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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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Ri(Tcl - Tp) + .?[А'г(-Тд + Tp - 2 T7 cosy-,) - 2^iT.,smv7]
|Zip(re + Tg + 2T7cosy?7) - 4A'1T7(A'1C0S97 -J- sin p,)
lo Fc77im, Rn- <ind Ysop.
1
- I J- ~ l-Г у N J'T 4- T.V-
2in^!' ~ ' V'~“ ' ~P'
1
|Zi|2(Ta + Tg + 2 T7 cos 97)
4To|i?i| V— — 1 - 1 “ •»
— 4 A|T7(Ai cos tp-i -f- /^isin^u,))
(4.161)
{4.itj'Z I
M 1 fi3)
4.3. Transformations between sets of noise pdr&msters
69
№1 \J(Ta + Tl3y- - 4 t;-
\Zi\:{Ta + Tp + 2TyCospy) - 4 Л i'T^Xi cos ipy 4- Rt 3;n
2 R\T7 sin. p-, — X['4- Ttj + 2TyCosp~,)
1 )Zi\2[Ta + Tp + 2TyCospy) - 4Aii,(A| cosy», + i?i.sin¥37)
Го r„, gni and Zy\
IRi\(TaTe - t2)
' n — To(Ta + Tp - 2 Ту cos ip*,)
9n — Ta + Te — 2 T., cos py
4 T0 \Ri\
П' Ri (Xa - Tp)
- Ta + Tp - 2 T, cos py
Л 2 Ty R\ sin py
■ I _______~ ______
J \Ta + Te - 2 Ту cos 97
To Temini 3n> arid ZF.
1 + 27- (Ы^а - 3» + y/(Ta + Tp)> - 4 T*]
971 =
Lo
Ta + Гд — 2 T-v cos
Zsof = №! V
4 r0 IЙ! I
f[Ta + Tj)2 - 4T2
Xa 4- i j — 2 T-y cos -w-/
+ J Ui -
2 X-, Д] sin p~, ''j
< < т Ip — 2 T, cos p7 j
To Ftm;n, Qnc, and Гsof:
fUi„ - 1 ■+ ~{piix, - TV, -7 v/(ZrTX^7- 4 7;0
One = (wX, - x/j +
^ io 4 v
Г SOF = ~ (it., + T;0 - Pl J\Ta 4- Т,зУ2 - 4 2-*)
(4.165)
(4.166)
(4.167)
(4.168)
(4.169)
(4.170)
(1.171)
(4.172)
(4.173)
70
4. Noise parameters
4.4 References
[1] Rothe, H. & Dahlke, W.: “Theory of noisy fourpoles”, Proc, IRE, vol. 44, pp. 311 -818, June 1956.
[2] Bauer, H. h R.othe, H.: ‘‘Der aquivalente Rauschvierpol ais YVelienvierpor, Archiv der elektrischen Ubertragung, vol. 10, pp. 241 - 252, 1956. Proc. IRE, vol. 44, pp. 811 -818, June 1956.
[3] Penfield. P.: “Noise in negative-resistance amplifiers”, IRE Trans, on Circuit Theory, vol. CT-7, pp. 166 - 170, June 1960.
[4] Penfield, P.: “Wave representation of amplifier noise”, IRE Trans, on Circuit Theory, vol. CT-9, pp. 84 - 86, March 1962.
[5] Engen, G. F.: “A new method of characterizing amplifier noise performance*’, IEEE Trans, on Instrumentation and Measurement, vol. IM-19, pp. 344 - 349, Nov. 1970.
[6] Meys, R.: “A wave approach to the noise properties of linear microwave devices”, IEEE Trans, on Microwave Theory and Techniques, vol. MTT-26, pp. 34 - 37, January 1978.
[7] Meys, R. & Milecan, М.: “Accurate experimental noise characterization ofGaAs FET’s at 18 and 20 GHz through the use of the noise wave model”, Proc. 11th European Microwave Conference, Amsterdam, 1981, pp. 177 - 182.
[8] Dobrowolski, J. A.: “A CAD-oriented method for noise figure computation of two-ports with any internal topology”, IEEE Trans, on Microwave Theory and Techniques, vol. MTT-37, pp. 15 - 20, January 1989.
[9] Engberg, J. & Larsen, Т.: <;Extended definitions for noise temperatures of linear noisy one- and two-ports”, IEE Proc. Part H, vol. 138, pp. 86 - 90, February 1991.
[10] Kurokawa, K.: “Power waves and the scattering matrix”, IEEE Trans, on Microwave Theory and Technique.s, vol. MTT-13, pp. 194 - 202, March 1965.
[11] Bachtold, W. & Strutt, M. J. O.: “Darstellung der Rauschzahl und der verfiibaren Verstarkung in der Ebene des komplexen Quellenreflexionsfactors”, A. E. U. Band 21,
pp. 631 - 633, 1967.
5
Noise measure and graphic representations
In this chapter the extended effective noise temperature and the extended noise factor for cascaded single response two-ports are derived. Then the extended noise measure of a single response two-port is introduced. The behaviour of the extended gain and especially the extended noise measure in both the source admittance plane and the source reflection coefficient plane are treated in the last two sections.
5.1 Two-ports in cascade
Often amplifiers consist of two-ports in cascade. This section computes the extended noise factor and the extended noise temperature of two-ports in cascade.
H H—* Fe, 1 Tec,l Fe,2 Tee,2 •
Ge ,

Figure 5.1: Noisy two-ports in cascade.
i
!
The definition of extended effective noise temperature (Equation (-J.4)) uses the exchangeable output noise power density for the amplifier alone ('without noise from the source). Single response amplifiers mean that each two-port has only one exchangeable earn at the appropriate frnnnenry. thus
„V' = TaGe = Т„С'Лв'Л---0'т [WHz-1! (.5.1)
! 71
72
5. Noise measure and graphic representations
The output noise power density from Figure 5.1 is Л* = к (reejGeiiGei2 ■ • ■ + Гев,2Сг,2 • ■ ■ Ge,m + ••• + Tce,mGe,,n) (5.2)
These two equations lead to
= Tcc.! + + -■ -'f- + • • ■ + ^''"mr------- M (5.3)
ед <Je5iU-e%2 С/еДе.З * ’ ‘
m rp
= Г»Д+Е™гг^- [K] ' (5.4)
i=2 l lj=l -.j
The extended noise factor is given by Equation (3.12) which for cascaded two-ports looks like Fe = 1 + T.c/Tq. Together with Equations (5.3) and (5.4) this leads to
Tee \ Tee 2 T„e 3 T--
Fe = 1 + г + +■■■ +77-
To G=tlTo G,1lGe,2T'o Ge.lG,^ ' ' ■ Ge,m^l'2’o
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