Can the parameter \$\alpha\$ and \$\beta\$ be used for any BJT?

Question

The reason I ask this question is because the statement in this wiki page. It says

The common-emitter current gain is represented by \$\beta_F\$ or the h-parameter \$h_{fe}\$; it is approximately the ratio of the DC collector current to the DC base current in forward-active region. It is typically greater than 50 for small-signal transistors but can be smaller in transistors designed for high-power applications.

Another important parameter is the common-base current gain, \$\alpha_F\$. The common-base current gain is approximately the gain of current from emitter to collector in the forward-active region. This ratio usually has a value close to unity; between 0.98 and 0.998. It is less than unity due to recombination of charge carriers as they cross the base region. Alpha and beta are more precisely related by the following identities (NPN transistor):

So I want to ask in common emitter or collector, can I use \$\alpha_F\$ as well as using \$\beta_F\$ in common base or collector

Answer 1

Given that \$\alpha\$ and \$\beta\$ are related by \$\alpha = \frac{\beta}{1+\beta}\$ as stated in the wiki article, obviously you can do your sums with either.

However, which is going to be easier to use? I personally always use \$\beta\$, regardless of the transistor configuration.

In common emitter \$I_c = \beta\times I_b\$, so I can say 'I need to control \$I_c\$ collector current, I need at least \$\frac{I_c}{\beta}\$ of base current to do it'.

But as \$\beta >> 1\$ (for most transistors), \$\alpha \approx 1\$, and \$I_c \approx I_e\$. You may object to the approximation, but given the way that \$\beta\$ varies with temperature, \$I_c\$, and between transistors of the same type, that is a far far better approximation than insisting that \$\beta\$ is constant. Any good transistor design will allow for operation with a range of \$\beta\$, at least \$2:1\$, preferably more.

Once you have made the approximation \$I_c \approx I_e\$, then common collector operation is given by 'I need to allow for a base current of \$\frac{I_c}{\beta}\$ to flow in the base circuit, without upsetting operation'.

With a common base stage, you say much the same thing, allowing an amount of base current, however you also say that the emitter to collector gain is slightly less than \$1\$, a fraction of \$\frac{1}{\beta}\$ less than one. The error of the gain from \$1\$ will usually be a smaller error than resistor tolerances and other sources of gain error.

Given that you can write an equation for \$\alpha\$, does that mean that you need to? For most practical engineering designs, the answer is no. If you are in college, and the tutor really likes to use \$\alpha\$, then the answer is yes.

Answer 2

Yes, You can Transform Beta into Alpha using special Transformations: Alpha is always less that one as Ie=Ic-Ib in common base configuration and Alpha is Ic/Ie (Beta is Current gain fromn Base to Collector or HFE in Common Emitter Config) so the difference between Ic and Ib is the current being Pulled out of the base by a negative bias in a PNP-BJT and a Negative Bias in an NPN bjt.

• A=Ic/Ie =>
• Ie=Ic-Ib =>
• Ic/Ie=-Ib/Ic =>
• Ie=Ic-Ib =>
• Ib=Ie/Ic Ic/(Ic-Ib) =>
• Ic/(Ic+Ie/Ic)) =>
• (Ic/Ie)/(Ic/Ie)+Ie/(Ic*Ie) =>
• A/(A+1) The definition of Alpha for Common Base Transistors

** Alpha is ideally near 1 as Iout is usually equal to Iim

• B = Iout/Iin =>
• B = -A*Ie/Ib =>
• B (Ic/Ie)A =>
• B = (-Ic/Ie)*Ie/Ib =>
• B = (-Ic/Ib) **The negative sign indicates there is a 180 degree phase shift when a base input is amplified and output at the Transistor Collector

This leads further to the demonstration that:L

B=A/(1-A)

&

1/(1-A)=B+1

If Beta is large the previous equation simplifies to:

B=1/(1-A)

Citation: Pages 40-46, "Large Amplification Transistor Circuits", Comey, 1860, Prentice-Hall, Jew Jersey

For Hybrid P Parameters R=Input Impedance, F=Forward Current Gain, R=Reverse Voltage, and O equals Output Admittance (1/Impedance). The "e" in "hfe" stands for "Common-Emitter", B in "hob" is "Common Base", and C in "hic"is "Common-Collector" so, although some may be ubiquitously used without proper thought of their nomenclature, it would be wrong to describe current gain in a Common-Base BJT as Hfe or Beta.