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12.5.4 Noise factor
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(12.24)
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An alternative way of representing amplifier noise is by means of its noise factor, F. In defining the noise factor of an amplifier, the source is taken to be at room temperature, denoted by T0, usually taken as 290 K. The input noise from such a source is kT0, and the output noise from the amplifier is N0,out FGkT0 (12.25)
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Here, G is the available power gain of the amplifier as before, and F is its noise factor.
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A simple relationship between noise temperature and noise factor can be derived. Let Te be the noise temperature of the amplifier, and let the source be at room temperature as required by the definition of F. This means that Tant T0. Since the same noise output must be available whatever the representation, it follows that Gk(T0 or Te (F 1) T0 (12.26) Te) FGkT0
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This shows the direct equivalence between noise factor and noise temperature. As a matter of convenience, in a practical satellite receiving system, noise temperature is specified for low-noise amplifiers and converters, while noise factor is specified for the main receiver unit. The noise figure is simply F expressed in decibels: Noise figure [F] 10 log F (12.27)
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Example 12.6 An LNA is connected to a receiver which has a noise figure of 12
dB. The gain of the LNA is 40 dB, and its noise temperature is 120 K. Calculate the overall noise temperature referred to the LNA input.
Solution
12 dB is a power ratio of 15.85:1, and therefore, Te2 (15.85 1)
4306 K
A gain of 40 dB is a power ratio of 10 :1, and therefore, Tin 120 4306 104
120.43 K
In Example 12.6 it will be seen that the decibel quantities must be converted to power ratios. Also, even though the main receiver has a very high noise temperature, its effect is made negligible by the high gain of the LNA.
12.5.5 Noise temperature of absorptive networks
An absorptive network is one which contains resistive elements. These introduce losses by absorbing energy from the signal and converting it to heat. Resistive attenuators, transmission lines, and waveguides are all examples of absorptive networks, and even rainfall, which absorbs energy from radio signals passing through it, can be considered a form
Twelve
of absorptive network. Because an absorptive network contains resistance, it generates thermal noise. Consider an absorptive network, which has a power loss L. The power loss is simply the ratio of input power to output power and will always be greater than unity. Let the network be matched at both ends, to a terminating resistor, RT, at one end and an antenna at the other, as shown in Fig. 12.5, and let the system be at some ambient temperature Tx. The noise energy transferred from RT into the network is kTx. Let the network noise be represented at the output terminals (the terminals connected to the antenna in this instance) by an equivalent noise temperature TNW,0. Then the noise energy radiated by the antenna is Nrad kTx L kTNW,0 (12.28)
Because the antenna is matched to a resistive source at temperature Tx, the available noise energy which is fed into the antenna and radiated is Nrad kTx. Keep in mind that the antenna resistance to which the network is matched is fictitious, in the sense that it represents radiated power, but it does not generate noise power. This expression for Nrad can be substituted into Eq. (12.28) to give TNW,0 Tx a1 1 b L (12.29)
This is the equivalent noise temperature of the network referred to the output terminals of the network. The equivalent noise at the output can be transferred to the input on dividing by the network power gain, which by definition is 1/L. Thus, the equivalent noise temperature of the network referred to the network input is TNW,i Tx(L 1) (12.30)
Since the network is bilateral, Eqs. (12.29) and (12.30) apply for signal flow in either direction. Thus, Eq. (12.30) gives the equivalent noise
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