# Capacitor Types and Active Filters

#### TrevorP

Joined Dec 8, 2006
55
Hey all,

I'm working on a little hobby project which has led me to designing a low-pass filter with a cut-off frequency of 150Hz (300pi rad/s). The input signal will have an amplitude of 1V and frequencies varying from 40Hz - 20kHz. Since this will be dealing with sound I've chosen a second-order Butterworth filter in a Sallen-Key configuration. I've derived the following two equations using the normalized Butterworth polynomials:

$$C_{2}(R_1 + R_2) = \frac{\sqrt{2}}{\omega_c}$$
$$C_1C_2R_1R_2 = \frac{1}{\omega_c^2}$$

(Using the circuit configuration shown here: http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Sallen-Key.svg/450px-Sallen-Key.svg.png)

Now, I have a couple of questions:

1. For this filter what kind of Capacitor should I use? This range of frequencies seems pretty much a grey-zone Tantalum Capacitors. Do I need to choose capacitors which are ideal for the range I want to pass, or the range I want to filter out?

2. What assumptions should I make when determining the components? Is it better to choose capacitors, then figure out resistor values? Is it safe to say C1 = C2 (so I don't have to buy two different capacitor values?)

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#### beenthere

Joined Apr 20, 2004
15,819
Tantalums are good for ripple filtering and sloppy time constants, but not for audio filtering. They are polarized, for one thing.

Your filter breakpoint is only as good as the component accuracy. If you can find a film capacitor with at least 5% accuracy (2% is much better), use that. Capacitor values jump more than resistor values, so select the capacitors first. You can always use multiple fixed resistors or even trim pots to get the correct resistance.

#### Wendy

Joined Mar 24, 2008
22,547
Three resistors in parallel should get you within 0.1% of anything, however if you are using a DVM their typical accuracy is around 1%, so that is more of a limiting factor I would think.

My understanding of electrolytics (of which tantalums are a subset) is they also drift a bit, as compared to other types. You can make a polarized capacitor into nonpolarized by putting them back to back, but this also halves the capacitance (and doubles the voltage). #### TrevorP

Joined Dec 8, 2006
55
Is there a good way to go about choosing capacitor values for something like this? I first tried setting C1 = C2, but that gives me imaginary values for the resistors. I finally figured out that if C1 > 2C2 I can solve for real resistances. So I tried 10nF and 1nF. But this gave me resistances of 79.2k and 1.42M. Then I tried 1uF and .1uF, and this gave me resistances of 75u Ohms and 15k. Is there a better way to do this than just guessing?

#### TrevorP

Joined Dec 8, 2006
55
Ok, so I got some reasonable numbers by plotting resistances as a function of Capacitances and getting reasonable numbers. Now, I have a question related to OP-AMPs and audio.

Is it better to couple and bypass the incoming audio signal, or use +/- supply lines to the op-amp? I have a ~8V DC supply, so would it better to somehow create a -8V source from that and then use that to drive the op-amp? (Are there voltage regulators that have positive and negative output?)

#### nickw1881

Joined Dec 25, 2009
31
I don't know what your goal is, but I have found that the easiest way to make a second order sallen-key active filter is to use one value of resistor and one value of capacitor, then put the filter opamp in a voltage follower configuration and use a second opamp to provide the gain. This way, you get a double pole at 1/(2piRC) with low peaking, and the second opamp will amplify the output to the required level.

You should be able to find switched capacitor inverter on digikey for very cheap.

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