Designers are under tight deadlines to create competitive circuits that meet stringent specifications covering performance, power, noise, and reliability.

There is a constant push to minimize silicon re-spins and that requires highly accurate verification.

Specialized analyses beyond typical methods need to be considered for analog circuits. While advanced process technologies provide the benefits of lower power and higher performance, designers must get more innovative to address growing design complexity due to a variety of factors. The prominent influencers are higher circuit density with noise vulnerability, decreasing supply voltage levels, increasing device and interconnect resistance and capacitance parasitics.

To properly verify these designs before silicon fabrication, specialized radio frequency RF analyses are required to accurately predict silicon behavior for which a high-performance RF simulation engine is needed. Both single and multi-tone Harmonic Balance analyses are essential in addressing these challenges for linear and moderately nonlinear periodic circuits such as LNA, PA, Mixer, Rx, Tx, etc.

along with some of the most common building blocks including VCOs LC-tank, ring and oscillators xtal, RTC, etc.

Why not just run the traditional AC, DC, transient, and transient noise analysis? Why require an RF engine with periodic analysis? To answer that, we need to understand what RF is first. RF applies to frequencies between 3 kHz to GHz.

A subset from 30 GHz to GHz is millimeter wave. These invisible waves are all around us as we immerse ourselves with the latest technological advancements in the mobile communication and networking world.

The analysis for any system that processes these frequencies needs to account for signal settling time and noise effects from within and around the system that can interfere with other signals in the system.

Some designers may be familiar with transient noise analysis TN where the use-model is straightforward. It produces noisy transient waveforms generated from random noise in circuit elements including resistors and transistors. The waveforms can often be postprocessed to get noise-related metrics.

TN analysis is an effective method for non-periodic circuits like PLLs and ADCs since periodic analysis may not be viable or may be very difficult to converge.

However, for periodic driven and autonomous circuits, RF analyses is a viable alternative. The disadvantages of running TN includes much longer simulation times, careful attention required for postprocessing, and no identification of top noise contributors. With the proliferation of mobile and wireless applications, device noise can be a limiting factor in meeting the increasingly stringent target specifications for RF blocks.

Traditional SPICE simulators cannot be used to predict this type of periodic noise since a long transient is required to allow the circuit to settle. It also entails several simulations and postprocessing steps that can be cumbersome and prone to user error.

Traditional SPICE also cannot accurately determine the noise in RF circuits such as mixers, LNAs, frequency dividers, oscillators, or PLLs.

Noise calculations in SPICE are based on small-signal linearized analysis of the circuit at its DC operating point, and this linearization affects proper frequency translation of noise due to circuit non-linearities.

In our experience, we have found that many designers find RF analysis confusing and even intimidating as it is not as straightforward as traditional analysis. Today, the two primary RF analysis methods are time-domain engine Shooting Newton or SN and frequency-domain engine Harmonic Balance or HB to verify periodic circuits for linearity, noise, and gain.

Both methods have their limitations and advantages. It is imperative to apply the most appropriate method, analyses, and options to maximize throughput for the required accuracy to garner maximum coverage and confidence before tapeout.

Periodic steady-state analysis can be thought of as an extension of SPICE operating point analysis. In SPICE, you apply DC signals to the circuit and the simulator computes the steady-state solution. That solution is the DC operating point at which you perform subsequent small-signal analyses.

In a periodic steady-state large signal analysis, you drive the circuit with one or more periodic sources.

The steady-state response is the response that results after any transient effects have dissipated. The large signal solution is the starting point for small-signal analyses, including periodic AC, periodic transfer function, periodic noise, periodic stability, and periodic scattering parameter analyses.

After calculating the DC operating point and running for some initial transient stabilization time tstab , we assume tstab is close to periodic steady state.

In SN, we start iterating in the time domain to solve for periodic steady-state solution. While the time domain view using PSS can show the net voltage waveform, the frequency domain view using HB can show output power at specific loading with various harmonics.

RF analyses are well suited for periodic driven and autonomous circuits. Driven circuits are driven by periodic time-varying independent sources and have a periodic solution.

Mixers, dividers, low noise amplifiers, transmit and receive chains, and power amplifiers are common examples of driven circuits.

In contrast, autonomous circuits contain non-time-varying independent sources. An autonomous circuit oscillates due to positive feedback, which results in a steady-state oscillation. Periodic autonomous circuits produce periodic time-varying outputs from non-time-varying sources.

The steady-state waveforms for the circuit are all periodic with the identical fundamental period. Ring oscillators, LC-tank oscillators, and crystal oscillators are periodic autonomous circuits.

Typical measurements from RF analyses focus on voltage gain in dB , power in dBm and linearity effects such as P1dB 1dB compression point and IP3 third order intercept point. Noise effects also can be accurately measured whereby Noise factor and Noise figure metrics are used.

Harmonic Balance is very well-suited for designs that have many reactive components as well as circuits in which time constants are large compared to the period of the simulation frequency, such as dispersive transmission lines.

Many linear models are best represented in the frequency domain at high frequencies. Usage examples include determining the spectral content of voltages or currents, calculating IP3, total harmonic distortion THD , and intermodulation distortion components, performing non-linear noise analysis, and load-pull analyses for amplifiers, etc.

Shooting Newton is very well-suited for most periodic driven circuits, especially non-linear circuits with sharp transitions such as switched-cap filter, divider and phase-frequency detector. Oscillators, such as ring and crystal, can also be target circuits.

SN accommodates a high number of harmonics. However, runtime and memory usage increase with time points or number of tones. SN is usually slower than HB for linear or moderately non-linear circuits.

HB is a frequency-domain analysis technique for simulating distortion in nonlinear electrical circuits and systems. In essence, it calculates the steady-state response of non-linear differential equations. It starts with KCL in the frequency domain and a chosen number of harmonics.

A sinusoidal signal applied to a non-linear component will generate harmonics of the fundamental frequency. HB analysis is most applicable for circuits that exhibit a linear to moderately nonlinear behavior, require high numerical accuracy and dynamic range, and use frequency-domain models such as tabulated S-parameters.

It is usually the method of choice for simulating circuits that are most naturally handled in the frequency domain such as analog RF and microwave designs that are excited with sinusoidal signals.

To perform an HB simulation, you only need to specify one or more fundamental frequencies and the order for each fundamental frequency. Within the context of high-frequency circuit simulation, HB offers several benefits over conventional time-domain transient analysis, wherein it obtains frequency-domain voltages and currents, directly calculating the steady-state spectral content of voltages or currents in the circuit.

The frequency integration required for transient analysis is prohibitive in many practical cases. It supports industry-standard netlist syntax and is seamlessly integrated into industry EDA design environments. The RF engine in AFS supports Shooting Newton and Harmonic Balance methods with recent innovations.

For silicon-accurate characterization, the AFS platform includes a comprehensive full-spectrum device noise analysis and integrates with Solido Variation Designer to deliver full variation-aware design coverage in orders-of-magnitude fewer simulations, but with the accuracy of brute force techniques.

The recently announced Analog FastSPICE eXTreme AFS XT technology further enhances performance for large post-layout netlists. There is no additional cost to existing and new customers.

AFS XT can handle over million element transient capacity and delivers mixed-signal simulation with Symphony Mixed-Signal platform. The AFS Harmonic Balance suite comprises of large signal HB analysis and small signal AC, transfer function, noise, stability, and scattering parameter analyses.

While single tone is supported for driven circuits and autonomous circuits, multi-tone is supported for driven circuits. It is most applicable for circuits with high dynamic range, for linear and moderately non-linear circuits and for circuits with distributed elements.

AFS HB solvers are further optimized for performance and convergence via automated intelligence algorithms. AFS HB utilizes multi-threaded capability for an additional performance speedup versus single core operations.

The AFS multi-core parallel feature MCP speeds up these simulations by 3. Table 1: AFS Harmonic Balance analyses. Large signal HB analysis determines periodic time varying operating points for single tone, and quasi-periodic time varying operating points for multi tone.

It allows a more effective verification that provides accuracy with a lesser number of simulations across all environmental corners, reducing the RF simulation complexity.

The Harmonic Balance method computes the periodic steady state of the circuit utilizing the frequency-domain, similar to the Shooting Newton method, which utilizes the time-domain. After a periodic steady-state solution is found, small signal analyses such as HB noise can also be run.

In this white paper, we focus on the application of Analog FastSPICE AFS Harmonic Balance HB engine that provides improved convergence, enhanced runtime and memory reduction via three case studies of circuits commonly simulated using HB.

We will provide a summary of performance and memory advantages of AFS HB.

However, runtime and memory usage increase with time points or number of tones. SN is usually slower than HB for linear or moderately non-linear circuits. HB is a frequency-domain analysis technique for simulating distortion in nonlinear electrical circuits and systems. In essence, it calculates the steady-state response of non-linear differential equations.

It starts with KCL in the frequency domain and a chosen number of harmonics. A sinusoidal signal applied to a non-linear component will generate harmonics of the fundamental frequency. HB analysis is most applicable for circuits that exhibit a linear to moderately nonlinear behavior, require high numerical accuracy and dynamic range, and use frequency-domain models such as tabulated S-parameters.

It is usually the method of choice for simulating circuits that are most naturally handled in the frequency domain such as analog RF and microwave designs that are excited with sinusoidal signals.

To perform an HB simulation, you only need to specify one or more fundamental frequencies and the order for each fundamental frequency.

Within the context of high-frequency circuit simulation, HB offers several benefits over conventional time-domain transient analysis, wherein it obtains frequency-domain voltages and currents, directly calculating the steady-state spectral content of voltages or currents in the circuit.

The frequency integration required for transient analysis is prohibitive in many practical cases. It supports industry-standard netlist syntax and is seamlessly integrated into industry EDA design environments.

The RF engine in AFS supports Shooting Newton and Harmonic Balance methods with recent innovations. For silicon-accurate characterization, the AFS platform includes a comprehensive full-spectrum device noise analysis and integrates with Solido Variation Designer to deliver full variation-aware design coverage in orders-of-magnitude fewer simulations, but with the accuracy of brute force techniques.

The recently announced Analog FastSPICE eXTreme AFS XT technology further enhances performance for large post-layout netlists. There is no additional cost to existing and new customers. AFS XT can handle over million element transient capacity and delivers mixed-signal simulation with Symphony Mixed-Signal platform.

The AFS Harmonic Balance suite comprises of large signal HB analysis and small signal AC, transfer function, noise, stability, and scattering parameter analyses.

While single tone is supported for driven circuits and autonomous circuits, multi-tone is supported for driven circuits. It is most applicable for circuits with high dynamic range, for linear and moderately non-linear circuits and for circuits with distributed elements.

AFS HB solvers are further optimized for performance and convergence via automated intelligence algorithms.

AFS HB utilizes multi-threaded capability for an additional performance speedup versus single core operations. The AFS multi-core parallel feature MCP speeds up these simulations by 3. Table 1: AFS Harmonic Balance analyses. Large signal HB analysis determines periodic time varying operating points for single tone, and quasi-periodic time varying operating points for multi tone.

All signals must be co-periodic with the fundamental frequency. After a periodic steady-state solution is found, the listed small signal analyses can be run. Achieving proper convergence in HB can be a challenge for complex designs.

Relaxation of convergence parameters is a logical approach, but it takes a toll on accuracy. Furthermore, verification complexity increases with increasing harmonics. Extracted netlists further introduce much more convergence complexity compared to schematics. Capacity refers to the number of elements contained in the netlist including active and passive devices, parasitic elements, etc.

As shown in figure 2, AFS RF analyses can easily handle designs with high element count. The ability to handle large netlists is crucial for RF analyses, especially as we move towards advanced process nodes. Ultimately, faster simulations without accuracy loss are needed to meet aggressive design deadlines.

Figure 3 shows examples of runtime and memory utilization benefits of AFS XT from AFS for a wide range of circuits. For periodic driven and autonomous circuits, choose your analysis engine wisely with the capabilities and benefits that AFS RF engines provide with both Shooting Newton and Harmonic Balance.

The Harmonic Balance suite comprises of large signal HB analysis and a variety of small signal analyses. March 24th, - By: Pradeep Thiagarajan.

By Pradeep Thiagarajan and Scott Guyton The world we live in is intricately connected by electronic systems that are expected to function flawlessly to satisfy consumer needs.

Why do we need periodic analysis? What is periodic analysis? RF Shooting Newton versus Harmonic Balance In our experience, we have found that many designers find RF analysis confusing and even intimidating as it is not as straightforward as traditional analysis.

Typical applications and measurements for RF analyses RF analyses are well suited for periodic driven and autonomous circuits. How does RF Harmonic Balance work? RF Harmonic Balance offerings The AFS Harmonic Balance suite comprises of large signal HB analysis and small signal AC, transfer function, noise, stability, and scattering parameter analyses.

Table 1 below summarizes the AFS RF Harmonic Balance offerings. Small signal summary HBAC is useful for measuring intermodulation distortion, conversion gain and RF-to-LO isolation etc.

Transfer function is computed from one input to multiple outputs and includes frequency conversion effects. HBXF is useful to determine image and sideband rejection and power supply rejection.

HBXF is the inverse of HBAC and determines the transfer functions from multiple input to one output. HBSTB is useful to determine stability in oscillators and switched capacitor circuits.

It can be used to measure loop gain when a large periodic signal is present that may cause non-linearity. After the needle is inserted, a small amount of blood will be collected into a test tube or vial. You may feel a little sting when the needle goes in or out.

This usually takes less than five minutes. There is very little risk to having a blood test. You may have slight pain or bruising at the spot where the needle was put in, but most symptoms go away quickly. A1C results tell you what percentage of your hemoglobin is coated with glucose.

The percent ranges are just a guide to what is normal. What's normal for you depends on your health, age, and other factors. Ask your provider what A1C percentage is healthy for you. Providers often use more than one test to diagnose diabetes. So, if your test result was higher than normal, you may have another A1C test or a different type of diabetes test , usually either a fasting blood glucose test or an oral glucose tolerance test OGTT.

If your A1C test was done to monitor your diabetes, talk with your provider about what your test results mean. Learn more about laboratory tests, reference ranges, and understanding results.

The A1C test is not used to diagnose gestational diabetes or type 1 diabetes. Also, if you have a condition that affects your red blood cells, such as anemia or another type of blood disorder , an A1C test may not be accurate for diagnosing diabetes.

Kidney failure and liver disease can also affect A1C results. In these cases, your provider may recommend different tests to diagnose diabetes and prediabetes.

The information on this site should not be used as a substitute for professional medical care or advice. Contact a health care provider if you have questions about your health. Hemoglobin A1C HbA1c Test. What is a hemoglobin A1C HbA1C test? An A1C test can show your average glucose level for the past three months because: Glucose sticks to hemoglobin for as long as the red blood cells are alive.

Red blood cells live about three months. Other names: HbA1C, A1C, glycohemoglobin, glycated hemoglobin, glycosylated hemoglobin. What is it used for? An A1C test may be used to screen fo r or diagnose: Type 2 diabetes.

With type 2 diabetes your blood glucose gets too high because your body doesn't make enough insulin to move blood sugar from your bloodstream into your cells, or because your cells stop responding to insulin.

Prediabetes means that your blood glucose levels are higher than normal, but not high enough to diagnosed as diabetes. Lifestyle changes, such as healthy eating and exercise , may help delay or prevent prediabetes from becoming type 2 diabetes.

Why do I need an HbA1C test? The Centers for Disease Control CDC recommends A1C testing for diabetes and prediabetes if: You are over age If your results are normal, you should repeat the test every 3 years. Modiano, D. Haemoglobin C protects against clinical Plasmodium falciparum malaria.

Nature , —, doi: Article ADS CAS PubMed Google Scholar. Taylor, S. Haemoglobinopathies and the clinical epidemiology of malaria: a systematic review and meta-analysis.

Lancet Infect Dis 12 , —, doi: Williams, T. Sickle cell trait and the risk of Plasmodium falciparum malaria and other childhood diseases. J Infect Dis , —, doi: Nat Genet 37 , —, doi:ng Red blood cell variants and malaria: a long story not yet over.

Article PubMed Google Scholar. Agarwal, A. Hemoglobin C associated with protection from severe malaria in the Dogon of Mali, a West African population with a low prevalence of hemoglobin S. Blood 96 , — CAS PubMed Google Scholar. Travassos, M. Hemoglobin C Trait Provides Protection From Clinical Falciparum Malaria in Malian Children.

Muehlenbachs, A. Hypertension and maternal-fetal conflict during placental malaria. PLoS Med 3 , e, doi: Umbers, A. Malaria in pregnancy: small babies, big problem.

Trends Parasitol 27 , —, doi: Desai, M. Epidemiology and burden of malaria in pregnancy. Lancet Infect Dis 7 , 93—, doi: Steketee, R. The burden of malaria in pregnancy in malaria-endemic areas.

Am J Trop Med Hyg 64 , 28—35, doi: Article CAS PubMed Google Scholar. Bouyou-Akotet, M. Prevalence of Plasmodium falciparum infection in pregnant women in Gabon. Malar J 2 , 18, doi: Patel, J. Absence of Association Between Sickle Trait Hemoglobin and Placental Malaria Outcomes.

Am J Trop Med Hyg 94 , —, doi: Huynh, B. Influence of the timing of malaria infection during pregnancy on birth weight and on maternal anemia in Benin.

Am J Trop Med Hyg 85 , —, doi: Cottrell, G. Submicroscopic Plasmodium falciparum Infections Are Associated With Maternal Anemia, Premature Births, and Low Birth Weight.

Clin Infect Dis 60 , —, doi: PubMed Google Scholar. Fairhurst, R. Abnormal display of PfEMP-1 on erythrocytes carrying haemoglobin C may protect against malaria. Microbes Infect 14 , —, doi: Article CAS PubMed PubMed Central Google Scholar. Srivastava, A.

Full-length extracellular region of the var2CSA variant of PfEMP1 is required for specific, high-affinity binding to CSA. Proc Natl Acad Sci USA , —, doi: Article ADS CAS PubMed PubMed Central Google Scholar.

Viebig, N. A single member of the Plasmodium falciparum var multigene family determines cytoadhesion to the placental receptor chondroitin sulphate A. EMBO Rep 6 , —, doi Gamain, B. Identification of multiple chondroitin sulfate A CSA -binding domains in the var2CSA gene transcribed in CSA-binding parasites.

J Infect Dis , —, doi:JID Disruption of var2csa gene impairs placental malaria associated adhesion phenotype. PLoS One 2 , e, doi: Cyrklaff, M.

Oxidative insult can induce malaria-protective trait of sickle and fetal erythrocytes. Nat Commun 7 , , doi: Kilian, N.

Hemoglobin S and C affect protein export in Plasmodium falciparum-infected erythrocytes. Biol Open 4 , —, doi: Ndam, N. Protective Antibodies against Placental Malaria and Poor Outcomes during Pregnancy, Benin. Emerg Infect Dis 21 , —, doi: Consequences of gestational malaria on birth weight: finding the best timeframe for intermittent preventive treatment administration.

PLoS One 7 , e, doi: Kelly-Hope, L. The multiplicity of malaria transmission: a review of entomological inoculation rate measurements and methods across sub-Saharan Africa.

Malar J 8 , 19, doi: Wooden, J. PCR and strain identification in Plasmodium falciparum. Parasitol Today 9 , —, doi: Core-Team, R. R A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria Download references.

and N. were supported by the European 7th Framework Programme contract no. is supported by the Intramural Research Program, NIAID, NIH. is supported by the Institut National de la Recherche Médicale.

We are grateful to the women who participated in this study. Institut de Recherche pour le Développement, UMR , Mère et Enfant face aux Infections Tropicales, Paris, France.

COMUE Sorbonne Paris Cité, Faculté de Pharmacie, Paris, France. Laboratory of Malaria and Vector Research, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Rockville, MD, USA.

You can also search for this author in PubMed Google Scholar. performed the experiments. designed the experiments and analysed the data; M. designed the experiments, analysed the data, and wrote the paper. Correspondence to Benoît Gamain. Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Open Access This article is licensed under a Creative Commons Attribution 4. Reprints and permissions. Tétard, M. Heterozygous HbAC but not HbAS is associated with higher newborn birthweight among women with pregnancy-associated malaria.