Issue link: https://iconnect007.uberflip.com/i/886239
October 2017 • The PCB Design Magazine 39 and Df data sheet values at 1 MHz are 3.5 and 0.005, respectively. If one segment of the plane model represents one square inch area, the FR406 laminate model at 1 GHz will have 226 pF capacitance and 0.022815 S conductance; the HK04J25 laminate model at 1 MHz will have 800 pF capacitance and 0.0257 S conductance. For a causal model, we need these parameters as a function of frequency, which can be read- ily calculated based on the chosen wide-band multi-pole model [12] . Figure 4 and Figure 5 show the causal dielec- tric parameters as a function of frequency for the FR406 and HK04J25 laminates. On both fig- ures the red dots on the left chart indicate the values provided by the data sheets. To obtain the series elements of the equiva- lent circuit, we can start with the DC sheet resis- tance and asymptotic high-frequency spreading inductance of the planes. The DC sheet resis- tance depends on the thickness and conductiv- ity of the conductor. Assuming one-ounce (30 um) pure cop- per for each plane, the sheet resistance is ap- proximately 0.6 mOhms for each square in each plane layer. The high-frequency spread- ing inductance is approximately 33 pH for each milli-inch dielectric thickness, resulting in a 132 pH for the 4-mil FR406 example and 33 pH want causal, lossy models, each segment needs to be represented with an RLGC network, where all four parameters are frequency dependent. For the frequency-dependent C(f) capaci- tance and G(f) conductance we can use one of the causal dielectric models, for instance the wide-band multi-pole Djordjevic-Sarkar model [8] . The material constants can be taken from the laminate data sheet or from measurements [9] . For instance, based on the data sheet [10] , a glass-reinforced FR406 4-mil core laminate at 1 GHz will have a Dk and Df value of 3.95 and 0.0161, respectively. If we chose an unreinforced HK04J25 1-mil polyimide laminate [11] , the Dk Figure 4: FR406 Dk(f) and Df(f) as a function of frequency (on the left) and C(f) and G(f) as a function of frequency for a one square inch of laminate (on the right). Figure 3: One segment of a generic, causal, lossy interconnect model. CAUSAL POWER PLANE MODELS