While a sample-and-hold circuit makes things easier for an ADC, it doesn't solve every problem.

### Sampling time, LSBs, and ASR

The time the sampling capacitor is connected to V_{in} is known as its **aperture**. If the signal changes during the aperture, the best we can hope to say is:

The captured voltage will be somewhere between the input's minimum and maximum values during the aperture.

That's a problem, but we already know how to solve it.

If we treat the unknown part of the captured voltage as noise, we can apply the same reasoning we used to define NFCR:

As long as the input changes less than 1/6th of 1LSB during the aperture, we can assume the error due to that change will only exceed 1LSB for 1 reading in 500 million.

That gives us a limit on how much the signal can change, and if we know how long the aperture is, we know how fast the signal can be allowed to change, aka: the **Aperture Slew Rate**

So, all you have to do is open up the datasheet for an ADC, look for something like 'aperture', 'sampling interval', or some other equivalent term..

... and you probably won't find anything.

Some high-end ADCs will tell you their sampling interval, but most don't. We can estimate minimum aperture times though, based on the number of RC time constants it takes to charge the sampling capacitor to Vin:

8 10
12 16
24 32 |
55ns 69ns
83ns 110ns
166ns 220ns |
72ns 86ns
100ns 127ns
183ns 237ns |

Those tell us how long the aperture lasts, and we know how much we can allow the voltage to change by calculating 1/6 LSB for an ADC's resolution and reference voltage. With those two values, we can figure out how quickly we can allow the signal to change.

A change in voltage over time is called a **slew rate**, and since this one is related to the aperture of a sample-and-hold circuit, I call it **aperture slew rate**:

8 10
12 16
24 32 |
3.25mV 814uV
203uV 12.7uV
49.7nV 192pV |
45.1kV/s 9.5kV/s
2kV/s 100V/s
272mV/s 810uV/s |

45.1 kilovolts per second sounds like a lot, but a 1Hz sine wave between 0V and 1V has a maximum slew rate of 3.14V/s. Increasing the amplitude so it swings between 0V and 5V takes the maximum slew rate to 15.7V/s.

The maximum frequencies you can read with an ADC while maintaining the aperture slew rate are:

8 10
12 16
24 32 |
14.4kHz 3kHz
637Hz 31.8Hz
86.6mHz 257.3uHz |
2.9kHz 600Hz
127Hz 6.4Hz
17.3mHz 51.6uHz |

Those frequencies are low, but remember they're calculated for a 10pF sampling capacitor charging from a source whose resistance is 1k. Lowering the resistance of the signal source will let the sampling capacitor charge faster, making it possible to measure higher frequencies.

The values are also calculated for less than 1LSB of error per sample. There's nothing to stop you from trying to measure signals faster than the values above, but you'll have to accept more error in your readings.

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