Bias Circuit

2.2 Fundamentals of Signal Amplification: The Linear
Circuit
The most fundamental property of a useful electronic voltage amplification device is that it
possess a transconductance that leads to the possibility of voltage gain. Transconductance is
defined as the ratio of the signal (ac, incremental) current out, iout δiOUT, and the applied
input signal voltage, vin δvIN. That is, transconductance gm is
Equation 2.3
For the BJT, iOUT iC and vIN vBE, while for the NMOS, iOUT iD and vIN vGS. Thus, (2.1) and
(2.2) can be used for the BJT and MOSFET, respectively, to obtain an expression for gm. The
results are
Equation 2.4
and
Equation 2.5
IC and ID are the dc (bias) currents of the transistors, so for comparison they can be made
equal. At room temperature, the thermal voltage is VT = 26 m. For the MOSFET, VGS is the
gate – source bias voltage and Vtn is the transistor threshold voltage. The difference, as in the
denominator of the transconductance expression, could typically be about VGS – Vtn = 500 mV.
The expression (2.3) suggests the linear model given in Fig. 2.2. Included in the model is an
input resistance, rin, which accounts for the fact that there can be an incremental current
flowing into the input terminal for an increment of input voltage. The model applies in general
to amplifying devices, including the vacuum tube (VT), BJT, JFET, and MOSFET. There exists a
wide range of magnitude of transconductance and input resistance between the devices. The
input resistance, though, affects only the loading of the input signal source; otherwise, the
relation of (2.3) applies in all cases, and the transconductance is the key to the gain for a
given device type. The input resistance is essentially infinite for the vacuum tube and the
MOSFET (common source) but can be as low as a few ohms in some configurations for the BJT
(e.g., common base).
Figure 2.2. Basic linear model of a voltage amplification device. Model
parameters are gm and rin.