246 Practical MATLAB® Applications for Engineers
and
2
2
1
1
22
R
S
R
QQS
rad/s
if QS > 10 then ω 1 = ωR (^) ( 1 – ^1
2 QS
(^) ) rad/s, and ω 2 = ωR (^) ( 1 + ^1
2 QS
(^) ) rad/s
where the BW is defi ned as BW = ω 2 − ω 1 or by BW = ωR/Q. Recall that the
BW represents the range of frequencies present in the output with a signifi cant
power content.
The frequency ωR is the geometric mean of the two frequencies given by ω 1
and ω 2 (or f 1 and f 2 ) as
R 12 ⋅
or
fffR 12 ⋅
R.3.53 Let us analyze now the simple parallel RLC circuit, shown in Figure 3.19, at
resonance.
The resonant frequency for the parallel case is still given by
f
R LC
1
2
The quality factor Q is given by
QCR
R
PR RRL
21
and the BW cutoff frequencies are given by the following equations:
1 2
2
2
1
2
1
2
1
2
114
R
RC RC C R R
C
L
CR L
FIGURE 3.19
RLC parallel circuit diagram of R.3.53.