\r\n\tThis necessitated a need to understand control theoretical concepts and system analysis in a discrete time domain, which gave rise to the area of discrete time control systems. This has helped control engineers and designers to theoretically ascertain the possibilities and limitations of a control system design implemented in a digital framework, whereas continuous time designs suffer from the essential mismatch in the nature of the underlying independent time variable in theoretical studies and practical implementation. Also, many practical systems are inherently discrete time in nature, sensors and transducers sample data only at fixed time intervals, and computers calculate the control input only in some finite time. \r\n\tTraditionally, fundamental concepts of discrete time control systems are derived from the continuous time counterpart upon time discretization of the latter and subsequent formal analysis. This gave rise to discrete time counterparts of system models and controllers in z-domain as well as in state space form. However, discrete time control system design and analysis matured as a discipline in itself with the advent of optimal and adaptive techniques solely based on discrete time approach. Robust nonlinear discrete time controllers were also developed utilizing the ideas of sliding modes, model predictive control, etc. \r\n\tThe techniques for parameter estimation and system identification are largely dominated by discrete time methods. Well-established Kalman filter and extended Kalman filters are developed in discrete time. Many discrete time stochastic filters are utilized in control systems to reduce the impact of noise and disturbance during practical implementation. \r\n\tDespite the developments in discrete time control designs and their usefulness in control system implementation, there are a few challenges like discretization effect on systems stability, communication loss, etc. which are also areas of serious research. With all its usefulness and limitations, discrete time control systems have found vast areas of application from process control and automation, robotics, network control systems and internet of things, control of networks and multi-agent systems, etc. \r\n\tThis book intends to provide the reader with an overview of detailed control system design methodologies in discrete time which are well-established in literature. Emerging areas of interest in discrete time systems catering to new and existing challenges are also welcomed.
",isbn:"978-1-83880-939-3",printIsbn:"978-1-83880-938-6",pdfIsbn:"978-1-83880-940-9",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"11adc19fee98d36348ba8456e6bf7bfb",bookSignature:"Dr. Sohom Chakrabarty",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/9253.jpg",keywords:"frequency domain, state space approach, model predictive control, sliding modes, LQR, LQG, parameter estimation, system identification techniques, Kalman filter, extended Kalman filter, discretization effects, communication loss",numberOfDownloads:52,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"August 12th 2019",dateEndSecondStepPublish:"September 2nd 2019",dateEndThirdStepPublish:"November 1st 2019",dateEndFourthStepPublish:"January 20th 2020",dateEndFifthStepPublish:"March 20th 2020",remainingDaysToSecondStep:"3 months",secondStepPassed:!0,currentStepOfPublishingProcess:4,editedByType:null,kuFlag:!1,editors:[{id:"196800",title:"Dr.",name:"Sohom",middleName:null,surname:"Chakrabarty",slug:"sohom-chakrabarty",fullName:"Sohom Chakrabarty",profilePictureURL:"https://mts.intechopen.com/storage/users/196800/images/system/196800.jfif",biography:"Mr. Chakrabarty obtained a PhD in control systems from Indian Institute of Technology Bombay, India, and currently holds the position of an Assistant Professor in Indian Institute of Technology Roorkee, India. He had also served as a Research Associate in University of Kent, UK, Visiting Faculty in Lodz University of Technology, Poland, and a Visiting Associate Professor of RMIT University, Australia. 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\n
1. Introduction
\n
Acute systemic inflammation is the host response to various insults, such as infection, trauma, hemorrhage, etc., and is mediated by the release in circulation of different cytokines, such as tumor necrosis factor alpha (TNF‐α) and interleukin‐1 (IL‐1), IL‐4, IL‐6, or IL‐10 [1, 2]. Such mediators possess both pro‐ and anti‐inflammatory properties. Furthermore, they are capable to activate the hypothalamo‐pituitary‐adrenal (HPA) axis and both the sympathetic and parasympathetic divisions of the autonomic nervous system (ANS), which subsequently may affect the immune response [1].
\n
However, safety mechanisms do sometimes fail, leading to a new continuum of disease—sepsis, septic shock, and multiple organ dysfunction syndrome (MODS). In this respect, patients develop nutrient deficiencies, which are associated with an increased risk of developing infections, organ failure, and death [3]. Consequently, artificial nutrition via the enteral or parenteral route is considered as an integral part of standard care. Recently, the concept of pharmaconutrition has emerged as an alternative approach, considering nutrition an active therapy rather than an adjunctive care [4]. Thus, specific nutrients have been designed to modulate the host immune response and suppress systemic inflammation. Moreover, lipid components of parenteral nutrition have been found to provide powerful bioactive molecules that may act to reduce inflammatory responses [5].
\n
Different clinical trials have shown that fatty acids from fish oil can be considered as powerful disease‐modifying nutrients in patients with acute lung injury and sepsis [6, 7]. Particularly, feeding with fish oil rich in the very‐long‐chain, ω‐3 polyunsaturated fatty acids (PUFAs), eicosapentaenoic acid (EPA), and docasahexaenoic acid (DHA) has been found to attenuate the production of different cytokines, chemokines, and other effectors of innate immune response [8]. In addition, the recent discovery of resolvins generated by EPA and DHA has shed more light on resolution of inflammation, as a possible mechanism of the anti‐inflammatory actions of ω‐3 PUFAs during systemic inflammation [9]. However, oral administration of these compounds is required for several weeks to affect metabolic and inflammatory pathways in humans. Nevertheless, it has been recently demonstrated that intravenous administration of fat emulsions rich in ω‐3 PUFAs can lead to their rapid incorporation into phospholipids of different cells, such as platelets or monocytes, within the first 2 days of feeding, reducing serum pro‐inflammatory cytokines over the next 7–8 days [10–12]. This may affect membrane fluidity, ion channel opening, or different signal pathways, leading to decreased production of TNF‐α and IL‐6 [8, 10]. The bypass of the intestinal process of absorption that is significantly delayed during critical illness could be another reason for such immediate effects.
\n
\n
\n
2. Anti‐inflammatory mechanisms of ω‐3 PUFA
\n
There are two types of naturally occurring essential fatty acids (EFAs) which cannot be synthesized in the body and need to be obtained in our diet, the ω‐6 series derived from linoleic acid (LA) and the ω‐3 series derived from α‐linolenic acid (ALA). Both the ω‐6 and ω‐3 series are metabolized by the same set of enzymes to their responsive long‐chain metabolites. In general, the term EFA includes all unsaturated fatty acids. In this respect, all EFAs are PUFAs, but all PUFAs are not EFAs [13]. The major metabolic pathways of ω‐3 include (1) incorporation into triglycerides that are found in circulating lipoproteins; (2) incorporation into phospholipids of either circulating lipoproteins as well or part of cellular membranes; (3) be circulated as free (nonesterified) fatty acids (FFAs) in the plasma, mostly bound in albumin; and (4) undergo oxidation generating substrates for ATP synthesis. ω‐3 PUFAs incorporated in membrane phospholipids are capable to affect membrane fluidity and membrane‐associated protein function. Furthermore, they can be cleaved by different phospholipases, giving rise to FFAs that subsequently are further oxidized to form various metabolites that are called eicosanoids (such as prostaglandins and leukotrienes) [8, 13]. These eicosanoids derived from EPA through different cyclo‐ and lipo‐oxygenases are generally considered less pro‐inflammatory in relation with their counterparts derived from the very‐long‐chain ω‐6 PUFA, such as arachidonic acid (AA). The major PUFA‐derived mediators are lipoxins, resolvins, and protectins which are highly active and are involved in different physiological and pathophysiological processes. In this respect, experimental studies have shown that protectin D1 (PD1) reduces inflammatory infiltration, enhances phagocytosis of apoptotic neutrophils by macrophages, and, finally, increases macrophage migration to sites of antigen presentation. As a result, these metabolites seem to both inhibit the initiation of an overwhelmed inflammatory response and accelerate at the same time its resolution [8, 13].
\n
The ω‐3 PUFA can also inhibit the activity of nuclear factor kB (NF‐kB), which is considered a pivotal pro‐inflammatory transcription factor and induces the expression of many pro‐inflammatory genes, mediating through the production of different cytokines, the innate immune response [8, 9].
\n
\n
\n
3. ω‐3 PUFA, the autonomic nervous system, and heart rate variability
\n
Different experimental studies have confirmed that there is a continuous cross talk between the brain and the immune response to different inflammatory insults during both an acute and chronic inflammation. In this respect, it has been postulated that the brain may coordinate and affect at the same time the immune response. The first mechanism is based on the activation of vagus nerve afferent fibers, which convey the information that an inflammatory response takes place, through different mediators, such as cytokines [14–16].
\n
Cytokines can activate visceral vagus afferent fibers which terminate within the dorsal vagal complex (DVC) of the medulla oblongata. The nucleus tractus solitarius (NTS) and the dorsal motor nucleus (DMN) of the vagus are part of DVC and give projections to hypothalamic paraventricular nucleus (PVN) that is responsible for the synthesis and release of corticotropin‐releasing hormone (CRH), with subsequent production of adrenocorticotropin hormone (ACTH) from the anterior pituitary. ACTH is the main inducer of the synthesis of immunosuppressive glucocorticoids from the adrenal cortex. DMN that is connected with NTS is believed to constitute the main site of origin of preganglionic vagus efferent fibers. NTS is also connected to rostral ventrolateral medulla (RVLM), which increases noradrenergic preganglionic neurons’ depolarization in the spinal cord [17]. In conclusion, the brain may alter the immune response through the activation of both the sympathetic (SNS) and parasympathetic nervous systems (PNS), as well as the activation of the HPA axis. In this respect, the SNS may induce local inflammatory response through α2‐subtype adrenoreceptor stimulation by norepinephrine (NE), in the early stage of inflammation. Nevertheless, stimulation of β2‐subtype adrenoreceptor‐cAMP‐protein kinase A pathway can also reduce pro‐inflammatory cytokine production [18–20], suggesting that SNS activation can both protect the organism from the detrimental effects of pro‐inflammatory cytokines and increase at same time local inflammatory response [21, 22].
\n
Apart from the SNS, a link between the PNS of the ANS and immunoregulatory processes has been suggested. Thus, acetylcholine is capable to decrease TNF‐α production from human macrophage cultures and immune cells located in the spleen upon stimulation with endotoxin, leading to its reduced release into the circulation. This effect is mediated by the specific α7‐subunit of the nicotinic acetylcholine receptor [23–25]. Acetylcholine is also effective in suppressing other pro‐inflammatory cytokines such as IL‐1β, IL‐6, and high mobility group box 1 (HMGB1) [26].
\n
A novel anti‐inflammatory mechanism of lipid‐diet immunosuppressive effects has been recently described by Luyer and colleagues [27]. They demonstrated that high‐fat enteral nutrition was able to lead to attenuation of systemic inflammation in rats subjected to hemorrhagic shock, through stimulation of cholecystokinin (CCK) receptors and subsequent activation of the cholinergic anti‐inflammatory pathway.
\n
In this respect, Tracey has suggested that for the development of new monitoring tools of the ω‐3 PUFA effects upon the cholinergic pathway in the clinic, new surrogate markers are needed [28], such as heart rate variability (HRV) analysis that is the variability of R‐R series in the electrocardiogram (ECG). HRV reflects both sympathetic and parasympathetic inputs upon the heart and can be estimated via frequency domain methods, which calculate the different frequency components of a heart rate signal through a fast Fourier transformation (FFT) of an R‐R time series [29]. The method displays in a plot at least three peaks—fast periodicities [high frequency (HF), 0.15–0.4 Hz] which are largely due to the influence of vagal tone—and has the largest impact on HRV. Recently, it has been found that central muscarinic cholinergic stimulation (usually in the context of balancing cytokine production) is also accompanied by activation of the HF component of HRV and an instantaneous increase in total variability [30]. Low‐frequency periodicities (LF, 0.04–0.15 Hz) are produced by baroreflex feedback loops, affected mostly by sympathetic modulation of the heart, and very low frequency (VLF) periodicities (less than 0.04 Hz) are related to vasomotor activity. The LF/HF ratio has been considered as a surrogate marker of sympathovagal balance [29, 31].
\n
Studying physiological signals of critically ill patients can easily identify “hidden” information, which can estimate variability and information content (entropy) as a measure of complexity, within time series [32]. It has been suggested that such measures are significantly altered during critical illness and may predict different outcomes of interest, such as the onset of septic shock and late organ dysfunction [33]. In addition, implementation of variability analysis of physiological signals at the bedside might give rise to new markers of disease. Such “physiomarkers” are generally considered more appropriate for better and more accurate early warning signs for patients, since they can be easily measured at the bedside. On the contrary, it has been repeatedly demonstrated that various “biomarkers” such as cytokines exhibit marked interdependence, pleiotropy (multiple effects), and redundancy (multiple cytokines with the same effect). At the same time, their plasma concentrations fluctuate from day to day and correlate poorly with classic physiologic variables in septic patients [33, 34].
\n
Both LF and HF frequency components and overall HRV are significantly reduced in septic patients, whereas the degree of attenuation has been found to be prognostic of survival [22, 35]. The reduction in instantaneous HRV has been associated with an overproduction of cytokines [36], whereas pharmacological stimulation of the efferent vagus nerve has been found to increase the HF component of HRV and inhibit at the same time TNF‐α secretion in septic animals [37]. Many studies have shown that oral supplementation of ω‐3 PUFAs increases instantaneous HRV, reduces LF/HF ratio, and confers protection against ischemia‐induced ventricular tachycardia and sudden cardiac death [38, 39]. In this respect, Christensen and colleagues [39] demonstrated that fish oil feeding can induce an incorporation of DHA into the membranes of granulocytes that is associated with a dose‐response increase in HRV and may protect against serious ventricular arrhythmias. In a recent study [40], the intravenous administration of fish oil with ω‐3 PUFAs, before endotoxin injection in healthy volunteers, was able to blunt fever response and sympathetic stimulation and enhance vagal tone, estimated with HRV analysis. This reduction was associated with a significant decrease in plasma norepinephrine and adrenocorticotropin hormone (ACTH) levels. Such effects of fish oil reflect an enhanced efferent vagal activity via a central‐acting mechanism due to a possible suppression of pro‐inflammatory cytokines, which have been found to inhibit central vagal neurons [8, 41].
\n
However, different interventional studies on ω‐3 PUFAs and HRV in patients with heart disease have found inconsistent results, with only 8 out of the 20 trials published so far, supporting a beneficial effect on HRV [42]. Thus, Mozaffarian et al. [43] found that individuals with the highest fish consumption (≥5 meals/week) exhibited 1.5 ms greater HRV than those with the lowest fish consumption. Moreover, this modest reduction in HRV was associated with only a 1.1% reduction in the relative risk for sudden cardiac death. As we have stated elsewhere [44], “reasons for such inconsistency might include heterogeneous populations, limited sample sizes or different study protocols with variable administered doses of ω‐3 PUFA and length of intervention.” Furthermore, “different methods of measurement of HRV with variable time of recordings could be an additional confounder” [42–44]. Another potential limitation of such measures could be associated with the fact that a reduction in pacemaker funny current rather than an alteration in autonomic neural output was found to be responsible for heart rate reduction and increase in HRV in an animal study with administration of ω‐3 PUFAs [45]. Nevertheless, a potential impact of autonomic tone on HRV cannot be evaluated in this study since experiments were performed in denervated hearts.
\n
In conclusion, an association has been suggested between increased HRV and fish oil administration in different groups of patients with cardiovascular diseases [38, 39, 42]. However, the possible relationship between HRV changes and inflammatory markers during fish oil feeding has not been studied yet, in septic patients. Thus, we think that a promising approach could be the assessment of the relationship between vagal activity estimated with HRV and inflammatory markers in septic patients, during parenteral fish oil feeding. In this case, we assume a beneficial effect of ω‐3 PUFAs on HRV and cytokine response, early in the course of disease.
\n
\n
\n
4. Clinical studies
\n
In Europe there are currently three available lipid emulsions containing ω‐3 fish oil for IV administration: Omegaven (Fresenius Kabi, Germany) that is a 10% fish oil emulsion supplement; Lipoplus/Lipidem (B Braun, Germany) that contains a mixture of 50% medium‐chain triglycerides (MCT) and 40% soybean oil (SO) that is rich in ω‐6 PUFA, such as LA and 10% fish oil; and Smoflipid (Fresenius Kabi, Germany) that is a four‐oil mixture of 30% soybean oil, 30% MCT, 25% olive oil, and 15% fish oil [13].
\n
Numerous studies in critically ill patients have found favorable effects of ω‐3 fish oil on different aspects of inflammatory response. Mayer and colleagues [10] randomized 21 septic patients requiring parenteral nutrition to receive an IV lipid emulsion rich either in ω‐3 (Omegaven) or ω‐6 (Lipoven) PUFAs. They were able to show that the first group within 2 days of infusion demonstrated a rapid incorporation of ω‐3 fatty acids into mononuclear leukocyte membranes. In addition, fish oil rich in ω‐3 was found to suppress generation of pro‐inflammatory cytokines from mononuclear leukocytes upon ex vivo stimulation with endotoxin. Heller and colleagues [46] demonstrated that IV ω‐3 PUFA administration (Omegaven) in 661 surgical critically ill patients improved survival and reduced infection rates, antibiotic requirement, and length of stay in a dose‐dependent manner. Moreover, IV fish oil was found safe, conferring significant clinical benefits when administered in doses between 0.1 and 0.2 gr/Kg/day. In two other studies evaluating fish oil parenteral administration in surgical patients admitted to the Intensive Care Unit (ICU), it was found that although a short‐term (<5 days) administration influences immune parameters, postoperative administration may further reduce length of stay and infectious complications in the ICU [12, 47]. In this respect Braga et al. concluded that ω‐3 should be given prior to surgery in order to enhance their anti‐inflammatory effects in the postoperative period [48].
\n
Barbosa et al. [11] evaluated the effects of IV fish oil administration (Lipoplus) for 5 days in 25 septic ICU patients. They found a significant decrease in IL‐6 plasma concentration, reduced hospital length of stay and amelioration in gas exchange during the sixth day of stay in the ICU.
\n
In 2014, Manzanares and colleagues [49] after aggregating six randomized controlled trials (RCTs) evaluating the effects of parenteral fish oil on relevant clinical outcomes in a heterogeneous group of critically ill patients were able to demonstrate a significant reduction in mortality and duration of mechanical ventilation. In 2015, the same group of researchers, after analyzing data from 10 RCTs involving 733 patients, was not able to find any survival benefit from parenteral fish oil feeding in septic patients [50]. Nevertheless, a reduction in the incidence of infections and a trend toward reduced duration of mechanical ventilation and length of stay in ICU were reported. Furthermore, intravenous fish oil feeding exhibited a nonsignificant trend toward reduced mortality. Since conflicting data have been originated from other systematic reviews and meta‐analyses [51, 52] “low sample size and heterogeneity of the cohorts included do not permit a final recommendation on the use of ω‐3 PUFAs as a pharmaconutrient strategy in septic ICU patients” [50].
\n
The European Society for Clinical Nutrition and Metabolism (ESPEN) Guidelines on Parenteral Nutrition in Intensive Care has suggested that both EPA and DHA can affect cell membranes and, subsequently, reduce the intensity of inflammatory response. As a result, fish oil‐enriched lipid emulsions might decrease duration of hospitalization in critically ill patients [53]. Canadian recommendations also endorse the use of fish oil‐enriched lipid emulsions when parenteral nutrition is indicated [54]. Finally, the American Society for Parenteral and Enteral Nutrition (ASPEN) in its recently published guidelines cannot recommend fish oil parenteral feeding in critically ill patients at this time, due to lack of availability on the market of these products in the United States, despite approval by the FDA in 2013 [55]. Nevertheless, it considers as appropriate its future administration either in patients with septic shock who are candidates for parenteral nutrition due to hemodynamic compromise, such as hypotensive (mean arterial blood pressure < 50 mm Hg); patients for whom catecholamine agents (e.g. norepinephrine, epinephrine) are being initiated and patients for whom escalating doses are required to maintain hemodynamic stability; or surgical postoperative patients who are not eligible for enteral nutrition (e.g. short bowel) [55].
\n
Different studies have also assessed potential differences between SO and fish oil lipid IV fat emulsions in septic patients. In a recent systematic review of 12 RCTS including 806 patients by Manzanares and colleagues, no significant difference in outcome benefits was found [56]. In another meta‐analysis of eight RCTS involving 391 patients by Palmer et al. [52], a significant reduction in hospital length of stay was demonstrated by nearly 10 days in those receiving ω‐3 fish oil in relation with either SO‐based or SO + MCT‐based lipid emulsions. However, no differences were seen between groups with regard to ICU length of stay, infectious complications, and mortality. The strongest evidence in favor of fish oil PUFAs than SO‐based lipid emulsions comes from small observational studies [55]. In this respect, data collected from an International Nutritional Survey showed a significantly lower ICU length of stay, reduced duration of mechanical ventilation, and reduced ICU mortality in septic patients receiving fish oil PUFAs when compared with SO‐based lipid emulsions [57].
\n
Another issue that has been tested in different RCTs is associated with safety and tolerability. Recently, a meta‐analysis of 23 trials involving 1503 patients receiving long‐term parenteral nutrition with IV fish oil found no evidence of any deleterious effects [58]. Consequently, ESPEN Guidelines on Parenteral Nutrition in Intensive Care suggests that lipids and essential fatty acids should be an integral part of the regimen to provide energy and should be administered at a rate of 0.7–1.5 gr/Kg over 12–24 h [53].
\n
Considering enteral administration of lipid emulsions rich in ω‐3 PUFAs in critically ill patients with sepsis and septic shock, strong evidence is still lacking. While early studies and meta‐analyses suggested reduced infection rates, ICU length of stay, and duration of mechanical ventilation, in both medical and surgical patients in a general ICU [59], Heyland and colleagues found a modest reduction in hospital length of stay, particularly in medical patients [60]. Furthermore and according to ASPEN Guidelines, current evidence does not support the use of enteral fish oil administration, particularly in medical ICU patients, due to heterogeneity of studies, variety of experimental and commercial lipid formulations, variable dosage of individual components, and increased costs [55]. Finally, two recent meta‐analyses showed that the effect of fish oil lipid emulsions on mortality in septic patients was not influenced by the route of administration (enteral vs. parenteral) [50, 61].
\n
\n
\n
5. Conclusions
\n
Many experimental studies have confirmed that ω‐3 PUFAs possess different anti‐inflammatory properties. Either through effect on membrane fluidity with subsequent attenuation of cytokine production or through indirect activation of the cholinergic anti‐inflammatory pathway (immunoreflex), fish oil lipids have demonstrated immune‐regulatory activities in different experimental settings. As a result, different investigators have evaluated their role in different groups of patients exhibiting systemic inflammation, such as surgical or septic patients treated in the ICU. However, extreme heterogeneity in patients’ populations, route of administration, doses and duration of therapy, as well as commercially available products limits generalizability of results derived from numerous systematic reviews and meta‐analyses. Consequently and since the current evidence is still too weak and sparse to make recommendations about the role of fish oil in the treatment of the critically ill, we suggest that HRV could be adopted as end point for monitoring nutritional manipulation of inflammatory response at the bedside, helping translation of basic science results into successful randomized controlled trials. In this case, we assume that ω‐3 PUFAs upon parenteral administration will be rapidly incorporated into the phospholipid membranes of different immune cell types, reducing the inflammatory response and increasing HRV.
\n
In this respect, 24 h recordings and longitudinal changes of HRV in two groups of septic patients with similar severity of disease and receiving parenteral nutrition with the same volume of glucose, nitrogen, and fat but different lipid composition could be tested. In the case that HRV metrics predict outcomes of interest, such as lower infection rate and/or attenuated organ dysfunction, such a study might identify a unique value of HRV analysis as a monitoring tool of inflammatory modulation by fish oil feeding, in septic patients. Another potential use of HRV in artificial nutrition of septic patients as has been suggested by Tracey [62] could be its adoption as a physiomarker to early identify patients with reduced vagal tone. In this case, a susceptibility to increased inflammation can be assumed, whereas HRV metrics might serve as an early alarm to identify patients who might benefit from pharmacological stimulation of the cholinergic anti‐inflammatory pathway, such as ω‐3 PUFAs [62].
\n
\n\n',keywords:"ω‐3 fatty acids, lipid emulsions, sepsis, heart rate variability, enteral, parenteral, nutrition, critical care, autonomic nervous system",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/54744.pdf",chapterXML:"https://mts.intechopen.com/source/xml/54744.xml",downloadPdfUrl:"/chapter/pdf-download/54744",previewPdfUrl:"/chapter/pdf-preview/54744",totalDownloads:479,totalViews:256,totalCrossrefCites:0,totalDimensionsCites:0,hasAltmetrics:0,dateSubmitted:"November 2nd 2016",dateReviewed:"February 21st 2017",datePrePublished:null,datePublished:"August 23rd 2017",readingETA:"0",abstract:"Different clinical studies have demonstrated that fish oil, rich in the very‐long‐chain ω‐3 polyunsaturated fatty acids (PUFAs), has immunomodulatory effects, suppressing the production of pro‐inflammatory cytokines in diverse groups of critically ill patients. Moreover, such compounds have been found to attenuate the inflammatory response within 2–3 days upon parenteral administration. Recent experimental data suggest that activation of the cholinergic anti‐inflammatory pathway constitutes a novel mechanism of such immune‐regulatory effects. Since enhanced vagal tone has been associated with decreased cytokine secretion, novel monitoring tools of its activity at the bedside are needed, in order to evaluate nutritional manipulation of inflammatory response in the critically ill. The present chapter provides an overview of the mechanisms of action through which ω‐3 PUFA modulates immune response in critically ill patients suffering from sepsis and septic shock. Furthermore, it summarizes the current evidence regarding clinical effects from administration of fish oil rich in ω‐3 PUFAs in septic patients. Finally, it presents data that suggest the existence of a continuous interrelation between immune status and autonomic nervous system during systemic inflammation and proposes novel tools of autonomic nervous system monitoring at the bedside, in order to assess pharmacological manipulation of immune response by ω‐3 PUFAs in acute illness.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/54744",risUrl:"/chapter/ris/54744",book:{slug:"sepsis"},signatures:"Vasilios Papaioannou",authors:[{id:"147093",title:"Prof.",name:"Vasilios",middleName:null,surname:"Papaioannou",fullName:"Vasilios Papaioannou",slug:"vasilios-papaioannou",email:"vapapa@med.duth.gr",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Anti‐inflammatory mechanisms of ω‐3 PUFA",level:"1"},{id:"sec_3",title:"3. ω‐3 PUFA, the autonomic nervous system, and heart rate variability",level:"1"},{id:"sec_4",title:"4. Clinical studies",level:"1"},{id:"sec_5",title:"5. Conclusions",level:"1"}],chapterReferences:[{id:"B1",body:'\nKoj A. Initiation of acute phase response and synthesis of cytokines. Biochim Biophys Acta 1997; 1317: 84-94.\n'},{id:"B2",body:'\nWebster JI, Tonelli L, Sternberg EM. Neuroendocrine regulation of immunity. Annu Rev Immunol 2002; 20: 125-163.\n'},{id:"B3",body:'\nGoode HF, Cowley HC, Walker BE, et al. Decreased antioxidant status and increased lipid peroxidation in patients with septic shock and secondary organ dysfunction. Crit Care Med 1995; 23: 646-651.\n'},{id:"B4",body:'\nJones NE, Heyland DK. Pharmaconutrition: a new emerging paradigm. Curr Opin Gastroenterol 2008; 24: 215-222.\n'},{id:"B5",body:'\nWanten GJ, Calder PC. Immune modulation by parenteral lipid emulsions. Am J Clin Nutr 2007; 85: 1171-1184.\n'},{id:"B6",body:'\nSinger P, Theilla M, Fisher H, et al. 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Democritus University of Thrace, School of Medicine, Alexandroupolis Hospital, ICU, Alexandroupolis, Greece
'}],corrections:null},book:{id:"5851",title:"Sepsis",subtitle:null,fullTitle:"Sepsis",slug:"sepsis",publishedDate:"August 23rd 2017",bookSignature:"Vijay Kumar",coverURL:"https://cdn.intechopen.com/books/images_new/5851.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"63844",title:"Dr.",name:"Vijay",middleName:null,surname:"Kumar",slug:"vijay-kumar",fullName:"Vijay Kumar"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},chapters:[{id:"56127",title:"Interaction of Host‐Microbial Metabolism in Sepsis",slug:"interaction-of-host-microbial-metabolism-in-sepsis",totalDownloads:778,totalCrossrefCites:1,signatures:"Beloborodova Natalia Vladimirovna",authors:[{id:"199461",title:"Prof.",name:"Natalia",middleName:null,surname:"Beloborodova",fullName:"Natalia Beloborodova",slug:"natalia-beloborodova"}]},{id:"54619",title:"Septic Shock in Older People",slug:"septic-shock-in-older-people",totalDownloads:511,totalCrossrefCites:0,signatures:"Mike Yoshio Hamasaki, Marcel Cerqueira César Machado and\nFabiano Pinheiro da Silva",authors:[{id:"171281",title:"Prof.",name:"Marcel",middleName:null,surname:"Machado",fullName:"Marcel Machado",slug:"marcel-machado"},{id:"200926",title:"Prof.",name:"Fabiano",middleName:null,surname:"Pinheiro Da Silva",fullName:"Fabiano Pinheiro Da Silva",slug:"fabiano-pinheiro-da-silva"},{id:"200928",title:"MSc.",name:"Mike",middleName:null,surname:"Hamasaki",fullName:"Mike Hamasaki",slug:"mike-hamasaki"}]},{id:"55046",title:"Kallistatin in Sepsis: Protective Actions and Potential Therapeutic Applications",slug:"kallistatin-in-sepsis-protective-actions-and-potential-therapeutic-applications",totalDownloads:522,totalCrossrefCites:0,signatures:"Julie Chao, Pengfei Li and Lee Chao",authors:[{id:"200172",title:"Prof.",name:"Julie",middleName:null,surname:"Chao",fullName:"Julie Chao",slug:"julie-chao"}]},{id:"54744",title:"The Role of Fish Oil Feeding Rich in ω‐3 Polyunsaturated Fatty Acids in Patients with Sepsis and Septic Shock",slug:"the-role-of-fish-oil-feeding-rich-in-3-polyunsaturated-fatty-acids-in-patients-with-sepsis-and-septi",totalDownloads:479,totalCrossrefCites:0,signatures:"Vasilios Papaioannou",authors:[{id:"147093",title:"Prof.",name:"Vasilios",middleName:null,surname:"Papaioannou",fullName:"Vasilios Papaioannou",slug:"vasilios-papaioannou"}]},{id:"56058",title:"Sepsis-associated Acute Kidney Injury",slug:"sepsis-associated-acute-kidney-injury",totalDownloads:1278,totalCrossrefCites:0,signatures:"Wiwat Chancharoenthana, Asada Leelahavanichkul and Somchai\nEiam-Ong",authors:[{id:"49591",title:"Dr.",name:"Somchai",middleName:null,surname:"Eiam-Ong",fullName:"Somchai Eiam-Ong",slug:"somchai-eiam-ong"},{id:"200624",title:"Dr.",name:"Wiwat",middleName:null,surname:"Chancharoenthana",fullName:"Wiwat Chancharoenthana",slug:"wiwat-chancharoenthana"},{id:"200625",title:"Dr.",name:"Asada",middleName:null,surname:"Leelahavanichkul",fullName:"Asada Leelahavanichkul",slug:"asada-leelahavanichkul"}]},{id:"54731",title:"Clinical Assays in Sepsis: Prognosis, Diagnosis, Outcomes, and the Genetic Basis of Sepsis",slug:"clinical-assays-in-sepsis-prognosis-diagnosis-outcomes-and-the-genetic-basis-of-sepsis",totalDownloads:857,totalCrossrefCites:0,signatures:"Alice Georgia Vassiliou, Stylianos E. 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1. Introduction
The significance of terahertz electronics is self-evident for readers of this book. The general consensus among silicon THz circuit designers (!) is that silicon will be the dominant technology for the lower end of the THz spectrum (300 GHz to around 1 THz) in light of recent breakthroughs of silicon circuits in terms of effective isotropic radiated power (EIRP), phase noise, and receiver sensitivity. For many applications, silicon circuits are on par or even superior to III/V compound technologies and optical-based techniques in this frequency range now. This chapter aims to introduce the reader to the fascinating world of silicon THz circuit design through a step-by-step approach: We examine conditions for extracting the most power gain out of a given active device. Popular topologies for silicon sources, detectors, and transceivers are discussed next, and this chapter concludes with a brief survey of THz interface options for efficient energy transfer between circuits and the outside world.
2. How to have THz power and radiate it too
Due to the excessive loss and scarcity of power gain for silicon devices in the THz region, one should strive to extract the most power out of a given device during the whole design phase. This involves making sure that the device is working under the optimum condition (i.e., the device is embedded in the right impedance environment for maximum power gain), the topology of the circuit is optimum for the intended application, and the power is transferred from the circuit through the most efficient interface. This section gives an overview of these areas.
2.1 Power gain maximization for a given active device
The active devices in THz circuits are connected to the rest of the circuits through passive elements, such as capacitors, inductors, and transmission lines. The overall circuit performance is decided both by the active device and these passive elements. Thus, to maximize the circuit performance, a “divide-and-conquer” approach is the logical choice. That is, we first find the “best” active device in a given technology under certain constraints such as power consumption or noise performance. We then decide the best passive network into which the device should be embedded. The problem is there is no such thing as “pure” active device; passive elements are always present in a given active device. Mason [1] has thus defined a figure of merit for active devices:
U=Y21−Y1224G11G22−G12G21E1
Gij is the real part of Yij in Eq. (1). The above FOM is called Mason’s invariant U, since it is invariant to passive embedding environments that are linear, lossless, and reciprocal [1, 2].
A device is active if its U is larger than one, which means this device is capable of providing real power. The maximum oscillation frequency (fmax) of a device is defined as the frequency where its U equals one, i.e., beyond which frequency it is no longer active. The maximum power gain of this device embedded in the two-port also drops to unity at the maximum oscillation frequency (fmax).
U is also the maximum power gain of the device after unilateralization, that is, when Y12 is made to zero. Generally speaking, higher U means higher power gain at a given frequency.
For a given two-port shown in Figure 1(b), the power gain is defined as
Figure 1.
The two-port representation of an embedded active device. (a) An active device embedded in a linear, lossless, and reciprocal passive network resulting in a two-port and (b) the two-port interfacing to signal source and load.
PL and PIN are the real power delivered to the load and to the two-port. V1, I1, and V2, I2 in Figure 1 are the voltage and current at port 1 and port 2, respectively. AV is the voltage gain of the two-port. Ys and YL represent the source and load admittance presented to the device. Is and Ys form the Norton equivalent circuit of the signal source.
For an unconditionally stable two-port (it does not oscillate for any passive load and source admittance) at a given frequency, the power gain could be maximized by biconjugate matching at the input and output. Conjugate matching is achieved when the load admittance is equal to the conjugate of the source admittance at a given node; biconjugate matching means that this condition is satisfied both at the input and the output port. For a given two-port, its maximum power gain is
Gmax=Y21Y12×k−k2−1E3
where K is the stability factor defined as
2×ReY11×ReY22−ReY12Y21Y12Y21E4
Biconjugate matching is possible when K is equal or greater than 1. For a given two-port, it is unconditionally stable when the following conditions are simultaneously satisfied:
g11≥0E5
g22≥0E6
K≥1E7
Keep in mind that unlike U, which is invariant to the embedding network, Gmax is sensitive to its environment. We can modify the embedding environment to make Gmax larger. It can be shown that the maximum Gmax for a given device is U+U−12. For a detailed discussion about U and Gmax, please refer to [3, 4, 5, 6] which present ways of designing the embedding network for maximizing Gmax while maintaining stability under process variations. The basic idea is to utilize feedback to generate negative resistance, such as adding capacitive degeneration to CE (common emitter) amplifiers or adding inductance to the base node of CB (common base) amplifiers.
Another important THz circuit is oscillators. Here, we need to make a distinction between amplifiers and oscillators. The former is one kind of driven circuit, the output of which is controlled by its input. Oscillators belong to the group of autonomous circuit, which generates time-varying signals without time-varying stimulus. By definition, amplifiers operate below fmax to provide power gain. For oscillators, the situation is more complicated: The power gain of active devices within the oscillator should be greater than unity to start the oscillation. As the oscillation amplitude grows, the power gain of the two-port (including device parasitic and loading) gradually compresses to unity when the circuit reaches steady-state oscillation. Thus, it could be argued that devices within oscillators operate at the fmax of its embedded two-port in steady-state oscillation. To take the gain compression into account, large-signal parameters should be used for the analysis.
Unlike analog circuit designers who deal exclusively with voltage and current gains, microwave circuit designers are more comfortable with power gain. Momeni [7] has thus shown a refreshing view about the optimum voltage gain and phase shift for a given two-port to oscillate at fmax:
AV=V2V1=AOPT=G11G22E8
ϕ=∠V2V1=ϕOPT=2k+1π−∠Y12+Y21∗E9
AOPT and ΦOPT are the optimum voltage gain and phase shift for the two-port at fmax. Equations (8) and (9) are derived assuming no clipping to the power rails occurs inside the circuit. If clipping happens, another set of equations apply for AOPT; ΦOPT remains the same [8, 9].
It can be shown that biconjugate matching automatically satisfies Eqs. (8) and (9) at fmax.
Under biconjugate matching, Gp reaches unity at fmax. Equation (2) can be rewritten as
We are now in the position to derive ΦOPT. First, we have to define the net power flowing into the two-port shown in Figure 1(b):
P=V1×I1∗+V2×I2∗E14
At fmax, the power gain of the two-port drops to unity, which means the real power consumed by the two-port equals the real power generated. Thus, the real part of Eq. (14) equals zero:
Since the above derivation is restricted to fmax, it would be interesting to observe the possible deviations of Eqs. (8) and (9) with respect to the two-port’s voltage gain and phase shift under biconjugate matching when operating at frequency below fmax. A SiGe HBT transistor is used as an example. The emitter width and length of the transistor is 0.12 and 2.5 μm, and the emitter current density is biased for peak fmax. The source and load admittance are adjusted for biconjugate matching under each frequency evaluated (Figures 2 and 3).
Figure 2.
Comparison of the phase shift of a SiGe HBT transistor under biconjugate matching and the optimum phase shift calculated with Eq. (9).
Figure 3.
Comparison of the voltage gain of a SiGe HBT transistor under biconjugate matching and the optimum voltage gain calculated with Eq. (8).
It is clear that Eqs. (8) and (9) are only strictly valid at fmax, but the optimum phase shift calculated with Eq. (9) tracks reasonably well with the results obtained with biconjugate matching over a wide frequency range.
2.2 Circuit topology for THz sources, detectors, and transceivers
Among the many potential benefits offered by THz application, the large bandwidth available is the most obvious one. However, a lot of design issues need to be addressed in order to truly harness this bandwidth potential. We discuss this problem in terms of SNR at the receiver:
SNR×B=PrkTBF=λ4πd2×PtGtGrkTFLE20
B is the receiver bandwidth. For communications, we would like B to scale with frequency. For imaging applications, sometimes B is not that important once it reaches certain value as only the range resolution scales with 1/B. The cross-range resolution scales inversely with wavelength λ. Thus, we lump SNR and B together for trade-offs. Pt and Pr are the power transmitted and received by the transmitter (Tx) and receiver (Rx). Gt and Gr are the gain of the transmitting and receiving antenna. K is the Boltzmann constant. T is the ambient temperature. d is the distance between the transmitter and receiver. F is the noise factor of the receiver. L represents the loss in the Tx and Rx system, and we assume it scales with f0.5 to f here.
Assuming constant drive power, Pt for terahertz transmitters approximately follows a Pt∝1/f2 relationship since the maximum unilateral gain U follows a -20dB/decade slope above fmax/2. F generally scales with f. SNR×B then scales with 1/f5.5 to 1/f6, which is a really disheartening result. This partly explains why the current silicon THz links are usually demonstrated with link distances ranging from centimeters to meters.
Before leaving this chapter in despair, we can try to manipulate Eq. (20) a little bit further:
SNR×B=116π2k×λ2Td2L×PtGtGrFE21
The first term is by all means beyond our control, and we do not want to change the second term for now. So, what can we do about the last term? It happens that if we were to keep the two-antenna size constants while increasing the frequency, Gt and Gr each come with a nice λ2 on the denominator. Equation (21) thus equals
Atp and εt are the physical area and the aperture efficiency of the transmitting antenna; εt is between zero and unity. For active phased arrays, Eq. (22) could be rewritten as
SNR×B=AtpεtNtPte4πkTd2L×NrGreFeE23
where Nt and Nr are the numbers of transmitters and receivers. Pte is the output power for each transmitter. Gre is the gain of the receiving antenna for each receiver. Fe is the noise factor of each receiver. For active phased arrays, antenna elements with their corresponding transmitters and receivers are evenly distributed with a pitch of about λ/2. Thus, Nt and Nr are proportional to 1/λ2. It is proven that for phased array with lossless combing, the Gr/F term in Eq. (22) scales with Nr [10]. Assuming constant εt and Gre with respect to f, we see that SNR×B scales with f−0.5 to f0!
The six orders of magnitude difference of SNR×B deduced from Eqs. (20) and (23) give us a hint of the size of the design space for silicon THz systems.
2.2.1 THz Sources
When talking about silicon THz sources, a plethora of options is available that varies in functionality, complexity, and performance. For incoherent imaging applications, the most important metrics are output power and efficiency, whereas for spectroscopy, the bandwidth is the most important specification. Perhaps the most demanding application is for THz communications, for which output power, power efficiency, tuning range, phase noise, harmonics, and spurious suppression are all important parameters. This subsection aims to give a brief and incomplete introduction to what has been done in this area.
THz signal can be generated either by frequency multipliers or by on-chip oscillators.
In multipliers, the MOS or bipolar transistor is driven heavily to generate highly nonlinear current. The intended frequency component is then extracted with other components filtered. If efficiency is important, the active device should be conjugate matched for the fundamental and the intended harmonic. The impedance presented to the device at other harmonics is usually short or open circuit to maximize energy transfer between the fundamental and the intended harmonic. But we should not be overzealous about this goal; usually taking care of the first two or three harmonics is enough since the higher harmonics are insignificant. The transistor also has to be biased correctly for maximum harmonic generation. For MOS transistor, the conduction angle is specified. Like power amplifiers, efficient MOS multiplier works in the class AB, B, or C region depending on the frequency, multiplication factor, and input power. For bipolar transistor, this efficiency is a function of Vbe (or collector current density) [11].
Relationship of phase noise between the harmonic and the fundamental for multipliers is [11]:
SoutΔω=N2SfundΔω+SharmΔω+SampΔωE24
where SoutΔω and SfundΔω represent the spectral density of phase fluctuations for the harmonic and fundamental signal with Δω radians offset from the carrier. It is in dBc/Hz form. N is the frequency multiplication ratio. The last two terms in Eq. (24) represent the added noise from the harmonic-generating device and the ensuing amplifiers (if any). The combined value is usually less than 3 dB for reasonably designed circuits.
Multipliers are usually compact and broadband, but they are not as efficient as (well designed) oscillators. A 90–300 GHz transmitter based on distributed quadrupler is designed for spectroscopy and imaging [12]. It resembles the distributed amplifier (DA) in that the input and output capacitance of active device are absorbed in the input and output transmission line. Differential quadrature signal is used to drive two groups of quadrupler diff-pairs, the current of which is then combined to cancel the second harmonic. As another example, quadrupler is used in an 8-element 400 GHz transmitter phased array to replace power amplifier [13]. This also simplifies phase shifter design since the fundamental signal only needs to be shifted within 90 degrees as the phase shift is multiplied by four.
In oscillators, the transistor is made unstable by intentionally introducing positive feedback around it. Steady-state oscillation occurs at the frequency where the open-loop transfer function equals −1 (Barkhausen’s criteria). Since the fmax of most silicon devices is below 300 GHz, harmonic generation is employed. The fundamental oscillation frequency is usually around 100 GHz for better phase noise, since larger oscillation amplitude and hence better SNR are easier to obtain at lower frequencies.
A high efficiency and scalable 4 × 4320 GHz oscillator array is built in SiGe BiCMOS technology [9]. The oscillator shown in Figure 4(a) oscillates at 160 GHz and is optimized for optimum transistor voltage gain and phase shift as discussed in Section 2.1. Y1 and Y2 represent the source and load admittance for the transistor. A transmission line with impedance Z0 and electrical length θTL is used to introduce feedback. The transmission line spans approximately a quarter wavelength at the second harmonic to transform the relatively small impedance of the gate node to high values at the drain node. Since harmonic signals are in the current form, boosting the output impedance at the harmonic frequency substantially improves output harmonic power. The DC-to-THz radiation efficiency is 0.54%. Early reports of THz oscillators based on push-push oscillators are less efficient than this partly due to the insufficient output impedance at second harmonic. As is shown in Figure 4(b), the cross-coupled pair in a push-push oscillator is effectively a diode-connected transistor at second harmonic.
Figure 4.
Topology of (a) self-sustained oscillator and (b) conventional cross-coupled oscillator and its equivalent circuit at second harmonic.
Frequency tuning of oscillators is usually done by varying the capacitance of varactor in the oscillation tank. Higher oscillation frequency translates to smaller capacitance, which is problematic for small varactors as its parasitic capacitance would swamp the variable capacitance. This would severely constrain the oscillator’s tuning range.
Shown in Figure 5(a) and (b) are the cross section of a NMOS varactor and its small signal model with its source AC grounded. To increase its Q factor, the minimum channel length is usually employed, which further increases the overlap capacitance (Cov) between the two terminals.
Figure 5.
Cross section of NMOS varactor (a) and equivalent circuit with grounded source (b).
A straightforward way to increase the tuning ratio of the varactor is to place an inductor to partially absorb the parasitic capacitance. A 300 GHz differential Clapp push-push VCO with 8.5% tuning range and phase noise of −85 dBc at 1 MHz offset is reported in [14]. Its simplified schematic and equivalent small signal circuit for calculation of the input impedance seen at the base is shown in Figure 6. Note that the base resistance, the depletion capacitance between base and collector, and the output resistance of the transistor are ignored.
Figure 6.
Push-push VCO with common-mode resonance: (a) schematic, (b) base input impedance for differential mode, and (c) input impedance for common mode.
The input impedance seen from the base is
ZB=−1jωCpi1+gm+jωCpi1/Rvar+jωCeffE25
where Ceff is
Ceff=Cvar×1−1ω2LdegCvar=Cvar×1−ω02ωOSC2E26
Rvar represents the loss in varactor; its conductance is 1/Q of the varactor at the evaluation frequency of the quality factor. The resonant frequency ω0 for Cvar and LDEG is set below the main oscillation frequency.
The equivalent series resistance and capacitance for ZB is
Another interesting property of the circuit is that the oscillation frequency for common mode is intentionally set to the second harmonic. Cr in Figure 6(a) and (c) forms a series resonator with the tank, raising the second harmonic voltage seen at the base significantly. This boosts the second harmonic generation. The output power for the two versions of the VCO is 0.6 dBm and 0.2 dBm, respectively.
As is evident from Eq. (27), the negative resistance seen at the base of the capacitively degenerated transistor could be used to mitigate the loss of the varactor [15]. This property is used in [16] to build a 300 GHz triple-push VCO. The tuning range is 8%, and the phase noise is −101.9 dBc/Hz at 1 MHz offset for the 100 GHz main loop. That translates to a phase noise of −80.28 dBc/Hz at 1 MHz offset for 300 GHz assuming noiseless multiplication.
An interesting observation is that inductors actually have better quality factor than varactors at higher frequency. A carefully designed inductor has a Q of 15–20 at 100 GHz, whereas the quality factor for varactor is around 2–5 at that frequency. It would be nice if we can replace the varactor with a high-quality metal-insulator-metal (MIM) or metal-oxide-metal (MOM) capacitor; we then need to figure out how to tune the inductance of these nice inductors. Figure 7 shows one such circuit [17] which is also based on Clapp oscillators.
Figure 7.
Schematics for (a) tunable active inductor and (b) complete VCO.
We know that inductance at the base generates a negative resistance and a positive inductance seen from the emitter, as LNA designers can attest to [18]. Careful derivation of ZE leads to the following results [14]:
ZE≈1gm−ω2LBBωT+ω2RBBωT2+jωRBBωT−1gmωT+ω2LBBωT2E29
Thus, we can tune the inductance by varying the gm of the transistor. For bipolar transistors, gm equals the emitter current divided by the thermal voltage VT (26 mV in room temperature).
The impedance at the emitter is mapped to the resonant tank through the transformer formed by LE and LT in Figure 7(b). The currents of the two active inductors are controlled by tail current source Q5. The second harmonic current is extracted through LC, and the degeneration resistor REE is used to improve common-mode rejection. Two versions of this VCO with different oscillation frequency are built; the tuning range are 3.5 and 2.8%, respectively. The harmonic power suffers due to the inclusion of REE, the output power at 201.5 and 212 GHz are −7.2 and−7.1 dBm, respectively. But the phase noise performance is very good, with −87 and −92 dBc at 1 MHz offset for the two VCOs. This translates to −83.5 and −89 dBc at 1 MHz offset if they oscillate at 300 GHz, which is comparable to the circuit shown in Figure 6 that generates 0 dBm at 300 GHz.
This raises interesting question as smaller output power usually means inferior phase noise performance. One possible explanation is that the noise current at the second harmonic in Q1 and Q2 of Figure 6 generates large noise voltage at the emitter since these nodes are open circuit due to resonance, thus amplifying the noise current at second harmonic. It should be noted that the phase noise could be improved substantially by breaking the noise current path at second harmonic [19].
A salient feature of Clapp oscillator is the inherent isolation of the load from the tank. This helps to preserve the quality factor of the tank, leading to a better phase noise and less load pulling (variation of oscillation amplitude and frequency caused by load variation). The problem of low output impedance at second harmonic is also mitigated in this topology as the base is isolated from the drain.
One starts to wonder if there is a way to further improve the phase noise performance. We know there is a trade-off between noise performance and power consumption, but we are kind of stuck here: We need larger transistor to burn larger power, but the larger capacitance of the device means smaller inductors in the tank, which complicates the design and ultimately degrades the Q. We need a larger design space here.
One way to do that is to build an array of N oscillators and lock them together. Theoretically the phase noise would drop by N as the SNR increases by N, and the output power would also increase by N. Better still, if we distribute them evenly with a certain pitch (normally λ/2) and radiate the power out collectively, the energy would focus in certain direction, improving the EIRP by N2. Tousi et al. shows one such design [20]:
Each individual oscillator shown in Figure 8 is a cross-coupled push-push oscillator. It is designed for optimum fourth harmonic generation by making sure that the gate is isolated from the drain at the fourth harmonic. The second harmonic is rejected by the narrow band on-chip antenna. Each oscillator is coupled to other oscillators as shown in Figure 8(a) through active phase shifters. Figure 8(a) forms a unit cell through which a 2-D oscillator lattice could be formed as shown in Figure 8(b). One nice feature of this design is the use of phase shifter as coupling elements, as this provides us with a new way of tuning the frequency of these injection-locked oscillators [21]:
Figure 8.
Block diagram for (a) a unit cell and (b) 2-D oscillator lattice.
Δf0f0=ksinΔϕtE30
Equation (30) is derived from the Adler’s equation under locked conditions. Δf0 is the frequency difference of the injected signal and the free-running frequency f0 of the slave oscillator. Δϕ(t) is the phase difference. K is a factor relating to the quality factor of the oscillation tank, amplitude of the injected signal, and the free-running oscillation amplitude of the tank.
Since the total phase shift through the loop in Figure 8(a) is 2kπ, the phase shift through the oscillator plus that of the phase shifter is constrained to a set of fixed values. The oscillation frequency of the whole array is changed if we apply a common shift to all the phase shifter in Figure 8(b). Interesting thing happens when we tune the phase shifter connected with an individual oscillator. If we apply a common shift to the four shifters, this disrupts the local loop momentarily as the instantaneous phase of the affected oscillator jumps to a new value to accommodate the change. This ability of changing the phase of radiating elements individually turns this design into a phased array. Measurements show that the beam could be steered ±50 degree in the E plane and ± 45 degree in the H plane. The frequency tuning range is 2.1%. The peak EIRP is 17.1 dBm, and the phase noise is −93 dBc at 1 MHz offset for this 338 GHz array, which show substantial improvements over single oscillators.
A brief comparison between multipliers and harmonic injection-locked VCOs is also in place: The former is generally compact and wideband. They add negligible phase noise if designed properly as dictated by Eq. (22). The biggest issue is the harmonics, which leads to annoying LO spurs that leads to spurious emission and corrupts received signals. The latter comes with higher efficiency and much higher harmonic rejection ratio, but the bandwidth is limited. The close-in phase noise is dominated by the source just like the multiplier, but the far-out phase noise is dominated by the VCO. For mm-wave frequency synthesizers, the two options generally achieve comparable phase noise performances [11]. Since we have to use multipliers to get from mm-wave to THz anyway, this same conclusion holds for THz. For communication applications, it is advisable to use PLL-locked or injection-locked VCOs to generate relatively high LO frequency and use multipliers to boost it to THz frequency (N-push VCOs does this in one place).
2.2.2 THz detectors
THz detectors utilize the nonlinearity of active devices to directly rectify THz signal to DC. A lot of devices could be used, like diode-connected NMOS transistor [22], CE (common emitter) [23] or CB (common base) connected [24, 25] SiGe HBT, CMOS-compatible Schottky diode [26], or P+/n-well diode [27]. THz reception with detectors is incoherent, that is, only the amplitude information is recovered at the receiving side, which limits THz detectors almost exclusively to incoherent THz imaging applications. The strength of THz detectors lies within their simplicity: They do not need LO (local oscillator) signal to do the THz down-conversion. The received THz signal self-mix themselves to DC through even-order nonlinearity of the device. This makes scaling extremely easy, as only low-frequency routing is needed, whereas LO-driven mixer needs cumbersome and power-hungry LO tree which quickly becomes unmanageable when the array gets large. A 1024 pixel NMOS detector array [22] in 65-nm CMOS process showcases the impressive scalability of THz detectors.
However, this flexibility comes with a price: The gain and noise performance of detectors is quite limited, and the specification “responsivity” and “noise equivalent power (NEP)” are used in place of conversion gain and noise figure. The responsivity is defined as the voltage output divided by received power, and NEP is defined as the output noise voltage density divided by responsivity.
The bandwidth of imaging application is usually below 1 MHz; thus, technologies with lower 1/f noise corner frequencies like SiGe HBT or P+/n-Well diode are preferred. The 1/f noise corner frequencies for SiGe HBT and P+/n-well diode are below 1 kHz and 10 kHz, respectively, whereas for NMOS transistor or Schottky diodes, the numbers are well above 1 MHz. For SiGe HBTs, it is shown that CB-connected topology has higher responsivity than CE-connected topology when operating above fmax [24].
The principle of THz imaging with detectors largely follow their optical counterpart: They use THz lenses to do the focusing. The problem is that THz wavelength is 2–3 orders of magnitude larger than visible lights, thus large and bulky THz optics are required for reasonable imaging resolutions. They require a lot of effort to set up the imaging setup with the invisible THz radiations [25]. This is the innate deficiency with incoherent imaging. Coherent imaging with THz transceivers could get rid of those optics.
2.2.3 THz transceivers
For transceivers working at lower frequencies, the transmitter and receiver are usually integrated on one chip, and they share the common RF port through switches or duplexers (bandpass filters tuned for simultaneous transmit and receive on different bands). Up to now, neither option is satisfactory for fully integrated silicon THz circuits.
One solution for integrated THz transceiver is to share the antenna and figure out ways to isolate the Tx (transmitter) and Rx (receiver). Park et al. have shown a fully integrated 260 GHz transceiver based on shared leaky-wave antenna [28]. The leaky-wave antenna resembles a lossy transmission line (TL); thus, the Tx and Rx ports could be placed on either end of the antenna. When the transmitter is working, the receiver is turned off and terminates the TL on its side. The same holds true for the receiving mode. The problem with the leaky-wave antenna is that they are relatively long (1.2 mm or 2.5 λ in this design). Statnikov et al. [29] have shown a fully integrated 240 GHz frequency-modulated continuous wave (FMCW) radar transceiver based on shared dual-polarization antenna. A quadrature hybrid coupler is used as a polarizer for the dual-polarization antenna and duplexer for the Tx and Rx. Isolation of the Tx and Rx depends on the orthogonality of left hand circular polarized (LHCP) and right hand circular polarized (RHCP) waves. The Tx and Rx interface with two orthogonal port of the branch-line coupler and are isolated from each other. In Tx mode, the branch-line coupler excites the LHCP mode of the antenna. When the transmitted wave hits a target and bounces back, it changes to RHCP and is subsequently routed to the receiver through the coupler. This scheme is not directly applicable for point-to-point communications, just like frequency-division duplexing (FDD)-based transceivers could not communicate directly with each other.
Another solution is to use two antennas. For FMCW radars, the leakage from the TX to the Rx results in strong interferences around DC [30]. This raises the noise floor in the range spectrum. With area permitting, the Tx and Rx antenna should be separated further apart for better isolation. The measured crosstalk between the two antennas with a separation of about 1.8 mm in a 160 GHz FMCW radar transceiver is below 31 dB [31]. This isolation might be adequate for FMCW radar applications, but it is still wanting for communications.
Transceiver-based THz imaging makes coherent imaging possible, as both the magnitude and phase information of the signal from targets are retained. With both information available, it is possible to get rid of bulky THz optics by sampling the THz field directly and do the focusing digitally. The THz field is usually sampled on a 2-D plane with different THz frequencies; this is fulfilled by raster scanning a FMCW transceiver (or the sample). For a given point in space, the round-trip phase delay from the transceiver to that point is a function of its position and sampling frequency. By raster scanning the transceiver or the sample under different frequencies, its phase delay variation is orthogonal to every other point in the sampling space. This forms the basis for the 3-D imaging through the back-projection algorithm. 3-D imaging based on SiGe FMCW transceivers is reported by several groups [32, 33], showcasing the great potential for low-cost THz imaging applications.
For communication applications, the modulation scheme plays a major role in deciding the transceiver architecture. Low-complexity modulation schemes like on-off keying (OOK) and binary phase shift keying (BPSK) lead to robust and power-efficient design, but the spectrum efficiencies are relatively low. Modulation schemes like 32 QAM and 128 QAM lead to much higher spectrum efficiency, but they are quite demanding on linearity and phase noise performance, and they require image-rejection architectures as the spectra of QAM are asymmetric around the carrier. The upper sideband (USB) and lower sideband (LSB) of the spectra become each other’s own image when converted to baseband, and image-rejection is needed to avoid signal corruption. Image-rejection modulation/demodulation is difficult in THz range as I/Q mixers are required. It is very difficult to guarantee phase and amplitude matching for the I/Q LO signal for adequate image-rejection at THz frequency.
A 210 GHz fundamental transceiver chipset with OOK modulation is demonstrated in a 32-nm SOI CMOS process [34]. Ideally speaking, power amplifier (PA)-based fundamental operation is more power-efficient than frequency multipliers. This helps to boost efficiency of the whole system as PAs are usually the most power-hungry circuits in transceivers. Perhaps the most difficult part of this design is controlling the oscillator pulling effect. Since the PA works at the same frequency as the on-chip VCO, significant coupling could occur between PA and VCO. The injection-locking effect would impact the phase noise performance heavily. The on-chip antenna used in this design only makes things more difficult. To improve the VCO performance, a stacked cross-coupled VCO topology is used to boost oscillation amplitude, improving its robustness in response to interferences.
A 240-GHz direction-conversion transceiver in SiGe BiCMOS technology is demonstrated with BPSK capability. BPSK is a constant-envelope modulation, which means the PA could be driven to saturation for better power efficiency. The spectra of BPSK modulation are symmetric around its carrier (symmetrically modulated), making direct conversion easier to implement as no image-rejection is needed. A 30 GHz LO signal is supplied to this transceiver, and on-chip ×8 multipliers are used for the 240 GHz LO generation. This helps to alleviate the detrimental effect of LO spurs caused by multipliers since they are separated by twice the baseband bandwidth (15 GHz). An on-chip antenna with 1-dB bandwidth of 33 GHz is achieved partly due to the local back etching (LBE) technology used. The silicon substrate below the antenna is removed, resulting in a low-loss air cavity below the antenna. The transceiver link is tested with 15 cm separation, and an impressive 6-dB bandwidth of 35 GHz is obtained. A 25 Gbps wireless link is demonstrated by this transceiver with no equalization. One problem with direct conversion using no I/Q demodulation is that the demodulated signal’s SNR is dependent on the phase difference between the Tx LO and Rx LO. A phase shifter is used in this test in case manual tuning is required to boost the SNR.
A 300 GHz QPSK transmitter for dielectric waveguide communication is demonstrated in a 65-nm CMOS process [35]. Again, off-chip LO signal is used to drive on-chip frequency multipliers. The targeted data rate is 30 Gbps, which translates to around 20 GHz baseband bandwidth for QPSK assuming a roll-off factor of 0.3. Thus, the off-chip LO signal frequency is set to 45 GHz. An on-chip quadrature modulator is used to modulate the baseband data to an IF frequency of 135 GHz. It is further shifted by a double-balanced mixer to 315 GHz. Such a high IF alleviates the need for image-rejection mixers since the image frequency falls completely out of band. A 30 Gbps QPSK is demonstrated with on-chip probing.
A 230 GHz direct-conversion 16-QAM 100-Gbps wireless link is demonstrated with a communication distance of 1 meter [36]. The I/Q mixer directly interfaces with on-chip antenna to avoid bandwidth limitation introduced by LNA. On-chip LO multiplier chain is used to convert the external 13.75–16 GHz LO to 220–256 GHz. The baseband bandwidth is around 14 GHz; this poses challenge as the spacing of LO spurs is comparable to this bandwidth. This leads to spurious modulation that overlaps with desired signal. Nevertheless, 100 Gbps with an EVM of 17% is demonstrated.
A 300 GHz 32-QAM and 128-QAM transmitter with 105-Gbps data rate is demonstrated in a 40 nm CMOS process [37]. As there is no PA available, an array of eight square mixers (i.e., mixing through the second-order nonlinearity) is power combined at the output stage. A heterodyne topology is used, and the LO frequencies for the two up-conversion stage are both set at 135 GHz. The IF frequency for the first stage is around 10 GHz, and high-pass filtering is used to suppress the LSB by approximately 10 dB. Single-balanced mixer is used in the first stage to intentionally leak LO signal to the second stage. The second-order nonlinearity of NMOS transistor is used to mix the (IF+LO) signal with LO leakage to obtain the desired intermodulation signal (IF+2LO). Unwanted second harmonics of LO and IF signal is canceled at the output rat-race balun. On-chip probing validates the operation; the 32-QAM modulation with an EVM of 8.9% is achieved with 105 Gbps. No on-chip antenna is used as this chip is intended to drive high-power THz devices like traveling-wave tubes.
2.3 THz interface for efficient power transfer
The THz interface serves as a gateway between the circuit and the outside world. The efficiency of this interface greatly impacts the performance of the overall system. A simple derivation of the transceiver’s link budget would highlight the importance of this interface (Figure 9):
PR=PT−IL2−IL0−IL1E31
Figure 9.
Link budget analysis of a THz transceiver system.
where PR is power received at the receiver, PT is the output power of the transmitter, and IL2 and IL1 are the loss for THz interface at the transmitter and the receiver. IL0 is the loss associated with the propagation medium. If the medium is free space, which is often the case, IL0 equals
IL0=20×log10λ04πd+GTX+GRXE32
λ0 is the free-space THz wavelength, d is the propagation distance, and GTX and GRX are the gain of antenna employed at the transmitter and receiver. Note that Eqs. (31) and (32) are in dB form. Also keep in mind that Eq. (32) is only valid under far-field conditions, that is, the radiation field seen by the receiver is not reactive and could be approximated by plane waves. Common criterion for far-field condition is that the receiver is separated from the transmitter by at least 2D2/λ, where D is the maximum overall dimension of the transmitting antenna.
To maximize PR, we have to minimize the loss at the interface and increase the gain of the antennas. This section covers both areas.
For THz silicon chips, grounded coplanar waveguide (GCPW) is the most prevalent medium for on-chip THz routing. It is a combination of coplanar waveguide with microstrip line. This configuration have several merits: First, the ground plane of the microstrip line shields the signal from the electrically thick silicon substrate, which reduces loss and prevents the signal from leaking into substrate modes; the coplanar waveguide makes interface with outside world easier, be it through flip-chip bonding or on-chip probing since the ground conductor lies in proximity with the signal trace.
A 90–300 GHz transmitter and a 115–325 GHz receiver are flip-chip bonded to a liquid-crystal polymer (LCP) substrate [12]. This connects the chip to the 100–280 GHz Vivaldi antenna on the LCP substrate. Such wideband antenna is extremely difficult to realize on-chip. As another example, a CMOS 300 GHz transmitter chip is flip-chip bonded to a GCPW-to-WG transition module [38] implemented on a low-cost glass epoxy PCB. Once transitioned to waveguide interfaces, the chip could be interfaced to a plethora of THz components like horn antennas and high-power amplifier modules. The packaging loss is 8 dB, which includes the transition loss (flip-chip bonding and the GCPW-to-WG), impedance mismatch, and loss in the epoxy material. It should be noted that gold stud bumping is used in both cases, which is compatible with conventional wire bonders and is quite convenient for R&D labs.
An effective way to lower transition loss is to radiate the THz signal directly from chip. Since the high permittivity silicon substrate readily traps the THz radiation, there are basically two lines of thoughts regarding on-chip antenna design. One is to accept this coupling and take this into account while designing antennas; the other is to eliminate the substrate mode altogether.
The first approach tries to make use of the electrically thick antenna to improve the antenna bandwidth. Metal reflector are placed underneath the substrate to reflect energy back, which is often the top layer of the PCB under the chip. To make sure the reflected power adds constructively with the surface radiation, the chip should be (2k + 1)/4λ thick [34, 39, 40]. The phase delay of the reflected wave increases linearly with frequency, which limits the bandwidth. Artificial magnetic conductor (AMC) reflector in place of the solid metal reflector on the PCB is used to compensate this phase shift [41], which extends the on-chip antenna bandwidth substantially. The antenna efficiency is within 0.5dB of the peak efficiency between 200 and 300 GHz. Note that the chip should be 1/2λ thick in this case as AMC introduces zero phase shift at the center frequency.
Although promising, allowing reflections within the substrate increases couplings between antenna elements and on-chip passive components. This makes circuit performance sensitive to antenna location and substrate dimensions (both lateral dimension and chip thickness), which is undesirable for designing arrays.
There are two widely adopted approach to eliminate the substrate mode. The first approach involves attaching a high-k dielectric lens on the back side of the chip, and the antenna radiates through the lens [22, 42, 43, 44]. This approach offers high directivity and improves efficiency. The most obvious drawback is the need for nonstandard packaging, which could be quite costly. An intuitive way of understanding why this structure can eliminate the substrate mode can be found in [8].
The second approach is more straightforward: The substrate is shielded from the radiating element using one or a few low-level metal layers. This eliminates the possibility of coupling with substrate modes, but it limits the bandwidth and radiation efficiency severely since the radiating element is only a few microns away from the ground due to the restriction of silicon backend process. The radiating element thus forms a high Q tank with the ground, and the bandwidth of the antenna is on the order of a few percent [13, 20, 25]. The obvious way to increase bandwidth and radiation efficiency is to lower the Q, which could be accomplished by increasing the volume of the resonant tank. One solution is to add a dielectric superstrate above the radiating element [45, 46], which diverts some of the electric fields from the dielectric layer below the radiating element, increasing the resonance volume considerably. The radiation efficiency increases with the superstrate till the onset of the TE1 mode, which limits the thickness of the superstrate to λ0/4εr−1 where εr is the dielectric constant of the superstate. Dielectric resonator antenna (DRA) is another option [47, 48]. This antenna composes of a dielectic resonator on top of the chip and a feed element in the top metal layer of the chip. The feed element is used to excite resonance inside the resonator, through which the THz signal radiates. The size of the resonator and relative position of feed could be adjusted for intended oscillation frequency and resonance mode. For a 270 GHz microstrip antenna, the gain is enhanced by 4 dB, and the 3-dB gain bandwidth is extended by 100% when an dielectric resonator is used [49].
For phased array applications, the patch antenna with ground shield is the most straightforward approach.
3. Summary
Silicon THz circuit design is an active research area open to innovations on multiple levels. We need better passive components, better circuits, and the most important thing is we need to come up with better ways of building THz arrays. Scaling is the key for significantly boosting the performance of silicon THz systems as we venture into this last untapped spectrum [50].
\n',keywords:"terahertz, detector, source, transceiver, silicon",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/67256.pdf",chapterXML:"https://mts.intechopen.com/source/xml/67256.xml",downloadPdfUrl:"/chapter/pdf-download/67256",previewPdfUrl:"/chapter/pdf-preview/67256",totalDownloads:135,totalViews:0,totalCrossrefCites:0,dateSubmitted:"January 22nd 2019",dateReviewed:"April 23rd 2019",datePrePublished:"May 21st 2019",datePublished:null,readingETA:"0",abstract:"With active devices lingering on the brink of activity and every passive device and interconnection on chip acting as potential radiator, a paradigm shift from “top-down” to “bottom-up” approach in silicon terahertz (THz) circuit design is clearly evident as we witness orders-of-magnitude improvements of silicon THz circuits in terms of output power, phase noise, and sensitivity since their inception around 2010. That is, the once clear boundary between devices, circuits, and function blocks is getting blurrier as we push the devices toward their limits. And when all else fails to meet the system requirements, which is often the case, a logical step forward is to scale these THz circuits to arrays. This makes a lot of sense in the terahertz region considering the relatively efficient on-chip THz antennas and the reduced size of arrays with half-wavelength pitch. This chapter begins with the derivation of conditions for maximizing power gain of active devices. Discussions of circuit topologies for THz sources, detectors, and transceivers with emphasis on their efficacy and scalability ensue, and this chapter concludes with a brief survey of interface options for channeling THz energy out of the chip.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/67256",risUrl:"/chapter/ris/67256",signatures:"Li Zhuang, Cao Rui, Tao Xiaohui, Jiang Lihui and Rong Dawei",book:{id:"8653",title:"Electromagnetic Materials and Devices",subtitle:null,fullTitle:"Electromagnetic Materials and Devices",slug:null,publishedDate:null,bookSignature:"Prof. Man-Gui Han",coverURL:"https://cdn.intechopen.com/books/images_new/8653.jpg",licenceType:"CC BY 3.0",editedByType:null,editors:[{id:"250649",title:"Prof.",name:"Man-Gui",middleName:null,surname:"Han",slug:"man-gui-han",fullName:"Man-Gui Han"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. How to have THz power and radiate it too",level:"1"},{id:"sec_2_2",title:"2.1 Power gain maximization for a given active device",level:"2"},{id:"sec_3_2",title:"2.2 Circuit topology for THz sources, detectors, and transceivers",level:"2"},{id:"sec_3_3",title:"2.2.1 THz Sources",level:"3"},{id:"sec_4_3",title:"2.2.2 THz detectors",level:"3"},{id:"sec_5_3",title:"2.2.3 THz transceivers",level:"3"},{id:"sec_7_2",title:"2.3 THz interface for efficient power transfer",level:"2"},{id:"sec_9",title:"3. Summary",level:"1"}],chapterReferences:[{id:"B1",body:'Mason SJ. Power gain in feedback amplifier. Transactions of the IRE Professional Group on Circuit Theory. 1954;1(2):20-25'},{id:"B2",body:'Gupta MS. Power gain in feedback amplifiers, a classic revisited. IEEE Transactions on Microwave Theory and Techniques. 1992;40(5):864-879'},{id:"B3",body:'Spence R. Linear Active Networks. 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