# Op-Amp Unity Gain Frequency

I'm tasked with finding the unity gain frequency of an op-amp using the datasheet specs provided to me (just a homework exercise, not a real op-amp). There is no direct spec given for "Unity Gain Frequency" or "Unity Gain Bandwidth" or "Gain Bandwidth Product", but it does provide a spec for "rise-time" (0.3 uS typical) as well as "slew rate at unity-gain" (0.5 V/uS typical).

I know there is a formula that shows that the bandwidth can be approximated by 0.35/tr, but I guess I'm not really understanding which rise time to use. In my mind, isn't rise-time and slew rate almost the same thing? If the rise time is defined as the time it takes to go from 10% to 90%, shouldn't the slew rate give me the same result? If I had a waveform move from 0V to 1V, it would take 1uS per the slew rate. 80% of that would give 0.8uS

Can someone help to determine which to use (rise time or slew rate)?? And maybe explain why there is a difference

• Which part number? Feb 1, 2020 at 17:25
• @Tony - Not a real part. A contrived homework assignment. Feb 1, 2020 at 21:46
• Nobody acknowledges my correct answer? Feb 1, 2020 at 21:47

The correct term to use to find Bandwidth is Rise Time (10~90%) BW=0.35/tR which is not current limited by external load capacitance, rather it is limited by internal unity-gain compensation capacitance.

Thus using Gain*BW = unity gain BW

Slew Rate is the result of current limiting at a specified load capacitance.

Where dV/dt=Ic/C and C is the specified load capacitance tested often with overdrive to input with a step voltage.

You are correct about rise time and slew rate being almost the same thing - sorta kinda maybe. The slew rate spec probably does not have any limitations on it, so it can be used to calculate the transition time for edges of any amplitude. The risetime spec probably has a qualifier on it, like risetime for a 5 V pulse, or risetime with +/-5 V power rails.

Also, risetime is the transition time for the entire 10%-90% part of the waveform. But, the slope of the waveform is not constant throughout. It slows a bit at the top and bottom as it begins its transition to the flat parts of the pulse. Slew rate can be thought of as the slope of the waveform at its fastest part (usually a small part in the middle).

• So which one should be used for the unity gain frequency? Feb 1, 2020 at 15:46
• No - rise time and slew rate are definitely NOT the same thing. The rise time is defined for small signals only and - in contrary - the slew rate is defined for large signals only which can bring the first stage in saturation. You should try to find the unity gain frequency from the shown frequency response information (open-loop gain vs. frequency)
– LvW
Feb 1, 2020 at 16:46
• It's the same thing for logic because of the input being saturated. Feb 1, 2020 at 17:49
• Interesting. Guess I never thought about determining the unity gain bandwidth of an op amp this way. First off, every op amp I've worked with has had some sort of open loop gain vs frequency plot provided. Second, I've always used op amps with feedback around them (or a bigger loop), and it is this feedback that provides the gain vs frequency response I are about. Feb 1, 2020 at 21:50
• Also, some devices use 20% to 80% as a definition for rise and fall time. Feb 1, 2020 at 21:57