First and second derivatives

[dbanner]

The second derivative of the function yields a negative sign(sinusoidal wave), this is the reason why we need to have an inversion of the second stage filter. If so, then why on some designs the double differentiation inverts both the first and second stage filters? Is there another stage which follows which ends up giving same result?

[Qiaozhi]

There could be 3 reasons I can think of for this:

1) The input signal to the differentiators is already inverted.
2) There is a further stage beyond the differentiators that corrects the inversion.
3) Sampling is being done on the other polarity of the signal.

Which schematics are you referring to as an example?

[dbanner]

Ok, just take the Tek st as example, in fact all of Payne's circuits seem to have first 2 filter stages in either channels inverted. But your point 2 above make sense. I wasn't sure about the math. TEK S-T REVISED_-_TEK LTD_0.pdf

[Carl-NC]

Although it is more natural to mentally process positive signals, it really doesn't matter when it comes to circuitry. You can design with either positive or negative 1st and 2nd derivative signals, and then design their subsequent circuitry around those polarities. I think that most VCOs (that I can think of) have a frequency proportional to input voltage (a "positive" response) so if you want to drive a VCO from the 2nd derivative you would want a positive-going output. You can then work backwards all the way to the preamp to determine all the other needed stage polarities. And if you do end up needing a polarity inversion somewhere along the way to make a proper 2nd derivative polarity, swapping the demod clocks are the easiest place to do that.

[dbanner]

Although it is more natural to mentally process positive signals, it really doesn't matter when it comes to circuitry. You can design with either positive or negative 1st and 2nd derivative signals, and then design their subsequent circuitry around those polarities. I think that most VCOs (that I can think of) have a frequency proportional to input voltage (a "positive" response) so if you want to drive a VCO from the 2nd derivative you would want a positive-going output. You can then work backwards all the way to the preamp to determine all the other needed stage polarities. And if you do end up needing a polarity inversion somewhere along the way to make a proper 2nd derivative polarity, swapping the demod clocks are the easiest place to do that.

Ok.

So feeding a sinusoidal signal into the inverting input of, let's say, an op amp unity gain buffer stage, would be the equivalent of placing a negative sign (-) on the sine function?

[Carl-NC]

A unity gain buffer is non-inverting, so you need to use an inverting opamp stage.

[dbanner]

A unity gain buffer is non-inverting, so you need to use an inverting opamp stage.

Ok. Thanks.