Transconductance

The Transconductance of a transistor is the current change through a transistor as a function of the voltage change over two specific gates, which can be interpreted as a "steering sensitivity" of a transistor.

Please note that transconductance $$g_m$$ can also be denoted as $$ s $$ in other languages than English.

$$ g_m=\frac{\Delta i_out}{\Delta u_in} $$

BJT
The transconductance of a Bipolar Juction Transistor is based on the equation:

$$ g_m=\frac{kT}{q}I_c $$

Here $$g_m$$ is the transconductance, kT a product of the Boltzmann constant and the temperature, q the magnitude of a electrical charge on a electron and Ic the current through the collector of the BJT.

$${q=1.602176565(35)×10^−19\ eV}$$

$${kT=8.6173324(78)×10^−5\ T}$$

T is always in Kelvin which is the teperature in Celcius plus 273.15. The typical Transconductance of a BJT is therefore at room temperature(20 degrees Celcius).

$$\ \frac{kT}{q} = 39.604 A/W$$

To calculate the transconductance you now only need to know the collector current at which your BJT is biassed.

MOSFET
The transconductance of a MOSFET can ben found on the datasheet of that specific mosfet. The Transconductance of a BS170 for example is 320mV.