Radio Frequency Integrated Circuit Design - Webs

78 Radio Frequency Integrated Circuit Design
The same type of analysis can be performed on the network in Figure
4.16(a). In this case,
R eq ≈ R�C 1 + C 2
C � 1
2
C eq ≈� 1
+
C 1
1
C 2� −1
4.6 The Concept of Mutual Inductance
(4.17)
(4.18)
Any two coupled inductors that affect each other’s magnetic fields and transfer
energy back and forth form a transformer. How tightly they are coupled together
affects how efficiently they transfer energy back and forth. The amount of
coupling between two inductors can be quantified by defining a coupling factor
k, which can take on any value between one and zero. Another way to describe
the coupling between two inductors is with mutual inductance. For two coupled
inductors of value L p and L s , coupling factor k and the mutual inductance M
as shown in Figure 4.17 are related by
k = M
√ L p L s
(4.19)
The relationship between voltage and current for two coupled inductors
can be written out as follows [3]:
Figure 4.17 A basic transformer structure.
Vp = j�L p I p + j�MI s
Vs = j�Ls Is + j�MIp
(4.20)