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
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.
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 to the region of dissipation. For a round conductor, this vector component points to the center of the conductor.
Note the following:
- A transmission line can carry energy in both directions.
- A transmission line can transport any number of signals at the same time.
- A transmission line is a path that allows energy to flow to a lower energy state.
- There is no way to tell if the field is carrying signal or energy. They are the same.
The transmission lines we will consider are the traces on circuit boards that make connections to capacitors, vias, conducting planes and cables and that connect logic signals between logic elements.