Home Power Monitor - Arduino ADC Speed

An important part of my home power monitor is the ability to measure the instantaneous power for a given circuit; this will allow me to calculate other important nerdy things like the power factor and reactive power.  This approach requires frequent sampling of the voltage and current waveforms so that the average power over many 60Hz cycles can be found.  There are two important points in making this work well:

• The voltage and current should be measured (ideally) simultaneously so that the power at that specific point in time can be determined.
• The rate at which new voltage and current measurements are made needs to be high enough that the accumulated samples form an accurate representation of the source waveform.  This is especially true if the current waveform has transients and nonlinearities (due to non-linear loads caused by power electronics).

Both of these factors are highly dependent on the speed of the analog-to-digital converter (ADC).  Assuming that multiple-channel simultaneous ADCs are not being used (which is the case for my system), separation in time between the voltage and current measurements will be entirely a function of the conversion time.  The measurement of the current can't start until the measurement of the voltage is complete.  Similarly, the rate at which the 60Hz voltage and current waveforms can be sampled is determined by how long it takes one voltage-current measurement pair to be made.

For the sake of simplicity, this prototype system I'm building now is going to use the Arduino's on-board ADC.  This ADC has a built-in multiplexer which has a reputation for not being very fast but since I am planning on using an external multiplexer to accommodate all the power circuits I want to measure (the Arduino can only mux in 8 channels, my plan calls for 13-16), I can get away with only using a single channel for the on-board ADC. 

The question that remains, then, is how fast the on-board ADC can do a conversion.  My prowling of the internet found some very experienced people who found a way to adjust the clock that the ADC uses when converting.  The ADC clock runs at a scaled down rate (prescaler) of the main system clock and the scaling rate can be changed programmatically.  A part of the documentation for the microprocessor used in my Arduino states:

The ADC accuracy also depends on the ADC clock. The recommended maximum ADC clock frequency is limited by the internal DAC in the conversion circuitry. For optimum performance, the ADC clock should not exceed 200 kHz. However, frequencies up to 1 MHz do not reduce the ADC resolution significantly.

Operating the ADC with frequencies greater than 1 MHz is not characterized.

Ignoring the actual results from the conversion, I decided to characterize the time it takes for the ADC to complete a given number of conversions.  The results from this test are below showing the conversion time for a varying number of conversions.  The last column is the difference in the 1 million conversions time as compared to the previous prescaler value.

Prescaler Value     1k conv.   10k conv.   100k conv.   1M conv.   Difference
2                     7.52us     7.43us      7.42us       7.42us    -
4                     9.53us     9.32us      9.30us       9.30us    1.88us
8                    12.78us    12.57us     12.55us      12.55us    3.25us
16                   19.15us    19.04us     19.04us      19.03us    6.48us
32                   32.19us    32.02us     32.00us      32.00us   13.00us
64                   60.28us    60.24us     60.24us      60.24us   28.24us
128                 112.24us   112.02us    112.00us     112.00us   51.76us


There are two reasons to feel confident in this data:

1. The conversion time is reasonably consistent across the various number of conversions.  There is not a dramatic difference in the calculated conversion time when the loop contained 1 thousand conversion and 1 million conversions.
2. The difference in conversion times scales very nearly linearly with the prescaler value.

Based on these results and the documentation's note that the ADC should operate reasonably well up to 1 MHz, I am planning on setting the prescaler to 16 giving me that 1 MHz conversion rate.  Doing the math: 16 channels at a conversion time of 19us per channel gives me a total of 304us to sample all channels.  With a 60 Hz waveform this allows 54 samples across all channels in one cycle.  This is maximum conversion rate I should expect; the test above does nothing with the conversion results except store them.  The arithmetic I need to do will slow the process down; characterizing that will be another test I'll have to do once the hardware is complete and I have a fuller start on the hardware.