# Op-Amp usefulness based on unity-gain Bandwidth (GBW) and Slew Rate

When selecting an operational amplifier (op-amp) for a particular application, it is important to consider its unity-gain Bandwidth (GBW) and Slew Rate. GBW is the frequency at which the op-amp's voltage gain starts to roll off and decrease. Slew rate is the maximum rate of change of the output voltage with respect to time.

GBW and slew rate both play a crucial role in determining the op-amp's ability to handle high-frequency input signals. The higher the GBW, the higher the frequency at which the op-amp can accurately amplify signals, while the higher the slew rate, the faster the op-amp can respond to changes in the input signal.

GBW is defined as the frequency at which the gain of the op-amp falls to unity, meaning that the op-amp is no longer amplifying the signal accurately. So if the input frequency is higher than the GBW, the op-amp will not be able to accurately amplify the signal, and the output waveform will become distorted. Unity-gain Bandwidth (GBW) is a measure of the maximum frequency at which an operational amplifier (op-amp) can amplify a signal without significant loss in accuracy. GBW is usually specified in hertz (Hz) and is one of the key specifications of an op-amp.

The formula for Unity-Gain Bandwidth (GBW) is,

$$GBW = \frac{dVo/dt}{A}$$

where, dVo/dt is the change in output voltage with respect to time and A is the closed-loop voltage gain of the op-amp. The GBW represents the frequency called unity gain frequency or the Cut-off frequency (fT) at which the closed-loop voltage gain of the op-amp starts to decrease from its maximum value of 1.

Slew rate, on the other hand, is the maximum rate of change of the output voltage per unit time, expressed in V/µs. A higher slew rate indicates that the op-amp can handle larger signal changes over a short amount of time. If the input signal frequency is too high, it may cause the output waveform to become distorted, even if the frequency is lower than the GBW.

The formula for slew rate at unity gain is represented mathematically as,

Slew Rate  = 2 * π * f  * Vpin

where f is input frequency and Vpin is input peak voltage. The frequency f is also called full-power bandwidth(FPBW).

If the voltage gain of op-amp is Av then for non-unity gain we have,

Slew Rate  = 2 * π * f  * Av*Vpin = 2 * π * f  * Av*Vpout

Since, Av=Vpout/Vpin

The following shows how the slew rate is measured,

Example calculation

Let's assume you have an input signal frequency of 1 MHz, and you want to choose an op-amp that can handle this frequency. If the op-amp has a GBW of 10 MHz, then it is capable of accurately amplifying the input signal upto frequency of 10MHz. However, if the slew rate is only 0.5 V/µs, the op-amp may not be able to handle the high-frequency input signal, and the output waveform may become distorted. So, it is necessary to choose an op-amp with a higher slew rate, for example, 2 V/µs, to ensure that the output waveform remains accurate.

Why the op-amp may not be able to handle the high-frequency input signal of 1MHz if the slew rate is only 0.5 V/µs?

The slew rate of an op-amp is the maximum rate of change of the output voltage in response to a step input signal. The relationship between slew rate, maximum allowable frequency is,

f = Slew Rate / (2 * π * Vp)

where, Vp is the maximum peak output voltage swing

Consider a sinusoidal waveform with a peak voltage (Vp) of 4V.

The maximum frequency the op-amp can usefully handle is,

f = 0.5 / (2 * π * 4) = 19.9KHz

Hence if the op-amp slew rate is only 0.5 V/µs, the op-amp may not be able to handle a high-frequency input signal of 1 MHz because the maximum frequency for a sinusoidal waveform with a peak voltage (Vp) of 1V is approximately 19.9KHz, which is much less than 1 MHz. In other words, the op-amp's output voltage cannot change fast enough to accurately follow the high-frequency input signal, causing distortion and loss of signal quality.

In conclusion, when choosing an op-amp for a particular application, it is important to consider both GBW and slew rate to determine its suitability for handling high-frequency input signals. The higher the GBW and slew rate, the more likely the op-amp will be able to accurately and quickly respond to the input signal. However, it's important to note that a high GBW doesn't necessarily mean that the op-amp is the best choice for all applications. Other specifications such as input impedance, output impedance, offset voltage, and slew rate should also be considered when choosing an op-amp for a specific application. Other parameters of Op-Amp such as input bias current, output offset current, input offset voltage, open loop gain, CMRR, input capacitance, SVRR and offset voltage are also important.

If you are interested in using op-amp in your electronics projects see the following tutorial on popular op-amp like LM324, LM393.

- Colpitts oscillator with LM358 and TL072 Op-Amps