4. Results and correct simulator settings

The HTFs obtained with Matlab and ADS can now be compared. Below, we show $G^{\left[i\right]}$ for $i$ between $-40$ and $+40$ in steps of $5$. The HTFs obtained with Matlab are shown in light green, the HTFs obtained with ADS are shown with dark green dashed lines. The difference between both is shown in red.

Figure 4.1 Using the default settings, we observe a large difference
between the HTFs obtained with ADS and the reference.

The error made in the analysis is small but not negligible. It is clear that some approximations are made in the default LSSS simulation of ADS. After some experimentation, we identified three parameters which influence the accuracy of the LSSS simulator:

• Matrix Solver ADS defaults to using a Krylov method to perform matrix inversion in HB. This introduces significant errors in the LSSS simulation. When Krylov is disabled, a significant improvement in accuracy will be obtained, at the cost of a much longer simulation time and larger memory requirements.
• Guard Threshold To increase sparseness in the matrices during the simulation, a Guard Threshold is used by default in ADS. Every value in the Jacobian matrix which is smaller than the Guard Threshold is set to zero. The small-signal behaviour of a circuit around its orbit is captured by this Jacobian matrix, so truncation in the Jacobian has a direct effect on the HTFs. The effect of the Guard Threshold is visible in the plot shown above: at higher frequencies, some of the HTFs jump to zero. To improve the accuracy of the LSSS simulation, the Guard Threshold is disabled by setting it to zero.
• Samanskii constant To speed up convergence, the Jacobian matrix in HB is not re-calculated in every step of the optimisation routine, but the Jacobian matrix is re-used a few times. The amount of re-use is controlled by a parameter called the Samanskii constant. To guarantee that ADS re-calculates the Jacobian in the final step of the optimisation, the Samanskii constant is set to zero.

When the simulator is configured correctly, the following comparison is obtained:

Figure 4.2 When configuring the simulator correctly,
the HTFs obtained with ADC match the reference

It is clear that the error made in the LSSS simulation of ADS is now determined by the numerical precision.