Derive the equation for Noise figure of Cascaded system in terms of individual Noise figures
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. Noise factor
For components such as resistors, the noise factor is the ratio of the noise produced by a real resistor to the simple thermal noise of an ideal resistor. The noise factor of a system is the ratio of output noise power (Pno) to input noise power (Pni):
To make comparisons easier, the noise factor is always measured at the standard temperature (To) 290°K (standardized room temperature).
The input noise power Pni is defined as the product of the source noise at standard temperature (To) and the amplifier gain (G):
Pni = GKBT0 (5-16)
It is also possible to define noise factor Fn in terms of output and input S/N ratio:
which is also:
where
Sni is the input signal-to-noise ratio
Sno is the output signal-to-noise ratio
Pno is the output noise power
K is Boltzmann's constant
(1.38 X 10-23 J/°K)
To is 290°K
B is the network bandwidth in hertz (Hz)
G is the amplifier gain
The noise factor can be evaluated in a model that considers the amplifier ideal and therefore amplifies only through gain G the noise produced by the input noise source:
or
where
N is the noise added by the network or amplifier
(Other terms as previously defined)
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2. Noise figure
The noise figure is a frequently used measure of an amplifier's goodness, or its departure from the ideal. Thus it is a figure of merit. The noise figure is the noise factor converted to decibel notation:
NF = 10 LOG Fn (5-21)
where
NF is the noise figure in decibels (dB)
Fn is the noise factor
LOG refers to the system of base-10 logarithms
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3. Noise temperature
The noise temperature is a means for specifying noise in terms of an equivalent temperature. Evaluating Equation 5-18 shows that the noise power is directly proportional to temperature in degrees Kelvin and that noise power collapses to zero at absolute zero (0°K).
Note that the equivalent noise temperature Te is not the physical temperature of the amplifier, but rather a theoretical construct that is an equivalent temperature that produces that amount of noise power. The noise temperature is related to the noise factor by:
Te = (Fn - 1) To (5-22)
and to noise figure by:
Now that we have noise temperature Te, we can also define noise factor and noise figure in terms of noise temperature:
and
The total noise in any amplifier or network is the sum of internally and externally generated noise. In terms of noise temperature:
Pn(total) = GKB(To + Te) (5-26)
where
Pn(total) is the total noise power
(other terms as previously defined)
For components such as resistors, the noise factor is the ratio of the noise produced by a real resistor to the simple thermal noise of an ideal resistor. The noise factor of a system is the ratio of output noise power (Pno) to input noise power (Pni):
To make comparisons easier, the noise factor is always measured at the standard temperature (To) 290°K (standardized room temperature).
The input noise power Pni is defined as the product of the source noise at standard temperature (To) and the amplifier gain (G):
Pni = GKBT0 (5-16)
It is also possible to define noise factor Fn in terms of output and input S/N ratio:
which is also:
where
Sni is the input signal-to-noise ratio
Sno is the output signal-to-noise ratio
Pno is the output noise power
K is Boltzmann's constant
(1.38 X 10-23 J/°K)
To is 290°K
B is the network bandwidth in hertz (Hz)
G is the amplifier gain
The noise factor can be evaluated in a model that considers the amplifier ideal and therefore amplifies only through gain G the noise produced by the input noise source:
or
where
N is the noise added by the network or amplifier
(Other terms as previously defined)
Back to Top
2. Noise figure
The noise figure is a frequently used measure of an amplifier's goodness, or its departure from the ideal. Thus it is a figure of merit. The noise figure is the noise factor converted to decibel notation:
NF = 10 LOG Fn (5-21)
where
NF is the noise figure in decibels (dB)
Fn is the noise factor
LOG refers to the system of base-10 logarithms
Back to Top
3. Noise temperature
The noise temperature is a means for specifying noise in terms of an equivalent temperature. Evaluating Equation 5-18 shows that the noise power is directly proportional to temperature in degrees Kelvin and that noise power collapses to zero at absolute zero (0°K).
Note that the equivalent noise temperature Te is not the physical temperature of the amplifier, but rather a theoretical construct that is an equivalent temperature that produces that amount of noise power. The noise temperature is related to the noise factor by:
Te = (Fn - 1) To (5-22)
and to noise figure by:
Now that we have noise temperature Te, we can also define noise factor and noise figure in terms of noise temperature:
and
The total noise in any amplifier or network is the sum of internally and externally generated noise. In terms of noise temperature:
Pn(total) = GKB(To + Te) (5-26)
where
Pn(total) is the total noise power
(other terms as previously defined)
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