Technical Article

# Understanding Collector Current in BJT Beta Variations

November 11, 2019 by Robert Keim

## This article looks at factors that can alter the functionality of a bipolar junction transistor (BJT) by causing variations in its forward current gain.

### The Importance of the Current Gain of BJTs

We saw in the previous article that BJT beta is both simple and complex: simple, because all you need to do to calculate collector current is multiply base current by beta; complex, because there are several betas to choose from. The “normal” beta (βF or βDC) refers to the large-signal current gain of a bipolar junction transistor operating in forward active mode.

Other betas represent the small-signal gain in forward active mode (βAC) and the large-signal gain for saturation mode (βforced) or reverse active mode (βR). And let’s not forget about hFE and hfe—these abbreviations, popular among the folks who write datasheets, are equivalent to βDC and βAC, respectively.

### Manufacturing Beta

Before we examine the operational conditions that cause variations in beta, I want to briefly discuss this parameter in relation to semiconductor characteristics. We won’t go into detail because this information probably won’t help you design better circuits, and if your goal is to design semiconductors, you’ll need much more information than I can provide.

It is possible to calculate beta from device parameters, and likewise we can manipulate device parameters in order to improve beta. I’m not going to reproduce the entire equation, but I’ll point out that the width of the base region, the doping concentration of the base region, and the doping concentration of the emitter region play an important role. More specifically, we can increase beta by making the base region narrower and by reducing the ratio of base doping concentration to emitter doping concentration.

### BJT Beta vs. BJT Biasing: How Collector Current Influences BJT Beta

You definitely can’t change the physical dimensions and doping concentrations of a purchased transistor, but you still can exert some influence over the value of the transistor’s beta, because beta is highly dependent on collector current (IC).

You might find this a bit confusing: if we’re performing amplification by causing variations in base current to generate higher-amplitude variations in collector current, how can we analyze the circuit if these variations in collector current will lead to variations in gain?

This is a good time to review the basic large-signal vs. small-signal concept. We think of a BJT amplifier circuit as living in two distinct but interrelated electrical worlds. In the large-signal world, biasing conditions place the transistor in an operational mode that makes amplification possible.

In the small-signal world, we superimpose small variations onto these biasing conditions and amplify only the variations. The large-signal and small-signal collector currents are not physically separate, but we can think of them as separate.

##### The straight blue arrows represent the large-signal portion of the base and collector current, and the sinusoidal red arrows represent the small-signal portion.

Thus, when we bias a transistor, we impose a large-signal collector current, and this is the collector current that we use when estimating beta. Yes, in theory, the small-signal variations in collector current influence beta, but we assume that the overall effect is not significant.

### Visualizing the Relationship Between BJT Beta and Collector Current

The following plots are examples of the relationship between beta and collector current. The basic trend is that beta decreases at the higher end of the IC range. I’ve seen plots in which beta decreases significantly at the higher end and the lower end of the IC range, but that appears to be less common.

### Other Factors That Affect Beta

All of the hFE vs. IC plots have different curves for different temperatures. This tells us that beta is influenced not only by collector current but also by temperature.

The magnitude of the changes is quite large, but notice that the curves cover a very wide temperature range. The relationship between beta and temperature is something to keep in mind if your application involves extreme temperatures, and you need to be especially mindful if the hardware could experience extreme changes in temperature.

You may have noticed that all the plots include a label that specifies the collector-to-emitter voltage (VCE). This parameter influences beta, but datasheets more readily provide detailed information on the β–IC relationship. If you’re concerned about how changes in VCE will alter a circuit’s behavior, you might have to do some experimentation.

### Conclusion

I hope that this short series on BJT beta has helped you to develop a more complete understanding of this important circuit-design parameter. If you have any additional insights or recommendations that you would like to share, feel free to make your contribution in the comments section below.

4 Comments
• V
vanderghast November 14, 2019

“It is possible to calculate beta from device parameters, and likewise we can manipulate device parameters in order to improve beta.”

Do you have any references available through the Internet (url) and free of access, about these “equations”, in particular, for the Gummel-Poon ( or Ebers-Moll) ‘s model used with LTspice? In particular, showing the influence of Ic for hFE and temperature of the junction, if possible.

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• RK37 November 21, 2019
Here is the LaTeX code for the equation that I was referring to: \beta=1/\left(\frac{D_p}{D_n}\frac{N_A}{N_D}\frac{W}{L_p}+\frac{1}{2}\frac{W^2}{D_n\tau_b}\right). My reference is a textbook, but you can probably find some relevant information online.
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• H
hugocoolens November 21, 2019

I have a scan of the beta behaviour of the BC546/7/8. It clearly shows a reduction of beta at low currents.
https://www.dropbox.com/s/r5yx6rfknjkf2n5/bc547_h_FE.pdf?dl=1
kind regards,
Hugo

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