Page 231 - System on Package_ Miniaturization of the Entire System

Mixed-Signal (SOP) Design 205

8000
7000

6000
Mag(Zin) 5000
4000

3000
2000

1000
0
0 0.5 1 1.5 2 2.5 3 3.5 4
Frequency in GHz
(a)
2
1.5
1
0.5
Phase(Zin) −0.5 0

−1
−1.5
−2
0 0.5 1 1.5 2 2.5 3 3.5 4
Frequency in GHz
(b)
FIGURE 4.53 Frequency response and rational function approximation for one-port inductor.
(a) Magnitude. (b) Phase.

established between the physical layout and the equivalent circuit. Interestingly enough,
except for inductor L , the remaining equivalent circuits have the same circuit topology
4
with different parasitic values. The parasitic values are consistent and scale with the
dimensions in the layout.
For arbitrary interconnections containing many resonances in the frequency
response, only nonphysical circuit models can be developed [58]. Once the coefficients
of Equation (4.21) are computed, the function can be represented in pole-zero form.
This can be expanded as low-pass, bandpass, high-pass, and all-pass filters as shown in
Table 4.8. Each filter can now be represented as an equivalent circuit. All of these circuits
concatenated together results in the overall network.