Transistor matching

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Tj & Tc are critical to any transistor measurement, particularly Vbe and hFE.

If you cannot set and check the accuracy of the Ic (or Id for FETs) then the resulting measurement is virtually useless.
but do not adjust the pot
means that you are applying the same Vbe (Vgs) to each device. That means that if the devices are unmatched then different Ic (Id) will flow and the result is that unmatched devices will be tested/measured at different temperatures, no matter how long you leave them to settle.

Once you find devices that using a constant Vgs result in the same Ic then you know that these devices are operating at the same test temperature. But they are selected for a combined Vbe and hFE. You still have to find out if they are matched.
To do this you need to separate out the Vbe testing from the hFE testing and group several batches of devices that measure the same hFE OR the same Vbe at the same Ic and then find which pairs in the batch measure the same Vbe and the same hFE.
That gives you matched sets/pairs.
Measuring Vbe alone, or measuring hFE alone, is a very quick test that is cheap to perform and give batches for further selection. Those two methods do not result in matched pairs.

Measuring for both Vbe and hFE to give matched pairs, takes at least ten times longer and more probably 100times longer for good matched pairs.
 
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