Is it possible to build an active second order all-pass filter using a single op-amp and no inductors? After Googling it I've found no less than three different circuit topologies, but when simulating them they all have a non-flat frequency response. I've also tried analysing them using some simple Laplace transforms and some algebra, but have failed to get anything similar to the transfer function that a second order all-pass filter should have. This might be because the algebra does get slightly messy, and I don't handle messy algebra very well when tired.
It would be great if such a circuit does exist, as I'm (purely for fun) designing a phasing network to obtain a fairly flat 90 degrees phase difference (quadrature) in the output over a fairly wide range of frequencies, to be used in a phasing SSB receiver for side-band rejection. Currently I'm using a software (called QuadNet) that outputs a phasing network for me, but it uses first order segments, which results in a whole lotta op-amps. The goal is to halve the necessary number of op-amps.
Just for reference; the transfer function of an all-pass filter takes on the following form $$\frac{s^2-As+B}{s^2+As+B}.$$
To be clear, I'm simply looking for a circuit topology that provides this transfer function (2nd order all-pass filter) using a single op-amp and no inductors, and nothing else. Assuming ideal components is totally fine for my purposes.
I'm eagerly awaiting enlightenment!