Hi John
The schematic you have shown, did you obtain it from somewhere?
For device matching, usually you are most concerned about base emitter voltage matching. This circuit is not set up for that.
What usually works well is a fixture with the base grounded, the collector attached to a positive DC source and the emitter connected through an appropriate value resistor to a negative DC source.
DMM connections are positive lead to ground and negative lead to emitter of device under test (DUT). Keep DUT wattage low during the test or it will take a long time for the reading to stablize. Keep your lead length short and ensure good connections.
All power sources should be well regulated sources or your readings will drift all over the place.
The positive supply voltage is less critical for absolute setting than the negative supply. It is just ensuring that the transistor is not in saturation.
For NPN small signal transistors my set up is:
Positive voltage source = 4VDC
Negative voltage source = -14VDC
Emitter resistor = 68,000 ohms 1/4W
This produces a Collector-Emitter current of ~200uA
For TO-3 NPN power transistors my set up is:
Positive voltage source = 3VDC
Negative voltage source = -14.3VDC
Emitter resistor = 100 ohms 10W. Mount this resistor away from the DUT as it will be dissipating ~1.5W and you do not want its heating effects screwing up your readings.
This produces a Collector-Emitter current of ~137mA and a DUT dissipation of ~1/2W
Do all your matching as close in time as possible to get the same ambient temperature in the room you are testing in.
It will take a while for the device to temperature stabilize and for you to get a stable reading. Be patient.
I have a long chart that I constructed of quadrille paper for sorting the devices, 8.5x11" sheets taped end to end vertically.
The lowest marking is 0.625V and then there is a major marking every five squares at 0.630, 0.635, 0.640 and so on up to 0.690. This will give you a millivolt resolution chart.
I lay this sheet on my working bench and lay the graded devices next to the millivolt gradation line corresponding to how the device graded out. Don't let your cat in the room or he/she will knock all your hard work off your chart
Your body heat temporarily affects the DUT as all bipolar semiconductors have a negative tempco on the base emitter junction. Wear gloves to minimize this or use needle nose pliers to install the DUT in the tester socket.
Hope this helps.