Measuring emitter & collector resistance

[Ian Fritz]

Hi all --

There was a question a while ago about how to measure emitter and
collector series resistances. I just ran across the answer in an old GE
Transistor Manual. I won't go through the theory, just mention that it
starts with the Ebers and Moll equations and simplifies to the case of a
saturated response with small (e.g., zero) load currents.

To measure R_e, you drive current I_b through the base-emitter junction,
with the collector open, and measure the voltage V_ce.  This is called
the "offset voltage" and turns out to be given by the function

V_ce = -(kT/q)(alpha) + (I_b)(R_e)

Since alpha is a function of I_b, this is a highly non-linear function
at low currents, but the second term dominates at high currents. So the
high-current slope of a plot of V_ce vs. I_b is the desired series
emitter resistance.

For the collector series resistance, you just swap the emitter and
collector in the obvious way and use

V_ec = -(kT/q) (alpha') + (I_b) (R_c).

The example in the manual shows data for determining R_c for a 2N2192.
The resistance is 0.08 Ohm and the plotted V_ec vs. I_b curve is linear
from about 0.5 to 3 mA.

It should be fun to try this out with some different devices.

Best regards,

  Ian