Effect of capacitor type in an active filter circuit?

Question

Below is a unity-gain low-pass filter implemented with a Sallen–Key topology:

If C1 and C2 is large, are electrolytic capacitors recommended? Similarly, if C1 and C2 is small, are any type of ceramic capacitors recommended?

What types of capacitors can be used if C1 and C2 are in uF range and nF range for a good filter application?

I cannot find information on this.

EDIT:

Lets say the desired LP active filter cut-off is 50Hz.

I go to this amazing Sallen-Key Low-pass Filter tool and set R1=R2=3.3k and C1=C2=1uf.

And I obtain 48Hz cut-off.

These tools do not show the types of the caps.

And depending on the opamp I get TOTALLY different results in SPICE simulations.

So basically some tools do not suggest an opamp and some tools do not suggest capacitor types. And some tools offer weird resistor values like 3.1235869804k

My specs are as follows

• Bandwidth -3dB = ___Hz
• Frequency tolerance = ___%
• Gain at DC = ____ with tolerance ____%
• Bandstop rejection >=____ dB at frequency ____ Hz
• Band pass ripple <1dB Butterworth?
• Maximum R value should be___ ? due to Iio error=___uA

I have tried http://www.ti.com/lsds/ti/analog/webench/webench-filters.page

and my result is ......

Answer 1

Unfortunately, electrolytic capacitors only work with a positive voltage on the positive terminal; they conduct in the other direction, so they are only really good for power supply decoupling.

Choose a ceramic capacitor with an NPO or COG dielectric. Other dielectrics vary dramatically with temperature, so your filter response will change as the circuit warms up or on a cold day.

Also keep in mind that ceramic capacitors often have a tolerance of 5 or 10%. You must use a capacitor with a value close to but lower than the calculated value, and leave space in your layout to put smaller capacitors in parallel so you can hit your target.

Answer 2

Last Edition

When considering large C , dont' consider more than ~0.33uF until you consider larger R's 1st . If OA has high input bias current that may cause Vio offset voltage, then Change 0 ohm feedback to Vin(-) to matched R load on Vin(+) then the offset is reduced to the spec for Iio input offset current.(Iio x Req + Vio= Vio_total) x gain > = Voutput offset error

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Any GOOD designer knows how to define specs before attempting to choose parts. LEARN THIS. by defining as much as possible the following;

• Bandpass f
• Bandpass gain
• Bandpass ripple ( possible with higher than 2nd order)
• Stopband f (important breakpoint)
• Stopband min attenuation.
• rise time , latency or group delay
• step response % overshoot and/or resonant frequency & Qu
• single or split supply
• input Z (optional)
• max DC offset error and gain error,
• Vin CMRR requirements ( and differential impedance balance)
• supply voltage , supply noise and power consumption.
• group delay distortion and Q are other ways to specify some of the above characteristics.

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http://www.ti.com/lsds/ti/analog/webench/webench-filters.page

e.g. Here a gain of 10 for a single supply with Vcc/2 = Vref

R2C2 product of the filter for example cannot approach the leakage Rp*C of the capacitor, otherwise unity gain no longer exists. Rp is equiv parallel leakage.

What rise time? t= 0.35/ f-3dB YOu largest R possible such that 2% * Iin*R is acceptable offset with matched R's on each OA input with 1% tolerance.

• Tantalum Polymer = 0.1CV is the DC leakage current thus 10uF @10V = 10uA =V/R (ref AVX)
  • so 0.1CV= V/R thus RC = 10 seconds for all values and voltages for Tant. polymer
• Plastic , metal film PET Polyester film (polyethylene terephthalate)
  T >= 1000 seconds for C> 1.0uFand > 5000 seconds (0.33~1uF) and 15000 seconds (<0.33uF)

So PET caps are your best bet. with values < 0.33uF and large R values. up to 15ks/0.1uF *1%error= 1.5GOhm for 150 seconds with 0.1uF as minimum but much higher is possible with DC gain error managed.

REF KEmet: R82 Series, Radial, 5 mm Lead Spacing,

XR7 are poor C values with sensitivity to large -dC/dV unless highV rated relative to operating range. In which case NPO/COG are much more stable and accurate and low leakage but lower k so smaller C range in same size.

Answer 3

Capacitors really look like this in the physical world:

The metal (in the leads and MLC layers) creates inductance called Equivalent Series Inductance or ESL. All materials have resistance (there are no superconducting capacitors) so the resistance of all the materials can be summed into an Equivalent Series Resistance or ESR.

Most of the time the datasheet of the capacitor will list the ESL and\or ESR. ESL's are usually in the nH range and ESR's in the mΩ range. Because of this, it usually only becomes a problem at higher frequencies. The figure below shows capacitor impedance's of various caps, the ESL and ESR create a cutoff at higher frequencies that reduces the capacitors ability to 'pass' high frequencies. The impedance doesn't get affected by ESL until about 1Mhz for a 2.2uf ceramic capacitor, so if your designing a filter with cutoffs below 1Mhz and below a 2.2uF capacitor you wouldn't even have to worry about parasitic effects.

Same goes for resistors, however the resistor model looks like this:

Source:EDN: Resistors aren't resistors

These effects are best modeled in a spice package, and you can get the ESL and ESR and use series model of a capacitor to see what effects they will have on your active filter circuit.

If you don't want to model it you can use a series impedance model in place of the capacitor or resistor where:

\$Z_{R} = R \$
\$Z_{L} = j \omega L \$
\$Z_{C} = \frac{-j}{\omega C} \$

And for a series model:

\$Z_{total} = Z_{R}+Z_{L}+Z_{C} = R +j \omega L+ \frac{-j}{\omega C} \$

And then use the \$Z_{total}\$ for each element to find the total transfer function (there are three parameters for each of the parasitic elements of each component).

$$ \frac{V_{out}}{V_{in}}= \frac{Z_3 Z_4}{Z_1 Z_2 + Z_3(Z_1 +Z_2) +Z_3 Z_4}$$

If there is a problem with parasitics, there are low-ESL capacitors and XY caps that are more expensive but better for high frequency applications.

Answer 4

You mention high time constant (very low cutoff frequency) filters. Others have made nice answers about capacitor ESL/ESR and high frequency effects, so I'll focus on low frequency stuff.

First, you got to decide what precision you want on the cutoff frequency and overall response of your filter. High value caps (like electrolytics) usually have extreme tolerances, like -20/+50%.

High-K ceramics like X7R change value with temperature (by a lot!) and also with voltage (which creates enormous distortion in your signal). They are also excellent microphones due to piezoelectric effects. Never use X7R/Z5U and the like in any kind of precision analog stuff! They are designed for decoupling, and excellent in that role.

Electrolytics' ESR varies with temerature, too, and the capacitance tolerance is huge. And there is dielectric absorption, which will screw your filter response at very low frequencies.

Only film and C0G ceramics types have reasonable precision, low temperature coefficient, and are generally what we would consider as "stable" in a wide, usable temperature range.

So, if you don't care about frequency response accuracy and only want a DC-blocking cap, then you can use electrolytics. In a filter, you'll have to worry about ESR, leakage, and dielectric absorption.

If you do care about accuracy, then your only choices are C0G/film types, which are only available in low capacitance values. Film caps are also expensive.

And large thru-hole film caps are microphonic, too, and subject to dielectric absorption... unless you use polystyrene or polycarbonate... which is even more expensive.

Bummer.

This is why you're going to implement your filter using one of these methods:

• Use FET input opamps and large resistor values, which allow smaller caps, which allows you to choose the good caps: C0G, PPS, polystyrene, polycarbonate, polypropylene... Most practical solution really...
• Obsess over low noise, pick an ultra low noise BJT input opamp, then pick low resistor values because of input current noise, then pick huge caps, then realize too late they are unaffordable and microphonic.
• Worst case is when you need to pass HF signal, but also filter LF out. This will get you a fast path with a fast opamp, and the lowpass implemented as a DC servo with a FET opamp.
• Sample the signal and use a digital filter. If you need low cutoff frequencies, then a slow sampling rate is OK, a micro implementing an IIR filter will do the trick. Of course you need to worry about rounding errors and quantization noise now. If your filter is placed before an ADC, then you should decide which parts of the filter you should implement in analog, and which parts in digital.

Answer 5

Besides all the answers already posted, if you really insist in using electrolytic capacitors, you can add two in series with common pins: see this answer.