555 oscillator queer behavour

[panos v]

I have a question concerning the function of the 555 oscillator in
astable mode.
In particular the external elements i have connected to the 555 are
those depicted at the
datasheets of all the 555 ics (LM555, NE555 etc). The 2 resistors are above
1K Ohm (Ra=1K & Rb=6.8K),
the C capacitor's value is greater than 0,0005uF (C=0,001uF) whereas a
0,1uF capacitor is connected
between the "Control Voltage" pin and the ground.
The above connection with the aforementioned values for the external
elements adjust the 555 so that
it theoretically produces a frequency of 98KHz, more or less. The problems
lies in the fact that the
experimental frequency, produced by the ic, is lower than the theoretical
by around 30KHz.
The discrepancy of theoretical and experimental value appears also in other
"valid-practical" values of
Ra,Rb & C with different deviations. I have also tried the LinCMOS version
of 555 (TLC555) with the same results.
Another odd phenomenon, equally unwanted with previous one, is the
shifting of the produced frequency whenever
the value of power supply of the 555 is changed, always ofcourse within the
allowed limits (4.5->16Volts).
The datasheets of the various 555 mention clearly that the HIGH and LOW
times, and hence the frequency, are
independent of the power supply.


Any help is wanted

panagiotis

 

[CFoley1064]

Subject: 555 oscillator queer behavour
From: panos v 2222@yahoo.gr
Date: 12/10/2004 6:24 PM Central Standard Time
Message-id: <opsith2nk434r7we@localhost

I have a question concerning the function of the 555 oscillator in
astable mode.
In particular the external elements i have connected to the 555 are
those depicted at the
datasheets of all the 555 ics (LM555, NE555 etc). The 2 resistors are above
1K Ohm (Ra=1K & Rb=6.8K),
the C capacitor's value is greater than 0,0005uF (C=0,001uF) whereas a
0,1uF capacitor is connected
between the "Control Voltage" pin and the ground.
The above connection with the aforementioned values for the external
elements adjust the 555 so that
it theoretically produces a frequency of 98KHz, more or less. The problems
lies in the fact that the
experimental frequency, produced by the ic, is lower than the theoretical
by around 30KHz.
The discrepancy of theoretical and experimental value appears also in other
"valid-practical" values of
Ra,Rb & C with different deviations. I have also tried the LinCMOS version
of 555 (TLC555) with the same results.
Another odd phenomenon, equally unwanted with previous one, is the
shifting of the produced frequency whenever
the value of power supply of the 555 is changed, always ofcourse within the
allowed limits (4.5->16Volts).
The datasheets of the various 555 mention clearly that the HIGH and LOW
times, and hence the frequency, are
independent of the power supply.


Any help is wanted

panagiotis

I'd try bringing the value of Ra up to 2.2K, Rb to 15K, and C to 470pF. The
equation will still give you just about the same frequency numbers, and you
won't be working the poor discharge transuistor quite so hard.

See if it works. That would cause both of your "Series of Unfortunate Events".

Chris

 

[John Popelish]

panos v wrote:

I have a question concerning the function of the 555 oscillator in
astable mode.
In particular the external elements i have connected to the 555 are
those depicted at the
datasheets of all the 555 ics (LM555, NE555 etc). The 2 resistors are above
1K Ohm (Ra=1K & Rb=6.8K),
the C capacitor's value is greater than 0,0005uF (C=0,001uF) whereas a
0,1uF capacitor is connected
between the "Control Voltage" pin and the ground.
The above connection with the aforementioned values for the external
elements adjust the 555 so that
it theoretically produces a frequency of 98KHz, more or less. The problems
lies in the fact that the
experimental frequency, produced by the ic, is lower than the theoretical
by around 30KHz.

According to the NS data sheet:

t1 = 0.693 (RA + RB) C
t1 = 0.693 (1k + 6k8) * .001e-6 = 5.4e-6 seconds

t2 = 0.693 (RB) C
t2= 0.693 (6k8) .001e-6 = 4.7e-6 seconds

frequency = 1/(5.4e-6 + 4.7e-6) = 99kHz.

So we agree on what is expected. Have you tried several different
capacitors? This one may be mismarked.

The discrepancy of theoretical and experimental value appears also in other
"valid-practical" values of
Ra,Rb & C with different deviations. I have also tried the LinCMOS version
of 555 (TLC555) with the same results.
Another odd phenomenon, equally unwanted with previous one, is the
shifting of the produced frequency whenever
the value of power supply of the 555 is changed, always ofcourse within the
allowed limits (4.5->16Volts).

Is the supply well regulated? Do you have a bypass capacitor across
the supply pins of the chip? For *stable* supplies, the voltage
should have a very minor effect on frequency. Bumpy supply voltages
have a pronounced effect on the cycle.

The datasheets of the various 555 mention clearly that the HIGH and LOW
times, and hence the frequency, are
independent of the power supply.

--
John Popelish

 

[Dominic-Luc Webb]

I have a question concerning the function of the 555 oscillator in
astable mode.
In particular the external elements i have connected to the 555 are
those depicted at the
datasheets of all the 555 ics (LM555, NE555 etc). The 2 resistors are above
1K Ohm (Ra=1K & Rb=6.8K),
the C capacitor's value is greater than 0,0005uF (C=0,001uF) whereas a
0,1uF capacitor is connected
between the "Control Voltage" pin and the ground.

I am not the expert even with simple things like 555 timers, but
I have used them a lot (perhaps proving I am not engineer)...
Following info on my datasheets, that second cap (as opposed to
the timing cap) is often 10 nF. I cannot say this is the problem.
However, with regard to the timing capacitor, I have found large
differences between different types of caps and also variation
between different manufacturers of same types of caps with same
value. Also, most of us in here (including me) are hobbyists and
use surplus store components, which includes resistors. I rarely
buy or use 5% or even 10% tolerance resistors. The unmarked ones
are claimed to be 20% tolerance. I find they are better than this
at room temperate, but maybe they are not stable in a live circuit.
And then there are differences between 555 timers from different
vendors and most of us are not using the stringently toleranced
military grade ones that are rated for higher temperature stability.
I note that the 555 can get hot in some circuits. Many, including me,
are guilty of trying to get this poor little IC to drive more than
the couple of hundred mW it was intended to sink or source.

I once added up all these variations that I actually encountered
using my usual surplus shop components and could easily account
for nearly twofold discrepancies in frequency. I also suspect that
the info in the datasheet is really and truly valid for tightly
toleranced components.

Another permutation was the steadily increasing frequency which
disappeared once I changed the timing cap for another with exactly
same value from same vendor. I think these tiny caps can get damaged
during soldering and then misbehave.


Dominic

 

[John Fields]

On Mon, 13 Dec 2004 18:58:55 +0100, Dominic-Luc Webb <dlwebb@canit.se>
wrote:

I have a question concerning the function of the 555 oscillator in
astable mode.
In particular the external elements i have connected to the 555 are
those depicted at the
datasheets of all the 555 ics (LM555, NE555 etc). The 2 resistors are above
1K Ohm (Ra=1K & Rb=6.8K),
the C capacitor's value is greater than 0,0005uF (C=0,001uF) whereas a
0,1uF capacitor is connected
between the "Control Voltage" pin and the ground.


I am not the expert even with simple things like 555 timers, but
I have used them a lot (perhaps proving I am not engineer)...
Following info on my datasheets, that second cap (as opposed to
the timing cap) is often 10 nF. I cannot say this is the problem.
However, with regard to the timing capacitor, I have found large
differences between different types of caps and also variation
between different manufacturers of same types of caps with same
value. Also, most of us in here (including me) are hobbyists and
use surplus store components, which includes resistors. I rarely
buy or use 5% or even 10% tolerance resistors. The unmarked ones
are claimed to be 20% tolerance. I find they are better than this
at room temperate, but maybe they are not stable in a live circuit.

---
With decent 5% carbon film resistors with predictable characteristics
being about as common as dirt, you really ought to consider
"upgrading".
---

And then there are differences between 555 timers from different
vendors and most of us are not using the stringently toleranced
military grade ones that are rated for higher temperature stability.

---
According to Signetics' original data sheet for the 555, typical
spec's for the commercial NE (commercial temperature range) device
are:

MONOSTABLE ASTABLE
---------------------+-------------+-----------
INITIAL ACCURACY 1% 2.25%
TEMP SENSITIVITY 50ppm/°C 150ppm/°C
VCC SENSITIVITY 0.1%/V 0.3%/V


This is with Ra or Rb vaying from 2k to 100k, C equal to 0.1ľF, and
Vcc either 5V or 15V.

Certainly nothing here should result in a twofold change in output
frequency.
---

I note that the 555 can get hot in some circuits. Many, including me,
are guilty of trying to get this poor little IC to drive more than
the couple of hundred mW it was intended to sink or source.

---
600mW absolute maximum according to Signetics, and with output drive
of up to 200mA, it's a little gutsier than it might seem to be at
first glance.
---

I once added up all these variations that I actually encountered
using my usual surplus shop components and could easily account
for nearly twofold discrepancies in frequency. I also suspect that
the info in the datasheet is really and truly valid for tightly
toleranced components.

---
The info in the datasheet has nothing to do with the tolerances of the
components, it only has to do with the capabilities of the 555 itself.
If you want to determine the total variation in whatever of the
output, then of course you have to determine the contributions of the
several components and determine how they'll affect the output.
---

Another permutation was the steadily increasing frequency which
disappeared once I changed the timing cap for another with exactly
same value from same vendor. I think these tiny caps can get damaged
during soldering and then misbehave.

---
Yes; there's usually a soldering time/temperature spec associated with
caps which should be followed if you expect reliable and predictable
operation. Bottom line though, and no insult intended, I suggest that
if you want to build stuff which is going to work the way you want it
to, stop buying junk.







--
John Fields

 

[Dominic-Luc Webb]

I have a question concerning the function of the 555 oscillator in
astable mode.
In particular the external elements i have connected to the 555 are
those depicted at the
datasheets of all the 555 ics (LM555, NE555 etc). The 2 resistors are above
1K Ohm (Ra=1K & Rb=6.8K),
the C capacitor's value is greater than 0,0005uF (C=0,001uF) whereas a
0,1uF capacitor is connected
between the "Control Voltage" pin and the ground.

Poster got deviation from expected frequency.

differences between different types of caps and also variation
between different manufacturers of same types of caps with same
value. Also, most of us in here (including me) are hobbyists and
use surplus store components, which includes resistors. I rarely
buy or use 5% or even 10% tolerance resistors. The unmarked ones
are claimed to be 20% tolerance. I find they are better than this
at room temperate, but maybe they are not stable in a live circuit.

---
With decent 5% carbon film resistors with predictable characteristics
being about as common as dirt, you really ought to consider
"upgrading".

I do not care to upgrade because I have no need. A discrepancy
between theoretical and actual frequency and duty cycle always
occurs and this can be fixed by swapping timing caps and use of
one or more potentiometers at Ra and Rb. I have indeed used the
high precision components and still needed to tune the 555 to
get the exact outcome I want.

There are two issues developing here. One is that the poster got
a large deviation. This is not likely due to the vendor of the 555,
but smaller scale differences do exist between vendors. It could be
due to a bad timing cap resulting from mismarking, inaccurate
construction or damage during soldering. The timing cap is my usual
first suspect.

I once added up all these variations that I actually encountered
using my usual surplus shop components and could easily account
for nearly twofold discrepancies in frequency. I also suspect that
the info in the datasheet is really and truly valid for tightly
toleranced components.

---
The info in the datasheet has nothing to do with the tolerances of the
components, it only has to do with the capabilities of the 555 itself.
If you want to determine the total variation in whatever of the
output, then of course you have to determine the contributions of the
several components and determine how they'll affect the output.

Yes, we all agree.

Yes; there's usually a soldering time/temperature spec associated with
caps which should be followed if you expect reliable and predictable
operation. Bottom line though, and no insult intended, I suggest that
if you want to build stuff which is going to work the way you want it
to, stop buying junk.

"Junk", as you refer to it, is the stuff of life for many hobbyists. I
have learned much from junk. I have fixed a lot of junk. I have built
junk, and I have encountered many people who have praised my junk. Indeed,
I even maintain "The Astronomy Junkyard"....

http://www.megspace.com/science/stp/

Heck, the universe revolves around junk!

Dominic

 

[John Fields]

On Tue, 14 Dec 2004 14:26:46 +0100, Dominic-Luc Webb <dlwebb@canit.se>
wrote:

I have a question concerning the function of the 555 oscillator in
astable mode.
In particular the external elements i have connected to the 555 are
those depicted at the
datasheets of all the 555 ics (LM555, NE555 etc). The 2 resistors are above
1K Ohm (Ra=1K & Rb=6.8K),
the C capacitor's value is greater than 0,0005uF (C=0,001uF) whereas a
0,1uF capacitor is connected
between the "Control Voltage" pin and the ground.

Poster got deviation from expected frequency.

---
Yes, I know. That's what he said.
---

differences between different types of caps and also variation
between different manufacturers of same types of caps with same
value. Also, most of us in here (including me) are hobbyists and
use surplus store components, which includes resistors. I rarely
buy or use 5% or even 10% tolerance resistors. The unmarked ones
are claimed to be 20% tolerance. I find they are better than this
at room temperate, but maybe they are not stable in a live circuit.

---
With decent 5% carbon film resistors with predictable characteristics
being about as common as dirt, you really ought to consider
"upgrading".


I do not care to upgrade because I have no need.

---
My post wasn't directed to you, but rather to the OP, who was
complaining about exactly the sort of thing which might be remedied by
using components with tighter tolerances.
---

A discrepancy between theoretical and actual frequency and duty cycle always
occurs

---
I disagree. The theoretical response of the device always lies within
a _band_ defined by the errors inherent in the device itself and its
peripheral components and, such being the case, the _actual_ response
will always lie somewhere within the realm of that band.

If it doesn't, _that_ is when the discrepancy occurs.
---

and this can be fixed by swapping timing caps and use of
one or more potentiometers at Ra and Rb.

---
Rather a sloppy way of "designing", don't you agree?
---

I have indeed used the
high precision components and still needed to tune the 555 to
get the exact outcome I want.

---
Yes, surrounding a device inherently capable of only 1% accuracy with
0.05% resistors and capacitors to try to achieve an initial accuracy
of 0.1% has its problems.
---

There are two issues developing here. One is that the poster got
a large deviation. This is not likely due to the vendor of the 555,
but smaller scale differences do exist between vendors.

---
Reading the data sheet(s) will resolve that issue.
---

It could be due to a bad timing cap resulting from mismarking, inaccurate
construction or damage during soldering. The timing cap is my usual
first suspect.

---
OK, but that's more than two issues.
---

I once added up all these variations that I actually encountered
using my usual surplus shop components and could easily account
for nearly twofold discrepancies in frequency. I also suspect that
the info in the datasheet is really and truly valid for tightly
toleranced components.

---
The info in the datasheet has nothing to do with the tolerances of the
components, it only has to do with the capabilities of the 555 itself.
If you want to determine the total variation in whatever of the
output, then of course you have to determine the contributions of the
several components and determine how they'll affect the output.


Yes, we all agree.


Yes; there's usually a soldering time/temperature spec associated with
caps which should be followed if you expect reliable and predictable
operation. Bottom line though, and no insult intended, I suggest that
if you want to build stuff which is going to work the way you want it
to, stop buying junk.


"Junk", as you refer to it, is the stuff of life for many hobbyists.

---
One man's meat...
---


--
John Fields

 

[Dominic-Luc Webb]

and this can be fixed by swapping timing caps and use of
one or more potentiometers at Ra and Rb.

---
Rather a sloppy way of "designing", don't you agree?

John, others,

Depends on the application. If I wanted high precision timing,
I would use a crystal and would say that not using this is a
sloppy design to begin with. The lack of use of a crystal by the OP
suggests that the design is permitted to be a little "sloppy".
If precision timing is not needed, the use of the crystal
would constitute a sloppy thinking process, because it just adds
extra components and cost and maybe even trouble-shooting and
additional failure modes to the design. At least where I live
there is a drammatic price and time difference in buying precision
components (online usually) and picking the lower precision
components off the shelf at the local surplus shop. It sounds like
the OP will be quite content, and learn much (just like me), with
common lower precision components and a little tuning with a trim
pot.

I note that many multimeters have cap testers. No idea how accurate
they are, but since the timing caps seem to have higher inaccuracy
than the rest of the typical astable 555 circuit, I would think checking
the capacitance would be informative in predicting the frequency. In
worst case, one could get relative values to compare caps, which is
still helpful.

BTW... when I write "theoretical", I mean specific equations for
frequency and duty cycle using stated values on components Ra, Rb
and C. These equations are only approximations regardless of how precise
components you add to the 555. A case in point, for instance, a couple
somewhat different constants for the frequency constant in the
numerator for the astable calculation exist (1.49 and 1.44). These values
are mentioned in books about the astable mode and are discussed
independently of vendor, yet they differ by about 3.4%. Until now, I have
never heard anyone claim otherwise and have expected to have easily 5%
deviation from calculated frequency and/or duty cycle. Maybe you know
something I do not?

Actually, I have been curious about where that constant comes from to
begin with.

Dominic

 

[John Fields]

On Wed, 15 Dec 2004 19:36:55 +0100, Dominic-Luc Webb <dlwebb@canit.se>
wrote:

and this can be fixed by swapping timing caps and use of
one or more potentiometers at Ra and Rb.

---
Rather a sloppy way of "designing", don't you agree?

John, others,

Depends on the application.

---
I disagree. Whatever the application, and whatever the precision
required, having to go back and redo work because of careless errors
made is sloppy workmanship.
---

If I wanted high precision timing,
I would use a crystal and would say that not using this is a
sloppy design to begin with.

---
And by that logic, not using an OCXO would constitute a sloppy crystal
oscillator design, and so on up the chain...
---

The lack of use of a crystal by the OP
suggests that the design is permitted to be a little "sloppy".

---
Lack of crystal? You must be joking; the poor guy doesn't even know
where a 2:1 error in output frequency is coming from, and you've got
him sitting down deciding how much slop he can live with, before the
fact!
---

If precision timing is not needed, the use of the crystal
would constitute a sloppy thinking process, because it just adds
extra components and cost and maybe even trouble-shooting and
additional failure modes to the design.

---
How on earth did this crystal manage to work its way into the
discussion? It's certainly not relevant to the discussion, which is
about where a 555 timing error is coming from.
---

At least where I live
there is a drammatic price and time difference in buying precision
components (online usually) and picking the lower precision
components off the shelf at the local surplus shop. It sounds like
the OP will be quite content, and learn much (just like me), with
common lower precision components and a little tuning with a trim
pot.

---
Yeah, great.
---

I note that many multimeters have cap testers. No idea how accurate
they are,

---
Read the multimeter spec's...
---

but since the timing caps seem to have higher inaccuracy
than the rest of the typical astable 555 circuit, I would think checking
the capacitance would be informative in predicting the frequency. In
worst case, one could get relative values to compare caps, which is
still helpful.

---
???
---

BTW... when I write "theoretical", I mean specific equations for
frequency and duty cycle using stated values on components Ra, Rb
and C. These equations are only approximations regardless of how precise
components you add to the 555.

---
They're _not_ approximations, they're exact.

To determine how closely the device will conform to the equations
however, the device specifications must be read.
---

A case in point, for instance, a couple
somewhat different constants for the frequency constant in the
numerator for the astable calculation exist (1.49 and 1.44). These values
are mentioned in books about the astable mode and are discussed
independently of vendor, yet they differ by about 3.4%. Until now, I have
never heard anyone claim otherwise and have expected to have easily 5%
deviation from calculated frequency and/or duty cycle. Maybe you know
something I do not?

---
I suspect that's probably true.
---

Actually, I have been curious about where that constant comes from to
begin with.

---
The short answer is, "Because of the voltage divider".

The long answer follows:

If you look at the "front end" of a 555, you'll find a voltage divider
and two voltage comparators hooked up like this:


Vcc
|
[R]
|
+----|-\
| | >
TH>-----------|+/
|
[R]
__ |
TR>-----------|+\
| | >
+----|-/
|
[R]
|
GND

The first thing to notice is that since the resistors are all equal,
the voltages on the inputs of the comparators connected to the string
will always be 2/3 Vcc and 1/3 Vcc. That is, they will be
ratiometric. On top of that, since the resistors are all made of the
same material and are very nearly isothermal, temperature changes
affecting one resistor will affect all of them, with the result that
the voltages on the inputs of the comparators connected to them will
stay constant for changes in temperature.

Now, looking at a simplified diagram of a 555 hooked up as an astable
multivibrator:


Vcc Vcc
| |
[R] [Ra]
| U1A |
+----|-\ +---------------->OUT
| | >---+ | |
TH>--+---------|+/ | +-----+ | +-----+
| | +--|R Q|--+ | |
| [R] | _| D |
__ | | U1B +--|S Q|---G Q1 |
TR>--+-+-------|-\ | +-----+ S [Rb]
| | | >---+ | |
| +----|+/ GND |
| | |
+-----------------------------------+--Vth
| |
[R] [C]
| |
GND GND


Assume that the circuit has just been powered up and that C is at 0V
and is just beginning to charge up toward Vcc through Ra and Rb.


Then, since

T = k (Ra+Rb) C (1)


and, since

Vcc - Vth1
k = ln ------------ (2)
Vcc - Vth2

where Vth1 is Vth at turn-on and Vth2 is Vth at 2/3Vcc,


if C needs to charge to 2/3 Vcc to get U1A+ to go more positive than
U1A-, we can say:

3 - 0
k = ln ------- = ln 3 = 1.1
3 - 2

and, therefore:

T = k (Ra_Rb) C = 1.1RC


Once U1A+ goes more positive than U1A-, the output of the 555 will go
low, Q1 will turn on, and C will begin to discharge through R2.
However, since C only charged to 2/3 Vcc before Q1 turned on and
started discharging C, it will only have to discharge to 1/3 Vcc
before it goes more negative than U1A. Since this a voltage ratio of
2:1 we can write

2/3Vcc
k = ln --------- = ln 2 = 0.693
1/3Vcc


so the discharge time will be

T = k (Rb) C = 0.693 Rb C


This time, when the cap discharges to 1/3Vcc and starts charging
again, the same situation will prevail. That is, there will be 1/3Vcc
across the cap and it will have to charge to 2/3Vcc before the cycle
will start anew, so it will charge to twice the voltage that was
across it when it started to charge, so the time constant will be the
same as when it was discharging, but now it will be charging through
Ra _and_ Rb, so the time to get to 2/3Vcc will be longer than the time
it took to get from 2/3 Vcc to 1/3 Vcc. That's the reason for the
asymmetrical duty cycle.

Finally, since frequency is the reciprocal of time, we can write

1 1
f = ------ = ---------- = 1.44 Rc
k RC 0.693 RC


and that's where f = 1.44 RC comes from.


The other values you've seen may have been generated considering
leakage and bias currents.

--
John Fields

 

[John Fields]

On Wed, 15 Dec 2004 18:06:13 -0600, John Fields
<jfields@austininstruments.com> wrote:

On Wed, 15 Dec 2004 19:36:55 +0100, Dominic-Luc Webb <dlwebb@canit.se
wrote:


and this can be fixed by swapping timing caps and use of
one or more potentiometers at Ra and Rb.

---
Rather a sloppy way of "designing", don't you agree?

John, others,

Depends on the application.

---
I disagree. Whatever the application, and whatever the precision
required, having to go back and redo work because of careless errors
made is sloppy workmanship.
---

If I wanted high precision timing,
I would use a crystal and would say that not using this is a
sloppy design to begin with.

---
And by that logic, not using an OCXO would constitute a sloppy crystal
oscillator design, and so on up the chain...
---

The lack of use of a crystal by the OP
suggests that the design is permitted to be a little "sloppy".

---
Lack of crystal? You must be joking; the poor guy doesn't even know
where a 2:1 error in output frequency is coming from, and you've got
him sitting down deciding how much slop he can live with, before the
fact!
---

If precision timing is not needed, the use of the crystal
would constitute a sloppy thinking process, because it just adds
extra components and cost and maybe even trouble-shooting and
additional failure modes to the design.

---
How on earth did this crystal manage to work its way into the
discussion? It's certainly not relevant to the discussion, which is
about where a 555 timing error is coming from.
---

At least where I live
there is a drammatic price and time difference in buying precision
components (online usually) and picking the lower precision
components off the shelf at the local surplus shop. It sounds like
the OP will be quite content, and learn much (just like me), with
common lower precision components and a little tuning with a trim
pot.

---
Yeah, great.
---

I note that many multimeters have cap testers. No idea how accurate
they are,

---
Read the multimeter spec's...
---

but since the timing caps seem to have higher inaccuracy
than the rest of the typical astable 555 circuit, I would think checking
the capacitance would be informative in predicting the frequency. In
worst case, one could get relative values to compare caps, which is
still helpful.

---
???
---

BTW... when I write "theoretical", I mean specific equations for
frequency and duty cycle using stated values on components Ra, Rb
and C. These equations are only approximations regardless of how precise
components you add to the 555.

---
They're _not_ approximations, they're exact.

To determine how closely the device will conform to the equations
however, the device specifications must be read.
---

A case in point, for instance, a couple
somewhat different constants for the frequency constant in the
numerator for the astable calculation exist (1.49 and 1.44). These values
are mentioned in books about the astable mode and are discussed
independently of vendor, yet they differ by about 3.4%. Until now, I have
never heard anyone claim otherwise and have expected to have easily 5%
deviation from calculated frequency and/or duty cycle. Maybe you know
something I do not?

---
I suspect that's probably true.
---

Actually, I have been curious about where that constant comes from to
begin with.

---
The short answer is, "Because of the voltage divider".

The long answer follows:

If you look at the "front end" of a 555, you'll find a voltage divider
and two voltage comparators hooked up like this:


Vcc
|
[R]
|
+----|-\
| |
TH>-----------|+/
|
[R]
__ |
TR>-----------|+\
| |
+----|-/
|
[R]
|
GND

The first thing to notice is that since the resistors are all equal,
the voltages on the inputs of the comparators connected to the string
will always be 2/3 Vcc and 1/3 Vcc. That is, they will be
ratiometric. On top of that, since the resistors are all made of the
same material and are very nearly isothermal, temperature changes
affecting one resistor will affect all of them, with the result that
the voltages on the inputs of the comparators connected to them will
stay constant for changes in temperature.

Now, looking at a simplified diagram of a 555 hooked up as an astable
multivibrator:


Vcc Vcc
| |
[R] [Ra]
| U1A |
+----|-\ +---------------->OUT
| | >---+ | |
TH>--+---------|+/ | +-----+ | +-----+
| | +--|R Q|--+ | |
| [R] | _| D |
__ | | U1B +--|S Q|---G Q1 |
TR>--+-+-------|-\ | +-----+ S [Rb]
| | | >---+ | |
| +----|+/ GND |
| | |
+-----------------------------------+--Vth
| |
[R] [C]
| |
GND GND


Assume that the circuit has just been powered up and that C is at 0V
and is just beginning to charge up toward Vcc through Ra and Rb.


Then, since

T = k (Ra+Rb) C (1)


and, since

Vcc - Vth1
k = ln ------------ (2)
Vcc - Vth2

where Vth1 is Vth at turn-on and Vth2 is Vth at 2/3Vcc,


if C needs to charge to 2/3 Vcc to get U1A+ to go more positive than
U1A-, we can say:

3 - 0
k = ln ------- = ln 3 = 1.1
3 - 2

and, therefore:

T = k (Ra_Rb) C = 1.1RC


Once U1A+ goes more positive than U1A-, the output of the 555 will go
low, Q1 will turn on, and C will begin to discharge through R2.
However, since C only charged to 2/3 Vcc before Q1 turned on and
started discharging C, it will only have to discharge to 1/3 Vcc
before it goes more negative than U1A. Since this a voltage ratio of
2:1 we can write

2/3Vcc
k = ln --------- = ln 2 = 0.693
1/3Vcc


so the discharge time will be

T = k (Rb) C = 0.693 Rb C


This time, when the cap discharges to 1/3Vcc and starts charging
again, the same situation will prevail. That is, there will be 1/3Vcc
across the cap and it will have to charge to 2/3Vcc before the cycle
will start anew, so it will charge to twice the voltage that was
across it when it started to charge, so the time constant will be the
same as when it was discharging, but now it will be charging through
Ra _and_ Rb, so the time to get to 2/3Vcc will be longer than the time
it took to get from 2/3 Vcc to 1/3 Vcc. That's the reason for the
asymmetrical duty cycle.

Finally, since frequency is the reciprocal of time, we can write

1 1
f = ------ = ---------- = 1.44 Rc
k RC 0.693 RC


and that's where f = 1.44 RC comes from.


The other values you've seen may have been generated considering
leakage and bias currents.

---
Aaaarrghhh!!!

Charge time = t1 = 0.693(Ra + Rb)C

Discharge time = t2 =0.693 (Rb) C

Total period = T = t1 + t2 = 0.693 (Ra + 2Rb) C

1 1.44
Frequency = --- = --------------
T (Ra + 2Rb) C


--
John Fields