III. Gm-C Filtering - Epublications - Université de Limoges

However, this feedback makes the filter become unstable. Indeed, the loop introduces
a new pole in system transfer function. Thus, a -90° phase shift appears in closed loop
operation, making the phase going below the critical -180° phase and the phase margin being
negative. To ensure stability, a zero is introduced by means of capacitor Cstab1, which is put in
parallel of the collector-base junction.
Figure 158 shows the results of a PZ analysis. It represents poles and zeros in the
complex plane. This is a parametric analysis with Cstab1 as parameter. When Cstab1 is small, the
real part of a pole is positive proving that the circuit is unstable. When Cstab1 increases, the
real part of the pole becomes negative, reaching the area where the circuit is stable.
Hence, there is a minimal value for Cstab1 so that the circuit becomes stable, and the
higher Cstab1, the higher the stability margins. However, Cstab1 decreases the operational
amplifier gain at high frequencies. As explained, a lower amplifier gain directly means lower
linearity, thus showing a trade-off between stability versus linearity.
Figure 158. Location of the poles and zeros of the Rauch filter transfer function when Cstab1 varies
IV.3.b.iii Enhancement of the Stability Margins
From the schematic simulations of the stability margins, it appears that phase and gain
margins are below the specifications. That is why a second capacitor Cstab2 has been added to
increase these phase and gain margins, as it may be seen in Figure 159. This capacitor is
placed between the emitters of the differential pair and the ground.
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