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Early Effect

Written by Andrew Levido

I have previously mentioned the Early effect in passing. It is the phenomenon where the collector current of a BJT transistor changes with collector voltage, even though the base current or voltage is held constant. The textbook explanation of the Early effect usually begins with a diagram like that of Figure 1.  As the collector-emitter voltage VCE is increased, the collector-base depletion region widens, and the base region narrows. This increases the charge gradient across the base region and results in increased current across the collector-base PN junction.

Figure 1

This explains (in high level terms) how the Early effect works but does not really help us electronics designers understand what it means in practice. A better way to get a handle on it is to consider the IC/VCE characteristic of a typical BJT shown in Figure 2. Each curve represents the relationship between VCE andIC for a fixed value of VBE. Note that most data sheets show this characteristic for fixed values if IB which is almost the same thing.

Figure 2

You can see that the slope of the characteristic curves in the active region is not horizontal as we would expect if IC was depended only on VBE. Instead, there is a positive gradient due to the Early effect. Increasing VCE with fixed VBE results in increasing IC. If we extend the gradients to the left as shown in the diagram, they will converge at a negative voltage VA, known as the Early voltage. The Early voltage is typically between 50 and 500V for modern BJTs. It is usually at the lower end for small-signal transistors of a given polarity. It is also typically lower for PNP transistors than NPN transistors of the same size.

To evaluate the impact of the Early effect let’s consider our go-to large-signal BJT tool, the simplified Ebers-Moll model. This gives us an equation for collector current in terms of base-emitter voltage (and some temperature-dependent constants):

Equation 1

There is no term for VCE here, so it stands to reason that Ebers-Moll predicts IC will be constant over the VCE range in the active area. We can add the Early effect to the model as shown below.

Equation 2

Now we have an additional term that models the increase in collector current with increasing VCE. This is helpful if we know VA, but in practice it is not usually published in BJT data sheets. It can however be estimated from the data sheet by extrapolating the slope of the published IC/VCE or IC/IB curves. I did this for a modern jellybean NPN BJT, the BC847, and came up with an Early voltage of around 100V.

In practice this would mean that a 10V change in VCE will result in a10% change in collector current, if all else is equal. Figure 3(a) shows a simple common-emitter amplifier circuit with a fixed VBE and a variable power supply. By Ebers-Moll alone we would expect the collector current to be constant over the supply range, but the Early effect means that we will see a 10% change in current. This is clearly not good if this was meant to be a constant current sink for example.

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Figure 3

We can eliminate the Early effect by adding a cascode transistor as shown in Figure 3(b). Here Q2’s base is held at a fixed voltage of 3V, so Q1’s collector is also held at a relatively fixed voltage of around 2.4V due to Q2’s VBE drop. Now the collector voltage of Q1 is fixed so no Early effect can occur, and IC will remain almost constant over the full range of the supply.

The Early effect, along with the Ebers-Moll model forms a solid base for the DC analysis of BJT circuits. Here is the “rule of thumb” – depending on the transistor, the Early effect will mean that collector current will typically increase 2-20% over a 10V collector-emitter voltage range, for a given set of base-emitter conditions. Keeping VCE as constant as possible (perhaps using a cascode configuration) is the cure, if this is going to be a problem for your application.

References

“Early Effect.” In Wikipedia, May 31, 2022. https://en.wikipedia.org/w/index.php?title=Early_effect&oldid=1090780447.

Horowitz, Paul, Winfield Hill, and Paul Horowitz. The Art of Electronics: The x-Chapters. Cambridge ; New York, NY: Cambridge University Press, 2020.

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Andrew Levido (andrew.levido@gmail.com) earned a bachelor’s degree in Electrical Engineering in Sydney, Australia, in 1986. He worked for several years in R&D for power electronics and telecommunication companies before moving into management roles. Andrew has maintained a hands-on interest in electronics, particularly embedded systems, power electronics, and control theory in his free time. Over the years he has written a number of articles for various electronics publications and occasionally provides consulting services as time allows.

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Early Effect

by Andrew Levido time to read: 3 min