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I have to design a frequency counter using a 555 timer as a pulse generator. I included a schematic for part of the circuit, but this is my first time using a 555, so I also included the original circuit that it is based off, just in case I didn't translate it correctly. As shown, the values for \$C\$ and \$C_1\$ are \$1µF\$ and \$.1µF\$ respectively.

schematic

simulate this circuit – Schematic created using CircuitLab

enter image description here

We have an equation for the frequency

$$ f=\frac{1}{T}=\frac{1.44}{(R_1+2R_2)C}$$

And one for the duty cycle

$$ D=\frac{T_{H}}{T} (100\%) = \frac{R_1+R_2}{R_1+2R_2} (100\%) $$

I was assigned a value of 90% for \$D\$ and a value .1s for \$T_{H}\$. Using these values in the duty cycle equation I find \$T=\frac{1}{9}\$. Then using the equation for frequency I get the following relationship $$ R_1+2R_2=1.6\times{10^5} $$

Does this mean I can make \$R_1\$ and \$R_2\$ any value as long as they obey the relationship described above? My instructor gave us potentiometers and I think we have to somehow incorporate those in this part of the circuit. So should I pick a value for \$R_1\$ and adjust the potentiometer to the appropriate value for \$R_2\$?

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You have two equations in two unknowns.. you need to solve them for R1 and R2. From the duty cycle equation:-

\$ R_1 + R_2 = 0.9R_1 + 1.8 R_2\$

Solving--I'll let you do your own algebra, you'll get unique values for R1 and R2 (given C = 1uF). I'll note that vvy's answer is slightly off (s/he does say "around").

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    \$\begingroup\$ Looks like I get \$R_1=128k\$ and \$ R_2=16k \$ \$\endgroup\$ – Lefty Nov 23 '14 at 1:20
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[1]Theoretically YES.
Practically there are some constraints like:
* You cannot realize every other resistance value. However, ratios(as in your case) can be realized to a good degree of accuracy.
* The 555 internal circuitry exhibits some finite delay which limits the max freq in astable mode.

Datasheets do contain the tricky information's about such limits.

[2] Nope! Your R1 + R2 should be around 142k for the required High_time of 0.1 sec. But the fall time 0.011 sec requires R2 around 15.7k. So that's the theory, now the trouble is practically finding those resistance values.
Good luck!

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