BJTs: Introduction

Transistors make the world go around. Look no further than the phone, tablet, or computer you are using to read this right now. There are a few billion transistors in each.

The most basic definition of a transistor is that they are switches. They can be on. They can be off. They can even be somewhere in the middle. We can do some fun things with a transistor when it is somewhere in the middle.

State	Resistance
On	0Ω (short)
Off	∞Ω (open)
Middle	Between 0Ω and ∞Ω

Another description for analog circuits: A potentiometer controlled by an electrical signal. There are of course some ket differences:

1. The transistor can reach ∞Ω where the potentiometer will have a specified finite maximum resistance.

2. The transistor can respond to higher frequency input signals than the mechanical potentiometer.

Transistor Types

There are many types of transistors.

The big two categories that we sort transistors into are:

1. Bipolar Junction Transistors (BJTs)

2. Field Effect Transistors (FETs)

Traditionally BJTs are introduced first but you could jumped to the FET chapters if you prefer.

A Simple Physical Model of a BJT

BJTs are basically 2 PN junction diodes built back to back

These are simplified models. They get the jobs done and are commonly used. The actual silicon looks different. I encourage you to find a good reference for semiconductor physics if you want to dig deeper into the topic.

We often talk about the junctions as the:

1. Base-Emitter Junction (B-E)

2. Base-Collector Junction (B-C)

Individually they behave like diodes. Together the “magic” happens.

If the B-E junction is forward biased and the B-C junction is reverse biased, the transistor is in the active region of operation, the first of four regions.

In the active region, current flows through the B-E junction as we would expect for a forward biased PN junction

The B-C junction, against our intuition, also allows current to flow. While majority carriers won’t cross the depletion region, minority carriers will.

The physics of semiconductors is a rich and deep subject. Go study it. In this book I am more interested in analyzing circuits with transistors.

V-I Characteristic

Just like with diodes, we can analyze circuits with BJTs using nodal analysis. I find it odd that most books shun methodical analysis in favor a seat-of-the-pants analysis. But I suppose that is why I started writing this book.

Nodal analysis needs:

1. KVL (still works)

2. KCL (still works)

3. Ohm’s law (BJTs are not resistors. What do we do here?)

Since transistors are constructed from similar semiconductor materials as diodes, their V-I characteristics are nonlinear too.

And since transistors are controlled by an additional input signal their V-I characteristics have a 3rd dimension. We must consider:

1. The current flowing into or out of the base (\(I_B\))

2. The voltage across the collector and emitter (\(V_{CE}\))

when calculating the current into or out of the collector (\(I_C\)).

In the active region we can use

\[ I_C=I_S\left(e^{(V_{BE}/V_T)}\right)\left(1+\frac{V_{CE}}{V_A}\right) \]

where

• \(I_C\) is the current into the collector

• \(I_S\) is the saturation current specified for the BJT

• \(V_{BE}\) is the voltage at the base with respect to the emitter

• \(V_T\) is the thermal voltage (~26mV @ 27ºC)

• \(V_{CE}\) is the voltage at the collector with respect to the emitter

• \(V_{A}\) is the Early voltage, named for James M. Early

3D functions such as the VI characteristic of a BJT cannot be printed in a data sheet or textbook. To get around this we find plots that use slices of the 3D surface like this

BJT CURVES LIKE A CURVE TRACER