If you use an op amp with a low slew rate, the shape of the waveform will change and distortion will worsen.
Its maximum output frequency (fmax) can be calculated from the slew rate.For simplicity, we will first explain the case of using op-amp in unity gain.
The slew rate (SR) is expressed as:
SR = ΔVo / Δtr or ΔVo/ Δtf
Waveform distortion occurs when the maximum value of the output signal differentiated by time becomes higher than this SR.
Let the voltage of the input sine wave with an amplitude of A be Vin = Asinωt. Then, no waveform distortion occurs if the maximum change (differential value) in the amplitude of the input signal is less than the slew rate.
Since the differential value of the input signal is dVin / dt = Aωcosωt, its maximum value is Aω. Therefore, the maximum frequency that does not cause slew-inducted waveform distortion is theoretically calculated as follows, where A is the input amplitude.
SR = Aω ＝2πfmaxA
fmax = SR / 2πA
If there is no unity gain, the voltage gain of the amplification circuit is multiplied by Av, then Vo = Av x Vin.
The same can be said for unity gain.
dVout / dt = AvAω cosωt
SR = AvAω =AvA2πfmax
fmax = SR / 2πAAv
In practice, it is necessary to set fmax, allowing an adequate margin for the required frequency.