Op Amp Large Signal Bandwidth, What is This All About?

by DarwinT

Well I've been taught in school only one thing about the bandwidth of an op amp, or perhaps it just didn't register enough in my brain that there's another kind of bandwidth, and all of a sudden I hear this large signal bandwidth, or sometimes referred to as the full-power bandwidth, about op amps. At first I thought that this "large signal bandwidth" thing should be pretty obvious and a no-brainer, until I got confused some and I realize it can't be ignored anymore. That I already know, and I wanted to know more about it. How come nobody explained this thing to me!

When you look at an op amp's datasheet (e.g. ADA4895-1), the manufacturer often publish the bandwidth on the front page, otherwise it can always be found in the collections of plots inside. It's basically the unity gain frequency of the open loop gain of the amplifier. What is not so obvious is that this doesn't apply to all level of signals you intend to use your amplifier with. There's this another thing called small signal bandwidth, and it is this bandwidth that shown on the datasheet. This truly is the real definition of the op amp's bandwidth. Aren't you confused yet?

This apparent confusion stems from the fact that op amps have limited slew rate, the maximum rate of change in the output that it can provide. This is inherent in the design of the amplifiers in order to limit its speed and make the operation stable. This slew rate limitation is what dictates the large signal performance of the amplifier, commonly referred to as a large signal bandwidth. But this large signal bandwidth we are talking about is not as defined as the op amp's published bandwidth, because it depends on three factors, the slew rate, the signal frequency, and the amount of output voltage.

The Op Amp Unity Gain Bandwidth

If you look at the plot of the op amp's open loop gain, the frequency where the gain crosses at unity (0 dB) is the unity gain bandwidth of the op amp, or just its bandwidth. It should not be confused with the closed-loop bandwidth, which is the -3dB frequency of the closed-loop amplifier, where the gain starts to roll of at -20dB per decade of frequency. The closed-loop bandwidth decreases as the closed-loop gain increases (Figure 2). So if the amplifier is wired in a unity gain configuration, the closed-loop bandwidth is equal to the op amp's unity gain bandwidth.

Figure 1 OP77 Open Loop Gain

Figure 2 ADA4500 Closed Loop Frequency Response

The Op Amp Slew Rate

Below is an op amp wired as a buffer, with a step signal applied at the input. The ideal op amp would simply follow the input without slewing at the output. Real world op amps couldn't simply do that and would exhibit slewing at the output, with what we call the slew rate often expressed in V per microsecond (V/us). This parameter is defined in the datasheet.

Figure 3 Buffer

Figure 4 Slew Rate

If we look into the innards of an op amp, the slew rate originates from the Miller capacitance, and the bias current of the differential stage. It happens when the differential stage saturates because of the large differential input seen by the amplifier, and all current is steered into the conducting transistor. The maximum current is the bias current, and is all being fed to the miller capacitor of the second stage. This current and the Miller capacitance set the limit to the slew rate, given by:

But you don't really need all this calculations, the datasheet should provide us the slew rate. But you'll agree it helps to better understand the problem.

The "Large Signal Bandwidth" Dissected

Consider applying a sinusoidal signal at the input at a certain frequency. The output will be the input multiplied by the gain (unity in this case), and depending on the amplitude, it should a be faithful representation of the input. But once the output exceeds the maximum slew rate of the device, we will have distortions at the output. Everything is fine as long the maximum rate of change in output voltage doesn't exceed the slew rate, and that the signal is within the closed loop bandwidth of the circuit. Remember the output starts to roll off once it hits the -3dB frequency, or the bandwidth.

Figure 5

The output of the amplifier can be expressed by the equation:

Around zero is where the rate of change of the output is at maximum. We can obtain this maximum rate of change by getting the derivative of the equation at time equals to 0 (t = 0).

Where Vp is the amplitude of the output signal.

As long as the above rate of change does not exceed the slew rate, the output will not experience distortion.You can determine if your signal will not exceed the op amp's slew rate by using the formula above. As an example, a 2Vp-p output at 1MHz will require the output to rise at 6.28V per microsecond (V/usec), which means the amplifier you are using should have slew rate greater than that value. Note that as the output amplitude gets lower, the value of the slew requirement decreases as well, and the limiting condition would now be set by the -3dB bandwidth of the circuit.

Comments and feedback welcome.

References:

The Art of Electronics 2nd Edition, 1989, by Paul Horowitz and Winfield Hill

Microelectronic Circuits, by Adel Sedra and Kenneth Smith