Small-Signal Analysis
COMSOL Multiphysics includes sophisticated and very general tools for small-signal analysis, which are available in the Semiconductor Module. Small signals are applied to features such as source, drain, or gate contacts by using the Harmonic Perturbation subfeature (a subnode in the Model Builder tree structure). This feature should be used in conjunction with the Small-Signal Analysis, Frequency Domain study. The Small-Signal Analysis, Frequency Domain study includes Stationary and Frequency Domain, Perturbation study steps. The Stationary study step 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.
To specify an AC voltage (with a DC offset) applied, for example, to the Thin Insulator Gate feature, the DC voltage should be specified as usual by typing it into the Voltage user input in the Terminal section of the settings for the feature. Next add a Harmonic Perturbation subnode to the Thin Insulator Gate node.
The Harmonic Perturbation subnode is available from the context menu (right-click the parent node) or from the Physics toolbar in the Contextual group.
The amplitude of the AC signal is typed into this Harmonic Perturbation feature. By default, the solution from a Small-Signal Analysis, Frequency Domain study contains both the Static (or DC) solution and the Harmonic Perturbation (or AC solution). When evaluating expressions in result analysis you can choose which part of the solution is displayed in the Evaluate expression for list (a range of other options are also available, which are described in the link below).
When evaluating the Harmonic Perturbation it is important that the Compute differential check box is selected so that COMSOL Multiphysics differentiates the solution at the linearization 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 graphs. Use the imag operator to obtain the imaginary part of a variable or an expression. To drive the system with several signals at different phases, enter complex-valued numbers into the Harmonic Perturbation subnode.
 
Care must be taken when computing quantities such as the transconductance and output conductance for a MOSFET. For example, if the drain is a Metal Contact with terminal name 1, then evaluating the global terminal current semi.I0_1 for the Harmonic Perturbation (with the Compute differential check box selected) gives the (complex) perturbation in the drain current, δIdrain. The output conductance is obtained by taking the absolute value of the perturbation and dividing by the amplitude of the voltage perturbation applied (for example 0.01[V]). Thus the output conductance (dIdrain/dVdrain) is obtained by evaluating the quantity: abs(semi.I0_1)/0.01[V]. It is not possible to evaluate the output conductance by evaluating the perturbation part of the expression: abs(semi.I0_1)/abs(semi.V0_1) because COMSOL Multiphysics linearizes the expression entered, computing the quantity: δIdrain/Vdrain−(Idrain/Vdrain2)δVdrain.
Alternatively, for complicated expressions, use the lindev operator, for example: lindev(semi.I0_2)/lindev(semi.V0_2). In this case, the Compute differential check box must be cleared.
In the COMSOL Multiphysics Reference Manual:
•
For details on the small-signal analysis study type see Frequency-Domain Perturbation Study Step in the Studies and Solvers section.
•
For details on postprocessing small signals see Results Analysis and Plots