Difference between using a first order low pass filter and a second order

So I have the following schematic. Basically what it does is , first it has an oscillator that produces a triangular wave (not from op amp output , but by taking a wire after the capacitor C1) . After that we have a band pass filter that is used to take the high frequencies and the DC offset from the signal , so we produce an AC sine wave. My question is for the third part(the red highlighted one) . I am asked to use a second order low pass filter like the one in the schematic. Why is that , why wouldn't I use a first order low pass filter , is there a difference in the wave if we use a first order low pass filter instead of a second order?

Εdit: I looked up the wikipedia entry which states:" The Bode plot for this type of filter resembles that of a first-order filter, except that it falls off more quickly." Can this be explained using the Xc (capacitive reactance) and solving the circuit?

• You've entered the circuit in a simulator. If you simulate the first order circuit and second order circuit, what difference do you see in the outputs? Dec 4, 2017 at 19:16
• Αctually I have a problem simulating this circuit , can't understand why , thus the question here. I am also shooting for a theoretical approach here . What is the best to use , why use this one here , does it change anything??
– user170589
Dec 4, 2017 at 19:17
• Sharper cut-off of course ! Dec 4, 2017 at 19:18
• @calcium3000 I actually explain what you are asking . The output of the first op amp is purposely left like that . I take the output in the wire between C1 and R1 so I get the triangular wave and not a square wave
– user170589
Dec 4, 2017 at 19:19
• No, the Vcc 20V is an input source. You need power for the op-amps, seen by the disconnected vertical pins with the + and - labels. Dec 4, 2017 at 19:24

1 Answer

It depends on your spec for harmonic distortion or SNR ratio with the harmonics being noise. It also depends on your group delay stability on the fundamental if DC phase stability matters.

Comparing the fundamental as a signal only and the rest as noise;

A square wave has a SNR of about 8dB.

A triangle wave has a SNR of about 16dB.

A 1st order LPF drops -3dB if the breakpoint is at the fundamental then -12dB per successive odd harmonic thus a gain in SNR of about 8dB to 9dB harmonic.

A 2nd order LPT doubles the above SNR improvement to 16~18dB
A 3rd order LPT triples to 24~27dB
A 4th order LPT quadruples to 32 ~36 dB improvement on the original 16dB triangle.

Whereas a -40dB 2nd order notch filter can do even better on 3f with the 2x-LPF and a recursive notch filter even better.

why wouldn't I use a first order low pass filter ?

It depends on your spec for sine spectral purity in dB ( 40dB ok ? or 50 or 60dB? )

• Does frequency stability matter? got specs? Need better purity? There is an easier way with an 8x clock Dec 4, 2017 at 20:04