Issue link: https://iconnect007.uberflip.com/i/652863
March 2016 • The PCB Design Magazine 51 dynamic models for passiVe components We can also run the simulation at different DC bias levels and show the equivalent capaci- tance at different DC bias voltages and we get a plot as shown in Figure 6. Note that even at 0V DC bias, the capacitance is just 35uF instead of the nominal 47uF. The reason for the differ- ence is the AC bias dependence of the part. This dynamic mod- el is based on measured data, where the excitation level is just a few millivolts, whereas the nominal capacitance is specified with a 0.5Vrms source voltage, and with the larger AC excita- tion the capacitance is bigger. The above simulation results used the AC SPICE simulation option, which linearizes the model at the given DC operat- ing point. For this reason the capacitance extracted from the AC simulation result would not change if the test current val- ue (I1 in Figure 1) changes. Of course we would need to scale the result, for instance with I1 = 0.1A, we would need to multiply the result by 10 to get the correct impedance, but beyond this scal- ing we would get the same result for any value of I1. With time-do- main simulations, however, we can expect the capacitor to show different capacitance values de- pendent on how the instanta- neous voltage changes across the part. This best can be shown if we simulate the capacitor model with a linear voltage ramp across the part. The current through the capacitor will be proportional to its capacitance multiplied by the voltage slew rate. This means as the voltage across the capacitor changes as the ramp moves, the cur- rent through the capacitor also changes according to the change of capacitance with voltage bias. To make sure that we capture the DC bias de- pendence, we need to select a slow enough ramp. The ramp voltage in our simulation changes four volts in four millisecond. This Figure 4: Impedance magnitude and real part as a function of frequency, shown for the GRM219R60G476ME44 part with 4V DC bias. Figure 5: Extracted capacitance (blue trace, left axis) and induc- tance (green trace, right axis) for the GRM219R60G476ME44 part with 4V DC bias.