Suggestions to clarify comparator circuit

Question

I'm confused with the next issue from school that I can't figure out and wasn't able to solve (this is homework already graded, but the teacher refused to explain me).

I was asked to design and implement a zero crossing detector using an op-amp (any op-amp, even the 741). I understand there are several ways to do this with opto, transformers,etc.

But the real issue was that this device must be able to detect the zero crossing and when the signal is at 90 degrees (in the positive and negative cycle).

So I made the circuits but separately. As in the next window detector:

(between 4.5 V and 5.5 V ) and

A non-zero level detector modified with the DC voltage source set to zero volts. If the sin-wave input voltage (Vin) is less than (Vref), the output remains at the maximum negative level. When Vin exceeds Vref, the output reaches its maximum positive value.

But if the output of the window is passed to the level detector it gets wrong result, since the level detector isn't a sinus signal but the square one, so how must they be wired together to make the 2 functions at the same time?

And is it valid to apply superposition to get the transfer function?

Thanks for your help.

Answer 1

Homework guidance: If you cause 90 degrees phase lag to the sinusoidal input by feeding it through an integrator you can use another zero crossing detector to show when the input is on its plus or minus peak.

In theory a differentiator would also do the trick, but it amplifies easily noise; needs band limiting. But it doesn't need DC free input like an integrator which would get saturated if there's DC.

Integrator has a drawback, too: It in practice drifts even with no DC in the input signal. Opamp non-idealities are the main causes of the drifting. 741 is not the finest selection in this sense. Offset voltage error is the same as a DC component in the input. Input bias current is another cause for drifting. The capacitor needs a discharging resistor which hopefully can be big enough. Otherwise it causes phase error.

A multistage RC filter can be designed to cause 90 degrees phase shift, but that works only at a fixed and known frequency.