}{qi_c}

Transistor current ratios

 \Delta V_{be} = V_T\  \ln  \frac{I_{c1}}{I_{c2}}
Where ,  V_T \cong 26mV at room temperature

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