COAXIAL TRANSMISSION LINES SKIN EFFECT BASIC INFORMATION

The components that connect, interface, transfer, and filter RF energy within a given system or between systems are critical elements in the operation of vacuum tube devices. Such hardware, usually passive, determines to a large extent the overall performance of the RF generator.

To optimize the performance of power vacuum devices, it is first necessary to understand and optimize the components upon which the tube depends. The mechanical and electrical characteristics of the transmission line, waveguide, and associated hardware that carry power from a power source (usually a transmitter) to the load (usually an antenna) are critical to proper operation of any RF system.

Mechanical considerations determine the ability of the components to withstand temperature extremes, lightning, rain, and wind, that is, they determine the overall reliability of the system.

The effective resistance offered by a given conductor to radio frequencies is considerably higher than the ohmic resistance measured with direct current. This is because of an action known as the skin effect, which causes the currents to be concentrated in certain parts of the conductor and leaves the remainder of the cross-section to contribute little or nothing toward carrying the applied current.

When a conductor carries an alternating current, a magnetic field is produced that surrounds the wire. This field continually expands and contracts as the ac wave increases from zero to its maximum positive value and back to zero, then through its negative half-cycle.

The changing magnetic lines of force cutting the conductor induce a voltage in the conductor in a direction that tends to retard the normal flow of current in the wire. This effect is more pronounced at the center of the conductor.

Thus, current within the conductor tends to flow more easily toward the surface of the wire. The higher the frequency, the greater the tendency for current to flow at the surface. The depth of current flow d is a function of frequency and is determined from the following equation:

d = 2.6/ √(μf)

where d is the depth of current in mils, μ is the permeability (copper=1, steel=300), and f is the frequency of signal in MHz. It can be calculated that at a frequency of 100 kHz, current flow penetrates a conductor by 8 mils.

At 1 MHz, the skin effect causes current to travel in only the top 2.6 mils in copper, and even less in almost all other conductors. Therefore, the series impedance of conductors at high frequencies is significantly higher than at low frequencies.

When a circuit is operating at high frequencies, the skin effect causes the current to be redistributed over the conductor cross-section in such a way as to make most of the current flow where it is encircled by the smallest number of flux lines. This general principle controls the distribution of current, regardless of the shape of the conductor involved.

With a flat-strip conductor, the current flows primarily along the edges, where it is surrounded by the smallest amount of flux.