The Forward Early voltage vAF is determined by extrapolating the curve of the IC versus VCE in the active region of operation where IC>= ICSAT till intercepts the the VCE axis in a voltage equals the forward Early voltage.

The equation of this straight line can be expressed as:

IC= ICSAT + VCE / rCE, where rCE IS the inverse of the slope of the I-V characteristics.

It is the incremental collector to the emitter resistance in the active region.

By definition, at IC=0, VCE= VAF, It follows that:

VAF= ICSAT X rCE.

WHICH IS THE PROOF OF THE ABOVE RELATION BY MUSTAFA FAYEZ..

Hello Raghu, you can calculate the early voltage from certain measurements as follows: you can draw the curve between Collector current and 

you can draw the curve between Collector current and Collectro-Emitter voltage. The slope of this curve is the output resistance which equals (Va+Vce)/Ic, you can then  caculate Va since u get Ic and Vce from the curve.

Check Sedra

http://www.amazon.com/Microelectronic-Circuits-Electrical-Computer-Engineering/dp/0199339139/ref=sr_1_1/181-4374515-8442007?ie=UTF8&qid=1450862858&sr=8-1&keywords=sedra

The Forward Early voltage vAF is determined by extrapolating the curve of the IC versus VCE in the active region of operation where IC>= ICSAT till intercepts the the VCE axis in a voltage equals the forward Early voltage.

The equation of this straight line can be expressed as:

IC= ICSAT + VCE / rCE, where rCE IS the inverse of the slope of the I-V characteristics.

It is the incremental collector to the emitter resistance in the active region.

By definition, at IC=0, VCE= VAF, It follows that:

VAF= ICSAT X rCE.

WHICH IS THE PROOF OF THE ABOVE RELATION BY MUSTAFA FAYEZ..

Thank you Mustafa and Abdelhalim.

From your replies, I get that ICSAT is the intercept on y-axis (Ic axis). It will be varying for different values of base current in the output characteristics. If so, how is the Early Voltage maintained constant? (Assuming the slope of the curve is almost constant)

 The slope of the curve is not constant. Experimentally the slope of IC versus VCE in the active region increases linearly with the ICSAT. This is proved also by direct measure of the small signal parameters of the transistor including hoe which is 1/ rCE. To this fact please see the link:http://www.zen22142.zen.co.uk/Theory/tr_model.htm

So, VA is constant with ICSAT and the and the parameter which changes is the rCE. such that rCE =VA/ ICSAT.

There is also a theoretical proof of this relation

In the active region we can express the collector current by:

IC= qDdelta n/ wb with q the electronic charge, d the diffusion coefficient of the minority carriers in the base delta n is the excess minority electrons at the edge of the base region adjacent to the emitter. and Wb is is the neutral base width.

If VCE increases Wb decreases and the slope of the excess minority carrier increases causing the early effect by increasing the collector current above its maturation value

Accordingly one can express IC as

IC= ICSAT( 1 + VCE/VA), DIFFERENTIATING THIS RELATION WE GET tCE= VA/ ICSAT.

wish you success. If you wish we can discuss the other spice parameters of the BJT.

Dear Raghuram, Dear Colleagues!

In the following answer you can find complete analysis of the Early voltage in case of constant voltage VBE and constant IB output characteristics. I gave this answer on a question on the researchgate by LUTZ VON wangenheim.

I will try to derive a relationship between the Early voltage VA for constant IB and constant VBE based on the basic relations in the bipolar transistor.

Assume that the transistor operates in the active mode such that theEJ i forward biased and he CJ is reverse biased.

According to the charge control model of the npn transistor the collector current is given by equation 1

IC= A Dn q delta n / Wbn with the symbol have their usual meaning and the reverse saturation current of the collector current is neglected.

The quasineutral base region width Wbn is that parameter what decreases by increasing VCE causing the collector current to increase. This effect is the Early effect..

Let us express Wbn by its value at VCB=0, Wbn0 and its incremental decrease dW because of increasing VCB and reverse biasing the collector junction, that is 

Wbn= Wbn0- dW, equation 2 , where dW is because of the collector pace charge widening in the base region.

Now let us expres IB in terms of the excess charges in the base region and emitter region

IB = A q delta n Wbn/ 2 Taun + A Dp q deltap / We ,wih Taun the minority carrier lifetime in the base region and We is the neutral region of the p-emitter.

The base current is composed of two components the recombination in the base region which is the first term, and the back infected current in the emitter which is the second term.

This IB relation is the most important one to explain the different observations concerning the Early voltage.

It is so, that The base current may be dominated by the recombination in the base region or may be dominated by back injected current. Integrated circuits very miniature transistors the base current is dominated by back injected base current.

In power transistors with the base width relatively larger, the base current may be dominated by the recombination in the base. With the improvement of technology, the base current is observed to be dominated by the back injection in the emitter.

There is remaining one fundamental equation to complete the required equations for the proof.

IT is the junction law of the EJ

delta n= nb0 exp VBE/ Vt with VBE>Vt,

delta p= pe0 exp VBE/ Vt with VBE>Vt,

The case of VBE is constant is straight forward,

Then delta n and delta p will be constants and the collector  current can be put in the form by combining equations 1 and 2

IC= ICSAT( I+ dW/ Wb0), With ICSAT, the collector current at VCB=0,

Now we come to the case of IB= constant and dominated by the back in injection in the emitter, IB= A q Dp delta p /we, From this equation if IB is costant, delta pwill be constant and from the junction law, VBE will be constant and consequently the collector current dependence on the neutral base width.

The last case, where the base current is dominated  by the recombination in the base region IB =A q delta n Wbn/ 2 Taun,

Combining with collector current and rearranging we get

IC= ICSAT ( 1- dw/ Wb0)^-2 = approximately ICSAT( 1+2 dw/ Wb0)

which means that the Early effect will increase in case of constant base current which is dominated by the recombination in the base.

In this way an explanation is introduced to Lutz observations concerning the Early effect in biploar transistors.

0 / 0 · Jun 5, 2015

How is the Early voltage defined? - ResearchGate. Available from: https://www.researchgate.net/post/How_is_the_Early_voltage_defined/1 [accessed Dec 30, 2015].