I was studying ADC basics from this document, AVR127: Understanding ADC Parameters. I have a question regarding the throughput calculation. The document reads,

Consider the case of single-ended conversion where one conversion takes 13 ADC clock cycles. Assuming the ADC clock frequency to be 1MHz, then approximately 77k samples will be converted in one second. That means the sampling rate is 77k.

May I know how they reached this value? (I know they divide the clock frequency by 13, but don't know why.) I am not able to find the logic behind it. If you can explain the math, it would be appreciated.

• Because one conversion ( of one sample) takes 13 clock cycles.
– user16324
Aug 26, 2022 at 16:29
• One conversion takes 13 clock cycles, there are 1 million clock cycles in a second, how many conversions are there in a second? Aug 26, 2022 at 16:30
• Thank you.If you don't mind can you provide a step by step explanation of how they arrived 77k
– Hari
Aug 26, 2022 at 16:33
• I have 1 million apples. If it takes 13 apples to make a pie, how many pies can I make? Aug 26, 2022 at 23:49

If the ADC clock frequency is 1 MHz, each clock lasts for 1 μs. So, if the ADC needs 13 clock cycles to compute a sample then it takes 13 μs to do so. That, is an effective sample throughput rate of 1/(13 μs) or approximately 76.92 kHz. • thank you. Is this 13clks,cycles is same as throughput rate(Data rate) of the ADC
– Hari
Aug 26, 2022 at 16:45
• @HARITO 13 clock cycles is what your ADC is stated as needing to compute a sample. The reciprocal of the time it takes to complete 13 clock cycles is then a frequency and, that frequency is the number of sample conversions per second. Data rate is something entirely different. Aug 26, 2022 at 16:48

Write it out with the units. Arrange the ratios to produce the desired unit and cancel out undesired units. (A unit in both the numerator and denominator cancels out).

In this case, you are given both ADC Clocks per second and ADC clocks per sample. You want to calculate samples per second and you want the ADC clocks unit to cancel out. When you write it out with the units you will see that you have to divide ADC clocks per second by samples per ADC clock to get ADC clocks to cancel out and leave you with samples per second.

1,000,000 ADC clocks      1 sample        76,923 samples
-------------------- * --------------- = ----------------
1 second          13 ADC clocks        1 second