An Op Amp Gain Bandwidth Product

I can see some chat on internet about the operational amplifier gain bandwidth product. People are interested in having a better understanding of this parameter, as it appears in any op amp datasheet and it is used in many articles and books. In this article I will describe this parameter and show you an example with Analog Devices’ ADA4004, which is a precision amplifier.

The Gain Bandwidth Product describes the op amp gain behavior with frequency. Manufacturers insert a dominant pole in the op amp frequency response, so that the output voltage versus frequency is predictable. Why do they do that? Because the operational amplifier, which is grown on a silicon die, has many active components, each one with its own cutoff frequency and frequency response. Because of that, the operational amplifier frequency response would be random, with poles and zeros which would differ from op amp to op amp even in the same family. As a consequence, manufacturers thought of introducing a dominant pole in the schematic, so that the op amp response becomes more predictable. It is a way of “standardizing” the op amp frequency response. At the same time, it makes the op amp more user friendly, because its stability in a schematic becomes more predictable.

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Build an Op Amp SPICE Model from Its Datasheet – Part 1

Why do you need to build your own Op Amp model? Most Op Amp manufacturers have SPICE models for their components and make them available for free. Then why should you know how to build one? Well, not everything has a model and that is why, sometimes, you have to build your own. Also, it may be necessary to study a circuit to see what happens if you change the Op Amp slew rate or bandwidth, offset, and so on. Sometimes the manufacturer own model does not work, as a user found out and posted a question in this forum. I told him that the model has a bug and advised him to build his own.

No matter the reason, building your own model is fun and rewarding and can only add to your overall understanding on how an Op Amp works. One note of caution. The model described here is a behavioral model. This means that the model will mimic the op amp functionality, but will not have any transistor or any other semiconductor SPICE models.

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An Ideal Operational Amplifier Simulation Model

You worked hard on your schematic, you calculated everything, you feel confident that it will work.  To be sure though, before committing the schematic to copper, you want to simulate it.  You develop a SPICE simulation schematic and, surprise, things don’t work.  What’s going on?

You start searching for bad connections in the simulation schematic.  You check the power supplies and the circuit biasing.  Finally, in desperation, you suspect the operational amplifier model that you downloaded from the manufacturer website, or found in the SPICE program library.  How do you troubleshoot your circuit?

First, split your circuit into small subcircuits, like a one op amp circuit.  Second, take aside, on a different simulation page, one of these subcircuits.  Is that working?  If that circuit is a non-inverting amplifier, as an example (Figure 1), and the output voltage is all over the place except your expected value, than replace your op amp with an ideal one and see if that circuit works.

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The RMS Value of a Trapezoidal Waveform – Part 2

In a previous article, to Derive the RMS Value of A Trapezoidal Waveform – Part 1, I showed how to derive the RMS value of a trapezoidal signal with a flat plateau and different rise/fall time values.  In some applications, the trapezoidal signal plateau is not flat, but rather a ramp, as shown in Figure 1.  A typical example is a DC-DC converter, where the transformer winding current might look like the signal in Figure 1.  Of course, in the DC-DC converter example, the amplitude is current and not voltage.  No matter, the calculations are the same.

This waveform is still considered a trapezoidal waveform. Let’s calculate its RMS value.

trapezoidal-waveform-2Figure 1

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Using the Summing Amplifier as an Average Amplifier

Sometimes people ask how can one use a summing amplifier as an average amplifier. The answer is simple, provided that one knows what kind of average one needs.

The summing amplifier can output the average of two, three or more signals. This is different than a signal average. The summing amplifier cannot, for example, output the average of a triangle signal. For that, you need an integrator to perform the average in the analog realm, or you need to sample the signal and calculate the average with a microcontroller. This type of average is the signal average in the time domain. I will write an article about the average of a signal in a near future.

In this post I will show you how to average two or more signals with a summing amplifier. In How to Derive the Summing Amplifier Transfer Function I wrote that the summing amplifier shown in Figure 1

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How to Derive the RMS Value of Pulse and Square Waveforms

The RMS value of a pulse waveform can be easily calculated starting with the RMS definition. The pulse waveform is shown in Figure 1. The ratio t1/T is the pulse signal duty-cycle. As shown in other articles in this website ( to Derive the RMS Value of a Trapezoidal Waveform and to Derive the RMS Value of a Triangle Waveform), the RMS definition is an integral over the signal period as in equation (1).

pulse signalFigure 1

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How to Derive the RMS Value of a Triangle Waveform

What is the RMS value of a periodic signal?  When a periodic signal is generated by a source connected to a load, a resistor for example, the RMS value is the continuous signal, the DC value which would deliver the same power to the load as the periodic signal.

This article shows how to derive the RMS value of triangle waveforms with different shapes and duty cycles.

The triangle waveform in Figure 1 has a slower rise time than the fall time.  In this case, the fall time is small so that it can be considered zero.  If it is not zero, read further on deriving the RMS value of a triangle with comparable rise and fall times.

triangle waveform with slow rise time, sharp fall timeFigure 1

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