Page 193 - System on Package_ Miniaturization of the Entire System

Mixed-Signal (SOP) Design 167

and C are the parasitic capacitances to the ground plane, L and L are the spreading
p2 s1 s2
inductance of the electrode plates, R and R are the series resistance of the electrode
s2
s1
plates due to conductor loss, and R is the dielectric loss. The dielectric loss to the
s1a
ground plane has not been included in the equivalent circuit since its effect on the
capacitor response is negligible. As an example, for a square capacitor with HL1 =
VL1 = 23 mils, LCP thickness = 0.92 mils and the distance to the ground plane of ∼8 mils,
the parameters in Figure 4.11 are C = 2.4 pF, C = 497 fF, C = 46 fF, L = 55.9 pH, L =
s2
s
p1
s1
p2
56.6 pH, R = 140 mΩ, R = 1 mΩ, and R = 66.7 kΩ. These parameters can be derived
s2
s1a
s1
by optimizing the equivalent circuit parameters to fit the frequency response obtained
from Sonnet [28] or other electromagnetic simulators.
Using the equivalent circuit or the frequency response obtained from an electro-
magnetic simulator, the effective capacitance and Q of the capacitor can be obtained as
⎛ 1 ⎞
C eff = ⎜ ⎛ 1 ⎞ ⎟ n = 12 ,
⎜ 2π f Im ag ⎜ ⎟ ⎟ (4.3)
⎝ ⎝ Y ⎠ ⎠
nn
Imag Y ( )
Q = nn n = , 12 (4.4)
Real Y ( nn )
The frequency response of these equations using the parameters extracted is shown in
Figure 4.12 from 1 to 9 GHz. As can be seen, the capacitance increases as a function of
frequency and resonates around 9 GHz after which it becomes inductive. The maximum
Q of 320 occurs at 1 GHz.
4.2.3 Embedded Filters
In addition to several performance improvements, multimode radio architecture
provides a method to efficiently conserve both power and real estate in the portable
multiband radio design. The multimode radio requires simultaneous multiband
operation of the key RF components such as the low-noise amplifier (LNA) [5], oscillator
[29], and filters [30–33]. A multimode filter is one that has more than one controllable

300
60.0
50.0 250
40.0
200
30.0
C 20.0 Q 150
10.0 100
0.000
50
–10.0
–20.0 0
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
Freq, GHz Freq, GHz
FIGURE 4.12 Frequency response of capacitor. (a) Capacitance. (b) Quality factor.