# What did my professor mean with this: gain-bandwidth product

After trying to ask multiple times my professor what he meant with this I still don't get it.

Basically I have an inverting amplifier with a specified gain-bandwidth product of 0.6 MHz. Now as I understand we have that the gain-bandwidth product is calculated multiplying the closed-loop gain with the bandwidth. Now the closed-loop gain is calculated with the ratio of resistances and it corresponds to 20 in my circuit. Therefore the bandwidth is 30 KHz. Now my professor tells me that the closed-loop gain must be in decibels in that formula and therefore it should be about 23 kHz. I don't get why the closed-loop gain needs to be in decibels in this formula, can someone please explain me?

• Your professor is incorrect. Your calculation is the right one. I think you meant "the closed-loop gain is 20 in my circuit" (not open-loop). Nov 9, 2019 at 19:07
• Yes, I meant the closed-loop gain, not open-loop. Thank you! Nov 9, 2019 at 19:10
• If the gain must be specified in dB we would have a problem in the unity-gain case because the gain is 0 dB. Nov 9, 2019 at 19:10
• Don't you mean closed loop gain is 20? What are the resistances then? As gain times bandwidth is constant then if gain is 20 bandwidth should be 30kHz. I don't see where the open loop gain suddenly comes in. Can you post the exact question in case there are some misunderstandings somewhere? Nov 9, 2019 at 19:11

The point of characterizing the gain-bandwidth product is that you will find that no matter what gain you configure using reasonable feedback resistors you will find

$$\left| A\right|\cdot f_{-3dB} \approx GBW$$

where $$\GBW\$$ is a characteristic of a particular op-amp.

Now as I understand we have that the gain-bandwidth product is calculated multiplying the open-loop gain with the bandwidth.

As said above, it doesn't matter what gain configuration you use, you will get pretty close to the same gain-bandwidth product.

Using the open-loop gain might be convenient. But using a gain of 10 or gain of -2 config might be more convenient.

Datasheets will normally say what gain they use, and it's not always open-loop, since loading effects and non-linearities will change the $$\GBW\$$ slightly.

Now my professor tells me that the open-loop gain must be in decibels in that formula and therefore it should be about 23 kHz. I don't get why the open-loop gain needs to be in decibels in this formula, can someone please explain me?

You'll have to say exactly what formula you mean.

In the formula I gave above, $$\A\$$ is the linear gain, not the decibel gain. (So you'd use 100,000 rather than 100, if you were using the open-loop gain of an op-amp with a gain of 100,000 or 100 dB)