# FAQ: How does a pole at high frequency prevent PID amplification of high frequency noise?

*Posted by Shreesh Mysore, 25 November 2002*

To understand this recall that high frequencynopise amplification is caused mainly by the "D" part of the PID controller. Consider the transfer function due to the D part (lets call it D(s)):

We see that as gets large, so does <mat>|D|</math>. To offset this effect, what we need is a means to limit high frequency gain, i.e., to bound the value of . Let us consider a modified version of D(s) as

with N being large. The interpretation is that we have "added" a high frequency pole to the transfer function.

So how does this help? At low frequencies (small s), we see that (because N is chosen large). Therefore, . Thus at low frequencies, the transfer function behaves just like the plain differentiatior (Ks) - our old transfer function. At high frequencies (s large), we see that s swamps out N, and hence . The high frequency gain is therefore limited by .