Effects of Collector Voltage on Large-Signal

Large-signal modeling is a common analysis method used in electrical engineering to describe nonlinear devices in terms of the underlying nonlinear equations. In circuits containing nonlinear elements such as transistors, diodes, and vacuum tubes, under "large signal conditions", AC signals have high enough magnitude that nonlinear effects must be considered.

"Large signal" is the opposite of "small signal", which means that the circuit can be reduced to a linearized equivalent circuit around its operating point with sufficient accuracy.

Differences between Small Signal and Large Signal

A small signal model takes a circuit and based on an operating point (bias) and linearizes all the components. Nothing changes because the assumption is that the signal is so small that the operating point (gain, capacitance etc) doesn't change.

A large signal model on the other hand takes into account the fact that the large signal actually affects the operating point and takes into account that elements are non-linear and that circuits can be limited by power supply values. You can't get 10 volts out of a 1.5 volt supply without transformers. A small signal model ignores supply values.

The Early Effect

As we have already seen, the depletion region around a reverse-biased PN junction gets wider as the reverse bias voltage increases, and narrower as the reverse bias voltage decreases. The same behavior holds true for the collector-base junction of any bipolar junction transistor (BJT) operating in its active region.

The first figure on the right shows an NPN transistor with a low collector voltage. As a result, the depletion region across the collector-base junction is narrow. At the same time the active base region (that part of the base not included in the depletion zones) is relatively wide.

The second figure shows the same transistor, but with a higher collector voltage. This means a wider depletion region around the collector-base junction, and a correspondingly narrower active base region. This means that free electrons in the base region spend less time there, and have a correspondingly smaller chance to recombine with holes in the base region. This is known as the Early effect, after James M. Early who identified and described what was happening.

Because of the Early Effect, the effective current gain of the transistor changes as VCE changes. The figure to the left shows the output characteristics of a typical BJT in common emitter configuration. Each curve in blue represents a fixed value of base current, IB, in increments of 10 µA. This particular transistor has a forward current gain (IC/IB) of 100 at VCE = 1V.

If there was no Early Effect, the blue curves would all be horizontal when VCE is high enough (above about 0.7V) to keep the collector-base junction reverse biased. That would mean that VCE would have no effect on IC or the current gain of the transistor. But, since the curves are not horizontal (and never are for real-world transistors), clearly the Early effect is real and does affect the behavior of the transistor.

As it turns out, there is indeed. Let's ignore the portion of the characteristic curves where the transistor is in saturation, and extend each of the main curves until it crosses the X axis. When we do this, we get the graph shown to the left.

Now we can see that all of these extended curves cross the X axis at the same point; in this case, at the point representing VCE = -50V. Disregarding polarity, this is known as the Early voltage (designated as VA) of this transistor. By "disregarding polarity," we mean that the Early voltage is always specified as a positive number. The same is true for a PNP transistor as for an NPN transistor. The importance of the Early voltage has to do with its magnitude only, not its polarity.

Looking at these lines, we note that they are straight lines on a graph that relates current to voltage. Thus, they are graphs of resistances. In fact, each line represents the output resistance of the transistor for that value of base current, IB. We typically identify this output resistance as ro, and compute it mathematically as: If VA is large enough and VCE can be kept small, we can approximate this expression as:If VA is large enough and VCE can be kept small, we can approximate this expression as: