Electromagnetic Fields and Waves: Notes, Solved Problems and Interactive Lab

Three short calculations tied to the applications. They use only $v = c / ε_{r}$ , the delay $R / v$ and the $1/ R$ of the retarded potentials, and no new physics. Numerical constants: $c = 3 \times 1 0^{8} m/s$ , Earth radius $R_{e} = 6371 km$ , all media nonmagnetic. A good way to use them: read the given quantities, produce the formula from the corresponding application yourself, and only then put the numbers in.

Worked example 5.5.1

Board, cable and chip

Given. A $15 cm$ stripline in FR-4 ( $ε_{r} = 4.4$ ), a $1 m$ coaxial cable with PE insulation ( $ε_{r} = 2.25$ ) and a $5 mm$ on-chip line in SiO $_{2}$ ( $ε_{r} = 3.9$ ), all with $μ_{r} = 1$ . The signal has a rise time $t_{r} = 50 ps$ . A differential pair may have at most $2 ps$ of skew.

Find. (a) $v$ and the delay on each line, (b) the length of the rising edge on FR-4 and on the cable, (c) the allowed length mismatch of the pair on FR-4, (d) the length of cable with the same delay as the $15 cm$ trace.

Try it yourself first.

cf. Application 5.5.1

Worked example 5.5.1: Board, cable and chip