I have designed this Sallen-Key to give a 2nd order low pass circuit with a cut-off frequency of 150Hz. Another design specification is that R1=R2 and C1=C2. The issue is when simulated on LT-Spice this sallen-key returns a low pass bode plot with a cut off frequency of around 100Hz. Have I calculated the resistor and capacitor values incorrectly? What could be causing this issue?
With equal values for both resistors and capacitors, the Q of the circuit is 0.5. At the natural resonant frequency of 2nd order filters, the Q value is the magnitude of the transfer function. So, at 159.15 Hz, the magnitude of the transfer function is half or down 6 dB. I expect that at around 100 Hz, the magnitude of the transfer function is down 3 dB.
Another design specification is that R1=R2 and C1=C2.
This will always mean a Q factor of 0.5 (critical damping = 1) and so, you would have to reduce both capacitors to produce a higher natural resonant frequency in order to get a 3 dB point at 150 Hz. It's the same for an RLC low pass filter too: -
In the design I've chosen R = 200 ohms, L = 100 mH and C = 10 uF to achieve a natural resonant frequency of 159.15 Hz and a Q of 0.5. In the upper graph I've position the cursor at 159 Hz and you can see that the magnitude of the transfer function is -6 dB.
In the lower graph I've moved the cursor to around 100 Hz and revealed that the magnitude is more like -3 dB.
Pictures from this interactive tool.
For the shown filter stage with equal components and a unity gain amplifier the Qp-value (pole quality factor) is Qp=0.5 and the POLE FREQUENCY is simply wp=1/RC=1000 rad/s or fp=159.2 Hz. This is the frequency where the phase shift is excatly -90 deg .
However, the pole frequency is identical to the 3dB cut-off frequency fo for Qp=0.7071 only (Butterworth response).
For Qp-values below 0.7071 (as in the present case) the 3dB cut-off fo is always lower than the pole frequency fp.
You should use a BODE diagram with better resolution (down to -10....-20 dB only). Then you will see that the display will be in accordance with these calculations.
Remark: In your case with Qp=0.5 there is a double real pole on the neg.real axis of the s-plane. For a SINGLE pole we have a 3dB cut-off at wp=wo. Hence, for a double pole we have -6dB at wp=1000 rad/s (fp=159. Hz)