Small-Signal Analysis of a MOSFET

This model shows how to compute the AC characteristics of a MOSFET. Both the output conductance and the transconductance are computed as a function of the drain current.

Introduction

The small-signal analysis is a mathematical approximation that allows to see the effect of incremental changes on the inputs of an electrical device on its output characteristics. For the MOSFET, two small-signal outputs are particularly interesting to get as they provide information on the device performance. Those are the transconductance (gm) and the output conductance (g0).

The MOSFET’s transconductance is defined as the ratio of the current change at the drain port to the voltage change at the gate port. The output conductance is defined as the ratio of the current change at the drain port to the voltage change at the drain port. The larger the transconductance, the greater the gain (amplification) the MOSFET is capable of delivering for a given gate voltage, when all other factors are held constant. Similarly, the larger the output conductance, the larger the drain current for a given drain voltage. Using small-signal analysis, an expression for the MOSFET’s output current (drain current) can be obtained showing the influence of these two variables:

Where id is the small-signal drain current, vgs the small-signal gate to source voltage, and vds the small-signal drain to source voltage.

The present model used the small-signal analysis to compute both gm and g0. To achieve this, the COMSOL Multiphysics model uses two study steps: a stationary step followed by a frequency domain perturbation study. The Stationary study is used to compute the linearization point for the equation system, which is the solution for the DC operating point in the absence of any AC signals. The Frequency Domain Perturbation study step then computes the response of the system to small AC deviations from the linearization point, correctly accounting for nonlinearities in the equation system.

Model Definition

The geometry and operation of the device are discussed in the DC Characteristics of a MOS Transistor (MOSFET) model.

This model adds a small AC voltage to the DC drain and gate voltage using the harmonic perturbation sub-feature. The model adds two studies to the existing MOSFET model.

In the first study the DC gate voltage is varied from 0 to 8 V under a constant drain voltage of 2 V using a stationary step. Using the same parameters, a 1 mV, 10 MHz AC signal is superposed to the gate voltage using a frequency-domain perturbation step. This first study is performed to determine the transconductance (gm) of the device as a function of the drain current.

In the second study it is the DC drain voltage that is varied from 0 to 4 V under a constant gate voltage of 2 V. The frequency domain perturbation step used the same 1 mV, 10 MHz AC signal but this time the signal is superposed to the drain voltage. The second study is performed to determine the output conductance (g0) of the device as a function of the drain current.

Results and Discussion

When evaluating the Harmonic Perturbation it is important that the check box is selected so that the COMSOL Multiphysics software differentiates the solution at the linearizion point when evaluating the expression. The solutions to Harmonic Perturbation studies are in general complex valued, with the argument representing the phase of the signal. By default, the real part of the solution is plotted in postprocessing. Note that evaluating the global terminal current semi.I0_2 for the Harmonic perturbation (with the check box selected) gives the (complex) perturbation in the drain current, δIdrain.

The transconductance is the ratio of the current change at the drain port to the voltage change at the gate port. The transconductance (dIdrain/dVgate) is obtained by evaluating the quantity -semi.I0_2/Vac (in COMSOL Multiphysics, the current at the boundary is positive when directed outward of the semiconductor material). It is not possible to evaluate the transconductance by evaluating the perturbation part of the expression -semi.I0_2/abs(semi.V0_4) because COMSOL linearizes the expression entered, computing the quantity dIdrain/Vgate-(Idrain/Vgate2)dVgate. A similar argument applies to the output conductance.

Figure 1 shows the transconductance as a function of the drain current. The transconductance increases rapidly with the drain current and reaches its maximum at about 80 μA. Figure 2 shows the output conductance as a function of the drain current. The output conductance decreases rapidly with the drain current.