# What is the physical significance of beta and alpha in BJT?

I have read in the book that beta is the ratio of collector current to the base current in common emitter configuration and alpha is the ratio of collector current to emitter current to common base configuration.

Also, I know that alpha and beta are the current gains in common emitter and common base configurations.

My questions are:

What does both the terms signify actually?

Why are we calculating these current gains?

And Why is there a range of beta for a particular transistor? What does minimum and maximum values of beta mean?

How much does these alpha and beta affects our Early Effect?

• I just saw this and the first thing popping to mind is that $\beta$ is the $\alpha$ and $\Omega$ of BJTs. ;) I'm having a silly day.
– jonk
May 22, 2021 at 23:26
• Yeah, got your point. Universe of BJT revolves around beta :) May 29, 2021 at 15:17

𝛼 and β are directly related - 𝛼 = β/(β+1); It doesn't matter what circuit configuration is used (or if any circuit is used at all -- these parameters are properties of the transistor, not the circuit).

However, in a common-emitter circuit, it may be more intuitive to consider β as the non-ideal factor, and in common-base circuits to use 𝛼.

The physical significance is that these parameters relate the effects of (usually considered non-ideal) base currents to collector currents. Beta for a transistor depends on the ratio of emitter doping to base doping, as well as the width of the base diffusion. It is quite constant over a range of current levels, and so is a useful parameter to use for calculations. Physically, however, a (BJT) transistor can be considered to be controlled by the base-emitter voltage; but since the current is exponentially dependent on this value, it is not generally used this way in a circuit (except in a current mirror).

A lot of circuit design involves making approximations or estimates of component performance because component parameters (especially transistors) are not precise, and may vary with temperature or current levels). Good circuits will setup components so that the performance remains acceptable (constant, or 'high enough') as component parameters may vary.

This often takes the form of 'sufficiently large' or 'close enough' calculations. This can for example be seen in opamp circuits where overall gain is defined by resistor ratios (which can be quite precise), where the equation's accuracy is acceptable if the opamp gain is 'high'.

• Thank you for this clarification. It was really helpful. However, there is another doubt popping out my mind: Why do we consider minimum value of beta to test the saturation? I had read this in a book that "if a transistor with minimum beta is saturated, then transistors with higher beta will also be saturated", why is that? May 27, 2021 at 2:02
• If a transistor is supplied with some amount of base current, then it will be saturated if the collector current (likely controlled by VSUPPLY/RLOAD) is less than beta*base_current. If beta is higher. then it can remain in saturation for even higher collector current loads. May 29, 2021 at 4:22

I never (need to) use $$\\alpha\$$ f , I always use $$\\beta\$$ (same as $$\h_{FE}\$$) for all configurations: Common emitter, common collector, common base.

If you make a schematic drawing and indicate the currents $$\I_b, I_c\$$, and $$\I_e\$$ and using $$\\beta = \frac{I_c}{I_b}\$$ then it is easy to write down $$\\alpha = \frac{I_c}{I_e}\$$ and then re-write that to express that using beta.

My point: using $$\\alpha\$$ for a common base is a choice. You can use it if you want and it makes your life easier. However I'd rather use $$\\beta\$$ as $$\\beta\$$ (or $$\h_{FE}\$$) can be found in the datasheet of a transistor. $$\\alpha\$$ is not in the datasheet but if I know $$\\beta\$$ then it is easy to know what $$\\alpha\$$ is. So I just don't need alfa.

Why are we calculating these current gains?

$$\\beta\$$ Is a current gain and a property of the transistor, as long as the transistor works in active mode, $$\\beta = \frac{I_c}{I_b}\$$ is true.

I see $$\\alpha = \frac{I_c}{I_e}\$$ more as a "helper" expression since it is mostly only useful in the common base configuration as in the common base the emitter is the input and the collector is the output. So really $$\\alpha\$$ is just the transfer function of the common base.

And Why is there a range of beta for a particular transistor? What does minimum and maximum values of beta mean?

Because it is almost impossible to manufacture transistors with a precise value for $$\\beta\$$. $$\\beta\$$ depends on the width of the base and doping levels which are hard to control. Some transistors have a very large range for $$\\beta\$$ like between 30 and 300.

In the factory all fabricated transistors are measured and the ones that do not have a 30 < $$\\beta\$$ < 300 are discarded.

You can buy transistors with a narrower range, for example 100 < $$\\beta\$$ < 200, then those transistors are "binned" meaning, they're measured and then marked depending on what their $$\\beta\$$ is.

To beginners this large range of $$\\beta\$$ often sounds like a huge problem. In reality it is not, we can design our circuits such that they can work with a $$\\beta\$$ that is for example at least 50. Then we just need to use transistors that have a $$\\beta\$$ that is always larger than 50, like a transistor that is specified to have: 100 < $$\\beta\$$ < 300. Yes, that 100 is 2x larger than the 50 we wanted but that's actually good meaning we get some "design margin".

How much does these alpha and beta affects our Early Effect?

The Early effect makes $$\\beta\$$ appear smaller as $$\V_{CE}\$$ increases and that is due to base with modulation. There is no easy to understand direct relation so as a beginner, don't worry about this too much.

• Are they 100% production tested? I would have thought that would be too much of an expense for a cheap party like a 2N3904 or a PN2222. May 22, 2021 at 12:38
• @Hearth When the transistors come from a reputable manufacturer then for sure they are 100% tested. The cost is limited by doing on-wafer testing (before the individual transistors are separated) and by testing in parallel (bed of nails and then testing for example 25 transistors in one go). Even dirt cheap transistors are used in expensive equipment and you don't want your customers to have to test the transistors before using them. I know that for example Nexperia can trace back for every transistor where and when it was measured and fabricated. May 22, 2021 at 12:50
• I would have thought that it would be possible to control β from design parameters well enough to work fine in properly designed circuits (i.e. ones that don't depend on the exact value of β). May 22, 2021 at 13:06
• *(base width modulation) May 22, 2021 at 16:23
• @Hearth Common practice for reputable manufacturers is that min/max characteristics, for example: $h_{FE,min}$ = 30, $h_{FE,max}$ = 300 are guaranteed and measured in production. Characteristics which only have a typical value might be "guaranteed by design" and not tested. What also happens is that only a few random devices from a batch are fully tested. Still every device will need to be tested for guaranteed parameters. Again. this applies to tier1 manufacturers, for Cheapy-Chinese manufacturers, I have no clue. May 23, 2021 at 10:43