LSNA Technology Library

On this page

• In a nutshell
• Sampling oscilloscope calibration
• Calibration
• Characterization
• Transistor Characterization and Modeling
• Behavioral Modeling
• Scattering Functions and “Large– signal S-parameters”
• Volterra
• Test Signals supporting LSNA technolgy

In a nutshell

• Sampling-based versus Mixer-based front-end
  This article presents the two common techniques to capture large-signal measurements and it discusses in details the pros and cons of each technique.
  (pdf - 275 KB)
• Theoretical background on LSNA Technology (with speakers notes)
  This presentation gives background about the technical aspects of the large-signal network analysis (LSNA) technology. It discusses the characterization and analysis aspects and gives an overview on the required measurement science, including the calibration aspects.
  (pdf - 1.5 MB)
• LSNA Technology and some of its applications (with speakers notes)
  This presentation explains some applications that have been realized with LSNA technology. Some applications were done by Agilent NMDG and others were done by research institutes working on this technology. The examples are there to give an idea about the capabilities but are in sense limited.
  (pdf - 3.5 MB)

Sampling oscilloscope calibration

• Quantifying the Maximum Phase-Distortion Error Introduced by Signal Samplers.
  Jan Verspecht
  IEEE Transactions on Instrumentation and Measurement, Vol. 46, No. 3, pp. 660-666, June 1997
  Quantifying the errors introduced by signal sampler imperfections is of interest to people who are doing frequency domain measurements. The phase-distortion introduced by the sampler is hard to quantify and is usually neglected. In this article upper bounds for this phase-distortion error are derived which are based upon simple assumptions, namely that the sampler weighting function is strictly positive, that it is limited in time and that the function has only one local maximum. The theoretical limits are applied in order to specify the accuracy of a calibration procedure for broadband sampling oscilloscopes.
  (pdf - 100kB)
• Broadband Sampling Oscilloscope Characterization with the "Nose-to-Nose" Calibration Procedure: a Theoretical and Practical Analysis.
  Jan Verspecht
  IEEE Transactions on Instrumentation and Measurement, Vol. IM-44, No. 6, pp. 991-997, December 1995
  In the past the “nose-to-nose” calibration procedure has been introduced as probably the most accurate method to determine the impulse response of broadband sampling oscilloscopes like the HP54124T. The method is based on the hypothesis “sampler kick-out equals oscilloscope impulse response”. This hypothesis was originally based on an intuitive approach and was later on verified experimentally (comparison with power measurements) as well as with SPICE simulations. Until now, however, there was no generalized mathematical evidence supporting this basic hypothesis. In this paper a mathematical theory is developed, which starts from a generalized sampler equivalent scheme, and which shows that, under conditions which are valid in practice, the sampler kick-out indeed equals the sampler impulse response. Experimental results are reported concerning the accuracy and precision of the calibration procedure. These experiments involve the investigation of experiment repeatability, noise, sampler linearity and timebase effects.
  (pdf - 125kB)
• Compensation of timing jitter-induced distortion of sampled waveforms.
  Jan Verspecht
  IEEE Transactions on Instrumentation and Measurement, Vol. IM-43, No. 5, pp. 726-732, October 1994
  The presence of timing jitter between the trigger signal and the sampling strobe in an equivalent-time sampling oscilloscope causes distortion of the recorded waveform. Two methods exist to estimate the waveform from the jittered measurements. One method, called the “median” method, is based on the calculation of the point-by-point median of a large set of waveform measurements. In this article it is shown that this method is asymptotically biased if noise is present and if the waveform is nonmonotonic. Another method, called the “pdf deconvolution” method, is based on an estimation of the jitter probability density function and on a technique to deconvolve this density function from the average of all recorded waveforms. To estimate the jitter probability density function, it is assumed that the waveform has a part which can very well be approximated by a ramp during a time span which is smaller than the standard deviation. In this article it is shown that a significant asymptotic bias is introduced by the method when this assumption is violated. A novel approach is proposed, based on a parametric model of the jitter probability density function, which results in an asymptotic unbiased estimate of the jitter probability density function. The method is experimentally verified, and it is explained why this method is especially useful when one is interested in the Fourier spectrum of the recorded waveform.
  (pdf - 133kB)
• Individual Characterization of Broadband Sampling Oscilloscopes with a "Nose-to-Nose" Calibration Procedure.
  Jan Verspecht, Ken Rush
  IEEE Transactions on Instrumentation and Measurement, Vol. IM-43, No. 2, pp. 347-354, April 1994
  A method is proposed to find the individual impulse response of broadband sampling oscilloscopes (HP54124T, 50 GHz bandwidth). The method is based on the fact that, when the oscilloscope is sampling a DC-voltage, pulses are launched from the sampler towards the input connector. These pulses contain information on the scope’s characteristic and can be measured by a second oscilloscope. This type of measurement is called a “nose-to-nose” calibration. Applying deconvolution techniques to the result of this measurement the characteristic of the two scopes can be found, assuming that the two scopes are identical. To avoid relying on this assumption, three oscilloscopes can be used. The “nose-to-nose” is then applied three times, with a different pair of scopes connected together each time. The individual characteristics of the three sampling oscilloscopes are then calculated.
  Both SPICE simulations and close correspondence between swept-sine measurements and this method indicate that it is probably the most accurate method available at this moment to calibrate broadband sampling oscilloscopes.
  Several measurement uncertainties and practical problems are identified. The phase contribution of the sampling aperture can never be determined by this method, but there is strong evidence that the effect is negligeable. Practical measurement problems are related to linearity of the samplers, additive noise, timebase jitter and timebase drift.
  (pdf - 187kB)
• Accurate Spectral Estimation Based on Measurements with a Distorted-Timebase Digitizer.
  Jan Verspecht
  IEEE Transactions on Instrumentation and Measurement, Vol. IM-43, No. 2, pp. 210-215, April 1994
  The timebase distortion present in an equivalent-time sampling oscilloscope introduces errors in the estimation of the values of the spectral components of a microwave signal when a classical discrete Fourier transform is used. In this article a method is developed to avoid these errors. The method is tested both in practice and with simulations. Two parts can be distinguished.
  At first, the timebase distortion is measured. This is done by digitizing a sinusoidal signal applied at the oscilloscope’s input, and by calculating the phase of the analytical signal of the digitized waveform. Other possible methods to measure the timebase distortion are discussed, and it is shown why the method used is the most appropriate for our specific application.
  The knowledge of the timebase distortion is then used to build a least-squares-error estimator for the values of the spectral components of a digitized microwave signal. An experimental verification is done, from which is concluded that the method effectively removes the spectral estimation errors due to a timebase distortion.
  (pdf - 100kB)

Calibration

• On-wafer absolute calibration
  As calibration reference planes are defined at probe tips for on-wafer measurement, one cannot connect the required power sensor and harmonic phase reference at the reference plane. This presentation explains how absolute calibration in an on-wafer setup is possible anyway.
  (pdf - 229 KB)
• “Triple A”: alignment addresses ambiguity
  In order to remove the ambiguity with respect to phase variation when using a component as a phase calibration element, proper alignment is required. This 4-slide-teaser puts things black and white. References are provided for those who are interested to go more in depth.
  (pdf - 365 KB)
• Phase stability study of a harmonic phase reference
  This slide set gives an overview of the typical phase stability tests that NMDG performed on a comb generator as candidate to become a harmonic phase reference (HPR).
  (pdf - 1.3 MB)
• Accurate On Wafer Measurement of the Large-Signal Behavior of a Nonlinear Microwave Device.
  Jan Verspecht, Peter Debie, Alain Barel and Luc Martens
  Revue HF, No. 2, pp. 35-45, 1996.
  A measurement setup and calibration procedure are described allowing the accurate on wafer measurement of phases and amplitudes of the spectral components of incident and scattered voltage waves at the signal ports of a nonlinear microwave device. A comparison is made between measurements performed with the setup and simulations based on a Root-model.
  (pdf - 130kB)
• Calibrated Vectorial "Nonlinear Network" Analyzers.
  Tom Van den Broeck, Jan Verspecht
  Conference Record of the IEEE Microwave Theory and Techniques Symposium 1994 , San Diego, California, USA, pp. 1069-1072, May 1994
  The vectorial nonlinear-network analyzer concept is introduced and realized in practice. A vectorial nonlinear-network analyzer excites a nonlinear microwave device-under-test with a combination of sinewaves of different frequencies and accurately detects the phase and amplitude of all frequency components of the incident and the scattered waves. A new, statistic efficient, absolute calibration procedure is developed based on a low crest factor multisine reference generator characterized by a broadband sampling oscilloscope. This makes the calibration traceable to the accuracy of a so-called nose-to-nose measurement.
  (pdf - 128kB)

• Calibration of a Measurement System for High Frequency Nonlinear Devices.
  Jan Verspecht
  Phd. Vrije Universiteit Brussel - Faculteit Toegepaste Wetenschappen
  promotor: Prof. dr. ir. A. Barel - copromotor: dr. ir. M. Vanden Bossche
  The research work described in the thesis is situated in a broad technological context. It is explained what vectorial “nonlinear network” analyzers are and why they are needed. The importance of traceable calibrations is highlighted, in general as well as applied to the vectorial “nonlinear network” analyzer.
  (pdf - 1.5MB)

Characterization

• State-of-the-art microwave device characterization using large-signal network analyzers.
  Maciej Myslinski (K.U.Leuven), Frans Verbeyst (NMDG), Marc Vanden Bossche (NMDG), and Dominique Schreurs (K.U.Leuven)
  17th International Conference Mixed Design of Integrated Circuits and Systems, Wroclaw, Poland, 24-26 June 2010
  This paper presents a snapshot of key large-signal network analysis capabilities enabling state-of-the-art microwave device characterization. An overview of different large-signal network analyzer configurations with the source- and load-pull techniques is given. Next, we report on the modulation capabilities that allow the characterization of high- and low-frequency effects which occur typically in active devices for wireless communication applications.
  Presentation (pdf - 1.5 MB)
• Calibrated Measurements of Nonlinearities in Narrowband Amplifiers applied to Intermodulation and Cross Modulation Compensation.
  Tom Van den Broeck
  IEEE MTT-S International Microwave Symposium Digest TH2C-6, 1995
  A vectorial nonlinear-network analyzer (VNNA) is absolutely calibrated in amplitude and phase for narrowband measurements of nonlinearities. Calibration is performed with a reference generator, characterized with a calibrated sampling oscilloscope. The reference signal, consisting of an upconverted baseband signal, is optimized for statistically efficient measurements. Using the calibrated VNNA, narrowband amplifiers can be measured, enabling compensation of intermodulation and cross-modulation.
  (pdf - 80kB)

Transistor Characterization and Modeling

• Large-Signal Modelling and Measuring go Hand-in-Hand: Accurate Alternatives to Indirect S-Parameter Methods.
  Dominique Schreurs and Jan Verspecht
  K.U.Leuven, div. ESAT-TELEMIC
  Classic large-signal device models are indirectly derived from small-signal S-parameter measurements. Due to the availability of the “Non-linear Network Measurement System” (NNMS), models can be based directly upon full two-port large-signal measurements, resulting in higher model accuracy. In this paper we discuss three large-signal measurement based modelling approaches.
  (pdf - 500kB)
• Easy and Accurate Empirical Transistor Model Parameter Estimation from Vectorial Large-Signal Measurements.
  D. Schreurs, J. Verspecht, S. Vandenberghe, G. Carchon., K. van der Zanden, B. Nauwelaers
  Conference Record of the IEEE Microwave Theory and Techniques Symposium 1999 , Anaheim, California (USA), June 1999
  The standard empirical non-linear model parameter estimation is often cumbersome as several measurement systems are involved. We show that the model generation complexity can be reduced tremendously by only using full two-port vectorial large-signal measurements. Furthermore realistic operating conditions can easily be included in the optimisation procedure, as we illustrate on GaAs PHEMTs.
  (pdf - 70kB)
• Direct Extraction of the Non-linear HEMT model from Vectorial Large-Signal Measurements.
  D. Schreurs, S. Vandenberghe, J. Verspecht, B. Nauwelaers, A. Van de Capelle
  KULeuven, div. ESAT-TELEMIC
  Non-linear models for microwave and millimetre wave devices are commonly based on DC and S-parameter measurements, due to the absence of vectorial large-signal measurements in the past. At present, accurate prototype measurement systems are being developed, which implies that new non-linear modelling techniques can be explored. We will show experimental results of a method that allows the direct extraction of the HEMT's state-functions from vectorial large-signal measurements.
  (pdf - 200kB)
• IM3 Suppresion using a Technology Independent Method based on Vectorial Large-Signal Measurements.
  D. Schreurs, T. Visan, S. Vandenberghe, H. van Meer, K. van der Zanden, B. Nauwelaers, and R. Bosisio
  K.U.Leuven, div. ESAT-TELEMIC
  The linearisation of power amplifiers is an important issue, as the analog and especially digital baseband signals to be communicated become gradually more complex. We show that the predistortion signal, needed to cancel the third-order intermodulation product IM3, can accurately and straightforwardly be determined from two-tone vectorial large-signal measurements. We demonstrate that this quasi-automatic procedure is independent of component technology and operation class. Furthermore, we indicate that a black-box model, that represents the measured intermodulation product’s dependencies, can be identified.
  (pdf - 90kB)
• Non-linear Device Modeling and Circuit Design based on Vectorial Large-Signal Measurements.
  Dominique Schreurs
  K.U.Leuven, div. ESAT-TELEMIC
  At present, precise vectorial large-signal measurement systems, like the HP Non-linear Network Mea-
  surement System, are being developed, which implies that new techniques to enhance non-linear circuit
  design can be explored. The most important aspect of non-linear circuit design is an accurate model
  of the non-linear device. Such non-linear models for microwave and millimetre wave devices are com-
  monly based on DC and S-parameter measurements. We will discuss a method that allows to directly
  extract the non-linear model of one- and two-port devices from vectorial large-signal measurements.
  (pdf - 343kB)
• Measuring Transistor Dynamic Loadlines and Breakdown Currents under Large-Signal High-Frequency Operating Conditions.
  Jan Verspecht, Dominique Schreurs
  IEEE MTT-S International Microwave Symposium Digest, Vol. 3, pp. 1495-1498, Baltimore, USA, June 1998
  The “Nonlinear Network Measurement System” accurately measures dynamic loadlines and breakdown currents of microwave transistors under highfrequency large-signal operating conditions. This measurement capability allows the designer to find optimal operating conditions for a given device without the need for large-signal models. Measuring RF breakdown currents allows the designer to tackle reliability issues in a way not possible before.
  (pdf - 100kB)

Behavioral Modeling

Scattering Functions and “Large – signal S-parameters”

• Microwave Network Design Using the Scattering Matrix
  Janusz A. Dobrowolski, Institute of Electronic Systems, Warsaw University of Technology
  Artech House Microwave Library
  October 31, 2010, 280 pages, ISBN: 978-1-60807-129-6
  Scattering parameters or S-parameters (the elements of a scattering matrix) describe the electrical behaviors of linear electrical networks when undergoing various stimuli by electrical signals. The parameters of the scattering matrix are highly useful to electrical engineers involved with microwave circuit and system design. This authoritative resource provides comprehensive and detailed coverage of the wave approach to microwave network characterization, analysis, and design using scattering parameters. For the first time in any book, all aspects and approaches to wave variables and the scattering matrix are explored. The book compares and contrasts voltage waves, travelling waves, pseudo waves, and power waves, and explains the differences between real scattering parameters, pseudo scattering parameters, and power scattering parameters. Moreover, professionals find clear methods for standard single-ended multiport network design and noise analysis. This in-depth reference is packed with over 1,100 equations and numerous illustrations.
  (link)
• High-frequency nonlinear amplifier model for the efficient evaluation of inband distortion under nonlinear load-pull conditions.
  G. Vandersteen, F. Verbeyst, P. Wambacq, S. Donnay
  Design, Automation and Test in Europe Conference and Exhibition. Proceedings - pp. 586 - 590, March 2002
  4-8 March 2002
  Designing complex analog systems needs different abstraction levels to reduce the overall complexity. The required level of abstraction depends on the accuracy and the purpose of the model. High-frequency amplifier modeIs can vary from simple transfer functions for efficient bit-error-rate analysis up to detailed transistor level descriptions for accurate load-pull prediction. This paper introduces a nonlinear black-box model for high-frequency amplifiers. It extends the linear S-parameter representation to enable both efficient system-level simulations and load-pull prediction. Both are demonstrated on the measurements of a high-frequency amplifier excited using a WLAN-OFDM modulation.
  (pdf - 347 kB)
• Measurement Based Behavioral Modeling of Components under Modulated Large-Signal Operating Conditions.
  Jan Verspecht, Frans Verbeyst, Marc Vanden Bossche
  Agilent Technologies, NMDG, VUB-ELEC
  It is shown in this paper how measurement based behavioural models can be build that accurately predict effects which are present under modulated large-signal operating conditions. The effects modelled include compression, AM-to-PM, spectral regrowth, harmonics, large signal-input match,...
  (pdf - 82kB)
• Network Analysis Beyond S-parameters: Characterizing and Modeling Component Behaviour under Modulated Large-Signal Operating Conditions.
  Jan Verspecht, Frans Verbeyst, Marc Vanden Bossche
  56th ARFTG Conference Proceedings, Broomfield, Colorado, USA, December 2000
  It is shown in this paper how the classical concept of the “network analyser” can be extended towards modulated and large-signal operating conditions. The concept is demonstrated by measuring the saturated behaviour of a MMIC amplifier, excited by modulated signals with CDMA characteristics. It is then illustrated how the measured data can be used to construct an accurate behavioural model.
  (pdf - 105kB)
• System Level Simulation Benefits from Frequency Domain Behavioral Models of Mixers and Amplifiers.
  Jan Verspecht, Frans Verbeyst, Marc Vanden Bossche, Patrick Van Esch
  Hewlett-Packard EEsof, VUB-ELEC
  Novel generic frequency domain behavioural models are constructed for mixers and amplifiers. The modelling is based upon three concepts: time-invariant describing functions, linearisation and multidimensional curve fitting. The model parameters can be calculated based upon measured or simulated data. Model performance is illustrated on practical examples.
  (pdf- 50kB)
• Accurately Characterizing Hard Nonlinear Behavior of Microwave Components with the Nonlinear Network Measurement System: Introducing `Nonlinear Scattering Functions'.
  Jan Verspecht, Patrick Van Esch
  Proceedings of the 5th International Workshop on Integrated Nonlinear Microwave and Millimeterwave Circuits, pp. 17-26, Duisburg, Germany, October 1998 (Invited Paper)
  This paper describes an original way of dealing with the measuring and modeling of microwave transistor nonlinear behavior. Although generalizations are possible, the method described in this particular paper deals with transistor behavior under a large signal one-tone excitation, with arbitrary impedance terminations for the fundamental and the harmonics. First the mathematical theory of the “nonlinear scattering functions” is described. Next the measurement set-up and the actual extraction of the model parameters is highlighted. Finally the model is implemented in a commercial harmonic balance simulator. Using the simulator, model verification is performed by comparing measured and modeled behavior.
  (pdf - 123kB)
• Characterizing Components Under Large Signal Excitation: Defining Sensible `Large Signal S-Parameters'?!.
  J. Verspecht, M. Vanden Bossche, F. Verbeyst
  49th ARFTG Conference Digest, Denver, Colorado (USA), pp.109-117, June 1997
  A measurement and black-box modeling technique is described enabling the characterization of nonlinear microwave components under periodic large-signal excitation. First, the mathematical model is theoretically described. The model is based on the assumption that the superposition principle holds for the effect of all spectral components, except the fundamental, of the incident travelling voltage waves. This assumption implies that, with fixed fundamental power and biasing conditions, the incident harmonics interact with the component as if it is a linear time-varying circuit. Since the superposition coefficients are a natural extension of the classical scattering parameters they are called “large signal s-parameters”. These coefficients are a function of fundamental power and biasing conditions. An automated set-up is described enabling to accurately measure these coefficients. The set-up is based on a “vectorial nonlinear network-analyzer”, which accurately measures the phase and amplitude of all spectral components of both incident and reflected travelling voltage waves. The experimental model extraction method is illustrated on a heterojunction bipolar and a field effect transistor, driven hardly nonlinear. The “vectorial nonlinear network-analyzer” is used in order to successfully verify the validity of the extracted model. The black-box model is finally integrated in a commercial harmonic balance simulator.
  (pdf - 115kB)
• Black Box Modelling of Power Transistors in the Frequency Domain.
  Jan Verspecht
  Conference Record of the 4th International Workshop on Integrated Nonlinear Microwave and Millimeterwave Circuits (INMMC'96), Duisburg (Germany), pp. 58-63, October 1996
  A frequency domain black box model for power transistors is proposed. It can accurately predict the behavior of the transistor for a one tone excitation with arbitrary fundamental and harmonic impedances present at the output. The model parameters can be extracted out of a limited set of “nonlinear network analyzer” measurements. Both simulated as well as measured results are given.
  (pdf - 87kB)
• Black Box Modelling of Hard Nonlinear Behavior in the Frequency Domain.
  Jan Verspecht, Dominique Schreurs, Alain Barel, Bart Nauwelaers
  Conference Record of the IEEE Microwave Theory and Techniques Symposium 1996 , San Francisco (USA), pp. 1735-1738, June 1996
  A black box model is proposed to describe nonlinear devices in the frequency domain. The approach is based upon the use of describing functions and allows a better description of hard nonlinearities than an approach based upon the Volterra theory. Simulations and experiments are described illustrating the mathematical theory.
  (pdf - 60kB)
• Describing Functions Can Better Model Hard Nonlinearities In The Frequency Domain Than The Volterra Theory.
  Jan Verspecht
  Annex Thesis Phd.
  In this text a new kind of model is proposed to describe nonlinear devices in the frequency domain. The approach is based upon the use of describing functions and allows the description of hard nonlinearities better than an approach based upon the Volterra theory.
  (pdf - 107kB)

Volterra

• Using Orthogonal Polynomials as Alternative for VIOMAP to Model Hardly Nonlinear Devices.
  Frans Verbeyst.
  47th ARFTG Conference Proceedings, June 1996
  Being a series approximation, VIOMAP is not well suited to model hardly nonlinear devices due to numerical problems. The prediction of two-tone behavior based on one-tone measurements of a microwave power amplifier which is driven deeply into compression, is used as test case to show the potentials of a possible alternative which is based on orthogonal polynomials.
  (pdf - 120kB)
• The Volterra Input-Output Map of a High-Frequency Amplifier as a Practical Alternative to Load-Pull Measurements.
  F. Verbeyst and Marc Vanden Bossche
  IEEE Transactions on Instrumentation and Measurement , Vol. 44, No. 3, pp. 662-665, June 1995
  Using a nonlinear black-box model based on the Volterra theory it is possible to describe the nonlinear behavior of a high frequency amplifier. Acquiring only a strongly reduced set of measurements it is easy to predict the load impedance curves anywhere on a Smith Chart. The classic load-pull approach involves the acquisition of a large amount of data and still lacks a description of the nonlinear behavior of the amplifier in deviating situations.
  (pdf - 174kB)
• Enhancing the Linearity of Digital Communication Channels Using IQ Predistortion Based Upon an Inverse VIOMAP.
  Frans Verbeyst and Marc Vanden Bossche
  presentation at the IEEE Microwave Theory and Techniques Symposium 1995 , Orlando, Florida, USA, May 1995
  Modeling a nonlinear device, based on measurements at the carrier frequency only, it is possible to predict its response to narrow-band signals like 16QAM. Using an inverse of this model to predistort the IQ signal may result in poor reduction of spectral regrowth due to unmodeled subtle side-effects. Based on two-tone measurements a better model can be extracted such that the linearity of the overall system is significantly enhanced.
  (pdf - 128kB)
• VIOMAP, the S-parameter equivalent for weakly nonlinear RF and microwave devices.
  F. Verbeyst and M. Vanden Bossche
  IEEE Trans. Microwave Theory and Techniques , vol. 42, No. 12, pp. 2531-2535, December 1994
  This paper presents the Volterra input-output map as an extension of the S-parameters towards weakly nonlinear RF and microwave devices. This ‘VIOMAP’ can be measured and it can be used to predict the behavior of cascaded nonlinear twoports.
  (pdf - 109kB)

Test Signals supporting LSNA technolgy

• Phase de-trending of modulation signals.
  For a generated or measured modulated signal, the phase relationship between the tones remains constant but the phase of the carrier can be arbitrary. Moreover, when comparing phases of the multi-tone between different measurements, the phase values will change for each measurement. This paper explains how to align several measurements of a modulated signal.
  (pdf - 185 KB)
• Design of a Microwave Multisine Source Using Allpass Functions Estimated in the Richards Domain.
  Tom Van Den Broeck, Rik Pintelon, Alain Barel
  IEEE Transactions on Instrumentation and Measurement, Vol. 43, No. 5, October 1994
  In this paper a low-crest-factor microwave multisine source is developed. This is a broadband, periodic signal with a low crest factor (peak factor to effective value ratio). The design method consists of generating a pulse with a broad spectrum, amplitude filtering to get the desired power spectrum, and phase filtering for lowering the crest factor. A new technique to realize microwave phase filters is described. First, the properties of a rational allpass function in the Richards variable are examined. This enables us to estimate the coefficients using a nonlinear optimization technique. The function is realized with coupled transmission line filters. Using this general technique, a microwave multisine consisting of 20 components in the band [100 MHz, 2 GHz] is realized with a crest factor of 2.
  (pdf - 115kB)