# Theory of Linear and nonlinear circuits - Engberg J.

ISBN 0-47-94825

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6.7. Transformation to common base and common collector

137

Figure 6.16: Mixed type input circuit.

G'n = К =

У' =

П'1 + из ni

Gn nj vnl2

i«i (^2 + п3)Ул -f nj n3 Y-ti)2

n2 + v ^ ( П2 + Пз) 71 з У22

П i ) nr

(n2 + пз ) пз Ay

Y-n

(6.137)

(6.138)

(6.139)

6.7 Transformation to common base and common collector

Equations (6.137) - (6.139) can be used to compute the common base (gate) noise parameters expressed by the common emitter (source) noise and small signal parameters. Let n2=0 and пз = щ and one gets:

Ghn = (6.140)

К = W-пЛ1 pc \Yn<+Y22e\2 " (6.141)

Y* = + |^b;e -\ 121 *. / i-;ie (6.142)

Transformation from common emitter ^ source) noise parameters to common collector (drain) noise parameters by use of the Z noise parameters gives the result:

(6.143)

(6.144!

138

6. Noise ol embedded networks

Z; = (l-|+ (6.145)

V ^ l Id/ ^21 <?

These results are also given in [14] and [15]. but expressed in a different way.

6.8 Noise computations in computer aided design programs

One type of popular optimization program comprises those based on the adjoint network. Without going into detail it is clear that uncorrelated noise contributions should be added as powers or power densities. Every one-port contains one noise generator which is uncorrelated to the other noise sources as they are physically separated. The two-ports contain two partly correlated noise generators which are separated into the equivalent noise two-port as shown in Chapter 4 and thus t-wo uncorrelated sources and a correlation immittance emerge. As equivalent noise multi-ports have not yet been developed to contain uncorrelated sources it is necessary to include correlation matrices.

Dobrowolskrs book on computer methods for microwave circuit analysis and design [16] includes linear noise computation of one-, two- and multi-ports.

6.9 References

[1] Engberg, J.: “Simultaneous input power match and noise optimization using feedback’’, R69ELS-79, Electronics Laboratory, General Electric, Syracuse, NY, 1969.

[2] Engberg, J.: “Simultaneous input power match and noise optimization using feedback", Proc. J^ih European Microwave Conference, Montreux, 1974, pp. 38-5 - 389.

[3] Rothe, H. & Dahlke, W.: “Theory of noisy fourpoles”, Proc. [RE, vol. 44, pp. S11 -818, June 1956.

[4] Lehmann, R. E. Heston, 0. D.: “X-band monolithic series feedback LNA”, IEEE Trans, on Micro-wave Theory and Techn.iqv.es, vol. MTT--33, pp. 1560 - 1566, Dec. 1985.

[5] Engberg, J.: *Noisc parameters of embedded noisy two-port networks’*. IEE Proc., vol. 132, part. II, Feb 1985.

[6] Albinsson, B.: “Noise parameter transformations of interconnected two-port networks", TEE Pmr : vol. 134, part H, pp. 125 - 129, April 1087.

[7] Hillbrand, H. к Russer, P. II.: "An efficient method for computer aided noise analysis of linear amplifier networks", IEEE Trans, on Circuit. Systems, vol. CAS-23, pp. 235 -238, April 1976.

6.9. References

139

[3] Dobrowolski, J. Л.: "A CAD-oriento.d 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 1969.

[9] Pucel, R. A., Struble, W., Hailgren, R. k. Rohde, V. L.: ;‘A general noise de-embedding procedure for packaged two-port linear active devices”, IEEE Trans, on Microwave Theory and Techniques, vol. MTT-40, pp. 2013 - 2023. November 1992.

[10] Twiss, R. O.: "Nyquist’s and Thevemn'.s theorems generalized for nonreciprocal linear networks”, Journal of Applied Physics, vol. 26, pp. 599 - 602, May 1955.

[11] Rohde, U. L.: "New nonlinear noise model for MESFETs including MM-wave application”, Dig. 1990 IEEE Integrated Nonlinear Microwave and Milliineterwaie Circuits Workshop, Duisburg.

[[*2] Char, B. W., Geddes, К. O., Gonnet, G. H.. Leong, B. L., Monagan, М. B. .fc Watt,

S. М.: ‘‘Maple V”, Springer, 1991.

[13] Hildebrand, F. 13.: '‘Methods of applied mathematics", 2ud edition. Prentice Hall,

1965.

[14] Stangerup, P.: ‘-Electronic noise calculation by computer'', ECR-58, Danish Research Centre for Applied Electronics, February 1976.

[15] Hagen, J. B.: '‘Noise parameter transformation for three-terminal amplifiers”, IEEE Trans, on Microwave Theory and Techniques, vol. MTT-3S, pp. 319-321, March 1990.

[16] Dobrowolski, J. A.: ■‘Introduction to computer methods for microwave circuit analysis and design”, Artech House, 1991.

Part II Non-linear systems

7

Noise in non-linear systems: Theory

This chapter deals with the theory of time invariant non-Linear noisy multi-port non-autonomous systems. The type of non-linear system considered may contain non-linear one- and multi-port non-linear elements and subsystems, the internal noise sources may be unmodulated (independent) or modulated (dependent), the system may contain dc sources, and the multiple signal input ports may be excited by multiple finite energy1 signals (also dc) and noise. The method of analysis is based on the use of Volterra series which requires an equivalent circuit description of the non-linear noisy system. The main objective of the present chapter is to derive expressions for the noise and deterministic response at arbitrary response ports in the situation where low level noise is analyzed. Low level noise refers to the situation where the noise is a small perturbation of the deterministic signal regime. This means that the non-linear contributions caused by a uon-linear mixing of noise with noise are insignificant.

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