Digital Circuit Boards: Mach 1 GHz

1.18 Poynting's Vector

When electrical energy moves, both an E field and an H field are required. The power density at a point in space is given by the vector cross product of the E- and H field intensities. This vector P in Equation 1.10 is called Poynting's vector. This vector exists at

1.10

all points in space and points in the direction of energy flow. For a pair of conductors carrying power from a battery to a load, the E field crosses between the conductors and the H field circles the current carrying conductors (Fig. 1.3).

Note that the E and H fields have directions perpendicular to the current path and perpendicular to the direction of power flow. The E field has units of volts per meter and the H field has units of amperes per meter, so the product has units of watts per meter squared.

N.B.

The energy supplied to a load is carried in the space between the connecting conductors and not in the conductors. This concept applies at all frequencies including dc. The P vector is greatest at points near the conductors.

It is important to view every pair of conductors as a transmission line. Fields carry the energy in the space between conductors at all frequencies. Fields that leave the circuit represent radiated energy. In this case, a component of Poynting's vector points in the direction of radiation. When there is heat loss, then a component of Poynting's vector points ...