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Rescaling resistors on a 555-timers

R

Rikard Bosnjakovic

Jan 1, 1970
0
I'm having an astable 555-timer with R1 = 8k2, R2 = 100, C = 1.5uF.

Using these formulas:

T1 = 0.693 * (R1 + R2) * C [ ms ]
T2 = 0.693 * R2 * C [ ms ]
F = 1.44 / [ (R1 + 2*R2) * C ] [ kHz ]

for my R1, R2, C, will yield these results:

T1 = 8.62785 (ms)
T2 = 0.10395 (ms)
F = 0.1142857 (kHz)

So far so good.


The problem is now that I need to lower C to 1uF and still try to retain
T1, T2 and F as much as possible. For 100% accuracy, I simply reevaluate
the equation and extract.

First R2:

R2 = T2 / (0.693*C)
R2 = 150k

then R1:

T1 / (0.693*C) = R1 + R2
R1 = T1 / (0.693*C) - R2
R1 = 12.3M

Verifying with the equation for F:

F = 1.44 / [ (12.3M + 2*150k) * 1u)
F = 1.44 / (12.6M * 1u)
F = 1.44 / 12.6
F = 0.1142857

This means that the new values for R1 and R2 are correct, since all of the
variables T1, T2 and F are correct.

However, a resistor of 12.3 megaohms sounds pretty silly, so going for
100% accuracy on T1 and T2 is probably not a good idea. What I'm doing is
not rocket science, but a small pulse generator. The problem is that I
don't have any 1.5uF-caps at home, and buying one of them will cost me
$12. That's not an option, and that's why I have to rescale the resistors
to fit my needs.

As a last resort, I can ofcourse use 1uF in parallell with two 1uF in
series to get 1.5 uF total, but I would prefer - if possible - just
changing the resistor values.

Unfortunately, this type of equation system is too difficult to me, so I
would appreciate a hand.
 
P

petrus bitbyter

Jan 1, 1970
0
Rikard Bosnjakovic said:
I'm having an astable 555-timer with R1 = 8k2, R2 = 100, C = 1.5uF.

Using these formulas:

T1 = 0.693 * (R1 + R2) * C [ ms ]
T2 = 0.693 * R2 * C [ ms ]
F = 1.44 / [ (R1 + 2*R2) * C ] [ kHz ]

for my R1, R2, C, will yield these results:

T1 = 8.62785 (ms)
T2 = 0.10395 (ms)
F = 0.1142857 (kHz)

So far so good.


The problem is now that I need to lower C to 1uF and still try to retain
T1, T2 and F as much as possible. For 100% accuracy, I simply reevaluate
the equation and extract.

First R2:

R2 = T2 / (0.693*C)
R2 = 150k

then R1:

T1 / (0.693*C) = R1 + R2
R1 = T1 / (0.693*C) - R2
R1 = 12.3M

Verifying with the equation for F:

F = 1.44 / [ (12.3M + 2*150k) * 1u)
F = 1.44 / (12.6M * 1u)
F = 1.44 / 12.6
F = 0.1142857

This means that the new values for R1 and R2 are correct, since all of the
variables T1, T2 and F are correct.

However, a resistor of 12.3 megaohms sounds pretty silly, so going for
100% accuracy on T1 and T2 is probably not a good idea. What I'm doing is
not rocket science, but a small pulse generator. The problem is that I
don't have any 1.5uF-caps at home, and buying one of them will cost me
$12. That's not an option, and that's why I have to rescale the resistors
to fit my needs.

As a last resort, I can ofcourse use 1uF in parallell with two 1uF in
series to get 1.5 uF total, but I would prefer - if possible - just
changing the resistor values.

Unfortunately, this type of equation system is too difficult to me, so I
would appreciate a hand.

Assuming R2=100k, and your formulas for T1, T2 and F are correct, I achieve
the next results:

T1 = 112ms
T2 = 104ms
f = 4.6Hz

So recheck your calculations.

There's no rocketscience in rescaling the R's. As you divide your capacitor
by 1.5, you'll have to multiply the resistors by the same amount. Just
substitute in the formulas. So R1=12k3 and R2=150k. Most commonly used
resistors have 5% tolerance. Capacitors even more. So R1=12k will be the
right choice.

petrus bitbyter
 
J

Jasen Betts

Jan 1, 1970
0
I'm having an astable 555-timer with R1 = 8k2, R2 = 100, C = 1.5uF.

Using these formulas:

T1 = 0.693 * (R1 + R2) * C [ ms ]
T2 = 0.693 * R2 * C [ ms ]
F = 1.44 / [ (R1 + 2*R2) * C ] [ kHz ]

I think you have the wrong units - should be seconds and Hertz,
for my R1, R2, C, will yield these results:

T1 = 8.62785 (ms)
T2 = 0.10395 (ms)
F = 0.1142857 (kHz)

So far so good.


The problem is now that I need to lower C to 1uF and still try to retain
T1, T2 and F as much as possible. For 100% accuracy, I simply reevaluate
the equation and extract.

First R2:

R2 = T2 / (0.693*C)
R2 = 150k

then R1:

T1 / (0.693*C) = R1 + R2
R1 = T1 / (0.693*C) - R2
R1 = 12.3M

Verifying with the equation for F:

F = 1.44 / [ (12.3M + 2*150k) * 1u)
F = 1.44 / (12.6M * 1u)
F = 1.44 / 12.6
F = 0.1142857

This means that the new values for R1 and R2 are correct, since all of the
variables T1, T2 and F are correct.

There's an easier way to do the math, if you divide the capacitance by 3/2
then multiply the resistance by the same amount.

12M is kind of high to use with a 555 -- hmm somhow you've gone from a
reasonable 8K2 upto 12M3 --- there's an error in your arithmetic...
All your answers are out by a factor of 1000

also How precise is the capacitor - it's pointless using 1% precision
resistors if the capacitor is temperature sensitive and only made to 10%
precision.

Ihe 12.3M should be 12.3K use a 12K resistor - that should be close enough,
the other resistor 150 ohms - a standard size,

Bye.
Jasen
 
D

Dan Hollands

Jan 1, 1970
0
--
Rikard Bosnjakovic said:
I'm having an astable 555-timer with R1 = 8k2, R2 = 100, C = 1.5uF.

Using these formulas:

T1 = 0.693 * (R1 + R2) * C [ ms ]
T2 = 0.693 * R2 * C [ ms ]
F = 1.44 / [ (R1 + 2*R2) * C ] [ kHz ]

for my R1, R2, C, will yield these results:

T1 = 8.62785 (ms)
T2 = 0.10395 (ms)
F = 0.1142857 (kHz)

So far so good.


The problem is now that I need to lower C to 1uF and still try to retain
T1, T2 and F as much as possible. For 100% accuracy, I simply reevaluate
the equation and extract.

First R2:

R2 = T2 / (0.693*C)
R2 = 150k

then R1:

T1 / (0.693*C) = R1 + R2
R1 = T1 / (0.693*C) - R2
R1 = 12.3M

Verifying with the equation for F:

F = 1.44 / [ (12.3M + 2*150k) * 1u)
F = 1.44 / (12.6M * 1u)
F = 1.44 / 12.6
F = 0.1142857

This means that the new values for R1 and R2 are correct, since all of the
variables T1, T2 and F are correct.

However, a resistor of 12.3 megaohms sounds pretty silly, so going for
100% accuracy on T1 and T2 is probably not a good idea. What I'm doing is
not rocket science, but a small pulse generator. The problem is that I
don't have any 1.5uF-caps at home, and buying one of them will cost me
$12. That's not an option, and that's why I have to rescale the resistors
to fit my needs.

As a last resort, I can ofcourse use 1uF in parallell with two 1uF in
series to get 1.5 uF total, but I would prefer - if possible - just
changing the resistor values.

Unfortunately, this type of equation system is too difficult to me, so I
would appreciate a hand.

Thats why if you need precise values variable resistors are used so that you
can tweak the R value to get the precise pulse width you need.

Dan

--Dan Hollands
1120 S Creek Dr
Webster NY 14580
585-872-2606
[email protected]
www.QuickScoreRace.com
 
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