Non-Linear Simulation by Harmonic Balance Techniques of Load Modulated Power Amplifier Driven by Random Modulated Signals

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Manuscript is well written and proposes a non-linear simulation of harmonic balance techniques of load modulated power amplifier driven by random modulated signals.

However, the authors should consider the following comments to help them revise their manuscript for further consideration and possible publication:

1. Starting with the proposed manuscript title, the authors should delete the part "Comparison with measured results.". This is because paper titles do not contain punctuation marks or multiple sentences.

2. The abstract should be re-written to meet the minimum standard for a journal article. I am not sure why the statement "To our knowledge, the full simulation, in the frequency domain, of a LMPA driven by a random modulated signal, and the comparison with measured results have never been published before and appears as a major innovation..." is placed in the abstract. The statement simply means that the authors are not even sure about the originality of their work. The statement should be deleted and the abstract re-written to highlight the proposed work and included some quantifiable results achieved in the manuscript.

3. Figure 1 needs to be improved for better readability.

4. Figure 9 should re-considered. part (c) of the figure should be deleted and the information in it captured in the body of the manuscript. Part (c) did not even feature in the Figure 9 label.

5. The conclusion should be revised and supported by the results achieved/reported in the manuscript.

Comments on the Quality of English Language

Moderate editing of English language required.

Author Response

First of all, the authors would like to thank again the editor, the associate editor, and the reviewers for their last useful comments and suggestions to improve the quality of the manuscript.

Below are written our responses in blue and italic according to the reviewer’s comments in black.

Our revisions in the manuscript are written in red to be highlighted.

Manuscript is well written and proposes a non-linear simulation of harmonic balance

However, the authors should consider the following comments to help them revise their manuscript for further consideration and possible publication:

1. Starting with the proposed manuscript title, the authors should delete the part " Comparison with measured results. ". This is because paper titles do not contain punctuation marks or multiple sentences.

We modified the title to cancel the punctuation marks or multiple sentences. The new title is an unique sentence and is the following one: “Non-Linear Simulation by Harmonic Balance Techniques of Load Modulated Power Amplifier Driven by Random Modulated Signals.”

2. The abstract should be re-written to meet the minimum standard for a journal article. I am not sure why the statement " To our knowledge, the full simulation, in the frequency domain, of a LMPA driven by a random modulated signal, and the comparison with measured results have never been published before and appears as a major innovation... " is placed in the abstract. The statement simply means that the authors are not even sure about the originality of their work. The statement should be deleted and the abstract re-written to highlight the proposed work and included some quantifiable results achieved in the manuscript.

As suggested by the reviewer, we remove the sentence “To our knowledge, the full simulation, in the frequency domain, of a LMPA driven by a random modulated signal, and the comparison with measured results have never been published before and appears as a major innovation in the frame of the simulation of future RF circuits and sub-systems for telecommunication applications.”.

We replaced it with the following one: “The time-domain measurement allows the validation of the new simulation technique through the comparison of both the measured and the simulated Error Vector Magnitude (EVM), the left and right Adjacent Channel Power Ratios (ACPRs) versus the average output power. This new simulation is then called Pseudo-Random Modulated Harmonic Balance (PRM-HB) simulation. The full PRM-HB simulation of a LMPA driven by a random modulated signal, performed in the frequency-domain at design circuit level, results in an advanced simulation tool in the frame of the design of RF circuits and sub-systems for telecommunication applications.”.

We also added this sentence in the abstract: “The non-linear microwave circuit and the driving Pseudo-Random Modulated (PRM) generator are integrally defined in the frequency-domain. The simulation is implemented and performed in a commercially available circuit simulation software.”

3. Figure 1 needs to be improved for better readability.

As suggested by the reviewer, we simplify the Figure 1, removing some unreadable figures and focusing on the flow-graph to generate the modulated voltage that drives the Amplifier under test to perform the PRM-HB simulation and calculates the input and output voltages and currents defined in the frequency-Domain. The Figure 1 also shows that the demodulation and post processing is realised after the PRM simulation in the data display thanks to AEL in-house XLIM defined functions and 6 post processing steps detailed in the text.

The new Figure one is the following one:

(New Figure in joined pdf file)

We also modified the title of Figure 1 by : “Principle of the proposed frequency-domain simulation by HB techniques of Pseudo-Random-Modulated signals (PRM-HB).”.

4. Figure 9 should re-considered. part (c) of the figure should be deleted and the information in it captured in the body of the manuscript. Part (c) did not even feature in the Figure 9 label.

As suggested by the reviewer, we deleted part (c) of Figure 9 and we add the previous information within the text.

The new Figure 9 and the associated text are the following ones:

“The schematic used for the [3.2-3.6] GHz asymmetric packaged Quasi-MMIC SI-DPA is given in Figure 9 [1]. This power amplifier is based on the use of an 8x275mm GH25-10 GaN HEMT for the main amplifier and a 2x8x275mm GH25-10 GaN HEMT for the peak amplifier.”

(New Figure in joined pdf file)

Figure 9. Layout (a), Demonstration board (b) of the realized asymmetric packaged Quasi-MMIC SI-DPA [1].

5. The conclusion should be revised and supported by the results achieved/reported in the manuscript.

As suggested by the reviewer, we revised the conclusion as follows:

6. Conclusion

The steady state and the non-linear stability simulations of a load modulated power amplifier (LMPA) driven by a random modulated generator are presented. The simulation is fully performed in the frequency domain by Harmonic Balance techniques. The demodulation of the output signal of the DUT is implemented, with optimal matched filters, as a software-defined demodulation, saving a lot of computation time.

This article presents a general methodology to perform a whole frequency-domain simulation of non-linear circuits driven by PRM microwave signals in the frame of almost-periodic HB. In the hereby-proposed methodology, the PRM microwave signals are generated by periodizing the pseudo-random bit sequences allowing almost periodic HB.

The simulated dynamic results of a Quasi-MMIC GaN LMPA: a Doherty Power Amplifier (DPA), are shown and compared to the measured results with a 16-QAM driving signal at 10MS/s.

The dynamic modulation criteria and power metrics (Adjacent-Channel Power Ratio (ACPR), Error Vector Magnitude (EVM)) simulated performances at design circuit level, in the frequency domain, are calculated and compared to the ones obtained with a specific THA-based time-domain calibrated test-bench developed at XLIM.

These comparisons between measured and simulated results present rather good agreements, especially in the OBO region where the EVM presents local minimum values.

To summarize, the PRM-HB simulation tool allows simulations of any High-Power Amplifier (HPA) driven with any random modulated signals at a circuit level in the frequency domain. It can be extended to multi-carrier applications as, for example, satellite transmissions.

The full simulation, in the frequency domain, including the steady state and the non-linear stability of a LMPA driven by a random modulated signal is, for the first time, presented. This new pseudo-random modulated Harmonic Balance simulation of the entire DPA is validated by large signal time-domain measurements of the realized DPA.

For telecommunication applications, this PRM-HB is an advanced and original improvement of the simulation tool of RF circuits and sub-systems, at circuit level. Effectively, it will help the circuit designers to have a deep insight and understanding of the operation of non-linear circuits when driven with modulated signals. The presented PRM-HB method will effectively complement the joint optimization of Power added efficiency, Output Power, RF Bandwidth, and linearity generally performed using Continuous Wave Harmonic Balance during the design process of Power amplifiers. The PRM-HB simulation during the first step of PA design process, at a circuit level, will then enable the electrical knowledge of the power amplifier in the presence of modulated signals as they are in real life with extraction of system-level criteria.

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This article proposes many simulations techniques and a simulation tool PRM-HB that allows simulations of any High-Power Amplifier (HPA) driven with any random modulated signals at a circuit level in the frequency domain. Also it presents the simulation of the steady state and the non-linear stability of a Load Modulated Power Amplifier (LMPA) driven by a random modulated generator, fully performed in the frequency domain.

The presented topic can be relevant for the telecommunication fields as it presents a basis for future physical research.

Full simulation in frequency domain of LMPA including the steady state and the non-linear stability, driven by a random modulated signal, was made. Many simulations were compared with measured data.

The methods are well described, but the authors have implemented a more abstract approach, even though the results are compared with measured results, it is not clearly described how the simulation tool will improve the future studies of this topic.

The contributions are not clearly highlighted. The state-of-the-art is is very summary presented. What are the original elements? What is the novelty of the paper?

The references are on topic and conclusive for the described studies.

 

 

Comments on the Quality of English Language

A proofreading is required. There are some paragraphs difficult to read and understand.

Author Response

First of all, the authors would like to thank again the editor, the associate editor, and the reviewers for their last useful comments and suggestions to improve the quality of the manuscript.

Below are written our responses in blue and italic according to the reviewer’s comments in black.

Our revisions in the manuscript are written in red to be highlighted.

This article proposes many simulations techniques and a simulation tool PRM-HB that allows simulations of any High-Power Amplifier (HPA) driven with any random modulated signals at a circuit level in the frequency domain. Also it presents the simulation of the steady state and the non-linear stability of a Load Modulated Power Amplifier (LMPA) driven by a random modulated generator, fully performed in the frequency domain.

The presented topic can be relevant for the telecommunication fields as it presents a basis for future physical research.

Full simulation in frequency domain of LMPA including the steady state and the non-linear stability, driven by a random modulated signal, was made. Many simulations were compared with measured data.

The methods are well described, but the authors have implemented a more abstract approach, even though the results are compared with measured results, it is not clearly described how the simulation tool will improve the future studies of this topic.

As suggested by the reviewer, we modified the conclusion to describe how the simulation tool will improve the future studies of the topic. The conclusion is now the following one:

6. Conclusion

The steady state and the non-linear stability simulations of a load modulated power amplifier (LMPA) driven by a random modulated generator are presented. The simulation is fully performed in the frequency domain by Harmonic Balance techniques. The demodulation of the output signal of the DUT is implemented, with optimal matched filters, as a software-defined demodulation, saving a lot of computation time.

This article presents a general methodology to perform a whole frequency-domain simulation of non-linear circuits driven by PRM microwave signals in the frame of almost-periodic HB. In the hereby-proposed methodology, the PRM microwave signals are generated by periodizing the pseudo-random bit sequences allowing almost periodic HB.

The simulated dynamic results of a Quasi-MMIC GaN LMPA: a Doherty Power Amplifier (DPA), are shown and compared to the measured results with a 16-QAM driving signal at 10MS/s.

The dynamic modulation criteria and power metrics (Adjacent-Channel Power Ratio (ACPR), Error Vector Magnitude (EVM)) simulated performances at design circuit level, in the frequency domain, are calculated and compared to the ones obtained with a specific THA-based time-domain calibrated test-bench developed at XLIM

These comparisons between measured and simulated results present rather good agreements, especially in the OBO region where the EVM presents local minimum values.

To summarize, the PRM-HB simulation tool allows simulations of any High-Power Amplifier (HPA) driven with any random modulated signals at a circuit level in the frequency domain. It can be extended to multi-carrier applications as, for example, satellite transmissions.

The full simulation, in the frequency domain, including the steady state and the non-linear stability of a LMPA driven by a random modulated signal is, for the first time, presented. This new pseudo-random modulated Harmonic Balance simulation of the entire DPA is validated by large signal time-domain measurements of the realized DPA.

For telecommunication applications, this PRM-HB is an advanced and original improvement of the simulation tool of RF circuits and sub-systems, at circuit level. Effectively, it will help the circuit designers to have a deep insight and understanding of the operation of non-linear circuits when driven with modulated signals. The presented PRM-HB method will effectively complement the joint optimization of Power added efficiency, Output Power, RF Bandwidth, and linearity generally performed using Continuous Wave Harmonic Balance during the design process of Power amplifiers. The PRM-HB simulation during the first step of PA design process, at a circuit level, will then enable the electrical knowledge of the power amplifier in the presence of modulated signals as they are in real life with extraction of system-level criteria.

The contributions are not clearly highlighted. The state-of-the-art is very summary presented. What are the original elements? What is the novelty of the paper?

As suggested by the reviewer, we modified the abstract, the introduction and the conclusion to better highlight the contributions and to better define the originality of the paper.

Abstract: The simulation of the steady state and the non-linear stability of a Load Modulated Power Amplifier (LMPA) driven by a random modulated generator, fully performed in the frequency domain by Harmonic Balance (HB) techniques, is presented. The non-linear microwave circuit and the driving Pseudo-Random Modulated (PRM) generator are integrally defined in the frequency-domain. The simulation is implemented and performed in a commercially available circuit simulation software.  The demodulation of the output signal of the LMPA is implemented, with optimal matched filters, as a software-defined demodulation. The simulated dynamic results of a Quasi-MMIC GaN Doherty Power Amplifier (DPA) [1], are shown and compared to the measured results with a 16-QAM driving signal at 10MS/s. The time-domain measurement allows the validation of the new simulation technique through the comparison of both the measured and the simulated Error Vector Magnitude (EVM), the left and right Adjacent Channel Power Ratios (ACPRs) versus the average output power. This new simulation is then called Pseudo-Random Modulated Harmonic Balance (PRM-HB) simulation. The full PRM-HB simulation of a LMPA driven by a random modulated signal, performed in the frequency-domain at design circuit level, results in an advanced simulation tool in the frame of the design of RF circuits and sub-systems for telecommunication applications.

We improved the presentation of the state-of-the-art in the introduction and we also add some arguments for the originality and the novelty of our PRM-HB simulation method which lie in the fact that a non-linear microwave circuit, driven by a pseudo-random modulated carrier is fully simulated in the frequency domain, at the circuit level. We also add more sentences to highlight the advantages of the PRM-HB method compared with simulation methods which need time-domain integration (circuit envelope for instance). The introduction becomes then:

1. Introduction

Today, in the new telecommunication standards (5G and beyond), the modulations with large Peak to Average Power Ratio (PAPR) become conventional. Therefore, it is mandatory that circuit designers have an accurate and reliable software design tool allowing, in the same HB simulation-frame the simulation of RF components or subsystems with Continuous Wave (CW) or with modulated RF sources, at circuit level. Many efforts have already been done in the past decades to reach this objective. In 1996, J.F. Sevic et al. [2] present an overview of the possibilities to simulate circuits driven by modulated generators in the frame of already published Harmonic Balance (HB) and Behavioral techniques. This article indicates that, at that time, the HB solver couldn’t give the solution using the classical Newton-Raphson technique and the direct inversion of the Jacobian matrix for HB simulations with a high number of frequencies. Later, to overcome the issue of the high number of equations to be solved, generated by modulated signals, V. Rizzoli et al. [3] proposed an “inexact Newton Harmonic Balance” method. Most recently, [4] and [5] give some examples of multi-dimensional HB method. For instance, in the journal of neural engineering, a team from Stanford University [4], after periodizing the input signal, managed to perform a neural transient stimulation by piecewise HB techniques. Today, thanks to the work of many mathematicians such as Galerkin [6], [7] Krylov [8] or Saad [9] for instance, commercially available simulators (Keysight PATHWAVE Advanced Design System (ADS)®, Cadence SpectreRF®, Mentor Graphics Eldo-RF®) allow the HB simulation of circuits with a number of nodes exceeding several hundred thousand and millions of equations to be solved. Therefore, these simulations can now be performed under periodic and almost-periodic regimes with reasonable computation time, with one to three non-harmonically related fundamental frequencies.

While transient and envelope simulations use time-domain integration and need time-domain models of the whole circuit, HB simulation leads to a system of equations solved in the frequency domain, with frequency-domain models, except for the non-linear elements modelled by time-domain equations coupled to Fourier transforms.

The main drawback of this design process is that designer must continuously switch between simulations in time/frequency domains with different schematics and/or models of the circuit depending on the desired time/frequency domain simulation.

At microwaves and millimetre-waves, passive elements include dispersive transmission lines, interconnections between circuits (wire bonding) or radiating elements, for instance. The models of these passive elements are generally extracted from Electromagnetic (EM) or S-Parameter ([S]) simulations. After verification of the Kramers-Kronig relationships to ascertain their feasibility conditions [10-11], they are well defined in the frequency domain. But the results may not be easily transposable into the time-domain

With a unified frequency-domain simulation-frame, designers will be able to switch easily from one kind of simulation (Continuous Wave (CW)) to another one (Modulated Carrier) without having to modify their workspace.

The application of a unified frequency-domain simulation method, at circuit level, leveraging Harmonic Balance technique is proposed here and constitutes a major advanced improvement for designers of microwave non-linear devices (Amplifiers, mixers, oscillators for example). This method also saves simulation time.

In the hereby-proposed method, the Pseudo-Random Modulated (PRM) signals are generated by periodizing the pseudo-random symbol sequences which could have been generated with an external software, such as Matlab^® for example.

The driving random modulated generator is first transformed in a Pseudo-Random Modulated (PRM) generator with two fundamental frequencies: the carrier frequency  and, on the other hand, the modulating frequency  given by the user-defined length of the modulating random symbol sequence . The random modulated generator becomes then an almost periodic signal generator. Figure 1 illustrates how a M-QAM modulated signal is generated from two initial pseudo-random sequences to the transmitted modulated signal in the plane p_outPA. The TX and the Amplifier Under test (AUT) are integrated in the same schematic. The equivalent Rx function is developed within the data display.

(see new Figure in joined pdf file)

Figure 1. Principle of the proposed frequency-domain simulation by HB techniques of Pseudo-Random-Modulated signals (PRM-HB).

In this new introduction, we need to add two new references [10] and [11] as shown below:

“After verification of the Kramers-Kronig relationships to ascertain their feasibility conditions [10-11],…”

Adding these references required shifting the values of other references in the text. These changes are noted in red in the text references.

The references are the following ones:

10. Saunders, C. S.; Steer M. B., Passivity Enforcement for Admittance Models of Distributed Networks Using an Inverse Eigenvalue Method, in IEEE Transactions on Microwave Theory and Techniques, vol. 60, no. 1, pp. 8-20, Jan. 2012, doi: 10.1109/TMTT.2011.2171500.
11. Charest, A.; Nakhla, M.; Achar, R.; Saraswat, D., Passivity Verification of Delayed Rational Function Based Macromodels of Tabulated Networks Characterized by Scattering Parameters, in IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 1, no. 3, pp. 386-398, March 2011, doi: 10.1109/TCPMT.2010.2099750.

Finally, to synthesize the improvements of our PRM-HB simulation method, we also revised the conclusion as previously given.

The references are on topic and conclusive for the described studies.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have improved the manuscript by incorporating the comments from the previous round of peer-review. I am happy to approve for publication. 

Comments on the Quality of English Language

Final proof-reading required.

Author Response

Dear Reviewer,

Thank you for your comments.

I'm uploading the final version of the paper with the corrections recommanded by the Academic Editor.

There are some minor bugs, such as:

1. 1. Please underline that bit sequences are different bit streams but no OFDM signals. Further in the text, it is OK.

We modified the title of Fig.1 to explain that it represents the principle of the PRM-HB simulation realized with 4 different bit sequence generators (Not OFDM signal generation in this example).

Figure 1. Principle of the proposed PRM-HB frequency-domain simulation by HB techniques of Pseudo-Random-Modulated signals (this figure shows an example of an M-QAM with N different bit sequence generators)..

 

2. 13. What is EDdyn? Units on the axis?

We modified text lines 366 and 367 to specify that DE is the acronym for “Drain Efficiency” with a unit in percentage (%) as specified on the axis. The text is the following one:

          The dynamic curve of the dynamic Drain Efficiency (   , follows the equivalent CW Drain Efficiency (DE) curve with more dispersion.

 

 

 

3. Line 339 What is THA?

 

We assume that you mean line 379. We modified the text to explain that the acronym THA is for “Track & Hold Amplifier”. The text is now the following one:

Figure 14 describes the proposed 6-channel time-domain measurement system based on the use of 4 Track & Hold Amplifiers (THA) [27].

Best regards,

Denis BARATAUD

 

Author Response File: Author Response.pdf