Radio Frequency Integrated Circuit Design - Webs

128 Radio Frequency Integrated Circuit Design
behave in an application when loaded with impedances other than 50�. It
would be more useful to extract an inductance and Q for both windings and
plot the coupling (k factor) or mutual inductance for the structure instead.
These properties have the advantage that they do not depend on the system
reference impedance.
In the following narrowband model, all the losses are grouped into a
primary and secondary resistance as shown in Figure 5.30.
The model parameters can be found from the Z parameters starting with
V1
I1 | = Z 11 = R p + j�(L p − M ) + j�M = R p + j�L p
I2 =0
Similarly,
Z 22 = R s + j�Ls
(5.30)
(5.31)
Thus, the inductance of the primary and secondary and the primary and
secondary Q can be defined as
L s = Im(Z 22)
j�
L p = Im(Z 11)
j�
Q s = Im(Z 22)
Re(Z 22)
Q p = Im(Z 11)
Re(Z 11)
Figure 5.30 Narrowband equivalent model for a transformer.
(5.32)
(5.33)
(5.34)
(5.35)