# Op-Amp: Gain Bandwidth Product and Frequency Response

Hey friends, welcome to the Kohiki.com So in this article, we will see the frequency response of the op-amp and we will also understand what is a gain-bandwidth product of the op-amp, and what is the significance of this gain-bandwidth product.

so these two parameters are very important aspects of an op-amp and it is quite often used by the designers for selecting a specific op-amp for any particular application.

## Op-Amp: Gain Bandwidth Product and Frequency Response

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## Frequency Response of the Op-Amp

so let us, first of all, see the frequency response of the op-amp. now so far we have assumed that the gain of the op-amp is very high and it is having a very high Gain Bandwidth Product and we have assumed Frequency Response that the gain of the op-amp is constant up to a certain band of frequencies.

But if you see the actual response then the actual response of the op-amp will look like this. That means the gain of the op-amp will be constant up to certain (Frequency Response) frequencies and if you go beyond this frequency then the gain of the op-amp will reduce at the constant rate of minus 20 dB per decade.

so this frequency is known as the cut-off frequency of the op-amp. so the cut-off frequency is the frequency where the gain of the op-amp will reduce by a 3 dB. Now in this frequency response here, the-axis represents the voltage gain of the op-amp and the x-axis represents the frequency on a logarithmic scale.

## Role of Internal Compensation Capacitor in the Frequency Response of the Op-amp

so in this frequency response if you see the cut-off frequency of the op-amp is very low and it used to be in the range of 10 to100 Hertz. so up to this frequency, (Frequency Response), the only op-amp will have a very high gain.

so we can say that in open loop configuration the bandwidth (Gain Bandwidth Product) of the op-amp is very low, and that is because all the op-amps which we are using today are internally compensated which means all the op-amps which we are using are having an internal composition capacitor.

so this internal composition capacitor ensures that the op-amp has a stable response at high frequencies. so now because of this internal composition capacitor, the open will have a single break frequency till the point the gain of the op-amp which is the unity.

so the frequency where the gain of the op-amp is unity is known as the unity gain frequency. so because of this kind of response we can predict the gain of any given frequency. (Frequency Response) Or in another way, suppose if you know the gain of the op-amp then we can predict the frequency of operation and that is particularly useful when we are using the op-amp in a closed-loop configuration.

so now suppose if op-amp is not internally compensated in that case you can have multiple break frequencies till the point the gain of the op-amp which is the unity gain frequency. (Frequency Response) And these multiple break frequencies can occur because of the stray capacitances and the load capacitances. so because of these break frequencies, the op-amp will become unstable at very high frequencies.

so that is the reason all the op-amps are internally compensated and because of that, the open-loop bandwidth (Gain Bandwidth Product) of the open is very low. (Gain Bandwidth Product) so because of this internal compensation is easy to predict the gain of the op-amp if we know the (Frequency Response) frequency of operation or in another way, if you know the gain of the op-amp then it is easy to identify the frequency of operation.

## Gain Bandwidth Product of Op-Amp

Gain Bandwidth Product of Op-Amp and that is particularly true when we are operating the op-amp in this particular region because in this region the product of gain and the frequency is constant. And that is known as the gain the bandwidth (Gain Bandwidth Product) product of the op-amp.

so let’s say if you are operating the op-amp at Unitygain frequency then the frequency (Frequency Response) of operation will be equal to one megahertz and at that frequency, the gain of the op-amp is 1. so the product of this frequency and gain will be equal to when megahertz. similarly, let’s say if you are operating the op-amp at this cutoff frequency FC, in that case, the gain of the op-amp is 10 to the power 5. (Gain Bandwidth Product) So, again the gain and the frequency product will be equal to one megahertz.

So, let us say we are using this op-amp in a closed-loop configuration and we have said the gain of open as a 40 dB which corresponds to100. so as you can see, in this particular region, the product of gain and frequency is constant and that is known as the gain than the product of the op-amp. And it will always be equal to the unity gain frequency (Frequency Response) of the op-amp. so using this gain-bandwidth (Gain Bandwidth Product) product, it is easy to identify the cut-off frequency of the op-amp whenever it is being used in the closed-loop configuration.

So, if you see the frequency response in frequency response we will get a constant gain of 40 dB till the point this gain line intersects the open-loop gain the response of the op-amp And beyond this intersection point the response of the op-amp will be similar to the open-loop response of the op-amp And this intersection point is known as the cut-off frequency (Frequency Response) of the op-amp. so below this cutoff frequency, (Gain Bandwidth Product) the gain of the op-amp will be constant.

so in this way whenever we are using the op-amp in a closed-loop configuration then we can get higher (Gain Bandwidth Product) bandwidth and we can find the bandwidth or the cutoff frequency (Frequency Response) in a closed-loop configuration by using this gain-bandwidth product. so for this particular response, we know that the unity gain frequency or the gain-bandwidth product on the op-amp is 10to the power 6 Hertz and we also know that the product of this closed-loop gain and the cutoff frequency will be constant and it will be equal to the gain-bandwidth product of the op-amp.

so from this, we can find the cut-off frequency of the op-amp which will be equal to this unity gain frequency divided by the closed-loop gain of the op-amp. so in this particular case, it will come out as a 10 kiloHertz. so in this way whenever we are using the op-amp in a  closed-loop configuration then in that configuration for the given gain can find the cutoff frequency (Frequency Response) of the op-amp. so, up to that cut-off frequency, (Gain Bandwidth Product), the gain of the op-amp will remain constant. now this relation is particularly true whenever we are using the op-amp in an anon-inverting configuration.

## Gain Bandwidth Product of Non-Inverting and Inverting Op-Amp

So In A Gain Bandwidth Product, There Are Two Types First Is Non-Inverting And the Second Is Inverting Op-Amp. So First We Are Talking About Non-Inverting.

### Non-Inverting Configuration

so for the non-inverting configuration if you seethe unity gain frequency or the gain-bandwidth product can be given by the expression closed-loop gain multiplied by the cutoff frequency (Frequency Response) of the op-amp. And for the inverting op-amp configuration, this gain-bandwidth product can be given by the expression this closed-loop gain plus 1, multiplied by the cut-off frequency of the op-amp.

so for the derivation of these equations, I will provide a separate note in the description very soon. so you can check that out. nowhere if you see whenever the gain of the op-amp is very high in that case the cutoff frequency fC will be equal to unity gain frequency. (Gain Bandwidth Product) But whenever this closed-loop gain is very low in that case the cutoff frequency for the inverting and the non-inverting configuration will be different.

so let us take the worst case, whenever the closed-loop gain of the op-amp is 1. So let us say we are using the op-amp in an inverting configuration and we have set the gain of to the unity.

so in that case, if you see the cut-off frequency of the op-amp will be equal to unity gain frequency divided by two.

While in the case of the non- inverting configuration, if we set the gain to the unity in that case the cutoff frequency will be equal to the unity gain frequency.

so whenever the gain of the open is very low in that case it is advisable to use the noninverting configuration over the inverting configuration.

## Example-Based On Non-Inverting Configuration

so now let us take one example based on this gain-bandwidth product.

so here we are using this op-amp in a noninverting configuration and for this configuration, we need the closed-loop gain of a hundred. And here we have been given this unity gain frequency that is equal to one megahertz. And we want to find the cut-off frequency fC for this configuration.

so we already know that for the non-inverting configuration the cutoff frequency fC will be equal to the unity gain frequency divided by the closed-loop gain of the op-amp.

So here the cutoff frequency fC will come out as at en kiloHertz.

So we can say that for this configuration the gain of the op-amp will be constant up to this ten kiloHertz frequency. Or we can say that the bandwidth (Gain Bandwidth Product) of the op-amp will be equal to 10 kiloHertz.

But now suppose in your application if you want the higher bandwidth (Gain Bandwidth Product) then what we can do. Either we can select an op-amp which is having a very high gain-bandwidth product or we can use the multiple stages of the op-amp. And we can distribute the gain of op-amp between these two op-amps.

so let’s say here we are distributing the gain of 100between this two op-amp and here both the op-amps are identical. That means the gain-bandwidth product of both the op-amp will be equal.

So, if we take the first stage, in the first stage the cut-off frequency of the op-amp will be equal to the gain-bandwidth (Gain Bandwidth Product) product divided by the closed-loop gain of the op-amp. And here we are assuming that the gain of the product of the op-amp is 1 megahertz.

So if you calculate then the cutoff frequency will come out as 100 kiloHertz. And the same is true for the second stage.

So here both the stages will have a cutoff frequency of 100 kiloHertz. And the overall cut-off frequency of the opamp will be equal to the cutoff frequency multiplied by the 2 to the power 1 by n minus 1. where n represents the number of stages which is being included in this system.

so here n is equal to 2 and the cutoff frequency-fC of the op-amp is 100 kilo, Hertz. So if you put all these values then the closed-loop cutoff frequency of the op-amp will come out approximately as 64 kiloHertz.

So in this way by using the multiple stages of the identical op-amp, we can increase the bandwidth (Gain Bandwidth Product) of the op-amp while keeping the same gain.

## You Tube Video

Here is a youtube video-based on Gain Bandwidth Product and Frequency Response Which Was Uploaded By w2aew

### How do you calculate gain bandwidth?

Quite simply, you need to answer this question:
How much data I want to be transferred across the network in a certain timeframe. and do the maths.
Example:
I have a “big” file of 10GB to download and I want it in 5 minutes.
Lets do the maths:
10 Giga Bytes = 10,000 Mega Bytes = 80,000 Mega bits (1 Byte = 8 bits)
5 minutes = 300 seconds.
Bandwith needed = 80,000 / 300 = 266.66 Mega bits / sec
To be able to download a 10GB file in less than 5 minutes, I will need at least a bandwidth of 267 Mbits/s

### Why is gain bandwidth product constant?

The gain-bandwidth product (GBW) is calculated by multiplying absolutely the worth of the gain with ω. that shows that the gain-bandwidth product could be a constant, as a result of it’s a product between 2 constants: the op-amp open-loop gain and also the corner frequency.

### What is the relation between gain and bandwidth?

The relationship is that, as gain will increase, the information measure, i.e. the frequency vary the op-amp will answer, decreases. as an example, say you set a gain of ten, you set in an exceeding frequency of 10Mhz, the output is ten times to input; i.e. the gain is ten.

### What is gain bandwidth product of 741?

Typically right down to one thousand at 1kHz, one hundred at 10kHz, and unity at regarding 1MHz. to create this simple to recollect we are able to say that the 741 includes a gain-bandwidth product of around a million (i.e. one megahertz because of the units of frequency ar Hz). victimisation HTMLEdit2 on a StrongARM hopped-up RISCOS machine.

### What is gain frequency?

The gain of associate degree device gate usually varies with the frequency of the applied signal. Unless otherwise explicit, the term refers to the gain for frequencies within the passband, the supposed in operation frequency vary of the instrumentation.

### What does gain bandwidth product mean?

The gain-bandwidth product (designated as GBWP, GBW, GBP, or GB) for AN electronic equipment is that the product of the amplifier’s information measure and therefore the gain at that the information measure is measured.

### What is the 3dB bandwidth?

The three dB information measure is that the frequency at that the signal amplitude reduces by 3 dB i.e. becomes [*fr1] its worth. The information measure of a bandpass filter is typically outlined because of the three dB information measure.

### How do you calculate frequency response bandwidth?

Bandwidth is outlined because of the frequency interval between lower discontinues and higher discontinue frequencies. The voltage gain (Av) of the electronic equipment for various input frequencies are often determined. A graph is often drawn by taking frequency (f) on X-axis and voltage gain (Av) on Y-axis.

### What is full power bandwidth?

Datasheets for operational amplifiers typically use the term (full-)power information measure to point the very best frequency at that the realizable peak-to-peak output voltage swing remains up to the DC output voltage varies. this can be conjointly generally represented because of the slew-rate-limited information measure. The full-power information measure

### What is full power bandwidth?

Full-power information measures The full-power information measure of AN op-amp is that the vary of frequencies during which AN op-amp operates with full power. This “full power region” is that the region from zero cps (DC) to the frequency at that the facility output is [*fr1] its DC power. this is often the region wherever the electronic equipment has the best gain.

so this is all about the gain-bandwidth (Gain Bandwidth Product) product of the op-amp. so I hope in this article you understood the frequency response and the gain-bandwidth product of the op-amp.

so if you have any questions or suggestions, do let me know in the comments section below. if you like this article hit the like button and subscribe to Kohiki.com for more such articles.