# Powers of 10 in cutoff frequency formula for capacitor

I need to know which values in this formula should have some powers of 10 applied.

I'm using the formula:

Fc = 1 / (2π R C)

to find the capacitor value needed in-line to cut low frequencies from a pair of 6-ohm tweeters I just bought. Their low freq is listed at 5k, but I'd like to start with a cutoff around 8k.

Wanting to cut off at 8kHz and solving for C, I use

1 / (2π * 6 * 8000) = 3.316e-06

Are there some powers of 10 to consider, like "well Ohms really means kilo-ohms, so multiply by 1k" or similar? Similar to how 1 Calorie = 1000 calories? Farads vs microfarads maybe?

I found a value the other day, looked for capacitors of that size, and they're the type used in safely starting air conditioners. At least I'm a decent at soldering. :-}

• You can find 3.3uF capacitors in a 0402 case - 0.04"x0.02", the size of a moderate grain of sand...they're just rated for 4V. What voltage do you expect to see in this application?
– vir
Commented Sep 8, 2022 at 19:51
• Note that a capacitor+inductor (here the speaker voice coil) = resonant tank. Tanks are noted for their ability to produce "resonant" voltages way higher than the input voltage. Now a speaker generally doesn't resonate (that'd sound awful) but it may be possible to have some certain frequency input create a higher-than-expected voltage across the capacitor. To prevent the cap from failing due to unforeseen over-voltage, choose a voltage rating that is significantly higher than anticipated. i,.e., if 200W and 35V are expected, I'd pick a 50V one. Commented Sep 8, 2022 at 21:13
• Thanks for all the information, this greatly helps. @rdtsc for my little 40-watt desktop amp connected to my computer, I figured that 16 volts would be a reasonable max limit. So I bought Panasonic film capacitors rated at 100v, as they seemed quite adequate, and were around a buck and a half each. But good point regarding resonant frequencies. I hadn't thought about that increasing what I'll call the back-voltage. Commented Sep 9, 2022 at 23:54

No 10X tricks here. That is a 3.3 microfarad capacitor, a common value.

Next you need to pick the type, polarized or not, & voltage rating.

For a speaker crossover you want a quality capacitor that doesn't have microphonic issues. A film capacitor is a good choice. These are always non-polarized (you want non-polarized).

Next calculate the voltage rating needed:

Power = Voltage squared divided by resistance.

Or, V = sqrt(P * R)

Your amp probably isn't more than 200W, so V = sqrt(200 * 6) = 35 V

Add some margin, you don't need much margin here since the power probably already has some margin.

Digikey sells quality components, that is where I buy most of my components.

• Excellent explanation Mattman944! That really clarified everything I need. Thanks Commented Sep 8, 2022 at 20:38

In that formula:
F = frequency in hertz
R = resistance in ohms