Searching operational amplifier (op amp) specifications for the perfect partner to your active filter can be a bit of a challenge as you look at the possible amplifier specifications.
First things first; do not consider using a current-feedback, comparator or instrumentation amplifier. Comparators are not tuned to be circuits that will accept precision gains and the feedback resistor of current-feedback amplifiers is very limited. Start by looking only at voltage-feedback amplifiers.
Selecting the correct voltage-feedback amplifier for an active filter circuit can be overwhelming. It takes a few times through an amplifier data sheet to come to this realization. But, in reality, there are only four specifications that you should consider when selecting an amplifier for any type of filter, whether it be a lowpass, highpass, bandpass or even a bandstop filter (Figure 1). Those are: 1) amplifier bandwidth, 2) input bias current, 3) input common-mode voltage, and 4) slew rate.
Figure 1
Today, I’m going to talk about amplifier bandwidth. I’ll explore input bias current, input common-mode voltage and slew rate in future posts.
When designing a filter, you should first determine the corner frequency (fC, lowpass and highpass) or center frequency (f0, bandpass and bandstop) of your filter, along with the rate of attenuation as the frequency increases and/or decreases.
Once this is complete, you’ll determine the approximation type (Butterworth, Bessel, Chebyshev, etc.). Many filter programs are available, such as the new Texas Instruments WEBENCH® Filter Designer, to help you through this process.
Once this is complete, you’ll need to select the proper amplifier.
With a unity-gain filter, the old “rule-of-thumb” is to make amplifier unity-gain bandwidth 100 times higher than fC or f0. This simple estimation will work for 1st order and 2nd order filters if Q (quality factor) is less than one. If a filter has a Q greater than one, gain errors will occur with this “rule-of-thumb” 100 x multiplier.
Determining Q for lowpass and highpass filters is different from bandpass and bandstop filters. For lowpass and highpass filters, Q of each stage is equal to:
The lowpass filter transfer function is:
The highpass filter transfer function is:
For bandpass and bandstop filters, Q of each stage is the ratio of the mid-frequency, f0 to the bandwidth at the two 3-dB points (f1 and f2).
You should use the equations below to determine the required frequency bandwidth for each stage of the filter with this equation.
If you want to select one amplifier for the entire filter, find the filter stage that has the highest Q.
Figure 2 shows a table of the Butterworth lowpass coefficients for filter orders 1 through 6.
Figure 2. Highlighted values are for a 4th order, Butterworth lowpass filter with transfer function coefficients1
The first column in Figure 2 describes the filter order. The second column describes the number of stages for that filter order. The highlighted area encompasses a two stage, 4th order, lowpass filter. The second filter (two pole) in this 4th order filter has the highest Q value (1.31).
As an example, assume A0 = 1 V/V and fC = 1 kHz. For this 4th order lowpass filter, the minimum amplifier bandwidth is 131 kHz (Qi = 1.31). Note that this is higher than 100 x fc! Also, the minimum amplifier bandwidth for stage one of this filter is 54 kHz. This is significantly lower than the 100 x fC value!
This change in an amplifier’s bandwidth is a surprise, but Eq. 5 is a good way to obtain a definitive answer.
If you are curious, spend some time examining various filters using the WEBENCH Filter Designer software. This software will tell you the acceptable minimum bandwidth for your filter amplifiers.
Be sure to check back for my future posts on input bias current, input common-mode voltage, and slew rate. Or better yet, email subscribe to the blog, and you’ll get an email whenever I post – about once a week. Just scroll up, and you’ll see the subscription box on the top right.