Figure 3 shows the voltages we get at the amplifier outputs; much more reasonable. The excursion down to ‑1.4 V, however, shows that we must be driving a lot of current through those Zener diode models. Sure enough, when you look, you see predicted spikes of nearly 2 A, assuming that your power supply can actually deliver that and that it ramps up instantaneously (rather unlikely, admittedly). I need some power Zener diode models!
The actual filtering story is actually not that bad at all. The ‘sting’ from the huge input step dissipates rapidly, absorbed by the transient protection diodes. The amplifiers come back out of saturation rapidly, because the clamps at the summing nodes hold them close to the supply. When this happens, the transfer function, and therefore the residual settling behaviour and stopband rejection, is restored. The entire system still settles to 0.1% in a speedy 67 ms and the behaviour of the circuit is actually now a lot less ‘nervous’ in terms of the ringing on the input step (Figure 4). The settling time to 1% is slower than the ‘ideal’ circuit, but this wasn’t a requirement for our original circuit anyway. The whole thing actually looks nice and clean from the outside, even though we know that terrible things are afoot internally.
When our input voltage jumps up instantly from zero to 180 V, the amplifiers spend a certain amount of time in a non-functional state, but the inherent settling time of the RC network formed by our fairly small total capacitance still allows an excellent settling time while the amplifiers are not working. Once the step has worked its way out of the system, all the amplifier terminals are operating at their correct values and the promised AC ripple rejection is obtained for steady-state operation. Most active filter topologies fall to pieces when their amplifiers overload – some even go unstable. The robustness of this particular configuration is another aspect that drives me to recommend it so highly.
Other points to note. We’re not limited to filtering positive input voltages – negative ones are fine too, as long as you remember to connect up any polarized capacitors correctly. And the voltage doesn’t have to be DC; any AC signal with frequency components sufficiently far below the cutoff frequency can be filtered in the same way. The source impedance can be reduced without limit too, as long as you can ensure that the amplifiers can deliver the current necessary for signals near the cutoff frequency. I’ve already had an audiophile amplifier designer get excited at the prospect of using this configuration in front of a voltage regulator, to ensure that input noise falls at a faster rate than the regulator loses supply rejection. Do plenty of simulation to ensure that under normal operating conditions you don’t get an excessive amount of the input signal appearing at the amplifier outputs.
So, my ‘umble apologies if it appeared last time as if I wasn’t aware of, or worried about, real-world behavior with real-world components. It turns out that even though the amplifiers stop working for a short while on that step input, the overall filter can still do the job intended. See if you can come up with some other ideas for where this approach can be used. Ripple begone!