What is the Early voltage equation in a transistor?
Technical Blog / Author: icDirectory Limited / Date: May 18, 2024 23:05
The Early effect, named after its discoverer James M. Early, refers to the variation in the effective width of the base in a bipolar junction transistor (BJT) due to changes in the applied base-to-collector voltage. Let%27s delve into the details:

1. Explanation:
- In a BJT, the neutral (active) base region is green, while the depleted base regions are hashed light green.
- Under increased collector–base reverse bias, the depletion region in the base widens, leading to a narrower neutral base region.
- The collector depletion region also increases, more than that of the base, due to the collector being less heavily doped.
- Base-narrowing has two effects:
1. Reduced recombination within the smaller base region.
2. Increased current of minority carriers injected across the collector-base junction, known as the Early effect.
- The increased current is shown in Figure 2.
- Tangents to the characteristics at large voltages extrapolate backward to intercept the voltage axis at a voltage called the Early voltage (VA), typically ranging from 15V to 150V (smaller for smaller devices).

2. Large-Signal Model:
- In the forward active region, the Early effect modifies the collector current ((I_C)) and the forward common-emitter current gain ((eta)).
- The equations are:
[ I_C = I_S left(e^{frac{V_{BE}}{V_T}} - 1
ight) ]
[ eta = frac{I_C}{I_S} ]
[ I_C = frac{eta}{1 + frac{V_{CE}}{V_A}} ]

Remember, the Early voltage is a crucial parameter in BJT design and analysis. If you have more questions, feel free to ask! ¹³

![Cross-section of an N-channel enhancement-mode MOSFET with the intrinsic body diodes indicated symbolically](https://www.digikey.com/-/media/Images/Article%20Library/TechZone%20Articles/2016/September/The%20Significance%20of%20the%20Intrinsic%20Body%20Diodes%20Inside%20MOSFETs/BodyDiode.png?la=en&ts=5e4c8a7d-6f0a-4f7e-9b3d-2b7e5b3c3a1b)¹

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(1) Early effect - Wikipedia. https://en.wikipedia.org/wiki/Early_effect.
(2) transistors - How is the Early voltage defined? - Electrical .... https://electronics.stackexchange.com/questions/173920/how-is-the-early-voltage-defined.
(3) (Solved) - Explain in detail, effect of Early voltage in transistor .... https://www.transtutors.com/questions/explain-in-detail-effect-of-early-voltage-in-transistor-determine-the-equivalent--10207723.htm.
(4) Understanding the Early Effect - Technical Articles - All About Circuits. https://www.allaboutcircuits.com/technical-articles/understanding-the-early-effect/.

icDirectory Limited | https://www.icdirectory.com/a/blog/what-is-the-early-voltage-equation-in-a-transistor.html
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