Theoretical analysis of sensitivity and Q-value for recursive active microwave integrated filters

High-Q active MMIC filters have very low tolerances for temperature drift and process parameter deviations. A theoretical analysis of how these problems limit the Q-value of recursive active MMIC filters is presented. Given that the highest tolerable deviation in filter gain is equal to 1 dB for a temperature drift of 5°C, the Q-value is shown to be limited to 30 if one assumes perfectly impedance matched circuit components. For a non-ideal matching of circuit components, the highest possible Q-value is shown to be also limited by the impedance matching of the filter. It is also found that the maximum allowed deviation in amplifier gain due to on-wafer process parameter derivations when high Q-values and a stable filter gain are required is very small, even if an automatic Q-controlling system is included. In this analysis, a first-order recursive active filter with a loop electrical length equal to 2π is assumed. The analysis shows that by cascading two first-order filters or by choosing a filter with a loop electrical length equal to n times 2π a decreased filter gain sensitivity can be achieved