i was seeing a data sheet of a transistor. it reads the gain or hFE value between 100 to 300. what does that mean. till now i was of the view that a transistor has a fixed gain value. if the gain varies then what are the conditions upon which it depends?

 

They do have fixed gain but hfe isn't an "exact science" and the gain of any particular transistor of that type will be between 100 and 300.

 

ok thanks. but is there any way by which we can determine the gain of a particular transistor?

 

My digital volt meter (DVM) has transistor sockets on the front for inserting transistors. It has two settings, PNP and NPN and shows the hFE on the display.

 

You can control the gain of a transistor by changing the collector current and any one of several other parameters. Check the specific transistor data sheet to see the many ways to affect Hfe.

 

....And you design circuits that do not depend on a particular value of hfe. It actually is much less of a problem than you might think. In fact it is actually a non-problem.

 

I had a similar issue earlier. You may find the thread of use/interest.
http://forum.allaboutcircuits.com/showthread.php?t=72928

 

Transistor gain varies with temperature, emitter current, base-emitter breakdown, and age. In saturated circuits gain variation is compensated by using a large margin, and in linear circuits gain is made dependent on passive components through the use of feedback.

 

β is a minimum spec.

With most transistor designs, it is the collector resistance (or reactance) divided by the emitter resistance (or reactance).

 

β is a minimum spec.

With most transistor designs, it is the collector resistance (or reactance) divided by the emitter resistance (or reactance).

Why is it a minimum spec if it is given as a range?

Also, I've always seen beta defined at the ratio of collector current to base current. Can you elaborate on how it relates to the ratio of collector resistance to emitter resistance, and how these resistances (or reactances) are defined?

 

Transistor gain varies with temperature, emitter current, base-emitter breakdown, and age. In saturated circuits gain variation is compensated by using a large margin, and in linear circuits gain is made dependent on passive components through the use of feedback.

To help quantify it, one can derive a relation using the Ebers-Moll model of the bipolar transistor. The relation is approximate since it uses a low frequency model and does not include all effects, but it still shows some of the basic behavior for most practical cases. The effective beta (defined as the ratio of collector current to base current) would be as follows and is a function of (temperature T, base emitter voltage Vbe and base collector voltage Vbc). Note that the alpha's and beta's with subscripts R and F are constants, and V_T is the thermal voltage KT/q.

\(\beta(V_{be}, V_{bc}, T)=\beta_F\ {{( e^{V_{be}/V_T}-1)-(e^{V_{bc}/V_T}-1)/\alpha_R} \over{(e^{V_{be}/V_T}-1)+\beta_F(e^{V_{bc}/V_T}-1)/\beta_R}}\)

This above relation is good for cutoff, saturation and the linear region.

In the linear region, the relation reduces to \(\beta_F\), a constant.

If the cutoff region is ignored (which it usually can be ignored because then the transistor is pretty much off anyway), then a relation for saturation and the linear region can be written in terms of the collector emitter voltage Vce, as follows.

\(\beta(V_{ce}, T)=\beta_F\ {{e^{V_{ce}/V_T}-1/\alpha_R} \over{e^{V_{ce}/V_T}+\beta_F/\beta_R}}\)

This relation is useful because it allows the Ebers-Moll model, which is a voltage controlled model, to be recast primarily into a current controlled model with \(I_c=\beta I_b\), and the saturation region operation, with dependence on Vce, can be modeled as a voltage controlled modification to the current controlled model.