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The Basic DC model for an NPN Bipolar Junction Transistor

Modified Current Definitions for our NPN Transistor Model Discussion

Modified Current Definitions for our NPN Transistor Model Discussion

There are two ways to create a model. One method is to know how the pieces are parts inside the device operate and use these principles to add all the pieces and parts and their interactions together to develop a “white box” model. The opposite way is to run signals or inputs into the device and see what comes out. From this “transfer equations” are written and the device is modelled using this “black box” method.

Transistors and other solid state devices have been modelled using the black box method.  Once the black box has been understood it was necessary to start understanding the interactions and try to make predictions on how changes of construction inside the device will change the operation.

For those of us only interested in using the transistors the black box model is fine.  We don’t have the equipment to grow the “Magic Crystals” and modify them but we do want to use them.  In this discussion of the NPN transistor I am going to break away from the IEEE standard convention where all currents are shown going into the transistor on all three connections.  As shown on the diagram in the first picture, I will refer to the emitter current in conventional current terms.  +Ie will be flowing from the emitter to the negative lead of the sources.  It is a minor change but it may cause you problems when you read other texts.   With some writing conventional current, some writing electron current, and the IEEE standard it is a mess any way we go.   I chose to break away because common sense says that if current goes in it must come out somewhere… or the transistor is going to get very very fat.  (Something I am going to have to come to terms with on my caloric intake!)

To “black box” test the  transistor using the circuit shown in figure one a voltmeter would be installed to measure the actual voltage on the Base and Collector terminals and all three currents would be monitored.  The resistances  are there to reduce the current and would be changed as needed.

The model of the transistor in the cut off region.

The model of the transistor in the cut off region.

Until the voltage on the Base terminal reaches a certain voltage, Vo, very little current flows through the Base lead and very little current flows through the Collector lead.  The transistor is said to be “cut off”.  This can be modelled as all three terminals completely disconnected, but usually it is shown with a very small amount of current flowing from the Collector to the Emitter.  This current is called Iceo.  This means the current flows from the Collector to the Emitter with the Base Open.   I normally refer to this as a leakage current, because it is not desired but the correct name is Iceo.  The current is very temperature sensitive and cause some major problems if the transistor gets hot.  (A rough estimate is the current doubles for each 10 deg C rise in temperature.)9*9

The model for the Saturation Region

The model for the Saturation Region

At the opposite extreme, if we have the base voltage above Vo and allow enough current to flow we can get to a situation where the collector voltage drops down below the base voltage and both junctions in the transistor are forward biased. This is called saturation.

In the saturation region the transistor acts like a resistor between the collector and emitter.  The model in this case specifically shows the value Vo, the magic voltage where things get turned on.  Some versions of this model show an ideal diode in series with the voltage source to highlight the idea that current cannot flow out of the transistor.  Many others do not show the diode, and I chose to not show it because I use three different models.  In this part of the operation, the base really is not in control of the rest of the transistor.  It is useful if we are using the transistor as a switch but we will not spend much time using the models in these two areas.  We will mostly be interested in the active region.

The model for the active region

The model for the active region

The active region is the middle region so it makes sense that we show most of the components of the other two regions.  In this region, the base voltage is above the magic value of Vo, (the barrier voltage, refer to the post on a diode).  However, base current is maintained at a value where it does not “loose control” of the collector current and put the transistor into saturation.  Iceo still exists, but if we are lucky and the transistor remains cool, it will be almost negligible in comparison to the major current flowing through the collector leg, the new symbol the dependent current source.

As shown in the model the dependent current source is controlled by a fixed current gain called Beta(β).  Ic = Ib X β.
To put this in English, the collector current is linearly controlled by the base current.

Our next goal will be to use these models to calculate the external resistors and voltage sources to obtain an good operating point to operate the transistor.   This is called setting the D.C. bias to obtain a quiescent current.   The transistor will be conducting current even with no signal and we will want it to have the ability to conduct more if there is a positive signal and to conduct less if there is a negative signal.   In other words we want to come up with a “happy medium”.

To get to that goal we will first have to learn how to read a real transistor datasheet  to get the value for beta, Vo, and the always critical values of power dissipation, and maximum voltages and currents the transistor can handle.   That will be the very next post.

Before ending this post I think a few equations are necessary:

The currents through the transistor are always (with the current directions shown in my modified picture 1.)
Ie = Ic + Ib

In the active region:  Ic = Ib*β+Iceo

Notice combining those two gives Ie= Ib(1+β)+Iceo.

There is another term we will deal with in the future called Alpha (α). It is not important for our point right now, but if you go to other sources in information you may run into it.  We will get there.

Hopefully, I have provided a good bite sized information… just enough to digest and enough to keep you interested.
More is coming.


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