Discussion
A Si n-p-n bipolar transistor has the following parameters collector current Ic = 6 mA, common emitter current gain factor hFE = 120, operational temperature T = 300°K. Determine the mutual conductance of small signal transistor.
Answer: A
The mutual conductance is about 0.23 mho.
For a bipolar transistor the small-signal transconductance depends only on the collector current and the thermal voltage:
\[ \begin{aligned} V_{T} &= \frac{kT}{q} \approx 25.9\ \text{mV at } 300\ \text{K} \\ g_{m} &= \frac{I_{C}}{V_{T}} = \frac{6 \times 10^{-3}}{25.9 \times 10^{-3}} \\ &\approx 0.23\ \text{S (mho)} \end{aligned} \]
The current gain hFE = 120 is not needed for gm; it would be used to find rπ = β/gm, about 520 Ω. 0.02 mho is ten times too small, and 2.3 or 4.33 mho would need currents of tens of milliamperes.
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