I am wondering if there can be other variations to achieve this secondorder low pass filter.
Sallen & Key discussed a large catalog of 2nd order active networks in their 1955 paper. Not just the one you posted. Something like two dozen specific configurations grouped into ten categories of equations.
Their paper's tagline, their very first two sentences in fact, is "In the frequency range below about 30 cps, the dissipation factors of available inductors are generally too large to permit the practical design of inductance-capacitance (LC) or resistance-inductance-capacitance (RLC) filter networks. The circuits described in the following pages were developed and collected to provide an alternative method of realizing sharp cut off filters at very low frequencies."
Without risk of distortion, one could say that their paper's primary purpose was to explore circuits that could replace the need for inductors. So the element in your question, "what if Z1 and Z2 were inductors," is pretty much antithetical to their purposes in writing.
That said, there are examples in their catalog where the values of \$Z\$ are complex impedances that are neither real nor imaginary but a combination of both. The following would be just one such example:
\$\quad\quad\quad\$Image may be NSFW.
Clik here to view.
In the above circuit, all four impedances are complex.
I understand the practical considerations of using an inductor(bulky). But, does it make sense theoretically?
Sallen & Key were focused squarely on the problems attending the use of inductors at lower frequencies. There's little to argue with, in such cases. Sallen & Key were right to look for alternatives.
The question may theoretically change when discussing higher frequencies and Sallen & Key didn't address that question. But there are problems.
In cases where it is important, capacitors can be readily found that have very little by way of annoying parasitics (ESR, ESL, and leakage), it remains very difficult and far more expensive (space, weight, and costs) to find inductors without significant parasitics.
Pretty much all inductors have unavoidable resistance and capacitance and tend to hold their design values over a narrower range of frequencies. This is problematic when designing active filters and complicates managing the active filter's performance in products. They also tend to be larger and heavier and almost always more expensive.
Finally, their are very very few cases where they can be used in ICs. I am thinking about hairpins, right now. But to be honest, I've no experience here. So I'm just guessing that there may be a few uses within an IC -- but only at very high frequencies, if so.
But in theory only? I suppose. But then I probably wouldn't call it "Sallen-Key" anymore. The authors were exploring the replacement of inductors in 2nd order designs. Not their use.
