What is the maximum frequency at which an op-amp can be used?

To use an op-amp at high frequency, it is necessary to take two factors into consideration: slew rate and Unity Gain Cross Frequency (fT).

If the slew rate is low for the frequency used, the square wave will become a trapezoidal wave and the sine wave will become a triangular wave.
Voltage gain decreases at frequencies above the 3dB cutoff frequency of the open-loop gain. In this part, not only does the voltage gain factor vary from product to product, but if a signal with a wide bandwidth is input, the gradient of the amplification factor causes waveform distortion. Please apply negative feedback to the operational amplifier so that the gain is flat up to the operating band.
Also, be careful of oscillations at frequencies close to unity gain. There is an explanation in the op amp e-learning 2.3. Oscillation. Oscillation. please refer.

 the op amp e-learning 2.3. Oscillation

  • Slew rate (SR):

Even when the ideal rectangular waveform (a fast-rising signal) is applied to the input of an op-amp, its output does not provide the ideal rectangular waveform as shown in Fig. 3.
A change in output voltage per 1 μs is called a slew rate.
As shown in Fig. 3, in the case of an op-amp with a low slew rate, a rectangular input signal appears as a trapezoidal signal at the output, and a sinusoidal input appears as a triangular signal at the output.

  • Unity Gain Cross Frequency (fT): 

Frequency at which the open-loop gain becomes unity gain (0 dB)
As shown in Fig. 2, an op-amp with a higher cut-off frequency provides a greater bandwidth with the same closed-loop gain.

Fig. 1 Definition of slew rate
Fig. 1 Definition of slew rate
Fig. 2 Unity Gain Cross Frequency and bandwidth
Fig. 2 Unity Gain Cross Frequency and bandwidth
Fig. 3 Slew-induced waveform distortion
Fig. 3 Slew-induced waveform distortion
Relationship between slew rate and signal frequency
Relationship between slew rate and signal frequency

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.

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