[sdiy] Making a HPF using a LPF...??

[Magnus Danielson]

On 04/11/2012 12:49 AM, David G Dixon wrote:
>> You can make a high-pass filter by summing for a low-pass
>> filter, but...<snip>
>
> Yes, but that's not now you would actually do the summing.

I wanted to show the consequence of such a summing. It's not what I 
would recommend.

> What you would
> do for a cascaded two-stage LPF, for example, is to sum the second-stage
> output with the input (or, more correctly, the input summed with the
> feedback, which is the actual input to the first stage), and with twice the
> inverted output of the first stage.  Hence, for a = 2 and b = 1,
>
> 2P LPF response:
>
> HLP2(s) = 1/(s^2 + 2s + 1)
>
> 1P LPF response:
>
> HLP1(s) = 1/(s + 1) = (s + 1)/(s + 1)^2 = (s + 1)/(s^2 + 2s + 1)
>
> input (0P LPF response):
>
> HLP0(s) = 1 = (s^2 + 2s + 1)/(s^2 + 2s + 1)
>
> Therefore:
>
> HLP2(s) - 2*HLP1(s) + HLP0(s) = (1 - 2s - 2 + s^2 + 2s + 1)/(s^2 + 2s + 1)
>
> = s^2/(s^2 + 2s + 1) = HHP2(s) = 2P highpass response.
>
> Again, this works very well, but only if the summing resistors are well
> matched.

As always when you play the sum-cancelling game.

Cheers,
Magnus