I've been using the ad8561 in the following circuit:
IN- connected to OUT- via few resistors (hystersis of few tens of mV) around 0V.
IN+ gets a sine wave signal with frequencies as low as 100Hz. When crossing the 0V point, the output toggles.
There are no oscillations on the output (due to low SR of the sine wave input).
Since the ad8561 is not a rail-to-rail input device, I've taken the LT1711 and I use it similarly (see below).
Vin is the sine wave signal. I've used hysteresis resistors of 50ohm/12.4K (20mV) and even 300ohm/10K (134mV).
On the LT1711 Ioh=10mA.
Both comparators are powered from +5V and -5V.
My problem: The ad8561 outputs are stable in Vin sine wave frequencies as low as 100Hz (and even lower).
With the LT1711 the outputs oscillate when Vin is 90KHz and lower.