How to mathematically determine the frequency of a tone based on components being used

My REAL question is how to choose the right components if you want a specific frequency spit out from a 555. In my particular case I want a potentiometer to control an output frequency from 16Hz to 33000Hz (roughly the tones audible to humans), and need to know the values of all the other components in the circuit.

I was perusing Forest Mims' Engineer's Mini-Notebook V2, and came across the following adjustable frequency tone generator. The image export is a little wonky, but it's readable. If you've got the book handy, it's on page 60. What caught my eye was the formula and given table of values. Looking at the values, they just didn't seem to make sense, and I cannot get that formula to make any sense on paper given the components in the schematic. Using the 555 calculator, I can't make the math match the table either. It appears, however, that with a 4.7ohm resistor as R2, a 0.1uF cap for C1, a 100k-470ohm pot will deliver a range from 14 to 30037Hz. to

I'm trying to understand what I'm missing. If it's a simple "the book is waaaay wrong", fine...but I ALSO want to make sure I understand the math for the future.

My understanding of the formula is that R1 is my potentiomer, in Ohms. R2 is a non-variable resistor, also in ohms. But which cap of the two gets plugged in to the formula? do I total the caps? and what unit of measure is used in the formula? uF? pF? nF? F?

Is the info in the book bad? Are the numbers I came up with by playing with the calculator a better guesstimate of component values? Or is there something else I'm missing?

• Your 4.7 uF capacitor is only to remove the DC from the speaker coil, and has next to no bearing on the frequency of operation. Such calculations are usually in ohms and farads, unless they explicitly denote that other units have been pre-factored in. Feb 11 '13 at 3:53
• There is a small error in the diagram: pins 7 and 8 should never be connected. There should be a small resistor in series with the 1M potentiometer. (1k or so is sufficient) For a symmetric output you could excahnge the 1k resistor and the 1M potentiometer. As is, the circuit will generate short spikes (which might actually be OK). The LSP symbol shown is also wrong: the symbol is for a piezo speaker, but the text states 8 Ohm, which indicates a conventional (coil) speaker. Feb 11 '13 at 13:14

The formula is correct, but it's normally given as:

period = 0.693×(R1 + 2R2)×C

Since frequency = 1/period and 1.44 = 1/0.693, your formula is equivalent to this.

R1 is the variable resistor in the schematic, R2 is the fixed resistor, and the capacitor C is the one attached to R2. Units are in ohms and farads.

In case you're wondering where the 0.693 comes from, it's the natural log of 2, and this derives from how the 555 timer operates, driving the capacitor voltage between 1/3 Vcc and 2/3 Vcc.

Be aware that in the example circuit, you cannot allow the adjustable resistor to go all the way to zero ohms, as this would then tie the DIS (discharge) pin of the 555 directly to the power supply. The first time the chip tries to discharge the capacitor, it will short out the power supply.

The formula is right, but the table looks wrong for the values shown.

For the pot at 470k and 1k, and 10nF for the cap (the 4.7uF cap is from the speaker to ground, so as Chris says doesn't factor in the calculations) you would get:

1.44 / (470e3 + 2e3) * 10e-9 = 305Hz

Similarly for the 47k case:

1.44 / (47e3 + 2e3) * 10e-9 = 2938Hz

As a sanity check I confirmed these in a SPICE simulation also. So, I'm not sure how they arrive at the table values.