4th order butterworth filter

Hi Sebdarmy,

When operating at single supply, you must provide a sufficient DC bias (reference) on the inputs of the amplifier which will raise the signals away from the negative rail (gnd). I would also suggest the Analog Filter Wizard to help you design your desired filter.

Regards,

Jino

Here are a few things to consider regarding this filter design:

1) LT1886 is NOT unity gain stable. What that means is that it must always operate with closed-loop gain Av >= 10V/V, or it will be unstable and oscillate. It can be used for gains < 10, but it requires an external compensation capacitor in order to make sure it stays stable, as described on p. 10 of the datasheet.

The way the output is tied to -IN for both LT1886's in this design guarantees unity gain, which means this op-amp is guaranteed NOT to be stable. Simulations may not show this correctly since this kind of behavior is hard to capture in models, so I would recommend NOT relying exclusively on simulations to know whether something will ring or not. Bench results are the only way to be sure.

2) Stacking multiples of the same poles causes the -3dB point to shift. Since the two sections of this filter are identical, there are two of each pole. When poles are stacked, their effects are doubled, so two poles in the same location lead to a -6dB point, not a -3dB point, at the frequency of choice. This means the cutoff will be below the desired 20MHz.

3) The Sallen-Key architecture as shown is vulnerable to capacitive drive problems. The output of the first amplifier is connected directly via feedback to C6, 220pF. At 20MHz, the impedance presented by C6 is only 36 Ohm, so the op-amp's output also sees C5, 120pF via the 47 Ohm R6, since 47 Ohm is not large enough to isolate the second capacitor. Although bigger resistors add noise, a resistor at least comparable to the impedance presented by the caps is necessary to isolate the caps from the output of the op-amp.

Most op-amps will oscillate or ring if they are driving significant capacitance. For LT1886 in particular, on p 6, the plot "Frequency Response vs Capacitive Load" shows 6dB of gain peaking at 60-70MHz while driving 200pF alone, and the peaking only gets larger and lower in frequency as more cap load is added. A significant gain peak leads to ringing too, since a gain above 1 will be present at a frequency when the poles' effect has started knocking the phase margin down. 

Given all of these significant problems, I would recommend a different design approach. Here are two designs that should meet your requirements, for a 3rd and a 7th order Butterworth-equivalent filter at 20MHz cutoff that is free of all of the above problems.

Please let me know if you have further questions.