7.2.6 ${\it f}_\mathrm{max}$ and Related Quantities

Expressing ${\it f}_\mathrm{max}$ as a function of small-signal equivalent elements, makes this quantity very sensitive to the approximation taken. Therefore, for circuit design ${\it f}_\mathrm{max}$ is best described considering frequency ${\it f}_\mathrm{c}$ where the stability factor ${\it k}$= 1, and the gain MAG=MSG available at this frequency. ${\it f}_\mathrm{c}$ is then determined from the transition MAG/MSG, and as both MAG and MSG have a defined slope as a function of frequency as given in Chapter 4, ${\it f}_\mathrm{c}$ can be determined based on a number of data points.

Figure 7.18: $f_c$ as a function of $C_{gd}$ for 4$\times$40 $\mu$m device.

Figure 7.19: Modeled $f_c$ as a function of gate-to-channel separation $d_{gc}$.

Fig. 7.18 supplies information for a given bias, which gate width is feasible for power application at a given frequency. Fig. 7.18 shows the measured and modeled (compact modeling) dependence of MAG/MSG for k=1 varying ${\it C}_{\mathrm{gd}}$ in a small-signal model. All other parameters are kept constant. It can be seen, that for lower ${\it C}_{\mathrm{gd}}$ the gain MAG/MSG rises, while the frequency ${\it f}_\mathrm{c}$ slightly drops. The overall effects is a rise of ${\it f}_\mathrm{max}$. In order to understand the variations of this important relation due to further process variations, Fig. 7.19 shows the sensitivity analysis of the ${\it k}$=1 point for a 4$\times$40 $\mu$m HEMT towards the gate-to-channel separation ${\it d}_\mathrm{gc}$ simulated with MINIMOS-NT. ${\it f}_\mathrm{c}$ rises significantly for decreasing gate-to-channel separation ${\it d}_\mathrm{gc}$. All other device parameters are kept constant.