# Op Amp Speed: Bandwidth or Slew Rate?

Op Amps are basic building blocks of analog circuits. They are used in several signal conditioning tasks such as voltage amplification, filtering, and mathematical operations. An important characteristic of an op amp is its speed. Ideally, op amps function infinitely fast with infinite gain at all frequencies, but in reality, they have finite speeds. There are two important concepts that relate to the speed of the op amp. It is the bandwidth and the slew rate. Both these concepts can be tricky to understand, esp how they relate to each other. In this blog we’ll try to answer the question “Bandwidth or Slew Rate?” intuitively.

But, what causes an op amp to have finite speed in the first place? This happens because real life op amps are limited by finite impedances at nodes. Impedance at a node is determined by the amount of resistance and capacitance at a node. As frequency increases, capacitance behaves more like a “short” leading to lower impedances and hence lower gains. Eventually, a point comes when the signal starts getting “lost”. It is this point which limits how fast an op amp can work. Below is a diagram which shows how an op amp responds to a step signal change. Both slew rate and bandwidth contribute to the total settling time of the signal.

Slew rate and bandwidth both determine the settling times

Now, let’s dive deeper and try to understand both slew rate and bandwidth conceptually.

#### Bandwidth

We design an op amp at DC biases. So we are basically spending quiescent power to make it “ready” to accept small-signals or rather small amplitude signals. These, when broken down with Fourier Transform, gives you the sum of very different frequencies ranging from small to very large. This is the domain of “small signals” and hence bandwidth. Higher the bandwidth, the op amp is able to amplify higher frequency signals, and hence have higher speeds. Electrically speaking, the frequency at which the signal gain is 1/sqrt(2) or 0.707 of the ideal value is the bandwidth of the op amp. This is the maximum frequency at which op amp can operate with expected behavior.

Example: For TI’s OPA333AIDBVT, gain bandwidth product is 350kHz i.e. for a closed loop gain of 1, the BW is 350kHz. For a gain of 2, it will be 175kHz and so on. An op amp becomes slower with higher closed loop gain – with the product of the gain and bandwidth constant.

#### Slew Rate

Now let’s say your small-signal becomes very large. For instance, instead of 1–2mV it becomes 2V. Now the op amp is confused. It was meant to handle small signals and comfortably operate within its bandwidth. Now we are in the large signal zone. Of course the op amp is going to get saturated, one of its differential pairs will have all the current, the other will have zero. This is the tail current which is then used to “transport” the 2V signal to the next stage. Changing voltage of anything instantly is impossible, as it will need infinite current to charge the caps “inherent” to a system. In our case, we use caps to do compensation and they can be as large as 10pF or so. And we don’t have infinite currents either. This gives rise to the slew rate!

What is the cause of this large signal change? It is because when power switches on in the system or when the input which is coming from the previous stage does a power cycle or switches. It’s in these cases we need large signal analysis.

Let’s talk a little more about the formula for slew rate.
All the biases of the op amp get fully saturated when op amp is in large signal mode, that’s why we need to go back to the Coulomb’s law which states that q = CV or I = CdV/dt — hence dV/dt = I/C which is the formula for the slew rate in the textbooks.

Example: For TI’s OPA333AIDBVT, slew rate is 160mV/us i.e. it takes the op amp 1us to increase its output by 160mV.

#### Bandwidth or Slew Rate?

Well, they operate together… The 2V signal will be in “slew-limited” till one side of the differential pairs is drained and then once the current starts building up in the drained differential side, it enters the “bandwidth” territory…

Settling time = Slewing time + BW Response time

Slew Rate is the maximum rate at which the op amp can respond to a large change in input signal. Bandwidth is the maximum rate at which it can respond to small change in signal. Both work together to determine the total settling time of a step response.

Some applications have a much more strenuous spec on bandwidth and their slew rate requirements are not too strict – this could be the case where the only real place where slew rate is handy is during start-up. But some applications such as motor drivers need the op amps to fully switch on or off, and that’s when slew rate requirement is much more stringent. It comes down to transport of electrical information from one stage to another. We are limited by how much currents we have to do this, and this creates the slew rate. In large signal zone its slew rate, in small signal zone its bandwidth. For fast op amps, we might need both a high bandwidth and a high slew rate.

Part Selection:
High slew rate op amps: TI’s OPA2743 series for slew rates above 10V/us.
High bandwidth op amps: TI’s LM6171 series for bandwidth above 100MHz

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