Hardware and Functional Development of Protection Devices and Systems - Digital Signal Processing in Power System Protection and Control - page 19

Fig. 3.6 Frequency response of a low-pass filter

For the first order RC four-pole its transfer function in frequency domain
amounts:

1
xC
xC þ R

1
xRC þ 1 :

H ð jx Þ¼ ¼ ð 3 : 2 Þ

From the very definition of cut-off frequency:

j ¼ 1

j H ð jx C Þ p 2 ð 3 : 3 Þ

it results that

RC ¼ 1
x C

ð 3 : 4 Þ

;

thus, for such a filter one can easily select the values of R and C. The frequency
response of the filter is shown in Fig. 3.7 . One can see that the characteristic is far
from ideal, which implies utilization of higher order filters (min. 2nd order),
having both higher slope in the transient region and better filtering properties in
pass and rejection areas, see Fig. 3.8 for the third order filter.

3.2.2 Sampling Process and A/D Conversion

If the input signal is a current in transient state caused by a short-circuit, it may be
represented in the form: