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In general, you can make a test jig with several types of sockets so as to allow the package types and pin configuations. One circuit will be required to measure beta for both BJT and FET. The pin configuration producing the largest beta will give you the pin definition. But, these days, some small portable testers have some schemes to measure the beta directly. As you know, most of the transistor manufacturers provide tha datasheet for their products on the internet.
By using the positive probe of the diode test on a digital multimeter it is possible to find the base. This will tell you if it is npn or pnp. You can pin it on a breadboard with collector (10k) and base bias resistor (1m) and 2 chances one pin is the collector or the other pin is the collector as it will only conduct one way.
You can make this: You take a multimeter, and tested in pairs of pins, next you look which this pairs have less impedance, then where your probe point is positive is the base and where is negative is emisor.
If you have a power supply, use a limiting resistor in series with the supply to limit the current to 100 uA. Then connect it to all pins in pairs in both combinations of polarity. The base-emitter will be the pair that has 0.6 V when forward biased and about 5-7 V when reverse biased. The collector-base pair will have 20-40 V breakdown when reverse biased. The polarity (npn or pnp) can also be deduced from these measurements.
One caveat is that once the BE junction has been broken down in the reverse direction, the noise of the transistor is increased.
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