# How do I properly size the components for an RC filter?

### Background

I'm filtering low-speed signals from some 5V automotive sensors. That is, their signal is within 0-5V and less than 1kHz. As such, I have selected a 1.3Kohm 1% resistor and a 0.1uF C0G capacitor, giving me a corner frequency of around ~1.2kHz. Both are 0603 packages.

### The Real Question

What I am curious on is... is there more to the filter than just the values? Does the package size of the RC components influence filtering, one way or another, based on the frequencies, or even voltages, that I'm working with? Aside from things like microphonics or temperature-based fluctuations (which I'm trying to deal with by going with C0G capacitors, etc)... is there anything else I should be looking at more closely?

• Just for clarity, by "size", do you mean physical dimensions or something else? – Alfred Centauri Jul 7 '12 at 0:00
• Yes. I know my resistors need to handle a given amount of power, but as far as physical dimensions go... I'm curious if package size is important here in regards to enhancing filter performance... or even if package size is critical to not hampering performance. – Toby Lawrence Jul 7 '12 at 0:28

It's a reasonable question. For much, much higher frequencies than you're working at, the non-ideal characteristics of physical components become significant and at higher still frequencies, electrical components can no longer be considered "lumped elements".

However, I think it's highly unlikely that any of these considerations are even remotely important for a simple 1st order filter with a corner frequency of 1kHz.

Consider, for example, classic vacuum tube audio / musical instrument circuits working over the audio band (20Hz - 20kHz), with much larger voltages, using point-to-point wiring and much larger, leaded components.

An simple first order passive R-C filter has a time constant of $\tau=R\cdot C$, and the cutoff frequency is $\frac{1}{2\pi RC}$. If you know your cutoff frequency, then fix R and set C or vice-versa. I think it's easier to find resistors over a broader range, so I prefer to pick an easy to source capacitance and let that drive my required resistance.

Resistors are rates for power, and you can use the equation $\frac{V^2}{R}$ to figure out what the required power dissipation will be for a given voltage drop and resistance is, and you should typically derate that by some amount (say 80%).

Capacitors have a voltage rating that must be respected. Capacitors also have something called an ESR or equivalent series resistance, which you typically don't need to worry about in filter applications unless your resisors are tiny, and in that case you should probably drop your capacitance by an order of magnitude and increase your resistance accordingly.

Both resistors and capacitors have coefficients that dictate how their electrical properties vary with temperature, which may or may not matter depending on your application.

• I went and modified the original post to give more details. I have sized both the resistor and capacitor for cost and requirements. Given my 5V input signals and the resistance I've chosen, I landed with 0603 being the simplest to source package size. So, with that in mind... my question would be: should I be striving for small packages for better filtering performance? Should I actually prefer bigger packages? etc etc – Toby Lawrence Jul 7 '12 at 0:47