Forward voltage of a diode connected to Vin through a resistor

`V`_in : Input voltage	[V]
`R` : External series resistance	[Ω]
`T`_j : Junction temperature	[°C]
Diode model
`T`_NOM : Nominal temperature	[°C]
`I`_s(`T`_NOM) : Saturation current	[A]
`n` : Emission coefficient
`E`_g : Energy gap	[eV]
`X`_TI : Temperature exponent
`R`_s : Ohmic resistance	[Ω]
`V`_f : Forward voltage	[V]
`I`_f : Forward current	[mA]

Calculation resulsts:

Note: The calculation model used here does not take into account the backward diode components.
In the high current range exceeding several tens of mA, the results may differ significantly from the calculations.

Formulas used

E_g : Energy gap [eV]
k : Boltzmann constant 1.380649 × 10^-23 [J K^-1] (exact)
q : Elementary charge 1.602176634 × 10^-19 [C] (exact)
n : Emission coefficient
T₀ : Nominal temperature in Kelvin. 273.15 + 27 [K]
T₁ : Junction temperature in Kelvin. 273.15 + T_j [K]
X_TI : Saturation current temperature exponent. Usually equal to 3 for junction diodes, 2 for Schottky barrier diodes.

$I_{s} = I_{s(T_0)}\left(\frac{T_1}{T_0}\right)^{\displaystyle\frac{X_{TI}}{n}}\exp\left(\frac{E_g q T_1 T_0}{n k (T_1 - T_0)}\right)$

$V_T = \frac{k T}{q}$

$V_\mathrm{f} &=& I_s R + V_\mathrm{in} - n V_T W_0\left( \frac{I_s R}{n V_T} \exp\left(\frac{I_s R + V_\mathrm{in}}{n V_T}\right)\right)$

For high V_in, such as V_in > 220 n V_T, the following Newton-Raphson method is used:

$f(V_f}) &=& \exp\left(\frac{V_f}{n V_T}\right) - 1 - \frac{V_\mathrm{in} - V_f}{I_s R}\\ f'(V_f}) &=& \frac{V_f}{n V_T}\exp\left(\frac{V_f}{n V_T}\right) + \frac{V_f}{I_s R}\\ {V_f}_\mathrm{n+1} &\leftarrow& {V_f}_\mathrm{n} - \frac{f'(x)}{f(x)}$

Appendix

fig.1 Example of a plot of calculation results

fig.2 Example of V_f characteristics of a real diode (Adapted from Nexperia, BAV70 datasheet)

Forward current as a function of forward voltage; typcal values

`V`_in に抵抗を介して接続したダイオードの順方向電圧

`V`_f calculator

Formulas used

Appendix

RESOURCES (External links)

SEE ALSO

Vin に抵抗を介して接続したダイオードの順方向電圧

Vf calculator

Formulas used

Appendix

RESOURCES (External links)

SEE ALSO

`V`_in に抵抗を介して接続したダイオードの順方向電圧

`V`_f calculator