# Limitations of op-amp phase shifter design

I want to implement a phase shifter using an op-amp, also known as active all-pass filter, according to this schematic:

simulate this circuit – Schematic created using CircuitLab

Formula for the phase shift is: π-2*arctan(2πfRC).

I think there are some limitations of this circuit:

1. Argument of the arctan will be always positive, that means resulting phase shift can be theoretically between π-0 = π and π-2*π/2 = 0. Negative phase shift or greater than π cannot be achieved.
2. Function arctan can only approach (asymptotically) π/2, so resulting phase shift will never be really zero. You can choose very large R (or C) to be very close, but with R as variable resistor this would have a negative side-effect of low resolution in the lower range of resistance.
3. You also cannot set R to zero to achieve π phase shift, as this would short the input of the op-amp to ground.

Are my assumptions about this circuit correct? Are there some workarounds, or other examples of active all-pass filters, which would allow to overcome this limitations?

• Negative phase shift is impossible anyway. You would need a circuit predicting the future for its input. Phase shifts greater than Pi or 2*Pi may be done using a chain of several shifters in series.
– Uwe
Apr 13, 2022 at 22:51

With only 1 cap , 90 deg shift is the limit. But you can always cascade circuits to get multiples of 90 deg. But of course this is a wide band shifter. A narrow band shift requires a BEssel BPF or a linear phase BPF with fewer flaws.

Or if you use a differentiator All Pass and a integrator all pass you can get 180 almost in 3 decades which is even better.

Using an integrator instead of a differentiator, you can reduce R to 0 as long as you have a low source impedance.

Argument of the arctan will be allways positive, that means resulting phase shift can be theoretically between π-0 = π and π-2*π/2 = 0. Negative phase shift or greater than π cannot be achieved.

Yes only positive phase shifts can be achieved with this circuit

You also cannot set R to zero to achieve π phase shift, as this would short the input of the op-amp to ground.

That is actually fine, you can connect the + terminal directly to ground, however that would also short the capacitor to ground and then the capacitor's pole would also slightly be dependent on the source (with an ideal source the cap wouldn't matter at all). It is much easier to buy components that vary resistance in a deterministic way rather than capacitance.

• When you swap R and C at the non-inv. input (RC lowpass instead of C-R highpass), the phase function will be between 0 and -180 deg.
• And wenn you connect both stages in series, the phase can assume values between -180deg and +180deg.