RTC without RTC ? How good is my crystal ?

Clock - I think that it's the most popular idea for a project with the MCU. It's not that hard from both software and hardware side to realize but not that trivial as well, not mentioning the fact that once realized it sits somewhere in the house, constantly reminding about itself and brings a kind of satisfaction :). There are a lot of options really to implement, a buzzer alarm, perhaps a thermometer, display and buttons servicing, perhaps maybe even serial port usage for NTP synchronization. But ...

The most challenging thing - like in every clock is the time reference source. There are a couple of options:

• well calibrated frequency source acting as an interrupt source
• Real Time Clock module with external crystal ( < 20 ppm )
• internal clock

These days RTC chips are so cheap and widely available that they are really the only reasonable choice, but if we're only planning to play around a bit with the software without paying much attention to accuracy and just for the sake of curiosity let's check how good the crystal to generate the system clock on the Arduino board is.

System Clock

System clock is generated using an external 16 MHz crystal. This crystal is not ideal, although it's quite stable - it may be surprising that it doesn't resonate exactly with the referenced frequency. In fact this frequency is a little bit different. 

Stability

A crystal accuracy is measured with ppms (parts per million). A typical crystal used to generate a system clock is something around +/- 50 - 100 ppm. Let's assume 80 ppm. The day has:

day = 24 * 60 * 60 = 86400 s

the hour

hour = 60 * 60 = 3600 s

If we would want to use this crystal as a reference for the clock application our clock would loose/gain:

per day:

86400 * 80 ppm = 86400 * 0,0008 = 6,91 s

per hour:

3600 * 80 ppm = 3600 * 0,0008 = 0,288 s

On the worst case it would be around 9 s per day. That's not that bad for a toy project.

Resonance frequency

Although the stability is quite satisfying, information about the exact resonance frequency is needed. How different is the resonance frequency of a typical 16 MHz crystal from the referenced 16 MHz ?

Using some code I can roughly measure it without using any laboratory equipment like frequency meters or oscilloscope. In fact I don't have access to this hardware and for most of the simple projects which I present here, although it would be helpful it's not a must.

The simplest way to estimate the crystal frequency is to use the code already created in libpca. Let's generate a tone of let's say 1 kHz frequency with a libpca beeper API. Now, Instead of connecting the buzzer I'll connect the pin to my laptop's microphone input directly and try to record it. The code is trivial:

Recorded signal:

1 kHz square signal recorded from OC0A pin.

This rough measurement shows that the full period took 45 samples at 44,1 kHz sampling rate, this gives the period of ~1,02 ms. The crystal clock period is 16000 shorter. After dividing the measured period of 1 kHz beep by 16000 and converting it to frequency, the answer is:

f =~ 15,68 MHz.

This means that our clock application will loose seconds. Every second measured will in fact be a 1,02 seconds in reality. This gives 1.2 seconds behind after every minute ! Of course the measurements done cannot be taken very seriously since they are done very inaccurately and without a proper tools, but keeping them in mind, let's write a simple application and see how much our "clock application" will be wrong from real time.



The above code is self explaining more or less, the "epoch" variable is incremented in the interrupt service routine every second (since interrupt happens every 1/256 s and epoch is incremented only when the cnt variable wraps). The time is send via Serial Port as a string.

After flashing it and running. I did some comparison between the measured time and the "real" time with a stopwatch. After an hour, Arduino has been a second behind. The crystal instability (80 ppm) results in 0,3 seconds behind. Assuming 0,7 second lost per hour I can roughly estimate that my crystal is less than 16 MHz by something around 3 kHz. So, it's more like 15,9968 MHz.

Conclusion

When building a real clock application RTC chip is a must, the system clock won't provide enough accuracy to be considered as a frequency reference good enough. Not mentioning the obvious advantage of having the RTC - the time is counted even if the main CPU is not powered, since most of them have a backup lithium battery circuitry.

The methods used to estimate the Crystal's resonance frequency cannot be treated serously with any level of confidence and used for a real production purpose, since they present no practical level of accuracy and the results are only a general hint.