f noise 10.8.1 Thermal or Johnson noise Reactive elements do not contribute to thermal noise but they do affect its frequency shape. Thermal or Johnson noise, first documented by J.B. Johnson of Bell Laboratories in 1928, is often called white noise. It is of a gaussian 10.8.3 Effective noise bandwidth nature which means it is completely random. Any circuit operating at a temperature above absolute zero (-273°C) will display thermal The effective noise bandwidth is defined as the width of a rectangu- noise. This random noise is caused by the random motion of discrete lar frequency response curve having a height equal to the the electrons in the conductive path. maximum height of the frequency response curve and correspond- The work of Johnson states that the available power per unit ing to the same total noise power (see Figure 10.15). It is given by bandwidth of thermal noise is given by Equation 10.25, where K is Equation 10.31. Boltzmann's constant (1.3805 X 10-23 joules/degree K), and T is the absolute temperature of the source in degrees K. (10.31) Noise power P = T T watts/Hz (10.25) Using measurements it has been shown that across the entire frequency range the available power P is directly proportional to the product of the system bandwidth B and the absolute tempera- ture of the source T. as in Equation 10.26, which may be expressed in dBm at room temperature as in Equation 10.27. |Hol2 (10.26) (10.27) 10.8.2 Noise voltage equivalence circuit A resistor is a good example of a thermal noise source, and therefore Frequency f a suitable equivalent circuit is an r.m.s. noise voltage generator connected in series with a hypothetically noiseless resistor having the same resistance. If these are connected in series with a load resistor, as shown in Figure 10.14. then the maximum noise power Figure 10.15 Effective noise bandwidth in the circuit may be calculated. The maximum power will be delivered with R = R. Therefore the maximum power is given by Equations 10.28 and 10.29, leading to Equation 10.30. 10.8.4 Sh