The need for measuring the gain of a transistor goes back to the early days
when the gain was fairly low and to get a good device for a particular
application you had to go through a whole batch and pick the best.
The DC current gain HFE for a transistor is:
This means we don't really need to know the gain but it is interesting to find out the value for those transistors you have in the junk-box or for a transistor you may have damaged during soldering. For this and other reasons we have designed the Combo-2 to give you the answers.
It gives you the gain for small signal devices, medium power devices and high power devices.
We mentioned in the main article that small signal devices have a gain in the range 70 - 450, medium power devices have a gain of 50 -200 and high power devices a gain of 10 - 110.
These are only approximate values and you could get a device with a value totally outside this range. For instance, some medium- to high-power devices are available in Darlington versions and have a gain of 1,000 to 30,000 - way outside the range of our Tester.
BUT if the device is BELOW the range specified above, I would suggest the transistor is faulty and damaged in some way.
This can quite often happen due to over-heating, if you don't use a heat-sink when soldering, or overheating when in use.
But this is getting away from our topic.
Let's get on with the theory.
The gain of a transistor is a very variable thing. Even from a single batch of transistors, the gain can vary from less than 70 to more than 400.
GAIN is one of the factors used to grade transistors and is one of the reasons why we have so many thousands of different types. You may have noticed the suffix 'A,' 'B,' or 'C' after a transistor type. These letters denote the gain category and although none of the transistors are faulty, the numbering and lettering combines with other factors that mean the transistor can only be used in a certain location such as low voltage, low gain or low frequency application.
Since the gain of a transistor varies according to many things such as manufacturing technique, the voltage of the supply (in which the transistor is placed), the frequency of operation of the circuit and the current passing through it, an infinite number of values can be created from a single type, so it is quite often difficult to know which to use and what to expect.
The only way we can cover this complexity is to discuss the three values commonly quoted in specification sheets.
What happens to a transistor, and how it behaves in a particular circuit is another matter and cannot be predicted in any way so we will content ourself with values that can be determined.
The most often quoted gain for a transistor is the optimum value - the one that is determined under ideal conditions. It is called the DC gain or βDC or HFE.
This is obtained from a circuit such as shown in figure 1. The circuit is set up and a graph drawn for the collector current when varying base currents are applied. The maximum gain is read from the graph.
This value is generally about 20% higher than the "AC" or "working" gain (to be discussed later) and that's why it is most commonly used.
But some purists don't think the above method is realistic as a transistor is not a static device but a dynamic amplifier such as when used in an audio situation. They want an "operating" value of gain. In other words they want an AC gain value.
In this case an amplifier is set up and varying signals are applied to the base for varying rail voltages.
Once again, the best gain is picked off the graph and used as the AC value or BETA or Hfe.
The third value of gain is the value that applies at the upper operating frequency of the transistor and does not concern us in this discussion. It is the highest operating frequency for the transistor and occurs when the gain falls to unity.
For most requirements, the difference between hfe and hFE can be ignored if you are working within the limits of the transistor.
Data sheets generally supply hFE or d.c. current gain and this is the value we obtain from the tester.
The current gain can be written as:
It does this in a very clever way. It knows that when a certain current flows through the 4k7 collector load resistor in the gain section, a voltage will be produced across this resistor to cause the detecting gate between pins 9 and 8 to change state and turn on the “gain LED."
By turning the "gain pot," the base current is increased until the transistor produces the required collector current and the value of gain is read oft the scale around the pot.
In other words all the mathematics has been done by the project designer and any transistor fined to the test socket will duplicate the values already worked out.
In most discussions, transistors are referred to as "transistors," but in effect the writer is referring to the first type of transistor to be invented (in simple terms), namely the bipolar junction transistor, or BJT.
They should be referred to as BJT's, but since this is such a mouthful, they are simply called "transistors."
Since the introduction of this type of transistor there have been a number of other developments such as the Field Effect transistor (the FET), the Darlington transistor and others that can be brought in to the transistor group.
Unfortunately our tester is not capable of testing these devices and you will get a false reading if you try to test them, so it is advisable to know the device you are testing is actually a "common" or "garden" transistor.
Most of the devices in your junk-box will be common NPN or PNP transistors and the tester will identify the base lead and provide a value of gain as well as an indication that the transistor does not have an obvious short between any of the junctions - so you shouldn't have any problems.
The gain we talk about in our projects, under the heading "HOW A CIRCUIT WORKS," is the OPERATING GAIN or STAGE GAIN. It is not the gain of the transistor.
For example, the first audio stage in our FM transmitters, such as the FM Bug, Ant, Amoeba, Cube of Sugar, VOX etc. has a STAGE GAIN of between 50-70.
This is the highest gain you will get, even if you are using a transistor with a gain (HFE) of 250 to 450.
If you are using a transistor with a gain below 250, the stage gain may drop to 30-50.
The problem is the gain of a transistor is almost totally "killed" when it is fitted into a circuit.
Why Is this so?
The reason for the drop in gain is due to biasing and coupling.
Figure 1 is a typical example. It is a self-biased stage with a 2M2 as the base bias resistor. We will see how this resistor reduces the gain of the transistor.
Let us assume the transistor has a gain of 250. When power is first applied, current flows in the 2M2 to turn the transistor ON. As the transistor turns on, the voltage across the 2M2 reduces because the voltage across it becomes less and this reduces the current to the base. A point is reached where the current through the 2M2 cannot turn the transistor ON any more. This is called the equilibrium point or quiescent point or balance point and the voltage on the collector is about 5v. The current through the 2M2 will be about 2uA.
The transistor cannot turn on any more due to the value of the 2M2 and the gain of the transistor.
If we supply an extra 1uA into the base of the transistor via the input line, the transistor will turn on more and produce a further 250uA in the collector circuit and drop the collector voltage another 2.5v.
But something else will happen at the same time to prevent the collector voltage dropping.
It's the current flowing through the 2M2 resistor. As the voltage on the collector drops, the current through the 2M2 will reduce and if the collector voltage drops to 2.5v, the current through the 2M2 will fall from 2uA to 1uA and so the collector will not fall to 2.5v but something between 2.5v and 5v.
The actual final voltage does not matter but you can see that the current flowing into the base is partially reduced (or cancelled) by the base bias resistor, due to the fall in collector voltage. Thus the transistor does not produce the 250 gain you expect.
In reality the gain is about 125.
Further losses are encountered by coupling capacitors between the stages.
We will see how this occurs.
Figure 2 shows a coupling capacitor between two stages.
When a sine-wave is processed by the first stage it is passed to the second stage via the capacitor.
The second stage will amplify this to produce a larger output but we want to investigate how and why the waveform on the collector of the first stage is reduced when the second stage is added.
The best way to see this is to remove the second stage.
With the second stage removed we will assume the waveform on the collector of the first stage is 8v.
When the second stage is reconnected, the waveform will fall to about 6v.
The reason for this is the second stage puts a LOAD on the first stage. After all, the energy to drive the second stage must come from somewhere and it comes from the first stage.
The "reduced swing, or reduced amplitude, on the collector" decreases the gain of the stage even further and the gain may fall from 125 to between 50 and 70.
This brings us to our conclusion. The gain of a transistor has almost no bearing on the gain you will get when it is connected to a stage.
The only way to determine the gain of a stage is to take measurements with a CRO.
To do this you must inject the input with a low-level signal from a sine-wave generator and record the amplitude. Then read the output of the stage.
Sometimes you will get quite a shock at the low gain. It can be as low as 10 – 50 for a stage you are expecting to be 100. The main reason will be due to poor design.
Figure 3 shows a transistor driving an 8 ohm speaker. This is where the problem lies. The transistor is NOT driving the speaker. It is merely discharging the 100u during the second half of the cycle. The 100 ohm resistor is DRIVING THE SPEAKER and since this resistor is such a high value, the speaker cannot expect to be driven very hard.
It is being driven at less than 10% of full output (due to the ratio of the 100R:8R) and this means the waveform will be less than 10% of rail voltage. It will appear that the transistor is not providing a good driving force but the fault lies in the poorly designed circuit.