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Theory of Linear and nonlinear circuits - Engberg J.

Engberg J. Theory of Linear and nonlinear circuits - Wiley & sons , 1995. - 154 p.
ISBN 0-47-94825
Download (direct link): noisetheoryoflinearandnonlinear1995.pdf
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Я 3 Ro G F i /"* 1^ = 1 ые
> 0 > 0 > 0 > 1 > 1 > 0
> 0 > 0 > 0 > 1 < 1 < 0
> 0 < 0 0 > 1 1 > (1
< 0 > 0 0 < 1 -A г 1 < 0
< 0 < 0 > 0 < 1 > 1 < 0
< 0 < 0 > 0 < 1 < 1 > 0
Table 5.2: Signs for Mc under various conditions
Ft should be noted that, tor a passive source. AF is positive for GK > L. which corresponds to a normal amplifier, and for Gt < 0, which holds for an amplifier wi' h negative re;v[ part of the output immit-anre. A’si > ' is negative when i: < ! Л -
which corresponds to an attenuator.
When m two-ports are going to be used for an amplifier the order of the two-ports for minimum noise is
0 < Mt,\ < M-.,% < з < •■■ < A/«.m !5.S]
76
5. Noise measure and graphic representations
In contrast, when a postamplifier is specified and a single preamplifier is required to precede the postamplifier, then one preamplifier must be chosen from several possibilities [2]. Here the minimum noise measure does not give enough information for the choice. This is demonstrated by writing the expression for the noise factor of the casca
e, 1 2
F',2 - 1
Сел
= 1+1-1
Fe.
= 1
1
(
1 -
1
gZ i
Fe, 1 ~ 1
F,-2 ~ 1
A/..1
e .2 - 1
(F, - l)
(Fe,2 - 1)
Suppose that a second stage is given. The second stage noise factor can be kept constant at the minimum value of FSl2, for example, by keeping the source immittance presented to stage two constant. Next, consider a candidate preamplifier with the real part of its output immittance positive. A lossless, passive two-port can be used to transform preamplifier output immittance to the value of stage two source immittance for minimum Fe,2. In subsequent comparisons of preamplifier candidates, let a lossless two-port transforming network, such as discussed above, be included with each preamplifier, with the net result that Fe,2 stays constant at its minimum value. It is seen that, given a particular second stage (the postamplifier), the first stage should be chosen such that the expression
V Ge,lA fe.2 - V
(5.9)
is maximized.
G.„ i Me,i Fe, 1 2
0 < G.,i < 1 < 1 0 > Fe,,
Gt, l > L МсЛ > F., 2-1 < о > Fc;2
Ge.l > 1 0 < М.,I > F.'2 - 1 > n и < FC' 2
Table 5.3: Throe common “f pfedinpiifier performances.
Table 5.3 shows the noise factor of a cascaded amplifier for three cases of exchangeable gain of the first two-port. Only the third case gives a lower noise factor for the cascaded amplifier. The first case in Table 5.3 corresponds to an attenuator;
5.2. The noise measure
its noise measure is negative and the cascaded noise factor greater than Fe 2■ In the second case, the preamplifier has a noise measure greater than the excess noise factor (the noise factor minus one) of the second stage, and again the cascaded noise factor is greater than Ft.2. The third case is the normal case, where the first stage noise measure is less than the excess noise factor of the second stage. The cascaded noise factor is lower than FZli- Here it is interesting to note that, from preamplifiers with the same noise measure, the one with the highest gain should be chosen.
The noise measure for m cascaded two-ports is derived from Equations (5.7), (5.5), and (5.6) as
Me = MC}i —7^—— G.^G,^ ■ ■ ■ Ge,m
\~J g 1.
+ Me,2 -y;------G„_3---Grtm -r • ■ • 4- —— (5.10)
Me - E ( r< _ 1 П j (5.11)
1=1 \ e j=m j
It is, however, normally much simpler to find the cascaded noise measure by computing the noise factor and the exchangeable gain of the cascaded two-ports and using the definition of the noise measure (Equation (5.7)).
When looking at this definition it is seen that
lim Me — Fe - 1
G«—'CO
This is also the case when cascading an infinite number of identical two-ports. Let these all have the noise factor Fe > 1 (~ a passive source) and gain Ge > 1, then
F — F 4- 4 4 ^
~ Ge G; ' GI
= 1 4- (Fe - 1) 4- (F. - 1) (4- {Fe - 11 ( + ■■■
\ О S / \ G '
1 —
]
Gn
\Ue/
F - 1
= 1 + —---------p = 1 -f
1 ~ (77
It should be noted that like the noi.se (actor, the exchangeable gain, and other noise characteristics, the noise measure is aiso a function of the source immittance.
Example 5.3 This example illustrates the importance of the noise measure and the effect of matching. Consider three amplifiers having the following noise parameters:
78
5. Noise measure and graphic representations
Rn,\ = 25 n Gn, i = 4.8 mS Y-r.i = 2.0 + j 12 mS
Rn, 2 = 24 Q Gn, 2 = 4.3 mS ^7,2 = 5.0 + j 9 mS
Rn, 3 = 6.25 гг Gn, з = 9.6 mS II 8.0 + j 14 mS
The amplifiers are unilateralized which means that their output admittances are constant whatever the source admittance might be. Let all output admittances be 10 mS and let that be the value of the source admittance as well. The exchangeable power gains of the amplifiers are
Ge,l = 4.0 Ge, 2 = 10 Ge, 3 = Ю
When all three amplifiers are used in cascade find the order giving the lowest overall noise factor. In order to find this the noise measure for each amplifier is computed.
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