54 The PCB Design Magazine • March 2016
back calculate the capacitance and can show it
on the same plot together with the AC simula-
tion results, see Figure 9.
The solid blue line is the same data we
showed in Figure 6; this was the result of SPICE
linearized AC analysis around the DC operating
point. The red dots are the capacitance values
calculated from the time-domain waveform of
Figure 8.
The very good agreement between the two
data series in Figure 9 proves that these dy-
namic models are actually nonlinear and the
capacitance changes instantaneously with
the voltage. The dynamic models allow us to
simulate the effect of bias dependence in LC
filters, power circuits and in many other ap-
plications. PCBDESIGN
References
1. DC Bias Effect in Ceramic Capacitors,
Quiet Power column.
2. DC and AC Bias Dependence of Capaci-
tors Including Temperature Dependence, Design-
Con East 2011, September 27, 2011, Boston.
3. Johanson Dielectrics Ceramic Capacitor
Aging Made Simple.
4. Murata Library of Dynamic Monolithic
Ceramic Capacitor Models.
Dr. Istvan Novak is a distin-
guished engineer at Oracle,
working on signal and power
integrity designs of mid-range
servers and new technology
developments. With 25 patents
to his name, Novak is co-author
of "Frequency-Domain Charac-
terization of Power Distribution Networks." To
contact Istvan, click here.
dynamic models for passiVe components
Figure 9: Comparison of capacitance vs. DC bias voltage simulated with AC run vs. time-domain ramp.
