If you open up the perennial favourite electronics textbook The Art Of Electronics and turn to the section on transistors, you will see a little cartoon. A transistor is shown as a room in which “transistor man” stands watching a dial showing the base current, while adjusting a potentiometer that limits the collector current. If you apply a little more base current, he pushes up the collector a bit. If you wind back the base current, he drops it back. It’s a simple but effective way of explaining the basic operation of a transistor, but it stops short of some of the nuances of how a transistor works.
Of course the base-emitter junction is a diode and not a simple potentiometer that sits between collector and emitter. The “better” description of these aspects of the device fills the heads of first-year electronic engineering students until they never want to hear about an h-paramater or the Ebers-Moll model of transistor function again in their entire lives. Fortunately it is possible to work with transistors without such an in-depth understanding of their operation, but before selecting the components surrounding a device it is still necessary to go a little way beyond transistor man.
The Simplest Biasing Example
Imagine for a moment a simple transistor circuit involving a single NPN transistor with its emitter grounded, its collector tied to the positive supply by a resistor, and a potentiometer between ground and supply allowing any voltage to be supplied to the base. Because the emitter is grounded, even if sometimes via a resistor, this transistor configuration is referred to as a Common Emitter amplifier. In this circuit if you were to start with the potentiometer at the grounded end then the transistor would be turned off, and no current would flow.
In an NPN transistor, the connection between base and collector is a PN junction, so as you might expect it shares its properties with the PN junction in a diode. A silicon diode starts to conduct when the voltage across it reaches about 0.6 V, and when the voltage from our potentiometer across our base-collector junction reaches 0.6 V, it also starts to conduct. A small current flows into the base, and since this is a transistor we’re talking about that results in a larger current flowing through the collector. We’re back to the little man in the Horrowitz & Hill cartoon, and the relationship between base current and collector current is called the transistor’s gain. You will see it quoted on data sheets, and for example a transistor with a gain of 100 would pass 100 mA at the collector for a base current of 1 mA.
When the base voltage is just over 0.6 V, a little current flows in the collector, but not much as the transistor is barely turned on. As our potentiometer moves upward the base voltage will increase, and there will be a corresponding increase in base current with an attendant increase in collector current. There will be a region during which the relationship between base current and collector current is close to linear, but eventually a point will be reached at which the collector current stops increasing no matter how much you increase the base current. At this moment the transistor is said to be saturated, or fully turned on, passing a current that’s limited by R1.
Making a More Practical Amplifier
Now, imagine for a moment our simple DC circuit used as an AC amplifier. We’re keeping the potentiometer, but also applying an AC source, a sine wave, to the base. As our sine wave rises and falls, so does the base voltage, and thus its current. If the base is held at the just-turning-on point of 0.6 V then the transistor will only be turned on during the upper part of the cycle, and if it is held near the transistor’s point of saturation then the transistor will only pass through the lower part of the cycle. In both cases half the cycle is missing at the collector. To amplify the whole cycle of our sine wave we must therefore hold the base with our potentiometer such that the transistor is in that close-to-linear region over the whole range of base current generated by the sine wave. Holding the base voltage of a transistor in this way is referred to as biasing it, and a transistor with this type of biasing will pass a constant standing current through its collector when connected to a supply and with no incoming signal such as our sine wave.
The classic transistor amplifier circuit then has a pair of resistors in series between supply and ground, forming a potential divider that gives the base its bias. The emitter is grounded, and another resistor lies between collector and the supply. A small incoming signal is provided to the base, and an amplified and inverted version of it appears at the collector. There are many variations and refinements of this circuit involving emitter resistors and bypass capacitors to modify the high-frequency response, but this simplest of circuits should be enough to understand its operation.
How then does one arrive at the values for the various resistors? For the dedicated mathematicians there are a set of formulae which can easily be found online and which it is better not to cut-and-paste here in the pretence that I and many other engineers have even given them a second look since university. For most others designing from first principles there are innumerable pieces of circuit analysis software, many of which trace their lineage from the venerable SPICE. I have met engineers who learned SPICE through the medium of punched cards, I learned it through a terminal into a VAX minicomputer, count yourself lucky if your introduction to it was through a desktop GUI. My simulator of choice, just to name one, is QUCS.
As always though, there is an “official” answer, and an “unofficial” answer. Do I reach for QUCS every time I wire up a 2N3904? Of course not. Like all who have gained familiarity with something through long practice, I imagine myself to be cleverer than SPICE. So I make a few guesses, then breadboard the resulting circuit, and make a tweak here or there if it isn’t quite right. For example I’d pick a collector resistor using Ohm’s Law to deliver the desired maximum current when the transistor is saturated, then make a few guesses with the bias resistors by making their total value over 10 times the collector resistor and the ratio of upper bias resistor to lower one being about 2 to 1. You can make hay in the comments and poke it full of holes based on your simulations, experiments, or experience, but this is really an exhortation to all readers to have a go and experiment with biasing in their own circuits.
Self-biasing, a Much Simpler Option
If a potential divider is too complex for you, there is another option. A so-called self-biasing circuit replaces the potential divider with a single high-value resistor (R6) from collector to base.
This circuit works on the principle that the base resistor is chosen to supply just the required current to turn the transistor on such that it remains in that just-about-linear region mentioned earlier. The base resistor is thus usually of a high value, typically in the several hundred kiloohm range. In the days of germanium transistors you would even see circuits without a bias resistor that relied on the higher leakage current of germanium devices, if you read our recent piece on [Clive Sinclair]’s writing you might have seen an example in one of the figures. As before if you prefer not to simulate it you can calculate the value of the base resistor depending upon the base current required to deliver your desired collector current, but again it’s a simple circuit to guess a resistor value for. A 1 kΩ collector resistor and a 330 kΩ base resistor has never failed me for a small-signal self-biasing audio amplifier, I’m nothing if not a creature of habit.
A month or so ago I wrote a piece bemoaning the lack of electronic fundamentals such as transistor biasing in a generation brought up on the Arduino or the Raspberry Pi. They are lucky enough to come out of their teenage years with useful skills such as the internals of a GNU/Linux OS or the intricacies of SPI interfacing, but analogue electronics at this level simply hasn’t come their way. This has been in part an attempt to address that problem, as well as something of a homage to the single transistor amplifier. I don’t by any means claim to have provided a comprehensive introduction tot he subject, but that handily leaves the door open for the chance to return in the future. Meanwhile if any of you have never picked up a 2N3904 and experimented with it rather than following someone else’s circuit, I hope you’ve been given some encouragement. Good luck!