Low Pass Filter

Winterstone said:

Hi mech_eng,

a short comment to your filter circuit.
It is an equal-component Sallen-Key topology with unity gain (the resistor in the feedback path has no effect) - and, thus, has a pole quality factor of only Qp=0.5.
This value is the lower limit for an active realization since this value can be realized also as a pure passive RC filter.
As a consequence, the magnitude response at the end of the passband (approx. 1 kHz) is not as "constant" as it could be.

Therefore, my suggestion: Increase the upper capacitor from 0.01uF to 0.02uF . This will give you a maximally flat response (Butterworth approximation) with Qp=0.707.
It is well known that such a lowpass response is a good trade-off between time and frequency domain. By the way: In this case, the 3-dB cut-off will be at 1.1 kHz.

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MrAl said:

Hi again,


Winterstone:
Oh you've talked to him before this?

Mech:
The calculation for the cutoff frequency is:
wo=(sqrt((sqrt(C1^2*R2^4+(4*C1^2-4*C1*C2)*R1*R2^3+(8*C2^2-8*C1*C2+6*C1^2)*R1^2*R2^2+(4*C1^2-4*C1*C2)*R1^3*R2+C1^2*R1^4)-C1*R2^2+(2*C2-2*C1)*R1*R2-C1*R1^2)/(C1)))/(sqrt(2)*C2*R1*R2)

but if the two capacitors are the same value so that C2=C1 then we have:
wo=sqrt(sqrt(R2^4+6*R1^2*R2^2+R1^4)-R2^2-R1^2)/(sqrt(2)*C1*R1*R2)

then using either formula the cutoff frequency in Hertz is:
fo=wo/2/pi


but the calculation for the amplitude is simpler:
w=2*pi*f with f in Hertz, then:
Ampl=Vin/sqrt((1-w^2*C1*C2*R1*R2)^2+(w*C1*R2+w*C1*R1)^2)

The phase shift is calculated from:
x=((1-w^2*C1*C2*R1*R2))/((1-w^2*C1*C2*R1*R2)^2+(w*C1*R2+w*C1*R1)^2)
y=((-w*C1*R2-w*C1*R1))/((1-w^2*C1*C2*R1*R2)^2+(w*C1*R2+w*C1*R1)^2)

then the actual phase shift in degrees is:
TH=atan2(y,x)*180/pi

and where atan2(y,x) is the two argument inverse tangent.

But if again C2=C1 then we have a simpler formula for the phase shift:
x=(1-w^2*C1^2*R1*R2)
y=(-w*C1*R2-w*C1*R1)
TH=atan2(y,x)*180/pi

where TH is again the phase shift in degrees.

The atan2(y,x) two argument function can be transformed into the atan(y/x) single argument form with a few changes and observation that the function changes for a certain threshold frequency but it's not worth the effort.

All these calculations of course assume a perfect op amp. With a real life op amp you may have to limit the input voltage level if it is a cheap op amp like the LM358 or go to a better quality op amp.

Audioguru has some interesting comments in the post that follows this one. The op amp will play an increasingly important role in the circuit as the frequency gets higher. It may be ok around 1kHz but up near 10kHz or so the input will have to be limited, but it's best to figure in the slew rate also to be sure.

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audioguru said:

The opamp has no power supply so it will not work.
The input of the opamp is not shown to be biased at half the supply voltage so it will not work.
The lousy old LM324 quad opamp is too slow to make a half-decent filter.
The LM324 has crossover distortion and is noisy (hiss).

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cowboybob said:

While I'm a big fan of bread boarding, sometimes a circuit simulator is just simpler.

Below is a TINA-TI3 (available free from TI.COM) circuit more or less similar to the one you provided:

It is a great aid, when analyzing signal filters, to employ a sweeping signal to the circuit to allow viewing the resultant effect(s) to the input signal.

This could also be seen using the TINA's on board oscilloscope. In this case, however, the signal analyzer gives a more definitive visual representation of the circuit's response to a variable frequency input to the circuit.

Other members on this forum prefer different simulators that are also free.

View attachment 66212

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cowboy, is this software is useful more than electronic workbench V5 , circuit maker or multisim ? Please, advice !

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Mechatronics Eng said:

audio, the supply is connected , but it is not shown. How can we bias an IC without a power supply !

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cowboybob said:

Mech,

Don't know. I'm only familiar with TINA. I think I'm the only one on this forum using it.

Probably any of the free sims would suit you as they probably all do pretty much the same thing and equally well (IMHO).

I did go so far as to buy the TINA Basic package, which has more test equipment, a greater variety of components in the parts library, etc. It will accept SPICE models and I like the instrument virtual icons (they look like real scopes, analyzers, with knobs and switches) etc). It was $90USD as I recall.

To me, it's more a case of what ever you get used to using after you've figured out all the little quirks of how and where to access the various features.

But I will say that after years (years) of real bread boarding, the sim hugely made the initial process of trying to see if, how, and why a circuit would perform a lot more fun (and not nearly as messy).

Keep in mind though that, as a rule, they do NOT completely eliminate the need for a "real world nuts and bolts" bread boarded circuit. But they'll get you much closer to something that works before you have to commit to the real thing.

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audioguru said:

ALL schematics must show a power supply!
We don't know if your supply voltage is high enough for the opamp and we don't know if it is dual-polarity or just a single positive supply.

Biasing:
The DC voltage of the Vin of your opamp circuit must be at about half the supply voltage which is 0V if the supply is dual-polarity. Then the input can swing up and down and the output will also swing up and down.

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