Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-24T06:02:59.740Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-analytic at the origin, behavioral models for active or passive non-linearity

Published online by Cambridge University Press:  05 March 2013

Jacques Sombrin
Jacques Sombrin*
Affiliation:
TéSA, 14-16 Port Saint-Étienne, 31000 Toulouse, France. Phone: +33 5 61 24 73 79
*
Corresponding author: Jacques Sombrin Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Most non-linear behavioral models of amplifiers are based on functions that are analytic at the origin and thus can be replaced by their Taylor series development around this point, e.g. polynomials of the input signal. Chebyshev Transforms can be used to compute the harmonic response of the model to a sine input signal. These responses are polynomials of the input signal amplitude. A second application of the Chebyshev transform to the first harmonic response or radio frequency (RF) characteristic will lend the carriers and intermodulation (IM) products for a two-carrier input signal, again polynomials. An important class of non-analytic non-linear behavior encountered in practice, such as hard limiters and detectors are either empirically treated or only approximated by an analytic function such as the hyperbolic tangent. This work proposes to generalize the polynomial non-linearity theory by adding non-analytic at the origin functions that, like polynomials, are invariant elements of the Chebyshev Transform. Devices modeled with these non-analytic at the origin functions exhibit intermodulation behavior significantly different from that of classical polynomial models, giving theoretical foundation to a number of important unexplained practical measurement observations.

Keywords

Power Amplifiers and LinearizersModelingSimulation and characterizations of devices and circuits
Type
Research Papers
Information
International Journal of Microwave and Wireless Technologies , Volume 5 , Special Issue 2: Special Issue on Power Amplifier Linearization , April 2013 , pp. 133 - 140
Copyright
Copyright © Cambridge University Press and the European Microwave Association 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Westcott, R.J.: Investigation of multiple FM/FDM carriers through a satellite TWT operating near to saturation. Proc. IEE, 114 (6) (1967), 726–740.Google Scholar
[2]Blachman, N.M.: Detectors, bandpass nonlinearities and their optimization: inversion of the Chebyshev transform. IEEE Trans. Inf. Theory, IT-17 (4) (1971), 398–404.Google Scholar
[3]Blachman, N.: Intermodulation in terms of the harmonic output of a nonlinearity. IEEE Trans. Acoust. Speech Signal Process., ASSP-29 (6) (1981), 1202–1205.Google Scholar
[4]Zhou, G.T.; Qian, H.; Ding, L.; Raich, R.: On the baseband representation of a bandpass nonlinearity. IEEE Trans. Signal Process., 53 (8) (2005), 2953–2956.CrossRefGoogle Scholar
[5]Loyka, S.L.: On the use of Cann's model for nonlinear behavioral-level simulation. IEEE Trans. Veh. Technol., 49 (5) (2000), 1982–1985.Google Scholar
[6]Kaye, A.R.; George, D.A.; Eric, M.J.: Analysis and compensation of bandpass nonlinearities for communications. IEEE Trans. Commun., 20 (5) (1972), 965–972.Google Scholar
[7]Gelb, A.; Vander Velde, W.E.: Multiple-Input Describing Functions and Nonlinear System Design. McGraw Hill Book Company, New York 1968.Google Scholar
[8]Rapp, C.: Effects of HPA-nonlinearity on a 4-DPSK/OFDM-signal for a digital sound broadcasting system, in Proc. Second European Conf. on Satellite Communications, Liège, Belgium, 22–24 October 1991, 179–184.Google Scholar
[9]Saleh, A.M.: Intermodulation analysis of FDMA satellite systems employing compensated and uncompensated TWT's. IEEE Trans. Commun., COM-30 (5) (1982), 1233–1242.Google Scholar
[10]Cann, A.J.: Nonlinearity model with variable knee sharpness. IEEE Trans Aerosp. Electron. Syst. AES-16 (6) (1980), 874–877.Google Scholar
[11]Schreurs, D.; O'Droma, M.; Goacher, A.A.; Gadringer, M.: RF Power Amplifier Behavioural Modeling. Cambridge University Press, Cambridge, UK 2009.Google Scholar
[12]Clarke, K.K.; Hess, D.T.: Communications Circuits: Analysis and Design. Addison-Wesley Publishing Company, Reading, Massachusetts 1971.Google Scholar
[13]Fager, C.; Pedro, J.C.; Borges de Carvalho, N.; Zirath, H.; Rosario, M.J.: A comprehensive analysis of IMD behavior in RF CMOS power amplifiers. IEEE J. Solid-State Circuits, 36 (1) (2004), 24–34.Google Scholar
[14]Pedro, J.C.; Carvalho, N.B.; Fager, C.; Garcia, J.A.: Linearity versus efficiency in mobile handset power amplifiers; a battle without a loser. Microw. Eng. Europe, August/September (2004), 19–26.Google Scholar
[15]Chapman, R.C.; Rootsey, J.V.; Poldi, I.; Davison, W.W.: Hidden threat – Multicarrier passive component IM generation, AIAA/CASI sixth Communications Satellite Systems Conf., Paper 76–296, Montreal, Canada, 5–8 April, 1976Google Scholar
[16]Shitvov, A.; Zelenchuk, D.; Schunchinsky, A.: Carrier-power dependence of passive intermodulation products in printed lines, Loughborough Antennas and Propagation Conf., 16–17 November 2009, Loughborough, UK, 2009, 177–180.Google Scholar
[17]Henrie, J.; Christianson, A.; Chappell, W.J.: Prediction of passive intermodulation from coaxial connectors in microwave networks. IEEE Trans. Microw. Theory Tech., 56 (1) (2008), 209–216.Google Scholar
[18]Hartman, R.: Passive intermodulation (PIM) testing moves to the base station. Microw. J., 54 (5) (2011), 124–130http://www.microwavejournal.com/articles/11103Google Scholar
[19]Khatri, H.; Gudem, P.; Larson, L.: Simulation of intermodulation distortion in passive CMOS FET mixers ». IEEE MTT-S Microwave Symposium Digest (2009), 1593–1596.Google Scholar
[20]Soury, A.; Ngoya, E.: A two-kernel nonlinear impulse response model for handling long term memory effects in RF and microwave solid state circuits. IEEE MTT-S (2006) Digest, 1105–1108.Google Scholar
[21]Cunha, T.R.; Lima, E.G.; Pedro, J.C.: A polar oriented Volterra model for power amplifier characterization. IEEE IMS (2009) Digest, 556–559.Google Scholar
[22]Lima, E.G.; Cunha, T.R.; Texeira, H.M.; Pirola, M.; Pedro, J.C.: Base-band derived Volterra series for power amplifier modeling. IEEE IMS (2009) Digest, 1361–1364.Google Scholar
[23]Verspecht, J.; Root, D.E.: Polyharmonic distortion modeling. IEEE Microw. Mag., (2006), 7 (3) 44–57.Google Scholar
[24]Verspecht, J.; Horn, J.; Betts, L.; Gunyan, D.; Pollard, R.; Gillease, C.; Root, D.E.: Extension of X-parameters to include long-term dynamic memory effects. IEEE MTTS (2009) Digest, 741–744.Google Scholar
[25]Cann, A.J.: Improved nonlinearity model with variable knee sharpness. IEEE Trans. Aerosp. Electron. Syst., 48 (4) (2012), 3637–3646.Google Scholar