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Title & Document Type: Spectrum Analysis: Signal Enhancement -
Application Note 150-4
Manual Part Number: 8554-8447
Revision Date: June 1975
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CHAPTER 1
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Basic Considerations
Definition of Sensitivity
Sensitivity, to be useful, needs to relate to how small a signal can be measured on the analyzer. The
CRTdeflection is always proportional to the total power which includes the signal and the noise. A signal
can be seen when it is equal to the noise power.
S+N
S=Nor-=2 (1), where
N
S = power of the signal
N = power of the noise
In this case, S + N will be twice the noise power or deflected 3 dB above the noise.
Available Noise Power
The input termination of a network (an amplifier, receiver, or spectrum analyzer) has a certain amount
of available noise power which is, in most cases, thermal noise. An impedance Z = R + jX at temperature
T generates across its open circuit terminals a voltage resulting from the random motion of free electrons
thermally agitated. This "noise voltage", en, can be defined by the equation:
en: = 4kTBR,
where
k = Boltzmann's constant 1.374x 10-23joule/oK
T = absolute temperature oK
R = resistive component of impedance
B = Bandwidth
J- ",
~
If the impedance Z = R. + jX is connected to a matched load with input impedance Z = Z. as shown in
Figure 1, maximum transfer of the noise power will occur. Noise power Pn will be dissipated in the load
resistance RL due to the noise voJtage generated in the original resistance R. The noise power will be:
P = (en/2)2 =~ = 4KTBR
n RL 4RL 4RL
Since there is equal noise voltage across source and load when R = RL
Pn = KTB (2).
r '
I I
I
I
I
I
I
R+jX RL -jX I
I
I
I
I
I
I I
L ----- NETWORK - - - - .J
Filure 1. Availablenoise power P. is equal to KTB.
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.~ y
1
.-
Equation (2) defines the available noise power from the source. In systems operating at frequencies
where voltages and resistances cannot be clearly defined, this equation becomes the usable expression,
containing terms that can be measured.
Noise Figure
Let us consider the network in Figure 2 with a power gain G which can be more or less than 1. In prac-
tice a network is never noiseless and decreases the signal-to-noise ratio.
St ~
G
N, N2
Fillure2.
.~
The noise figure of the network may be defined as the ratio of input signal-to-noise power ratio to the
output signal-to-noise power ratio. .
. StiNt St N2
NOIse figure F =-=-'-,where
~/N2 Nt 52
St = input signal power
Nt = input noise power
~ = output signal power
N: = output noise power
'N
Since ~ = StG F = Nt~
. H the network is noiseless, the output noise will just be equal to the amplified input noise. In other-
words, N2 = NtG and F= 1. When F > I, there is degradation of the input signal-to-noise ratio. The out-
put noise power Nt, from a noisy network is made up of two terms:
.
. The first due to the amplification of the input noise power N.G
The second is the amount of noise power generated by the noisy network and is
-
equal to (F 1) N,G. So that Nt = N.G + (F - 1) N.G = FN.G
We have seen Nt is the input noise power or the available noise powj!r; that is, Nt = KTB. It follows
then that
Nt = FkTBG (3).
Sensitivity of a Spectrum Analyzer
We can use equation (3) to figure out the output noise power or sensitivity of a spectrum analyzer.
Unfortunately, the gain is unknown and we prefer to define the total input noise power which is the
output noise power divided by the gain.
.
2
~ Equation (3) becomes
N = FsAkTB (4) with FSA = Spectrum analyzer noise figure.
x;:.' It's more convenient to express the formula in dB
10 log N = 10 log FSA+ 10 log kT + 10 log B
At room temperature, T = 290okand 10log KT= -204 dB, a value which is constant in normal utilization.
(VVehave an error of 0.4 dB for t = 23