2.2.1 Thermal Noise

Chapter 2.2.1 Thermal Noise

Radio Frequency Integrated Circuit Design Second Edition Book
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Radio Frequency Integrated Circuit Design Second Edition Book

  • Issues in RFIC Design: Noise, Linearity, and SignalsTo find the total noise due to a number of sources, the relationship of the sources with each other has to be considered. The most common assumption is that all noise sources are random and have no relationship with each other, so they are said to be uncorrelated. In such a case, noise power is added instead of noise volt-age. Similarly, if noise at different frequencies is uncorrelated, noise power is added. We note that signals, like noise, can also be uncorrelated, for example, signals at different unrelated frequencies. In such a case, one finds the total output signal by adding the powers. On the other hand, if two sources are correlated, the voltages can be added. As an example, correlated noise is seen at the outputs of two separate paths that have the same origin.2.2.1  Thermal NoiseOne of the most common noise sources in a circuit is a resistor. Noise in resistors is generated by thermal energy causing random electron motion [1–3]. The thermal noise spectral density in a resistor is given by: resistor4NkTR= (2.1)where T is the temperature in Kelvin of the resistor, k is Boltzmann’s constant (1.38 ´ 10-23 joule/K) and R is the value of the resistor. Noise power spectral density has the units of V2/Hz (power spectral density). To determine how much power a resistor produces in a finite bandwidth, simply multiply (2.1) by the bandwidth of interest Df: 24nvkTR f=D (2.2)where vn is the rms value of the noise voltage in the bandwidth Df . This can also be written equivalently as a noise current rather than a noise voltage: 24nkT fiRD= (2.3)Thermal noise is white noise, meaning it has a constant power spectral density with respect to frequency (valid up to approximately 6,000 GHz) [4]. The model for noise in a resistor is shown in Figure  Available Noise PowerMaximum power is transferred to the load when RLOAD is equal to R. Then vo is equal to vn/2. The output power spectral density Po is then given by: 224onovvPkTRR=== (2.4)Thus, available power is kT, independent of resistor size. Note that kT is in watts per hertz, which is a power density. To get total power out Pout in watts, mul-tiply by the bandwidth, with the result that: