n = (Fosc / (16 * BAUD)) - 1: May Not Always Be Appropriate...

Log in or register to post comments
Go To Last Post
9 posts / 0 new
Author
Message
microcarl
microcarl's picture
Level: Raving Lunatic
Joined: Sun. May 30, 2004
Posts: 8363 View posts
Location: Cincinnati, Ohio
#1
Posted by microcarl: Tue. Dec 23, 2014 - 09:24 PM
  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 1

While working through my Arduino "Brain-Fart" dilemma:

 

https://www.avrfreaks.net/forum/most-epic-brain-fart-2014

 

I came to a conclusion...

 

I have never been a proponent of the n = (Fosc / (16 * BAUD)) - 1 equation.  I've always gone to the data sheet and looked up the appropriate value needed to derive the desired BAUD rate for a given crystal frequency and defined what the BAUD rate is with the following:

// USART0 = 115.2K BAUD @ 18.432MHz
#define BAUD_115_2K 9

I did, at one time, use the n = (Fosc / (16 * BAUD)) - 1 equation to prove to myself that this equation worked.

 

Well, while in the fog of my "Brain-Fart", I decided to see if I could employ the use the BAUD rate equation to verify what the BAUD should be and, here is what I discovered.

 

For any of the "Magic" frequencies: 14.7456MHz, 18.432MHz, etc., the BAUD rate calculation resolves to numbers that are exact whole numbers - meaning, there is no fractional part.

 

But... for crystal frequencies that don't resolve to whole number results, such as 1.000MHz, 4.000MHz, 8.000MHz, 12.000MHz, 16.000MHz, 20.000MHz, the formula doesn't seem to be the most appropriate approach and, here is why:

 

For a, say, 16.000MHz crystal, the resulting BAUD constant when calculating for a BAUD rate of 115.2K BAUD works out to:

n = (Fosc / (16 * BAUD)) - 1 = n = (16.000MHz / (16 * 115200 BAUD)) - 1 = 8.680555... - 1 = 7.680555...

 

I don't know how it is for GCCAVR, WinAVR or some of the other AVR C compilers but, rather than rounding 7.680555... up to 8 when moving from a float to UNSIGNED INT, ImageCraft's ICCAVR C compiler truncates the result of the equation to the value of 7.  The issue is that, according to the data sheet BAUD charts, deriving a BAUD rate of 115.2K BAUD when using a crystal frequency of 16.000MHz and a BAUD constant of 8 inherently produces an error of -3.5%.

 

For a BAUD constant of 7 the BAUD rate is:

BAUD = Fosc / (16 * (UBRR + 1)) = 16000000 / (16 * (7 + 1)) =  125000 BAUD >>> from the datasheet <<<

 

% error = 100 - ((115200 / 125000) * 100) = 100 - (0.92 * 100) = 100 - 92 = +8% error.

 

While I have only performed the error resulting due to fractional truncation for one BAUD rate, I suspect the error will be proportionally as bad, across all of the BAUD settings, using the much touted n = (Fosc / (16 * BAUD)) - 1 to derive BAUD rates with non BAUD friendly crystal frequencies.

 

I think I'll keep using hand fed BAUD constants presented in the data sheet BAUD charts.

 

 

You can avoid reality, for a while.  But you can't avoid the consequences of reality! - C.W. Livingston

Tags:

AVR Microcontrollers, megaAVR and tinyAVR
Top
theusch
theusch's picture
Level: 10k+ Postman
Joined: Mon. Feb 19, 2001
Posts: 39611 View posts
Location: Wisconsin USA
Posted by theusch: Tue. Dec 23, 2014 - 11:08 PM
  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

Carl--Much ado about nothing.  Yes, in the case of your truncation example, rounding up would be a bit better.

 

However, both resulting numbers are "bad" and outside the band of reliable serial comms.

 

Like driving off the shoulder 3.5 meters on the right and 8.5 meters on the left.  Neither is good.

 

-- Many of us use "Wizards" that help with this type of thing when building an app.

-- Many of use use avrcalc and/or kavrcalc to check settings.

-- Many of us >>only<< use magic frequency crystals in our USART AVR8 apps.

-- When the above "only" is violated, then indeed the datasheet chart and/or tools mentioned above are consulted.

 

(Somewhere in that equation there had better be a cast to UL ...)

You can put lipstick on a pig, but it is still a pig.

I've never met a pig I didn't like, as long as you have some salt and pepper.

Top
kk6gm
kk6gm's picture
Level: Raving Lunatic
Joined: Fri. Sep 11, 2009
Posts: 3716 View posts
Location: Sacramento, CA
Posted by kk6gm: Tue. Dec 23, 2014 - 11:41 PM
  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

Add rounding (the (8*BAUD) being 1/2 of the divisor):

 

n = ((Fosc + (8 * BAUD)) / (16 * BAUD)) - 1

Top
Who-me
Who-me's picture
Level: Raving Lunatic
Joined: Sun. Mar 25, 2007
Posts: 2215 View posts
Posted by Who-me: Wed. Dec 24, 2014 - 02:23 AM
  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

microcarl wrote:

 

I think I'll keep using hand fed BAUD constants presented in the data sheet BAUD charts.

 

I agree, and I usually document the actual Baud, and in many cases check that against the USB-UART device baud choices too.

 

This pastes into CCalc

// FOsc=16M; Baud=115200; BaudDiv = round(FOsc/(16*Baud))   BaudDiv = 9
// TrueBaud = FOsc/(16*BaudDiv)      TrueBaud = 111111.1111
// BaudErr = 1-Baud/TrueBaud         BaudErr = -0.0368
// and this for USB Baud
// USB_Baud = 12M/(round(12M/Baud))  USB_Baud = 115384.6154
// or
// USB_Baud = 12M/(round(12M/TrueBaud))  USB_Baud = 111111.1111

 

ie a design can  set 111.111k Baud @ uC, and set that on most USB-Bridge parts, for lowest errors.

 

Top
Koshchi
Koshchi's picture
Level: 10k+ Postman
Joined: Wed. Nov 17, 2004
Posts: 15674 View posts
Location: Vancouver, BC
Posted by Koshchi: Wed. Dec 24, 2014 - 06:06 AM
  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

We have seen people spend weeks trying to write the "best" set of defines to calculate the proper UBRR value taking into account rounding, deciding when to use U2X, calculating the error, producing warnings when no appropriate value is found, etc., all to avoid the 10 seconds it takes to calculate the value by hand. I never saw the point. In the time it took to create the defines you could have done the hand calc a thousand time.

Regards,
Steve A.

The Board helps those that help themselves.

Top
joeymorin
joeymorin's picture
Level: 10k+ Postman
Joined: Tue. Jul 17, 2012
Posts: 11391 View posts
Location: Location, Location
Posted by joeymorin: Wed. Dec 24, 2014 - 06:19 AM
  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 2

Why write macros for anything, then?

 

The point of any macros is that once written, you can deploy them in (ideally) any circumstances, regardless of considerations like F_CPU.

 

That's what the macros in <util/setbaud.h> do, which btw handle rounding neatly.

"Experience is what enables you to recognise a mistake the second time you make it."

"Good judgement comes from experience.  Experience comes from bad judgement."

"Wisdom is always wont to arrive late, and to be a little approximate on first possession."

"When you hear hoofbeats, think horses, not unicorns."

"Fast.  Cheap.  Good.  Pick two."

"We see a lot of arses on handlebars around here." - [J Ekdahl]

 

Top
stevech
stevech's picture
Level: Raving Lunatic
Joined: Tue. Dec 18, 2001
Posts: 6148 View posts
Posted by stevech: Wed. Dec 24, 2014 - 06:20 AM (Reply to #6)
  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

 

download: avrcalc

http://www.avrcalc.com/

 

or one of its cousins.

 

Last Edited: Wed. Dec 24, 2014 - 06:21 AM
Top
Koshchi
Koshchi's picture
Level: 10k+ Postman
Joined: Wed. Nov 17, 2004
Posts: 15674 View posts
Location: Vancouver, BC
Posted by Koshchi: Wed. Dec 24, 2014 - 08:12 PM
  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

Why write macros for anything, then?

Generally I don't, especially for something as trivial as calculating UBRR.

download: avrcalc

Why? It is two divides to get the value, one more divide if you want the amount of error. 

Regards,
Steve A.

The Board helps those that help themselves.

Top
microcarl
microcarl's picture
Level: Raving Lunatic
Joined: Sun. May 30, 2004
Posts: 8363 View posts
Location: Cincinnati, Ohio
Posted by microcarl: Wed. Dec 24, 2014 - 08:56 PM (Reply to #8)
  • 1
  • 2
  • 3
  • 4
  • 5
Total votes: 0

Koshchi wrote:

Why write macros for anything, then?

Generally I don't, especially for something as trivial as calculating UBRR.

download: avrcalc

Why? It is two divides to get the value, one more divide if you want the amount of error. 

Obviously, for me, working two divide operations isn't a problem.

 

But even with that, it's just so much easier to look at the BAUD tables in the data sheet and get the BAUD constant and the percent error, as well.

 

To me, the n = ((Fosc / 16) / BAUD) - 1 is better used as a tool, to discover if some other frequency other than what is listed in the BAUD charts will have little enough error to work with.  For instance, will Fosc = 4.096MHz work for a given BAUD and, what error will you be working with?

 

Other than that, it's the BAUD charts...

 

 

You can avoid reality, for a while.  But you can't avoid the consequences of reality! - C.W. Livingston

Last Edited: Wed. Dec 24, 2014 - 09:06 PM
Top