A common problem that engineers are faced with is the need to determine the closed-loop bandwidth of their operational amplifier (op amp) circuit. Some data sheets specify unity-gain bandwidth while others specify gain-bandwidth product . What is the difference between these terms and how are these specifications used to determine bandwidth?

Gain-bandwidth product is defined as the open-loop gain multiplied by the bandwidth. The gain-bandwidth product can be used to calculate the closed-loop gain bandwidth. For example, if the gain-bandwidth product is 1 MHz and the closed-loop gain is 10, then the closed-loop bandwidth is 100 kHz (1 MHz/10 = 100 kHz)

GBW/closed-loop gain = closed-loop bandwidth. The gain-bandwidth product is valid for any open-loop gain, as long as the A_OL curve has a single, dominant pole which will be a −20 dB/decade slope (see Figure 1).

The unity-gain bandwidth is the closed loop bandwidth when the open-loop gain curve is 1 V/V (0 dB). In the case of a single pole A_OL curve, the unity-gain bandwidth and the gain-bandwidth product are the same (Figure 1). Many op amps, however, have additional poles and zeros at high frequency that shift the unity-gain bandwidth. Figure 2 shows an example of an op amp where the higher frequency poles affect the slope of the A_OL curve so that the unity-gain bandwidth is not equal to the gain-bandwidth product. Note that in this case the gain bandwidth product of 80 MHz is valid for gains greater than 100. For gains less than 100 the actual gain bandwidth product will be between 80 MHz and 45 MHz. In the event that the gain bandwidth product is not specified, you can estimate the bandwidth graphically using the A_OL curve.

Table 1 (below) shows the data sheet table corresponding to the A_OL curve given in Figure 2. Note that the gain-bandwidth product is specified for two different closed-loop gains (1, 100). In fact, the gain-bandwidth product specified at unity gain could be called unity-gain bandwidth. Furthermore, note that the gain-bandwidth product specified at a closed-loop gain of 100 is valid for gains greater than 100 (Gain ≥ 100). The gains between 1 and 100 have to be graphically estimated using the A_OL curve.

Some amplifiers are not stable for low gains. In these amplifiers the secondary poles and zeros are well within the amplifier’s bandwidth. This type of amplifier allows for wide-bandwidth operation at lower quiescent currents, stable for gains greater than 12. Figure 3 shows the A_OL curve for the OPA847, a voltage feedback op amp. Table 2 gives its data sheet table. Note that the gain-bandwidth product is constant for gains greater than 50. The bandwidth for gains less than 50 is given at a few discrete points. This device does not have a unity gain bandwidth because it is not unity gain stable. However, they cannot be used in lower gains.

In this article we explained how to calculate closed bandwidth using the gain-bandwidth product and to eliminate confusion between the terminology unity-gain bandwidth and gain-bandwidth product. Furthermore, we showed how to graphically estimate bandwidth using the A_OL curve. Lastly, we introduced amplifiers that are not stable at unity gain.

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About the author

Arthur Kay is an applications engineering manager at TI where he specializes in the support of amplifiers, references, and mixed signal devices. He focuses a good deal on industrial applications such as bridge sensor signal conditioning. He has published a book and an article series on amplifier noise. He received his MSEE from Georgia Institute of Technology, and BSEE from Cleveland State University.