Variation-Aware Circuit Macromodeling and Design Based on Surrogate Models - Simulation and Modeling Methodologies, Technologies and Application - page 254

samples, each a function of the ten parameters described above. Although an analytic
equation for g m is used in this work, the modelling methodology is general and can
employ simulations or measurement results given that they have the same input and
output parameters.
Kriging basis functions are used to construct the surrogate model with the neces-
sary coefficients being optimized using the MATLAB toolbox Design and Analysis of
Computer Experiments (DACE) [20]. The device width is assumed to be 10 µm . The
finalized model is tested for accuracy using the root relative square error (RRSE)
metric where RRSE can be given by Equation (1).
The g m model is constructed using a total number of 2560 input samples, and tested
with 6400 samples other than the input samples. The resulting model yields an RRSE
of 3.96% indicating to a high level of accuracy.
The model can be used to observe the changes in g m with respect to its input para-
meters. Examples of this are provided in Figure 8. The graphs provide critical insight
to the designer about the fundamental relations and trade-offs between the chosen
process parameters, terminal voltages, and temperature. Higher g m values are ob-
tained with smaller V th,0 , L eff , and t ox , as well as larger µ 0 . This information becomes
especially vital when variability of the circuit performance that depends on g m must
be considered. In the example of an RF cascode low-noise amplifier , voltage gain A v ,
input and output return ratios, S 11 and S 22 , as well as the optimum noise impedance,
Z opt , are complex functions of the g m value of the common source transistor [21]. Any
(a) (b)
(c)
Fig. 11. 3D graphs showing the trade-offs between the different inputs on the modeled g m