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910 ⏐⏐⏐ RESONANCE
For an ideal current source (R s � ∞ �), or if R s k R p, the equation
reduces to
Q p
The quality factor is now defined by
Q l ≥ 10, R s k R p
(20.50)
Rs � Q
Qp � � (20.51)
2 R
l Rl ��
Quite obviously, therefore, R s does have an impact on the quality
factor of the network and the shape of the resonant curves.
If an ideal current source (R s � ∞ �) is employed, or if R s k R p,
and Qp � Ql Ql ≥ 10, Rs k Rp BW
The bandwidth defined by f p is
f p
(20.52)
BW � f2 � f1 � �� (20.53)
Q
By substituting Q p from above and performing a few algebraic manipulations,
we can show that
BW � f 2 � f 1 � � � � (20.54)
clearly revealing the impact of R s on the resulting bandwidth. Of course,
if R s � ∞ � (ideal current source):
I L and I C
Z Tp � Q2 lR l
� XLp
Q
Qp � � � �
2 Q l
�
Ql
2 Q l
�
XL/Rl 2 Rs � Q lRl �
XL
2 lRl �
XL
1
�
2p
Rl
BW � f2 � f1 � �� 2pL
p
1
�
RsC
R s � ∞ �
(20.55)
A portion of Fig. 20.30 is reproduced in Fig. 20.31, with IT defined as
shown.
As indicated, ZTp at resonance is Q2
l R . The voltage across the paral-
l
lel network is, therefore,
VC � VL � VR � ITZTp � IT Q 2 lRl XL
R l
� L
ƒ r