2 Level Calculation

Transmission of information also is transmission of energy. Thereby, losses in the communication channel cannot be avoided, resulting in a decrease of available power throughout over the transmission link (Figure 2-1). If the power has been decreased so much that the receiver cannot be activated, amplifiers must be used along the transmission line. They can amplify the signal up to the level it had at the beginning of the transmission. These amplifi-ers also increase the level of the noise produced in the transmitter, along the line, and in the receiver. For the calculation of the link budget or the drawing of the level chart, in infor-mation transmission often logarithmic values are used, named levels. Attenuation a or gain g of a transmission line are given in the logarithmic ratio of two electrical values of the same unit, measured at the two points of the transmission system that should be compared. This leads to smaller values compared to the linear values of the real physical world.
Figure 2-1: Compensation or power losses at line segments 1, 2 and 3 by use of amplifiers: a) schematic of the line, b) level diagram of the line. 

The concept of levels comes from hydraulic construction. There it is used to define the water-level at different positions based on a reference point. Corresponding declarations have then been used in other areas as information technology. The general definition of a level is:
The level gives the logarithm of an absolute value A2 of a physical quantity in relation to an-other absolute value A1 of the same physical quantity.
In practice, the natural logarithm as well as the base-ten-logarithm is used for the logarithmic ratio. Although level declarations are actually dimensionless, the numerical value of the ration is described by 

  • Neper (Np), in case of natural logarithm
  • Bel (B), in case of base-ten-logarithm

named after the Scottish mathematician John Napier und the American inventor Alexander Graham Bell. For practical reasons, the pseudo unit Bel often is too large. Therefore, the decibel (dB) as a tenth of a Bel is used.