V₍CE(sat)₎ Calculator Using Ebers–Moll Model for a BJT

V₍CE(sat)₎ Calculator Using Ebers–Moll Model

Calculate the collector–emitter saturation voltage using the simplified Ebers–Moll model:
\[ V_{CE(sat)} \approx V_T \ln\left(\frac{I_{CS}}{\alpha_F\,I_{ES}}\right) \] where \(V_T\) is the thermal voltage, \(I_{ES}\) is the emitter saturation current, \(I_{CS}\) is the collector saturation current, and \(\alpha_F\) is the forward common‐base current gain.

* Enter all currents in amperes (A) and voltage in volts (V). Ensure that \(\frac{I_{CS}}{\alpha_F\,I_{ES}}>1\).

Step 1: Enter Parameters

Example: 1×10⁻¹⁶ A

Example: 1×10⁻¹⁴ A

Example: 0.98

Example: 0.026 V at 300 K

Formula: \( V_{CE(sat)} \approx V_T \ln\left(\frac{I_{CS}}{\alpha_F\,I_{ES}}\right) \)


Practical Example:
For example, if \( I_{ES} = 1 \times 10^{-16} \) A, \( I_{CS} = 1 \times 10^{-14} \) A, \( \alpha_F = 0.98 \), and \( V_T = 0.026 \) V, then:
\[ \frac{I_{CS}}{\alpha_F\,I_{ES}} = \frac{1 \times 10^{-14}}{0.98 \times 1 \times 10^{-16}} \approx 102.04, \] \[ V_{CE(sat)} \approx 0.026 \times \ln(102.04) \approx 0.026 \times 4.625 \approx 0.1203\, \text{V}. \]