Methodologies of Microwave Amplifier Design

Methodologies of Microwave Amplifier Design 2.1 ACTIVE DEVICE SELECTION This chapter discusses various methodologies used in the design of single stage microwave amplifiers. Reaching the desired goals of gain, power loss and noise performance requires first selecting a suitable active device (transistor) that meets these goals. The rapid advances in transistor fabrication have permitted the traditional Si transistors to operate in the GHz re- gion. the increase for higher frequency operation drove the innovation of new novel devices with new materials, architectures and geometries Possibly the most significant difference be- tween microwave transistors and the lower frequency ones is in the area of materials. Although low-frequency transistors are fabricated mostly from silicon, the use more costly compound semiconductors like gallium arsenide (GaAs) and indium phosphide (InP) proves to be more economical at microwave frequencies because of their performance advantages over silicon. The demand for higher frequencies also produced sophisticated material c onfigurations like the heterojunction transistors which have no low-frequency counterparts. At low frequencies, microwave transistors can be broadly categorized into: the bipolar junc- tion transistors (BJTs) and the field-effect transistors (FETs). At lower frequencies, FETs con- tains the junction FET (JFET) and the metal oxide FET (MOSFET), structural characteristics limits their high frequency operation. GaAs metal semiconductor FET pushed the frequency of operation well into the GHz region. However, in the intervening decades, bipolar device caught up and now it is common to find BJTs operating at the GHz region. The selection of a suitable transistor for the required application is based on the targeted goals of gain, noise and power loss performance. In the following sections, the GaAs HJ-FET transistor NE3210S01 from Renessa Electronics will be used to illustrate the various meth- ods for selecting the appropriate terminations used in constructing matching networks for both narrowband and wideband operation. 2.2 MATCHING NETWORKS TOPOLOGIES Impedance matching involves transforming one impedance to the other. This process is useful in circuits where the mismatch between the source (ZS) and load (ZL) prevents maximum power transfer. Theorem states that for a maximum transfer of power from source to load. Load impedance (ZL) must be equal to the complex conjugate of the source impedance. Complex conjugate is complex impedance having the same real part with an opposite imaginary one. For example, if the source impedance is ZS =R+jX, then its complex conjugate must be ZL =R-jX. For a pure resistive load, equations (2.1) and (2.2) aided with Fig.2.1 shows that a maximum 4 power transfer occurs when RL=RS. VO= VS L RL + RS RL (2.1) PO= V2 S(RL+ RS)2 (2.2) (a) (b) Figure 2.1: (a) Pure resistive circuit with VS=1V and RS=1à ¢Ã¢â‚¬Å¾Ã‚ ¦, (b) Maxim power is delivered to the load when RL=RS The same concept can be applied to AC circuits with complex load and source. Equation.2.3 aided with figure Fig.2.2 shows that a maximum power transfer to the load occurs when XL= XS. The value of the power delivered to the load is given by: 1|VS|2 RL PO= 2 (R + RL )2 + (XS + XL (2.3) )2 Where the resistance RS and RL and the reactants XS, XL are the real and imaginary parts of ZS and ZL. The target in applying impedance matching to make the load impedance look like the complex conjugate of the source impedance to attain maximum power transfer to the load. This is shown in Fig. where a matching circuit is placed between points a,b shown in Fig to transfer the load impedance to the complex conjugate value of the source impedance. Since we are dealing with reactances, which are frequency dependent, the matching can occur only at single frequency. That is the frequency at whichXL= Xand, thus, cancellation or resonance occurs. At the surrounding frequencies, the matching becomes worse. This is the main problem in broadband matching where perfect or near perfect matching along the required bandwidth is required. The methods for narraowband and wideband matching is presented later in this chapter. In Fig.2.3b, numerous topologies can be used as a matching network. The shape of the topology can vary from a simple L, Ï€or T networks to a complex ladder circuit or filter design. The concept of matching network can be explained using the two simple L-Matching topologies shown in Fig.2.4a,2.4b. Both B and X values in Fig.2.4 must be chosen to satisfy the condition ZL=ZS*. To achieve this condition, both analytical methods, mostly with the aid of a computer, and graphical procedures, using the Smithchart, can be used. (a) (b)(c) Figure 2.2: (a) AC circuit with complex ZS and ZS, (b) For XS=j5, Maxim power is delivered to the load when XL=-j5 (c) For XS=-j5, Maxim power is delivered to the load when XL=j5 For the case of RL  ¿ Ro, the topology of Fig.2.4a is preferred, where B and X are given by:   RL  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   22 XL ± B= ZoRL+ XL−ZoRL (2.4) R22 L+ XL X= BZoRL−XL 1 − BXL (2.5) For the condition of RL ¡Ro the topology of Fig.2.4b is used with B and X given by: 1  Ã‚  Ã‚   Zo−RL B=  ± oL (2.6) X=  ±Ã‚   RL(Zo−RL) −XL(2.7) In both topologies of Fig.2.4, B and X represent either an inductor (L) or capacitor (C). The result is four simple L-matching networks as shown in Fig.2.5. (b) Figure 2.3: (a)Circuit before the matching network(b) Circit after adding the matching network. (a)(b) Figure 2.4: L-Matching topologies, a) used when RL  ¿ Ro, b) used when RL  ¡ Ro 2.3 NARROWBAND DESIGN METHODOLOGIES Analytical Solution Graphical Solution CAD Solution WIDEBAND DESIGN METHODOLOGIES Analytical Solution Graphical Solution CAD Solution (b) (c)(d) Figure 2.5: Four basic L-matching Networks

Introduction to Philosophy Essay

1. What are the main branches of philosophy? Do philosophers have the same answers to the same philosophical questions? Why? Philosophy is a way of thinking about the big questions in life, from the existence of men to its morality. It is an activity which sharpens our reason. The word was coined by Greeks , meaning â€Å"the love of wisdom†. Philosophy can be divided into six big issues it is interested with. * First, the question about the nature of the world and the existence of Men which is under the domain of Metaphysics or also called Ontology. From the word â€Å"meta† which means beyond and â€Å"physics† which means physical it deals about beyond physical world- the spiritual. It also attempt to answer the ultimate reality of life, our reason of very existence, Who and what God is and, how everything relates to it. * Second, what are the right ways to think and build arguments which is under the field of Logic. It tries to distinguish the valid reasons from the fallacies. It also examines the different general forms that argument may take. It is primarily studied in the disciplines of philosophy, mathematics, semantics, and science. * Third, How do we know and how do we think we know which is under the area of Epistemology. From the Greek words †episteme† which means knowledge and â€Å"logia† which means study, it basically deals on how do we acquire knowledge and what is the basis for true knowledge. * Fourth, Ethics which generally centers on the morality of our actions. It differentiates wrong from right and studies character’s actions based in his intentions. This field of Philosophy is vital and applied to other disciplines such as business, medicine, science, robotics, and education. * Fifth, Issues about laws, liberty, rights, property and , politics fall under the Political Philosophy. It is also one of the sub-fields of Political Science. Its purpose is to lay bare the fundamental problems and concepts which frames the study of Politics. It also studies the great thinkers of the past which shapes politics such as Socrates, Plato, Adam Smith and Hobbes. * Lastly, Aesthetics which deals on what is beautiful. Mainly it tries to answer questions which deals in art- music, painting, poetry, and such. It attempts to distinguish what is beautiful, what has taste, and what has artistic value. Philosophy can also be subdivided into three specific categories which are, Philosophy of Mind, Philosophy of Language, and Philosophy of Science. These are branches which deal to questions their respective field of subject matters such as what exactly is a mind? how does language work? and Does science has responsibility to humanity? An Educator can ask a question to his students and would receive different responses . We can even expect complex answers to a simple question. It is because people view things in different perspectives, have different degree of intelligence, exposed to different environment, influenced by different people and ideas, and have personal insights and experiences which differ from one person to another. People thoughts varies and no idea can be of an exact match of another. In my opinion, Humans’ mind are like his fingerprint, We all have our fingerprints but its design- the curves and lines is unique in each individual. There might be similarities in ideas between individuals but in some point they contradict. For example, the two famous philosophers, John Locke and Thomas Hobbes both support the â€Å"Social Contract Theory† in which men enter a mutual agreement to surrender some of their liberty to authority in return of protection, both also, believe that men can exist without government and speak of its dangers in this kind of state-State of Nature. For Hobbes, the entire time that man is in a state of nature, he is in a state of war. He states that â€Å"if any two men cannot enjoy the same thing, they become enemies and in the way to their end†¦. endeavor to destroy or subdue one another† (Wootton, 158). Locke too points out risks, saying that without the â€Å"law of nature† everyone may execute decisions, leading to a state of war (Wootton, 290). However, despite of the similarities, Locke believes that people enter to social contract to seek peace and avoid the fear of death and living in State of Nature is brutish and chaotic while Hobbes believes that State of Nature is important and do exist in some ways such as among governments and leaders. Locke’s view on State of Nature is pessimistic in contrast to Hobbes which he thinks has some potential benefits. Philosophers do not have the same answer to a certain question. Each philosopher present different examples and take different stand on a certain idea. 2. Why has philosophy lost importance in the priorities of contemporary man? Philosophy had the paramount role during the ancient education. It created great and wise thinkers such as Socrates, Plato, and, Seneca and influenced bright minds such as Descartes, Adam Smith, and Karl Marx. Although the subject Philosophy is only introduce in higher level of studies in modern years, it diffuses its idea and being applied to core subjects such as mathematics, science, and language. Philosophy is still vital in learning until today. The decreasing value given in philosophy arises in the way modern man receive and gather information. Core subjects like Science should teach us to Inquire, to Analyze, to Think, and to Search- which are roles of philosophy but, Educators and with the convenience at reach, Students are being spoon-fed with facts from books and other resource materials instead of encouraging them to explore. They are bound with rules and regulations without giving them a chance to ask why they should follow orders. Students fail to analyze things because most Educators present facts and inculcate it to them through rote memorization instead of validating it. Learners learn facts but never learn to reason. They become man of knowledge but never become man of substance. The decreasing importance of philosophy in modern days is ascribed partly, to us Educators for failing to emphasize and apply its essence to the students. We teach the students to be dependent on the facts provided in books and internet, for we believe that it offers a vast amount of information forgetting that one’s mind can offer limitless insights on a certain topic. 3. Why should philosophy be restored to its former prominence in the priorities of contemporary man? Philosophy is vital in man’s learning and improvement. Giving answers to man’s most perplexed questions or even to the simplest question that bother us gives us sense of satisfaction and purpose in life. In modern times, Philosophy is essential in choosing decisions that has impact on our future such as career path, religion, core beliefs, and even to work or business. Philosophy should never be undermine and be restricted to as a mere subject. It is a way of thinking and essential in making a wise decision hence, should be integrated in daily living. 4. How does western philosophy differ from the eastern? In General, Western Philosophy promotes individualism and more interested in finding and validating the truth while Eastern Philosophy is more interested in finding the balance within one’s self in order to live in harmony with others and thus promoting collectivism. Also, East philosophy which emerged in China is spiritual in nature as opposed to West which starts from Greece is naturalistic and subject to research. Individualism of the West gives meaning to the worth a person as an individual. It gives stress on liberty and self-reliance. â€Å"Man is directly a natural being. As a natural being and as a living natural being he is on the one hand endowed with natural powers, vital powers — he is an active natural being. These forces exist in him as tendencies and abilities — as instincts. On the other hand, as a natural, corporeal, sensuous objective being he is a suffering, conditioned and limited creature, like animals and plants. †¦ A being which does not have its nature outside itself is not a natural being, and plays no part in the system of nature. A being which has no object outside itself is not an objective being. â€Å" Marx, Critique of Hegel’s Philosophy in General (1844) â€Å"Self-expression is individuality, and our individuality is our self, which ought to be our chief concern† Ernest Dimnet (1928) The Art of Thinking p. 250 â€Å"If a man does not keep pace with his companions, perhaps it is because he hears a different drummer. Let him step to the music which he hears, however measured or far away. † Henry David Thoreau, Walden: Or, Life in the Woods (1854), chapter 18, p. 210. Collectivism of the East emphasizes the interdependence of individual among others. â€Å"If I am walking with two other men, each of them will serve as my teacher. I will pick out the good points of the one and imitate them, and the bad points of the other and correct them in myself. † â€Å"Without feelings of respect, what is there to distinguish men from beasts? † Confucius â€Å"A leader is best when people barely know he exists, when his work is done, his aim fulfilled, they will say: we did it ourselves. † â€Å"Being deeply loved by someone gives you strength, while loving someone deeply gives you courage. † Lao Tzu â€Å"The highest education is that which does not merely give us information but makes our life in harmony with all existence. † Rabindranath Tagore.

Summer Sport Camp at State University

14th MANCO Linear Programming Approach for Irrigation Scheduling – A case Study H. MD. AZAMATHULLA, Senior Lecturer, River Engineering and Urban Drainage Research Centre (REDAC), Universiti Sains Malaysia, Engineering Campus, 14300 Nibong Tebal, Pulau Pinang, Malaysia; email: [email  protected] usm. my, [email  protected] com (author for correspondence) AMINUDDIN AB GHANI, Professor, REDAC, Universiti Sains Malaysia, email: [email  protected] usm. my NOR AZAZI ZAKARIA, Professor, REDAC, Universiti Sains Malaysia, email: [email  protected] usm. my CHANG CHUN KIAT, Science Officer, REDAC, Universiti Sains Malaysia, email: [email  protected] sm. my Abstract There is an increasing awareness among irrigation planners and engineers to design and operate reservoir systems for maximum efficiency to maximize their benefits. Accordingly, significant work has been done on reservoir operation for known total irrigation demand and on the optimal allocation of water available to c rops at the farm level. Very few studies have been conducted to derive optimal reservoir operation policies integrating the reservoir operation with the on-farm utilisation of water by the various crops.This present paper deals with the development of model — Linear Programming (LP) — to be applied to real-time reservoir operation in an existing Chiller reservoir system in Madhya Pradesh, India. Keywords: Cropping pattern, Water resource management, Irrigation management, Optimization 1. Introduction In most developing countries, a huge share of the limited budget goes to creating facilities for irrigation. Construction of reservoirs requires very high investment and also causes socioeconomic and environmental issues.Water in the reservoir has multiple claimants and needs to be optimally utilized to generate maximum benefits through proper operation, which must remain consistent despite uncertain future inflows and demands. According to the World Commission on Dams, ma ny large storage projects worldwide are failing to produce the anticipated benefits (Labadie, 2004). Similarly, small storage projects made for local areas in developing countries, like India, are also failing to meet expectations.The main cause identified at various levels of discussion, as reported by Labadie (2004), is inadequate consideration of the more mundane operation and maintenance issues once the project is completed. For existing reservoirs, optimum operation is critical, since all the expected benefits are based on timely water releases to meet the stipulated demand. Real-time operation of a reservoir requires making relatively quick decisions regarding releases based on short-term information. Decisions are dependant on the storage in the reservoir and information available in the form of forecast hydrologic and meteorological parameters.This is especially important during floods and power generation, where the system has to respond to changes very quickly and may need to adapt rapidly (Mohan et al. 1991). For reservoir systems operated for irrigation scheduling, real-time operation is not very common because of longer decision steps. Traditionally, the reservoirs meant for irrigation purposes are operated on heuristics and certain rules derived from previous experiences. This defies the concept of water-management; much of the water is lost, which in turn leads to loss of revenue.In the early 1960s, mathematical programming techniques became popular for reservoir planning and operation; pertinent literature is available. An excellent review of the topic is given by Yeh (1985), followed by Labadie (2004) and Wurbs (1993). Along with simulation studies, Linear Programming (LP), Dynamic Programming (DP) and Non Linear Programming (NLP) are the most popular modelling techniques. A comparative study on the applicability and computational difficulties of these models is presented by Mujumdar and Narulkar (1993).Many of the aforementioned techniques ha ve been implemented in realistic scenarios, and many reservoir systems worldwide are operated based on the decision rules generated from these techniques. However, there exists a gap between theory and practice, and full implementation has not been achieved yet (Labadie, 2004). 1 14 & 15 February 2009 Kuching, Sarawak The basic difficulty a reservoir manager faces is to take a real-time optimum decision regarding releases according to the future demand and inflow. This leads to the problem of optimization of the stochastic domain.Two approaches of stochastic optimization are practised: i) Explicit Stochastic Optimization (ESO), which works on probabilistic descriptors of random inputs directly and ii) Implicit Stochastic Optimization (ISO), which is based on historical, generated or forecasted values of the inputs through the use of Time Series Analysis or other Probabilistic approaches. The ESO approach has computational difficulties; ISO methods are simple, but require an addition al forecasting model for real time operation. In the case of irrigation reservoirs, decision making at the reservoir level depends upon the water demand arising at the field level.In order to operate the reservoir in the best possible way, it becomes imperative to understand the processes occurring in the crop-soil-water-atmosphere system. This helps not only in the estimation of accurate demands, but also ensures optimum utilisation of water. If the processes at the field level are also modelled properly and integrated with the reservoir level model, the goal of water management can be achieved in the best possible way. Dudley et al. (1971) pioneered the integration of the systems in the determination of optimal irrigation timing under limited water supply using a Stochastic DP model.Dudley and his associates then improved the model (Dudley and Burt, 1973; Dudley, 1988; Dudley and Musgrave, 1993). Vedula and Mujumdar (1992, 1993) and Vedula and Nagesh Kumar (1996) have also contrib uted to this area. Their approach was to derive a steady state reservoir operation policy while maximizing the annual crop yield. DP-SDP and LP-SDP were used in the modelling. However, for real-time reservoir operation, Vedula and Nagesh Kumar (1996) stressed the need to forecast inflows and rainfall in the current season to implement the steady state operation policy.As a result, the ESO model has to be supplemented with an ISO model to get a policy for the current period. As an extension to the work of Vedula and Mujumdar (1992), a significant contribution to the real-time reservoir approach was presented by Mujumdar and Ramesh (1997). They addressed the issue of short term real-time reservoir operation by forecasting the inflow for the current period, a crop production state variable and a soil moisture state variable. Their work was based on SDP, but had all the limitations of SDP regarding the curse of dimensionality.Against this background, a model for the derivation of real-t ime optimal operating policy for a reservoir under a multiple crop scenario is proposed in the present study. The primary issue is that the reservoir gets inflows during the wet season (monsoon season) and is operated for irrigation in the dry season (non-monsoon season). The reservoir storage and the soil moisture level are considered to be the principal state variables, and the irrigation depths are the decision variables.An optimal allocation model is embedded in the integrated model to evaluate the irrigation water depth supplied to different crops whenever a competition for water exists amongst various crops. The model also serves as an irrigation-scheduling model because it specifies the amount of irrigation for any given fortnight. The impact on crop yield due to water deficits and the effect of soil moisture dynamics on crop water requirements are taken into account. Moreover, a root growth model is adopted to consider the effects of varying root depths on moisture transfer. The only stochastic element in the season is the evapotranspiration. The handling of stochasticity has been accomplished through dependability based forecasting in an ISO model. The rest of the variables, such as soil moisture status and the reservoir storage status, at the beginning of any period are considered to be state variables. The basic formulation is based on a LP model and is later transformed into a GA framework. 2. The Model Formulation and Concept The real-time operation model proposed in the present study integrates the reservoir level and a field level decision (Figure 3).It considers the soil-moisture status and the reservoir storage as the state variables and the applied irrigation depths as decision variables. The formulation is based on the conceptual model for soil moisture accounting and the reservoir storage continuity relationships. A major emphasis is laid on maintaining soil moisture in a state such that the evapotranspiration from the crops takes place at a rate that achieves better results in the form of increased yields from the crops. To assess the timing of irrigation water application, the soil moisture status of the crop is an important parameter.Whenever the soil moisture status approaches a critical limit, irrigation is applied. Thus, the soil moisture status is monitored either by physical measurement or through soil moisture models. Soil moisture models are more popular since they do not require a lot of instrumentation to be installed in the field. Soil moisture models can be formulated either by a physical approach (Fedders et al. , 1978) or a conceptual approach (Rao, 1987). The conceptual approach has been used by Rao et al. (1988), Rao et al. (1990) and 2 14th MANCO Hajilal et al. (1998) for the problem of irrigation scheduling.Vedula and Mujumdar (1992) utilised the conceptual model in their study. The same concept is adopted in the present study. Figure 3 Flow chart of real-time operation of reservoir 3 14 & 15 Februa ry 2009 Kuching, Sarawak 3. The Conceptual Model In the conceptual model for the Crop-Soil-Water-Atmosphere (CSWA) system, the basic assumption is that the soil acts as a reservoir, the main inputs to the reservoir are rainfall irrigation, and the main outputs are evapotranspiration, percolation and drainage. The extent of the reservoir is considered to be up to the effective root zone at the particular time.The soil water reservoir is governed by a continuity equation: ? ik +1 ED ik +1 ? ? ik ED ik ? IRR ik + AET i k = RF k (1) The conceptual model stated by Eq. 1 is used to compute the irrigation to be applied for the LP model with area as a decision variable. The following parameters are important for the conceptual model. Figure 1 shows the sketch for the conceptual reservoir. In the context of the conceptual model two parameters are important: IRRk RFk AETk EDk ?k Figure 1 Conceptual model Variation of Evapotranspiration with the Available Soil Moisture Evapotranspiration as a function of the available soil moisture is expressed as: kAETi k = PETi k if aai ? Zww (2) or AETi k = k aai PETi k Zww where AETi k (3) is the actual evapotranspiration that has occurred from crop i in fortnight k (mm), PETi k is the potential evapotranspiration in a particular geographical location (mm), Zww is the critical available moisture limit (mm/cm) = (Zf? Zw) d, Zf is the field capacity for the soil (mm/cm), Zw is the permanent wilting k point for the soil (mm/cm), d is the depletion factor and assumed to be 0. 5 in the present study, and a ai is the average available soil moisture over a fortnight (mm/cm). The average available soil moisture over a fortnight is given by ik + aik +1 a= 2. 0 k ai where otherwise aik = ? ik ? Zw if aik < Zww aik = Zww k +1 A similar expression can be used for ai . 4 14th MANCO Root Zone Depth Growth The root depth data in relation to the time stages are prepared according to the Linear Root Growth Model (adopted by Narulkar, 1995). The model assumes that maximum root depth is achieved at the start of the yield formation stage. It remains at the maximum depth until the maturity stage. A minimum depth of 15 cm is considered in the first fortnight to account for the conditions of bare soil and an area with sparse crops.The root depth model is shown in Figure 2. Life span of group Growth stages of group V F G Root Depth Max. Depth Figure 2 Root Depth growth model Relative Yield Ratio The yield of a crop is affected by water deficits and the rate of evapotranspiration. The rate of evapotranspiration tends to decrease depending on the available moisture content. There are many methods to model the phenomenon. However, the model used in the present study is the most commonly-adopted model. The relative yields are computed on the basis of the expression given by Doorenbos and Kassam (1979) YaiAETi k ? k? = 1 ? Ky ? 1 ? ? PET k ? ? Ymi i? ? (4) Equation (4) gives a yield ratio for a single period only. However, the aggregate ef fect of moisture deficits over all fortnights of crop growth is also evaluated. The final yield ratios computed for the crop during various time periods of a season is computed by a multiplicative model (Rao et al. , 1990). The determination of the yield ratio is very important since they reflect the operation policy for an irrigation system. The expression is given by ? AETi k Yai ncr ? = ? ?1 ? Ky k ? 1 ? ? PET k ? Ymi i =1 ? i ? (5)Water Requirements of the Crops The model derived for an optimal crop pattern uses predetermined irrigation demands. On the basis of this, the optimisation model selects an appropriate area for an individual crop. The irrigation demands are determined using the conceptual model stated in Eq. 1. The irrigation requirements may be calculated by substituting a value of critical soil moisture content instead of soil moisture in either of the fortnights k and k+1 and replacing the values of actual evapotranspiration by potential evapotranspiration and re arranging the terms of Eq. : ( ) IRRik = ? cr EDik +1 ? EDik + PETi k (6) 5 14 & 15 February 2009 Kuching, Sarawak where ? cr is the critical soil moisture content below which the actual evapotranspiration may fall below the potential rate. 4. Integrated LP Formulation In the objective function, the weighted sum of all the actual evapotranspiration values is maximised. The weights are assigned according to the yield response factors for individual crops in individual periods. The objective is to maximise the actual evpotranspiration rate to minimise the deficits in the yields.The available soil moisture in any time period in the objective function is indirectly maximised: ncr np ? a k + aik +1 ? Ky k MaxZ = ? ? ? i ? 2. 0 ? Zww i =1 k =1 ? (7) subject to the following constraints: 1. Soil moisture continuity ? aik + aik +1 ? PET = RF k ? 2. 0 ? Zww ? ? ik +1 EDik +1 ? ? ik EDik ? IRRik + ? (8) ? ik +1 ? aik +1 ? bik +1 = ZW (9) where with physical bounds ? ik +1 ? 4. 0 a 2. k +1 i ( 10) ? 0. 9 (11) Reservoir continuity ncr A k S k +1 ? B k S k + ? i =1 S k +1 ? 31. 1 5. IRRik * AREAik = ? ID ? Ao RE k Eff (Maximum Reservoir Capacity M m3) (12) (13) Crop Simulation ModelThe optimisation model presented above yields some irrigation depth values that are based on forecasted values for the reference evapotranspiration. This reference evapotranspiration, in turn, is based on a dependability model. However, the actual evapotranspiration value differs from these values, and thus, before going into the next fortnight, the soil moisture status must be updated with the applied irrigation and actual climatic factors. The formulation for crop simulation is as follows: First compute the final soil moisture with the following relation ? ik = (? ik +1 EDik +1 + IRRik ?Fkcik APET k + ARF k ) / EDik If (14) ? ik +1 < 3. 1 ?k ? Fkcik +1 APET k +1 Fkcik +1 APET k +1 ZW + ARF k +1 ? ? i EDik + IRRik +1 ? + ? 2. 0 2. 0 ? EDik +1? ik +1 = ? k +1 k +1 Fkci APET EDik +1 2. 0 ( ) (15) or 6 14th MANCO ? ? ik = ? ik ? 1 ? EDik ? 1 ? ? Fkcik APET ? Fkcik APET Fkcik APET + Zw + ARF k + IRRik ? ? EDik ? 2 . 0 2 . 0 2 . 0 ? (16) or ? k ? 1 ? k ? 1 Fkcik APET ? Fkcik APET Fkcik APET ? k k ? ? = i ? EDi ? Zw? ? ? EDi ? ? + IRRi + ? ? 2. 0 2. 0 2. 0 ? ? ? ? k i (17) The computed soil moisture status of the crops is used in the next fortnight to compute the demand. . Stochastic Analysis of Evapotranspiration It was previously stated that the data regarding the climatic factors is uncertain in nature and the determination of these factors beforehand is impossible. However, there is a general trend to assume the expected values for these factors and carry out the operation. The concept does not give a clear picture of the actual scenario and the appropriate weights for the individual growth stage of the crops are not assigned. The present study proposes a different method of forecasting the expected values for the climatic factors.The method of analysis starts with the co mputations of dependability values of reference evapotranspiration factors from the available data. The dependability of realisation of any stochastic variable is defined as the probability of equalling or exceeding that variable with a particular value. Mathematically, P(x ? X ) (18) where P (. ) is the probability and x is the variable under consideration and X is a stipulated value of the variable. A traditional method of estimation of the dependability value is the use of standard frequency formulae (e. . Wiebull’s formula or Hazen’s formula). In the present study, a detailed probability analysis for the data is performed. The data is fitted to a standard probability distribution and the best fitting distribution is tested through the Kolmogorov Smirnov Test (Haan, 1977). Once the values corresponding to different dependabilities are evaluated, dependability values for reference evapotranspiration are assumed to be different in different growth stages. The analysis is performed on the basis of the yield response factor.A high yield response factor signifies greater sensitivity towards the deficits, and thus, a higher level of dependability is assumed for the evapotranspiration data and a lower level of dependability is assumed for the rainfall data. This will ensure a higher value of irrigation required for the crop in the sensitive period. As a result, the crop will be safeguarded against any poor moisture content conditions. 7. LP Model Formulation for Optimal Cropping Pattern At the start of each dry season, depending on the storage volume in the reservoir, the crop pattern must be determined.To evaluate the crop pattern, another LP model is used. In this model, irrigation depths are calculated from Eq. (6). The formulation is as follows: The objective function is MaxZ = C1 X1+ C2 X2+ C3 X3 (19) which is subject to the following constraints: 1. Total available area X1+X2+X3? A (20) where X1, X2, and X3 are the decision variables related to the area of individual crops;C1, C2, and C3 are the cost coefficient for each crop in Indian Rupees (1 US $ = 50 INR); and A is the maximum area available for irrigation. 2.Area of each individual crop: 7 14 & 15 February 2009 Kuching, Sarawak The area under each crop is required to be constrained; thus, there are lower and upper bounds on the area under each crop. The lower bounds indicate the minimum area that can be allocated to a crop, while the upper bound indicates the maximum. In the present study, the lower bounds were defined for all the crops except cash crops, while the upper bounds were defined considering the present cropping pattern. The constraints can be expressed as Li? Xi? Mi (21) here Li corresponds to the lower bound of the area for the ith crop and Mi corresponds to the upper bound on the area of the ith crop. 8. Model Application The developed models were applied to the Chiller reservoir system in Madhya Pradesh, India (Latitude 23o23’ N and Longitude 7 6o18’ E). In the central part of India, many reservoir projects have been constructed for irrigation, but no irrigation is available from these reservoirs during the monsoon period (from June to September). The area receives about 90 to 95 % of its rainfall during the Monsoon season. The rainfall then becomes runoff to the reservoirs.These reservoirs are designed to contain the runoff in the monsoon season, but there is no runoff during non-monsoon months. The present formulations are specially suited for these types of reservoirs. Non-monsoon rainfall is rare and provides little runoff. A systematic data base was prepared for the various physical features of the reservoirs, including the meteorological and hydrological data such as evapotransiration, details of crops in the command area, details of net returns from individual crops and soil properties collected from the College of Agriculture, Indore, India. . Results and Discussion Optimum Crop Pattern A separate computer p rogram was run before the real time operation program to determine the optimum crop pattern for all possible storage values. The results of the optimum crop pattern are stated in Table 1. The results indicate that from a storage level of 31. 10 M m3 to a storage level of 26. 06 M m3, the cropping pattern is same as the one that has been adopted in the project formulation. However, below a storage level of 26. 06 M m3, the crop pattern changes suddenly, and wheat (ordinary) is not recommended by the model.The area of wheat (hybrid) also gets reduced when the rainfall storage is below this level. However, the area for Gram is full, up to a storage level of 15. 83 M m3. The change in cropping pattern indicates that efficient water usage is maintained. Table 1 Optimum Cropping Pattern for Different Live Storage Values Area (ha) for different crops Live storage (M m3) Wheat (ordinary) Gram Wheat (hybrid) 4. 3230 342. 910 120. 00 8. 2379 427. 580 500. 00 12. 3246 15. 8632 20. 7581 26. 098 6 28. 8610 30. 1250 31. 1000 300. 0 300. 0 300. 0 300. 0 1084. 015 1100. 000 1100. 00 1100. 000 1100. 000 1100. 000 1100. 000 500. 00 855. 00 1434. 00 1700. 00 1700. 00 1700. 00 1700. 00 Results from Real-Time Operation Model The real-time operation model gives an optimal operating policy for the available storage in the present fortnight considering the future. The model also yields the values of irrigation to be applied to individual crops in the fields. In the wake of deficient water supplies, the model distributes the available water over the time for different crops optimally. The sample results of the present model are stated in Table 2.The available moisture to the crops is not affected, and generally the soil remains at the upper limit of the available soil-moisture. This 8 14th MANCO is because the crop pattern is predicted according to the availability of the storage in the reservoir. The results are indicative of successful application of the real-time operation strategy proposed in the present work. Table 2 Sample Results Showing the Soil Moisture, Available Soil Moisture, Storage, and Irrigation to be applied for Different Crops for a Real-Time Reservoir Operation Model (LP) Live Storage in the Reservoir 31. 1 M m3 FORTNIGHTPARAMETER 1 2 3 4 5 6 7 8 9 10 11 Reservoir Storage (M m3 ) 29. 28 28. 17 26. 30 22. 22 Crop 1) Soil Moisture (mm/cm) 3. 76 3. 89 3. 84 3. 07 2) Available soil Moisture 0. 9 0. 9 0. 9 0. 87 (mm/cm) 3) Applied Irrigation (mm) 53. 62 90. 63 92. 87 36. 04 Crop 1) Soil Moisture (mm/cm 3. 90 3. 07 3. 28 3. 15 2) Available soil Moisture 0. 9 0. 87 0. 9 0. 9 (mm/cm) 3) Applied Irrigation (mm) 68. 76 22. 27 60. 67 41. 59 Crop 1) Soil Moisture (mm/cm — – 4. 00 2) Available soil Moisture —0. 9 (mm/cm) 3) Applied Irrigation (mm) — – 94. 21 19. 68 14. 64 10. 87 Wheat (ordinary) 3. 54 3. 30 3. 22 0. 9 . 9 0. 9 5. 62 4. 24 3. 63 3. 60 3. 17 0. 9 4. 0 0. 9 – -. — — 163. 9 8. 44 23. 02 GR AM 3. 28 3. 66 0. 9 0. 9 19. 94 102. 6 — — 3. 23 0. 9 3. 47 0. 9 — — 37. 64 53. 15 Wheat (hybrid) 3. 06 3. 48 3. 32 0. 86 0. 9 0. 9 0. 00 33. 17 — — 3. 28 0. 9 3. 38 0. 9 3. 18 0. 9 3. 19 0. 9 37. 19 162. 9 0. 00 36. 09 0. 0 3. 4 0. 9 26. 96 127. 9 78. 89 Relative Yield Ratios Relative yield ratios computed for different crops at different live storage values are shown in Table 3. The relative yield ratios for all the crops become one if live storage in the reservoir is equal to or greater than 28. 9 M m3. The GA model is found to be better for application in real world operation of the reservoir. Table 3 Relative Yield Ratio for Different Live Storage Values Computed With a Real-Time Reservoir Operation Model Relative yield ratio for Live different crops storage LP (M m3 ) Wheat Gram Wheat (hybrid) (ordinary) 4. 3230 0. 9677 1. 000 8. 2362 0. 9083 1. 000 12. 3246 0. 9576 1. 000 – 0. 989 1. 000 20. 7581 26. 0986 1. 000 0. 987 0. 987 0 . 911 0. 952 28. 8610 1. 000 0. 987 1. 000 30. 1250 31. 1000 10. – 15. 8632 1. 000 1. 000 1. 000 1. 000 1. 000 1. 000 ConclusionA real-time model using an integrated Linear Programming Model for a reservoir system meant for irrigation has been developed in the present study to obtain an optimal reservoir operating policy that incorporates field level decisions, while also deciding the appropriate time and amount of water to release from the reservoir. 9 14 & 15 February 2009 Kuching, Sarawak From the analysis, the following conclusions can be drawn: The developed model can be successfully applied to irrigation supporting reservoir systems. Furthermore, the models ensure an optimum reservoir release over different time periods.In addition, they also ensure optimum allocation of the available water over the different crops in the fields. While allocating the water to different crops in the fields, the model takes into account the critical growth stages of the crops and allocate s sufficient water to each crop to safeguard it against any ill effects of water deficits. The optimum crop pattern model used in the study will only allow productive irrigation, so the amount of wasted water is reduced. Acknowledgements The authors would like to express sincere thanks to Universiti Sains Malaysia for the financial support of this work.Nomenclature AETi k k Actual evapotranspiration in period k from crop i (mm) APET ARFk Ak and BK Ao d Actually occurring potential evapotranspiration in period k (mm) Actual rainfall value in the fortnight k Constants relating the storage to reservoir evaporation Area of spread at dead storage level Depletion factor EDik Effective root zone depth of a crop i in period k (cm) k +1 i ED Effective root zone depth of a crop i in period k+1 (cm) Eff Fkcik ID Overall efficiency Crop evapotranspiration coefficient Industrial supply from the reservoir (mandatory release) IRRikIrrigation applied to crop i in stage k (mm) k Ky Yield response fa ctors for a crop i in period k PETi k RE RF k Potential evapotranspiration in a particular geographical location (mm) Rate of evaporation in fortnight k k Sk Sk+1 Zf Zw Zww Rainfall in period k (mm) Reservoir storage at the beginning of period k Reservoir storage at the end of period k Field capacity for the soil (mm/cm) Permanent wilting point for the soil (mm/cm) Critical available moisture limit (mm/cm) ? ik ? ik +1 Final soil moisture in a particular time stage k for a particular crop i (mm/cm) Yai Ymi Actual crop yield Maximum crop yieldInitial soil moisture in the time stage k in for a crop i (mm/cm) 10 14th MANCO References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. Doorenbos, J. , and Kassam, A. H. (1979). Yield Response to Water. Irrigation and Drainage Paper, 33, FAO, Rome. Dudley, N. J. , Howell, D. T. , and Musgrave, W. F. (1971). Optimal intraseasonal irrigation water allocation. Water Resour Res. , 7(4), 770-7 88. Dudley, N. J. and Burt O. R (1973). Stochastic reservoir Management and system design for irrigation, Water Resources Res. 9(3), 507-522. Duldley, N J. 1988). A single decision-maker approach to irrigation reservoir and farm management decision making, Water Resources Res. , 24(5) 633-640. Dudley, N. J. and Musgrave, W. F. (1993). Economics of water allocation under certain conditions. In Biswas, A. K. ; et al. , ed. Water for sustainable development in the twenty-first century. Oxford University Press, Delhi. Fedders, R. A. , Kowalic, P. S. and Zarandy, H. , (1978). Simulation of field water use and crop yield. Centre for Agricultural Publishing and Documentation, Wganingen. Haan, C T. (1977). Statistics methods in hydrology, Iowa State Press, Iowa.Hajilala, M. S. , Rao, N. H and Sarma, P. B . S. (1998). Real time operation of reservoir based canal irrigation systems, Agricultural Water Management, 38, 103-122. Holland, J. H. , (1975). Adaptation in natural and artificial syste ms, University of Michigan Press, Cambridge Mass. Labadie, J. W. (2004). Optimal operation of multi reservoir systems: State-of-the-art review, J. Water Resour. Plan. Manage. 130(2), 93–111. Mohan, S. , Raman, S. , and Premganesh, G. , (1991). Real-time reservoir operation. IWRS, 11(1), pp. 35-37. Mujumdar, P. P. , and Sandeep Narulkar. , (1993).Optimisation models for multireservoir planning and operation†, Hydrology Review, Vol. VIII, No. 1, pp. 29-52. (Pub: Indian National Committee on Hydrology, Roorkee, India) Mujumdar, P. P. and Ramesh, T S. V. , (1997). Real time reservoir operation for irrigation, J. Water resources research, Vol. 33, No 5, 1157-1164. Narulkar, S. M. (1995). Optimum real-time operation of multi reservoir systems for Irrigation scheduling. Ph. D Thesis submitted at I. I. T. , Bombay, India Oliveira, R. and Loucks, D. P. , (1997). Operating rules for multi reservoir system, Water Resources Research 33(4), 839–852. Rao, N. H. , (1987).Field test for a simple soil-water balance model for irrigated areas. J. of Hydrology, 91, 179-186. Rao, N. H. , Sarma, P. B. S. and Chander, S. (1988). Irrigation scheduling under a limited water supply. Agri. Water Management, 15, 165-175. Rao, N. H. , Sarama, P. B. S. , and Chander, S. (1990). optimal multicrop allocations of seasonal and interseasonal irrigation water. Water Resour. Res. , 26(4), 551-559. Reddy, J. M. and Nagesh Kumar, D. (2006). Optimal reservoir operation using multi-objective evolutionary algorithm, Water Resources Management, Springer, 20, No. 6, 861-878. Reddy, J. M. and Nagesh Kumar, D. (2007).Optimal reservoir operation for irrigation of multiple crops using elitist-mutated particle swarm optimization, Hydrological Sciences Journal, IAHS Press, UK, Vol. 52, No. 4, 686-701, Sharif, M. and Wardlaw, R. (2000). Multireservoir System Optimization Using genetic algorithms Case Study. J. Comp. in Civ. Engrg. ASCE, 14(4), 255–263. Shie-Yui L. , Al-Fayyaz T. A. , and Sai L. K. (2004). Application of evolutionary algorithms in reservoir operations, Journal of the Institution of Engineers, Singapore, 44(1), 39-54. Vedula, S. and Mujumdar, P. P. (1992). Optimal Reservoir Operation for Irrigation of Multiple Crops. Water Resour. Res. 28(1), 1-9. Vedula, S. and Mujumdar, P. P. (1993). Modelling for Reservoir Operation for Irrigation. Proceedings of Intl Conf. on Environmentally Sound Water Resources Utilisation, Bangkok. Vedula, S. and Nagesh Kumar, D. (1996). An integrated model for optimal reservoir operation for irrigation of multiple crops, Water Resources Research, American Geophysical Union, 32, (4), 1101-1108. Wurbs, R. A. (1993). Reservoir system simulation and optimization models. J. Water Resource Manage. ASCE 119 (4), 455–472. Yeh, W. W. G. (1985). Reservoir management and operation models: A State of the Art Review, Water Resour. Res. 21(1), 1797-1818. 11

Teaching As A Middle Level Educator - 994 Words

I believe the ultimate goal of teaching is to inspire and encourage students to learn and discover new concepts in an enjoyable way. I see teaching as an art and a skill that is mastered as time goes on. Through my study I have developed methods and reasoning for my teaching philosophy. As a middle level educator, the foundation of my philosophical beliefs is guided by constructivism. Constructivism entails me as a teacher to know my students learning needs and to integrate what I learn into my methods of teaching. As a constructivist, I believe that when students work collaboratively they develop a learning community that is strong. Another belief is that when teaching is built on the prior knowledge of students, there is fairness and the classroom is equitable for all. Another benefit to the young adolescents is when he or she realize they possess knowledge, they are motivated and will be engaged with the lesson. My instruction will support all cultures and learning modalities. The roles of teachers, students, and parents are essential for the success of the young adolescents. Each depends on the other. It is a teacher’s duty is to create a positive learning environment for all students. It is a teacher’s responsibility to motivate students with engaging lessons while having high expectations to encourage students to complete work to their best ability. Teachers are accountable for the academic performance of every student. It is a teacher’s job to establishShow MoreRelatedThe Most Important Lesson Of My Life1609 Words   |  7 Pagesme. It is in this that I have learned the most important lesson of my life. Learning isn’t defined by a set of rules, it is defined by each individual personally. Why can’t this type of learning be applied to a classroom setting? Why can’t we as educators allow students to learn in whatever way they deem appropriate for themselves? It is definitely possible, and definitely necessary. This†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦, I believe. Young adolescents experience a very specific period of their lives where many changes will occurRead MoreThe Determinants Of Learning For Nurses Educators758 Words   |  4 PagesLearning In a variety of settings, nurses are responsible for the education of patients, families, staff, and students. Lengths of stay and staffing pattern, and cultural differences are challenges that influence learning that nurse educators must be aware. The role of educator includes assessment of learner, their progress, providing information, feedback, reinforcement, and evaluation. Before learning can occur the learner’s needs, their readiness to learn, and learning style must be assessed. ReadinessRead MoreThe Music Of A Music Educator1264 Words   |  6 Pageshave a chance to make it into the musical business. A music educator is a rewarding job because they help students learn about general music, choral or voice music , instrumental music, or a combination of all music. A music educator job consists of teaching classes or individuals the different types of music. In both class and individual teaching the students being taught can have a range of ages, abilities, and grade levels.When teaching students the teacher plans lessons to suit individuals ofRead MoreTeaching And Teaching Through Problem Solving1360 Words   |  6 PagesI enjoyed talking and reading about teaching through problem solving because the way it was structured throughout the chapter was presented in a way that communicated its relevance to the audience. Since actively reading this chapter I’ve been able to build on my knowledge of problem solving and incorporate a few new methods into my problem solving technique. The chapter, â€Å"Teaching Through Problem Solving†, in Elementary and Middle School Mathematics Teaching Developmentally, by Walle, Karp, andRead MoreMy Teaching Philosophy1217 Words   |  5 Pageseducation, I always wondered what grade level best fitted me. Could it be Elementary, where children have been stereotyped as uncontrollable little brats, Middle School, where the students are depicted as uncontrollable, rebellious students, or High School, oh gee whiz? I have decided that I would pursue a career in Elementary School. The grade level I hope to teach is at the elementary school level. My current goal is to either teach the 4th or 5th grade level. Moreover, throughout the semester I haveRead MoreThe Music Of A Music Educator1342 Words   |  6 Pagesopportunity to make it into the musical business. A music educator is a rewarding job because they help students learn about general music, choral or voice, music, instrumental music, or a combination of all music. To begin with, a music educators job consists of teaching classes or individuals the disparate types of music. In both class and individual teaching, the students being taught can have a range of ages, abilities, and grade levels.When teaching students the teacher arranges lessons to suit individualsRead MoreStudent Engagement And Motivation For A Diverse Group Of Learners1087 Words   |  5 Pagesterritory of being a classroom teacher. The students that attend Stafford Middle School are no different. I chose to complete my research on the topic of student engagement and motivation for a variety of reasons. Stafford Middle School, where I teach, underwent a massive transformation this school year from housing only six-hundred students to now housing twelve hundred. These students were pulled from their schools in the middle of middle school to be transferred to another school, often resulting in aRead MoreEducating Students Of All Ages Essay1464 Words   |  6 PagesEducating s tudents of all ages is important. But middle school is such a critical time for students, and if they are not taught correctly it can mess them up down the road. Everything at this age is essential to their future because it sets the standard of how they will view education from then on. Middle schools are specially made for ages 10-14 because the needs for these transitioning students are met in middle schools. In middle school, young adolescents are beginning to go through major changesRead MoreGraduation Speech On Middle School Teachers1499 Words   |  6 PagesIt is said that teaching is one the profession that creates all other professions. Everyone has been in contact with a teacher in some way or another. We understand that without teachers we would most likely be nowhere. Especially middle school teachers, who teach us during the time when we are most developing who we are, and what we want to do with ourselves. Have you ever thought about what it’s like, to be the person behind shaping all of tomorrow s wonderful minds? Hopefully, your questionsRead MoreQuestions On Financial Literacy Education798 Words   |  4 Pagesencouraged for use in the classroom. This particular question sets to find out the relationship of FLE Educators personal beliefs and how they affect FLL overall personal financial satisfaction. An Integrative Essay and the Posing of One Research Question: According to Tisdell, Taylor and Sprow Forte a complex interaction exist between educator’s beliefs and their pedagogical approach to the teaching practice in the classroom. Similarly, learners are affected by emotions and money when making financial