# Choosing resistor values for a 555 timer

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.

simulate this circuit – Schematic created using CircuitLab

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 $R_2$?

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").

• Looks like I get $R_1=128k$ and $R_2=16k$ Nov 23 '14 at 1:20

[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!