How to Determine the Bandwidth of an Op Amp Circuit

Determining the bandwidth of an op amp in a given configuration requires understanding several interrelated circuit configuration factors and op amp specifications. Below is a structured explanation of how gain, input amplitude, and other parameters affect op amp bandwidth, and how to compute or estimate it in practical circuits. Note that this tutorial is mainly applicable to voltage-feedback op amps.

⚙️ Gain-Bandwidth Product (GBP) is a Good Starting Point

Most op amps specify a Gain-Bandwidth Product (GBW or GBP) in their datasheet. The GBP tells you how much "gain times bandwidth" you can get from a particular op amp. If you want a higher gain, you'll have a smaller bandwidth, and vice versa. To use the GBP specification to calculate bandwidth:

• Bandwidth = GBP / Gain
• Example: If an op amp has a GBP = 10 MHz and the op amp will configured for a closed loop gain = 10 V/V → Bandwidth = 10MHz / 10V/V = 1 MHz

This formula holds true whether the op amp is in a non-inverting configuration or inverting configuration. For the inverting configuration gain is an absolute value. 

Note: This rule applies well in unity-gain stable, linear region configurations, for voltage-feedback op amps.

🔊 Signal Amplitude and Op Amp Bandwidth

The bandwidth or frequency response of an op amp is also affected by a signals amplitude level. You will often find an op amp specification called small-signal bandwidth (SSBW). An example of a SSBW specification from an op amp's datasheet is shown below, it is rated up to 105MHz with a 20mVpp output signal with gain of 1. This specification often represents the best case bandwidth of the op amp. But in many applications it is not realistic since the signal amplitude is small (20mVpp in the example below) and the op amp is configuration is a gain of 1. This example op amp datasheet also includes a large-signal bandwidth at 2Vpp which is almost an order of magnitude less then the SSBW (105MHz versus 14MHz). You can see with a gain configuration of 1, the op amp's bandwidth drops as signal amplitude increases. Also notice from the example datahsheet the GBP (referred to as GBWP in this datasheet) is almost right in the middle of SSBW and LSBW. This is where things get confusing if your op amp will be configured for a gain of 1. If you are working with a signal that has an amplitude of 25mVpp (close to SSBW) do you use the GBP spec along with a gain of 1 to get your bandwidth? This approach assumes your bandwidth drops by over a half with just a 5mVpp amplitude change (SSBW at 20mVpp). If your signal is 1.95Vpp do you use GBP at 50MHz with a gain of 1 and then assume a small increase of 5mVpp drops the bandwidth by over a half to 14MHz (LSBW)? One way to deal with this bandwidth uncertainty is to turn to the slew rate specification. 

The slew rate of an op amp is the maximum rate of change of its output voltage over  time, typically expressed in volts per microsecond (V/µs).

Slew Rate=  delta Vout (max) / delta time

How to determine the slew rate of a signal is shown below, where the signal of interest is drawn in red. Slew rate can be measured on the rising or falling edge of a signal. It is typically measured at the 10% and 90% amplitude points of the signal. Often an Oscilloscope is used measure the slew rate of a signal. If the input signal's slew rate is higher than the op amp's slew rate specification the output signal's slew rate will be limited.

Obviously the slew rate of a signal and the bandwidth of a signal are related or else we would not be talking about slew rate. The mathematical relation of the two specifications for various signal types is beyond the scope of this tutorial. But we can look at them both from the simplest signal type example: a perfect sinewave. If our input signal is a perfect sinewave then the relationship between bandwidth and slew rate can be expressed as:

Sine wave frequency = Slew Rate / 2 x Pi x Vpeak

If we assume we are inputting a sinwave signal with an amplitude of 1Vp, then the maximum frequency (or bandwidth) that our example op amp can support:

100V/us / 2 x Pi x Vpeak =  100,000,000 / 6.28 x 1 = ~15.9MHz

This calculation tells us that the maximum bandwidth of a 1Vp sinewave that this op amp can handle without any bandwidth or slew rate limitations is 15.9MHz. If you are working with a signal that is a non-sinewave (which most of us are) then using slew rate specification is often the easier way to determine if the op amp has the bandwidth to properly pass your signal with no slew rate limiting or amplitude attenuation. 

📊 Op Amp Datasheet Plots Related to Bandwidth performance

Op amp datasheets will often include various plots that show its frequency response or bandwidth over various conditions. As an example below are some frequency response plots from the datasheet of the same example op amp that we looked at previously. As we can see from some of the example plots below that the op amps bandwidth is also dependent on load conditions, both resistance and capacitance. These plots are just meant to be an example, different op amps will most likely have different frequency response plots. When considering load conditions that the op amp has to drive:

• The lower the load resistance the lower the op amp's bandwidth. This is because the op amp has to output higher current.
• The higher the load capacitance the lower the op amp's bandwidth. Since higher capacitance means lower output impedance, the op amp has to output more current

⚙️ Op Amp Bandwidth Conclusion

In this tutorial we looked at important op amp specifications that help you understand the frequency response or bandwidth of an op amp based on how the op amp circuit is configured and aspects of the signal used with the op amp. We also looked at example frequency response plots that further provide details on the bandwidth of the op amp in a particular configuration and with known load conditions. Unfortunately when working with op amps there is no one simple formula or recipe to understand bandwidth over a variety of configurations, signal types, and load conditions. One way to deal with this ambiguity, is to select an op amp that has plenty of bandwidth margin when analyzing these different specifications as a whole, but this approach is not always possible or cost effective. Another approach you can take is to use the various free "SPICE" software modeling tools available to verify the bandwidth performance of your op amp circuit with different signal conditions using software models created by the op amp manufacturers themselves. Lastly, you can always spin up PCBs for doing real world testing of the op amp you want to evaluate. This is my favorite approach, but it should be done more as a step 2 or 3 after the other approaches because it is costly and time consuming.