555 Timer Calculations 1

[Nuke101]

Hi, my first post.

In the 555 timer calculations there are some parts of the formula i just cant find much info on. Im referring to these:
For a 555 Mono T = 1.1 RC

For a 555 Astable F = 1 / 0.693C( R1+2R2 )

My question is, where does the numbers .693 and 1.1 come from ?
I know just about everything about the operation of a 555 timer but this part ive been stumped on for quite some time, perhaps someone can fill me in or maybe point me to some appropriate info ?

 

[dhwilliams]

The 555 has, internally, 3 equal resistors in series and connected across the supply voltage. This produces 2 reference voltages, 1/3 of supply and 2/3 of supply. When the trigger input goes below 1/3 of supply the output goes high and when the threshold input goes above 2/3 of supply the output goes low - see 555 data sheets. The timing capacitor is charged or discharged via the timing resistor(s) and the voltage across a capacitor while charging follows an exponential rule as described in the following URL, specifically equations 4.6 and 4.7

http://www.unf.edu/coas/natsci/physics/physics2/lab/manual/lab4-0305.pdf

The 0.693 and 1.1 you refer to are the numerical values which, when substituted in the exponential formula, will give the appropriate time for the capacitor to charge or discharge between the reference values.

My mathematics is not good enough to do the calculations to prove this but I don't think it's important once you understand the principle.

 

[Nuke101]

dhWilliams, thanks for your reply.

Im having a problem getting the PDF file, you referred to, to open (using adobe acrobat reader). All i get is blank pages and a font error prompt. Can you perhaps give me the key words you used in your search and i could prolly hunt it down ? It appears to be what im looking for.

Thanks again, most appreciated.

 

[dhwilliams]

I can't remember what I used to get that link but I have just put "exponential capacitor charging formula" (without the quotes) into Google and that returned 988 hits, one of which gives 2 formulas, 1 for charging and 1 for discharging:

http://www.utsc.utoronto.ca/~quick/PHYA10H3F/Manual/LMB08The.pdf

Again this is a PDF so if you can't read it I suggest you download the latest Acrobat Reader.

 

[Nuke101]

dhWilliams,thanx again, the pdf file opened with no problems and was very helpful.

After an exhaustive search ( and a splitting headache) using some of your terms as well as some others, i think im finally getting out of the dark with these RC time constants.

Although i still havent completely figured out the origin of the formula for the 555 timer, ive learned a thing or two about RC time constants.
I guess more than anything else i needed to know just what the symbols used in the calculus differencial equation for determining RC time constants meant. Heres the link that i found most helpful in that regard:

http://www.allaboutcircuits.com/vol_1/chpt_16/8.html

Using a derivitive of the formula i think i may have found where the 1.1 came from used in the monostabe. Im no math wiz but it goes something like this: (using 1 second as the RC time constant).

T = -RC 1n (1/3)
= -1 x 1n (0.333)
= -1 x 1n x 0.333
= -1 x -1.0986
= 1.0986
rounding off gives T = 1.1RC used in the monostable formula. Does that look about right ?

Im still searching and working on te astable part, i'll post if i make any progress.

Thanx again.

Nuke.

 

[dhwilliams]

As far as your derived formula is concerned, I'll take your word for it! But it does look convincing...

When you are considering the astable you will have to use both the charging and discharging variants of the formula to calculate the "mark" and "space" separately then add them to get the period, not forgetting that you only charge/discharge between 1/3 supply and 2/3 supply.

Dave

 

[IRstuff]

The only problem is that the equation in the link can never provide an argument for the log that's less than 1.

TTFN

 

[Nuke101]

IRstuff, Thanx for your reply.

Can you please explain what you mean ? I'd like to find out as much as i can about these RC time constants and the associated formulea and perhaps some reading this might like to know about them as well.

Dave, please dont take my word for it, like i said im no math wiz ;-p , after looking over my so-called "derived"
formula again, i think it may be flawed. First off i shouldnt have used 1 sec as the RC constant, RC in this instance is an unknown. Secondly i dont think 1/3 was suppose to be changed to a decimal (.333), it just happened to work out to 1.1 when i took the exponential (or its inverse 1n)of it on my calculator, so i guess it was just a fluke.
I also found out that this procedure also works for the astable in finding where .693 comes from, like this:

t = exp(1n(1/2))RC
= 1(1n(2))RC
= 0.6931718 RC

Rounding off gives .693RC used in the astable formula. Why this works im really not sure, but it works !

Nuke.

 

[IRstuff]

It's fine, just some sloppiness in fractions. The timing equation is RCln(1/(1-delta/total)

delta/total=2/3 in the monostable mode, so the denominator is 1/3, resulting in RCln(3)~1.1RC

see:

http://www.play-hookey.com/digital/timer_555.html

for the rest, although the Philips app note has something slightly different for the astable mode:

http://www.web-ee.com/primers/files/555AN.pdf

TTFN

 

[Nuke101]

IRstuff, thanx for the explaination and the links(book marked them).
It as been an eye opener and has cleared up a few misunderstandings i was having.I guess now i can go away alittle wiser.

Thanx guys.