# What is the advantage of a Sallen-Key filter over a normal second order filter?

Wikipedia links to a Sallen-Key filter as a active low pass, so I tried it out with LTSpice.

The frequency response and phase response are not linear, instead frequency response even gets higher after 10kHz. Why is that, and why would I use a Sallen-Key filter instead of a "normal" low pass filter?

The Sallen-Key is on the blue line.

• Your "normal" second order appears to be a cascaded pair of first order filters. It'll always be overdamped. Sallen&Key allows full control of the damping factor. And above 10kHz you're running out of gain bandwidth product from the ancient LM324. Mar 1, 2017 at 21:32

What you call "normal" is a simple two-stage RC filter with very bad selectivity (two real poles only). In contrast. the Sallen-Key topology is capable of producing a second-order lowpass response with much better selectivity (higher pole Qp) and various possible approximations (Butterworth, Chebyshev, Thomson-Bessel,...).

However, there is one big disadvantage of the Sallen-Key structure - if compared with other active filter topologies (multi-feedback, GIC-filters, state-variable,...): There is a direct path (in your example: C4) from the input network to the opamp output.

That means: For frequencies much larger than the cut-off frequency the output voltage from the opamp is - as desired - very low. However, there is a signal coming directly through the C4 path which creates an output signal at the finite output resistance of the opamp. And this resistance is increasing with frequency!

As a consequence, the damping charactersitics of this filter are not as good as it should/could be. And thats what you have observed: The magnitude shows a rising characteristic for larger frequencies. (This unwanted damping degradation is not caused by limitations of the gain-bandwidth product).

Improvement: The situation can be improved by scaling the parts values: Smaller capacitors and larger resistor values.

Comment 1: This undesired property of any opamp circuit with a feedback capacitor (between output and input circuitry) can be observed also for the classical MILLER integrator.

Comment 2: So - are there any advantages the Sallen-Key filters have in comparison to other active filter structures? Yes - there are. Lets compare the two most frequently used topologies:

(1) Sallen-Key has very low "active sensitivity" figures (sensitivity against opamp non-idealities) and rather high "passive sensitivity" figures (sensitivity against passive tolerances).

(2) Multi-feedback filters (MF): High "active sensitivity" and low "passive sensitivity" figures.

Both sensitivities are rather important properties of all filters because they determine the deviations between desired and actual filter response (under IDEAL conditions all filter types would have identical performance properties).

• Now that you have added "the situation can be improved by scaling the parts values: smaller capacitors and larger resistor values" I can upvote your answer with complete peace of mind. :) Mar 1, 2017 at 22:13
• 'This is not caused by limitations of the gain-bandwidth product' - The output resistance of a closed loop system is directly determined by the gain, so I think the connection is stronger than you are suggesting. If the GBW was higher, the inflection point in the response would be higher too Sep 21, 2019 at 7:08
• I did not mention the GBW product at all. The effect I have mentioned is caused by the (desired) lowpass characteristics (decreasing opamp output signal) and - at the same time - an increased contribution of the direct path between input and output (through the feedback capacitor).
– LvW
Sep 21, 2019 at 8:01
• There is one sentence in the answer which suggests that the decreasing opamp output is not a result of limited GBW product. That's the only part which doesn't convince me immediately Sep 21, 2019 at 8:23
• The decreasing opamp output is, of course, the result of the desired lowpass function.
– LvW
Sep 21, 2019 at 10:44

At really high frequencies, such as higher than UnityGainBandWidth, the opamp has lost control of its Vout. Notice how this inverting single-pole lowpass has NON-INVERTING response to the fast input pulses. The Cfeedback allows the input charge to appear directly on the output.

Here is the circuit, and the OpAmp params:

The only reason the BODE (2nd screen-shot) has attenuation at higher frequencies is 'CL' 15pF forming LowPass with the 2 resistors into VirtualGround. [ If you want better High Freq attenuation, install 470pF cap to ground at middle of the 2 input resistors.]

You'll have fun, by editing the Amplifiers ROUT. And by enabling that input filter capacitor. And editing out that 15pF Cload.

This example is one of those BUILTIN (no SPICE knowledge needed) to Signal Wave Explorer, free to download from robustcircuitdesign.com for 19 unique days of use.

And Walt Jung, of Analog Devices, discussed this frailty of LPF decades ago.

Here is example of an opamp's MEASURED Zout (near 500MHz, looks like 10pF. 31 Ohms), for Active and for ShutDown modes:

• Note that this revelation ignores the prudent design that makes the input impedance much greater than the open loop output impedance. In this case Rout is 1k and Rin (dc)=1.5k which at test waveforms > 1Mhz as shown above makes the circuit a high pass filter that is obviously a poor choice of values. Scaling for a >10x higher Rin must be remembered to attenuate this weakness in GBW limitation. Notwithstanding if large signals above BW of OA are expected, prefiltering is essential. Mar 3, 2017 at 16:47
• The feedthru with rising f makes the Multiple Feedback cct a better choice over the Sallen-keys filter which has feed-forward pass-thru on the feedback cap where the Zout rises from lack of BW. Mar 3, 2017 at 16:51

You may choose from many configurations depending on your specs for group delay, Q, bandpass ripple, bandstop attenuation , skirt steepness.

Both Sallen-Key and Multiple Feedback can achieve the same results.

see below.

Both can achieve high gain limited by the GBW of the OP you choose.

This TI software can design any active filter and allows you choose from either configuration and choose resistor tolerances which selects the appropriate value. It doesn't allow you to specify input impedance so you can scale all RC values to suit this.

I chose Bessel response, so group delay is flat.