Page 27 - Analog and Digital Filter Design

24 Analog and Digital Filter Design

The designer must determine the cutoff frequencies, the stopband attenuation,
and whether a lowpass, highpass, bandpass, or bandstop filter is required. Some-
times this specification will be supplied by the system designer, but this may be
left to the filter designer to decide for him or herself.

Phase Response
Radianslsec are used as the unit of frequency measure because in an analog filter
this gives a value for reactive impedance, which is directly proportional to the
frequency. Ohms law states that current can be expressed as the ratio of voltage
to load resistance. This is true for DC measurements with a purely resistive load.
For AC measurements with loads that include reactive elements like capacitors
and inductors, the current can be expressed as the ratio of voltage to load imped-
ance. If there is some reactance in the load, the current through the load is not
in phase with the voltage across it.

VOLTAGE AND CURRENT
PHASE FOR CAPACITORS

1
w
0 0.5
3
h o
J
; 4.5
Q -1

I."
TI ME
-VOITAG E-C U RRE NT

VOLTAGE AND CURRENT
PHASE FOR INDUCTORS

-1.5 1'
TI ME
C
-VULT AG E - u R RE N T
Figure 1.6 (a and b)
Voltage and Current Phase Relationship for Capacitors and Inductors