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The rotational nature of the Kerr solution leads to an interesting effect known as frame dragging. We imagine dropping a particle in from in nity with zero angular momentum. This particle will acquire an angular velocity in the direction in which the source is rotating. An easy way to describe this phenomenon is to

Even the best nonverbal skills can t make a bad presentation good. But bad verbal skills can ruin your great content. As an executive speech coach, if I had the opportunity to improve just one area for a client, I would choose nonverbal mannerisms. Improve the way you look and sound when you say the words you ve prepared, and you ll give a better presentation.

Note: This chart is for a 0.07" thick (or greater) PCB. 14 12 Current (Amps) 10 8 6 4 2 0 0 50

30 C

45 C

FIGURE 16.5 Baseline (Jouppi) 1 oz. internal conductor chart. [The baseline (Jouppi) charts represent the author s personal data collection.]

Note: This chart is for a 0.07" thick (or greater) PCB. 3.5 3.0 Current (Amps) 2.5 2.0 1.5 1.0 0.5 0.0 0 5

10 45 C

25 10 C

30 5C

FIGURE 16.6 One-ounce internal conductor chart (fine line). [The baseline (Jouppi) charts represent the author s personal data collection.]

2-oz External 0.07" Thick Polyimide PWB Air 14 12 10 Current (Amps) 8 6 4 2 0 0 50 100 150 200 250 300 Cross Sectional Area (Sq-Mils)

Authenticity Is Essential: Be the Power of You by Susan Waldman When presented with what, for most of us, is the daunting task of speaking before a large audience or group of peers, it s tempting to conjure up the persona of someone whose presentation style has impressed you in the past. Maybe if you can somehow channel his or her charisma, style, or presence, your audience will be moved, your presentation a success, and your impression long lasting.

10 C

20 C

30 C

consider the momentum four vector and the components of the metric tensor. Looking at the inverse components of the metric (11.13) consider the ratio 2mar g t = = tt g (r 2 + a 2 )2 a 2 sin2 (11.17)

45 C

FIGURE 16.7 Two-ounce external conductor chart. (The baseline (Jouppi) charts represent the author s personal data collection.)

2-oz External 0.07" Thick Polyimide PWB Air 3.5 3 2.5 Current (Amps) 2 1.5 1 0.5 0 0 5 10 5C 15 10 C 20 20 C 25 30 C 30 45 C 35 Cross Sectional Area (Sq-Mils)

FIGURE 16.8 Two-ounce external conductor chart (fine line). (The baseline (Jouppi) charts represent the author s personal data collection.)

Copper weights Half-ounce copper traces are similar in temperature rise for the same size cross-sectional area as the 1 oz. traces. An increase in temperature rise of 10 to 15 percent over the 1 oz. traces is observed for 2 oz. traces, and 15 to 20 percent increase for 3 oz. traces for the same cross-sectional area.The higher percentage is for a 45 C rise and the lower percentage is for a 10 C rise. Board material The FR-4 versus polyimide board material properties did not have a significant impact on trace temperature, which is determined primarily by the thermal conductivity of the dielectric laminate material construction. Table 16.2 lists measured thermal conductivity values for each of the test boards.The column labeled kz presents values through the thickness of the board and represents the resin thermal conductivity.The values in columns kx and ky are in-plane and the difference is attributed to the influence of the glass fiber.

TABLE 16.2 Dielectric Thermal Conductivity Material FR-4 Polyimide kx (w/in.-C) 0.0124 0.0138 ky (w/in.-C) 0.0124 0.0138 kz (w/in.-C) 0.0076 0.0085

Copper Planes One factor that has significant impact on the temperature rise of a trace for a given current level and trace size is the influence of copper planes. Whether they are power, ground, or simply thermal planes, the copper planes help spread the heat and lower the temperature rise of what would otherwise be a hot spot. When designing with baseline charts, the copper planes add margin to the design. Multiple planes have more of an impact on lowering the temperature rise of a trace, although a single plane of 1 oz. copper is the starting point from the baseline configuration.

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