# How can I determine if a Sallen-Key filter will be stable using LTSPICE and analytical expressions?

I am trying to determine if a Sallen-Key filter that I designed will be stable. In order to do this, I am trying to simulate the filter in LTSpice and measure its open-loop phase margin.

The filter is designed to have a cutoff frequency of 150kHz, but the operational amplifier that I would like to use, the LMV358, has a GBW of 1MHz. This means that the open loop gain at high frequencies will be very low.

I have set up the simulation below to try and estimate the open-loop gain (V(FB) / V(INB)):

As you can see the magnitude of the open-loop gain seems about right. But the phase seems wrong to me.

• Why is the phase increasing?
• Why is it starting out at -180°?

Analytically, I can estimate the frequency of the Op-Amp dominant pole response and that introduced by the output capacitive load, which in this simulation seems tobe fairly small.

The poles introduced by the filter however are estimated under the assumption of infinite open-loop gain, which is not valid anymore here since the loop gain drops to low values around the supposed filter cutoff frequency. How can I estimate the effect of C2 and C3 in this case?

Also, one final question:

• Should I use another operational amplifier with a higher GBW?
• I don't think the GBW is much of an issue; but many other things could be. What kind of signal amplitude will be fed in to the circuit (and needs to come out of it as you want gain of 1)? Jul 19, 2023 at 20:33
• @Justme are you thinking about saturation of the opamp? Or slew rate limitation? It should not saturate in its bias point, and the small-signal input should be rather small. Either way, the signal should be a 5V DC value max. The filter is only there to clean it up a bit. Jul 19, 2023 at 20:43
• The output amplitude starts to drop at 50 kHz or so already. At 200 kHz amplitude can be only below 2Vpp. And if it is powered with 5V, the input supports voltages only up to 4V. Jul 19, 2023 at 20:51

That is a classical representation of a typical open loop gain and phase shift. No need to worry; this is as you would expect with a "twist" at high-frequencies.

Why is the phase increasing?

The phase begins at -180° and by 1Hz has risen to -90&deg. This is because an open-loop op-amp exhibits the behaviour of a very high-gain system fed into a low-frequency low-pass filter (think integrator). Pretty normal and nothing strange happening at all.

Above 10 kHz other things take over and, feed-through of your input signal will be one of these because the op-amp output impedance is no-longer less than a few ohms as seen at low frequencies and you will get your input signal passing through C2 to the output or, in your test circuit, V3 will couple to the no-inverting input.

Why is it starting out at -180°?