UART Baudrate Error Budget

[N9WXU]

I was reviewing a Cypress data sheet for the CYW4390 and saw a line in the UART chapter saying that the total baud rate error budget for both ends had to be less than 2%.  With a large dependence upon internal oscillators these days, it seemed a good time to discuss these error budgets.  Is 2% reasonable or conservative?

First here is a quick back of the envelope calculation for link budget for UARTS.  I will assume "perfect" rise & fall times, and 8, none, 1(8n1) framing.

There are a total of 10 bits in a byte with 8n1 so each bit is 10% of the total byte time.  If your link budget is larger than 10%, you will miss a bit.  BUT WAIT... all UART implementations I am aware of try to sample in the center of the bit.  Generally, this is done by oversampling 16x and using the center 3 samples as a majority detect.  If you consider that slipping the byte time by 1/2 a bit time will cause a missed bit, our link budget is now 5%.  If you KNOW you are talking to a PERFECT receiver, then you can accept the entire 5% error.  (Of course, you can assume your design is perfect and pass the blame to the other side, but then you would not be reading this.). I am sure that perfect transmitters & receivers are not possible, so we shall reasonably accept 1/2 the responsibility for the link budget, making our baud rate error specification 2.5%.

Hmm.  Something still seems rotten.  The data sheet states that the TOTAL budget is 2%.  Our envelope scribblings say 5%.  What gives?

Here is a good writeup by Maxim Integrated (https://www.maximintegrated.com/en/app-notes/index.mvp/id/2141) that adds some more details.  Essentially, you have an uncertainty of ±1 sample-time detecting the START bit and a terrible link would have a 50% chance of detecting the midpoint of the stop bit.  The short of the story is a ±3 sample-time error budget out of a needed 152 sample-times (160 sample times less 1/2 a bit time) or ±2% error budget for the link.  That assumes you are over sampling 16x.  On a PICmicrocontroller, the UART has a high speed mode (BRGH = 1) which changes the sampling rate to x4 instead of x16.  This can have a profound effect on the error budget due to the ±1 bit sampling uncertainty.

So here are a few recommendations:

1) Always use the MAXIMUM sampling rate available in your UART.

2) Consider a crystal (20ppm) or a resonator (0.5%) or if you must use an internal oscillator, I hope your temperature & power supply is stable so your oscillator accuracy is good.

3) Consider using the auto baud features and internal oscillator tuning features if they are available in your controller.

Good Luck

[Orunmila]

I lost you a bit at the end there, so you say +-2.5% is pretty close to correct but it does not take the sampling into account, if you do - that reduces to +-2% error budget which means that if the 2 devices drift apart more than 4% (the one goes up 2% and the other one goes down 2%) - you will start seeing errors?

That sounds about right for what I was expecting...

But how much does that change with BRGH to 4x? 

Does that mean the budget becomes close to 1% ?

 

[N9WXU]

Those are great questions.  So here is the answer with the same procedure.

10 bit-times * 16 provided 160 total sample times in a byte.  The error threshold occurs 1/2 a bit time early so you subtract 8 sample for 152 total sample times as the baseline.

Then the article assumed additional errors of ±25% and ±37.5 for the two test cases.  .25 * 16 == 4 and .375 * 16 == 6 less 1 bit for sampling uncertainty and you get ±3 and ±5 sample times of allowable mismatch out of 152 sample times.

If we rework the numbers for x4 sampling and x8 sampling we get the following:

x4 Sampling (PIC BRGH = 1)

10 * 4 == 40 - 2 == 38 total sample times.

.25 * 4 == 1 and .375 == 1.5. less 1 for sampling uncertainty and you get ±0 and ±1 (rounded .5 up to 1 for a 'good" link)

So you just can't receive a bad link (50% chance of catching the last bit) and on a reasonable link (75% chance of catching the last bit) you have a 1/38 == ±1.3% link budget.  

If BRGH is set, you need a fantastic signal and you get a ±2% link budget.

x8 Sampling (AVR U2Xn bit set)

10 * 8 == 80 - 4 == 72 total sample times to the edge of acceptability.

.25 * 8 == 2 and .375 * 8 == 3 less 1 for sampling uncertainty and you get ±1 and ±2.

Total Link Baudrate Error is 2/72 == ±2.7% and 3/72 == ±4.2%.  Essentially, the lower oversampling means the middle is sampled more broadly which increases area where the edges can be caught.

 

[Orunmila]

Ok I think I get it now. 

We can separate the quality of the link from the basic budget. We know on a perfect link the slew rate is instant. I will do a 10% bit time slew rate for the table calculation as that is typically what I like to have.

Sorry I was too lazy to do the 8x, but it is somewhere inbetween.

Over  Sampling	Samples from  Start to centre  of stop bit	Budget without Sampling  Uncertainty	As %	Sampling  Uncertainty	Error Budget with Sampling  Uncertainty	Clock Error Budget Ideal slew	Clock Error Budget 10% bit slew
4x	38	+-2 sample periods	5.26%	1 period	+-1 sample period	+-1.32%	+-0.52%
16x	152	+-8 sample periods	5.26%	1 period	+-7 sample periods	+-2.3%	+-2.03%

 

From the PIC16F18875 datasheet the clock accuracy is +-2%, which means that from 0 to 60C between 2.3V to 5.5V you can use the internal oscillator for 2 devices to communicate realiably only if both devices are oversampling at 16x, if you want to use 4x over sampling you will not get reliable communication as the clocks cannot remain within +-0.52%. 

 

 

[N9WXU]

Ok.  That looks more like what I suspected.  Thanks for checking the math.

That 1/2% error budget in x4 mode will be challenging for most systems.  You will need short cables and/or low baud rates.