Phase shift due to finite length of circuit conductors.
On a particular type of circuit board, assume a signal travels at 2/3 of the speed of light. Suppose a high-speed system using this type of board can tolerate a phase shift in a sine-wave signal due to propagation delay of only 15° before failing to work.
Calculate the maximum length Imax (in m, or a suitable subdivision such as cm or mm) that a circuit-board trace carrying this signal can have at each of the following frequencies without encountering excessive phase shift due to the propagation delay along the trace:
(a) f= 10MHz,
(b) f=30 MHz,
(c)f= 500 MHz, and
(d) f=2.5GHz.