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  • Title: ACEMarketModelingIntro
  • Type: Notes
  • School: Iowa State
  • Course: ECON 308
  • Term: Spring

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Behavior, Modeling Learning, and Interaction Networks in Dynamic Market Economies An Agent-Based Computational Approach Presenter: Professor of Economics and Mathematics Department of Economics Iowa State University Ames, Iowa 50011-1070 http://www.econ.iastate.edu/tesfatsi/ tesfatsi@iastate.edu 1 Leigh Tesfatsion Outline The complexity of real-world decentralized market processes Agent-based computational economics (ACE) and dynamic market modeling 1. Normative Analysis: Example ACE double-auction market performance study 2. Qualitative Analysis/Theory Generation: Example An ACE two-sector trading world 2 What is a Market ? A market is any context in which trading (buying and selling) of services, physical assets, and/or financial assets takes place 3 The Complexity of Real-World Decentralized Market Processes Distributed local interactions Two-way feedbacks mediated by interactions Micro Agent Interactions Macro Strategic behaviour & uncertainty Possible existence of multiple equilibria Critical role of institutional constraints 4 Simple Example of a Competitive Decentralized B1 B3 B2 SupplyB(pB), DividendB(pB) Standard Market Economy H2 H4 H1 H3 Hash Firms pH SupplyH(pH), DividendH(pH) Bean Firms pB Fictitious Clearing House ConsumerShareholders pB ,pH, DividendB, DividendH Demand(pB,pH,DividendB,DividendH) 5 Plucking Out the Fictitious Clearing House! B1 B3 B2 H2 H1 H3 Hash Firms H4 Bean Firms Firm-Consumer Connections?? ConsumerShareholders 6 Without the Fictitious Clearing House Careful attention must now be paid to Market Organization Who trades with whom? [e.g. business-to-business (B2B) transactions, business-to-consumer (B2C) transactions, etc.] In what types of market structures does this trading take place? [e.g. double auctions, single-sided auctions, exchanges, bilateral trades, etc.] Learning Behavior and Strategic Interaction Price/quantity discovery processes Formation of buyer-seller interaction networks 7 Market Organization Two basic forms of trading: 1. Bilateral trading (Seller Buyer) 2. Mediated trading (Seller Mediator Buyer) 8 Example 1: Bilateral B2B & B2C Trade (B2B=Business To Business, B2C=Business To Consumer) Can Firms B1 B3 B2 H2 H1 H3 Hash Firms H4 B2B Bean Firms B2C ConsumerShareholders B2C 9 (Producers Retail Stores Consumers) B1 B3 B2 Example 2: Mediated Trade H2 H1 H3 Hash Firms B2B Retail Bean Retail Hash Stores Stores H4 Bean Firms B2C ConsumerShareholders B2C 10 Key Types of Market Mediators Broker Facilitates trade by matching buyers with sellers Does not take a position in the assets he/she trades (i.e., does not maintain an inventory of the assets) Earns profits through commissions charged to buyer/seller Examples: Stock broker; Real estate broker Facilitates trade by matching buyers with sellers Takes a position in the assets traded ( makes the market ) Earns profits by selling high and buying low Examples: Bond dealer; Car dealer; Retail store owner 11 Dealer Key Types of Mediated Market Forms Auction markets Centralized facility (clearing house) managed by brokers Examples: Art auctions, U.S. Treasury bill auctions, etc. Over-the-Counter (OTC) Exchanges (Hybrid of Auction and OTC) Centralized facility conducted through specialized broker/dealer intermediaries Examples: Retail stores, New York Stock Exchange, Wholesale Power Markets Decentralized facility managed by dealers Examples: NASDAQ stock market, gov t bond market 12 Learning Behavior & Strategic Interaction in Markets Price/Quantity Discovery amount to produce and/or the most profitable price to charge per unit in order to compete for business against rival sellers for purchase and which sellers are willing to accept the lowest prices for the items they wish to purchase For sellers, seeking to determine the most profitable For buyers, seeking to determine what items are available Buyer-Seller Interaction (Relational Goods) How to behave in longer-term relationships (e.g., job situations, servicing contracts, loan contracts, repeat purchases from same supplier, etc.) Trust, honesty, punctuality, etc. 13 Key Types of Market Procurement Processes that Must Be Carried Out Terms of Trade: Set production and price levels Seller-Buyer Matching: Identify potential suppliers/customers Compare/evaluate opportunities Make demand bids/supply offers Select specific suppliers/customers Negotiate supplier/customer contracts Trade: Transactions carried out Settlement: Payment processing and shake-out Manage: Long-term supplier/customer relations 14 Can ACE help? How might Agent-based Computational Economics (ACE) modeling tools facilitate the study of decentralized market economies? 15 ACE and Normative Market Analysis Key Issue: Does a market arrangement ensure efficient, fair, and orderly market outcomes over time despite efforts by participants to game it for individual advantage? ACE Approach: Construct an agent-based world capturing salient aspects of the market arrangement. Introduce self-interested traders with learning capabilities. Let world evolve multiple times. Observe/evaluate market outcomes. 16 Illustrative Issue: What are the performance ACE Approach: ACE and Qualitative Market Analysis capabilities of decentralized markets? (Adam Smith, F. von Hayek, John Maynard Keynes, J. Schumpeter ...) Construct an agent-based world qualitatively capturing Introduce traders with behavioral dispositions, needs, goals, beliefs, etc. Let the world evolve. Observe the key aspects of decentralized market economies (firms, consumers, circular flow, limited information, ) degree of coordination that results. EXAMPLES: Decentralized exchange economies without a central clearing house ( Walrasian Auctioneer ), ZI agent double-auction markets, 17 Application 1: ACE Study of a Mediated Double-Auction Market Design IEEE J. Nicolaisen, V. Petrov, L. Tesfatsion, Transactions on Evolutionary Computation,5(5),2001,504-523 http://www.econ.iastate.edu/tesfatsi/mpeieee.pdf Key Issue Addressed: Relative role of structure vs. learning in determining performance of a double-auction design for a day-ahead electricity market. 18 Key Issues We Address market structure: Sensitivity of market performance to changes in RCON = Relative seller/buyer concentration RCAP = Relative demand/supply capacity trader learning: Sensitivity of market performance to changes in Individual learning via Reinforcement Learning (RL) Social mimicry via Genetic Algorithms (GAs) 19 Market Performance Measures Market Efficiency: Actual total net benefits extracted from the market relative to maximum possible total net benefits (competitive benchmark). extracted total net benefits are distributed among the market participants. Market power: The manner in which 20 Dynamic Flow of DA Market: Simple View World Constructed. World configures DA Market and Traders, and starts the clock. Traders receive time signal and submit asks/bids to DA Market DA Market matches sellers with buyers and posts matches Traders receive posting, conduct trades, and calculate profits Traders update their exp s & trade strategies 21 Dynamic Flow of DA Market: Detailed View COMPETITIVE EQUILIBRIUM BENCHMARK CALCULATION (OFF-LINE) (OFFTraders Buyers Init. Sellers Traders Submit true reservation values as bids/asks Auctioneer Matches bids/asks Competitive equilibrium outcomes Auctioneer Traders Submit strategic bids/asks Matches bids/asks Clearing prices, quantities Traders Receive auction results Updating & learning Report runs rounds End ACTUAL DOUBLE-AUCTION PROCESS DOUBLE(DISCRIMINATORY- PRICE DOUBLE AUCTION WITH STRATEGIC BIDS/ASKS) (DISCRIMINATORY22 Structural Treatment Factor Values (tested for each learning treatment) RCAP 1/2 Ns = 6 Nb = 3 Cs = 10 Cb = 10 Ns = 3 Nb = 3 Cs = 20 Cb = 10 Ns = 3 Nb = 6 Cs = 40 Cb = 10 Ns = Number of Sellers Nb = Number of Buyers Cs = Seller Supply Capacity Cb = Buyer Demand Capacity RCON=Ns/Nb RCAP=NbCb/NsCs 1 Ns = 6 Nb = 3 Cs = 10 Cb = 20 Ns = 3 Nb = 3 Cs = 10 Cb = 10 Ns = 3 Nb = 6 Cs = 20 Cb = 10 2 Ns = 6 Nb = 3 Cs = 10 Cb = 40 Ns = 3 Nb = 3 Cs = 10 Cb = 20 Ns = 3 Nb = 6 Cs = 10 Cb = 10 23 2 R C O N 1 1/2 True Total Demand and Supply Schedules (True Reservation Values) Cell (3,1) Price ($/MWh) B 1,4 Price ($/MWh) B 1,4 Cell (3,2) 37 35 S1 37 35 17 16 S1 B 2,5 17 16 S2 B 2,5 S2 B 3,6 12 11 S3 12 11 S3 B 3,6 10 20 40 60 80 120 Power (in MW=MWh per Hour) 10 20 Power 40 60 24 The Computational World Public Access: // Public Methods The World Event Schedule, i.e., a system clock that permits inhabitants to time and synchronize activities (e.g., submission of asks/bids into the DA market); Protocols governing trader collusion; Protocols governing trader insolvency; Methods for receiving data; Methods for retrieving World data. Private Access: // Private Methods Methods for gathering, storing, and sending data; // Private Data World attributes (e.g., spatial configuration); World inhabitants (DA market, buyers, sellers); World inhabitants methods and data. 25 The Computational DA Market Public Access: // Public Methods getWorldEventSchedule(clock time); Protocols governing the public posting of asks/bids; Protocols governing matching, trades, and settlements; Methods for receiving data; Methods for retrieving Market data. Private Access: // Private Methods Methods for gathering, storing, and sending data. // Private Data Data recorded about sellers (e.g., seller asks); Data recorded about buyers (e.g., buyer bids); Address book (communication links). 26 A Computational DA Trader Public Access: // Public Methods getWorldEventSchedule(clock time); getWorldProtocols (collusion, insolvency); getMarketProtocols (posting, matching, trade, settlement); Methods for receiving data; Methods for retrieving Trader data. Private Access: // Private Methods Methods for storing, gathering, and sending data; Methods for calculating expected & actual profit outcomes; Method for updating my ask/bid strategy (LEARNING). // Private Data Data about me (history, profit function, current wealth, ); Data about external world (rivals asks/bids, ); Address book (communication links). 27 What Do DA Traders Learn? Asks (Offers to Sell) and Bids (Offers to Buy) Ask for each Seller i = reported supply qiS of real power in Mega-Watts (MWs) together with a reported unit (i.e., per-MW) price pi in dollars $ per MW Bid for each Buyer j = reported demand qjD for real power in MWs together with a reported unit price pj in $ per MW Action choices for sellers = Their possible ASKS Action choices for buyers = Their possible BIDS 28 How Might DA Traders Learn? One possibility: Reactive Reinforcement Learning (RL) Asks . Given past events, what action should I take now ? Examples: Three-parameter RL based on human-subject experiments (Roth-Erev, 1995,1998), Modified Roth-Erev RL for electricity double auctions (Nicolaisen, Petrov, Tesfatsion, IEEE TEC, 2001) 29 How Might DA Traders Learn Another possibility: Anticipatory Learning Asks . If I take this action now, what will happen in the future ? Examples: Q-Learning (Watkins, 1989); Temporal-Difference Reinforcement Learning (Sutton/Barto, 1998) 30 MRE = Modified Roth-Erev RL (Nicolaisen et al.,2001) Learning Method Used for This study: Reactive Reinforcement Learning choose Action Choice a1 Action Choice a2 Action Choice a3 update normalize Choice Probability Prob1 Choice Probability Prob2 Choice Probability Prob3 rk Choice Propensity q1 Choice Propensity q2 Choice Propensity q3 Each trader maintains action choice propensities q, normalized to action choice probabilities Prob, to choose actions. A good (bad) profit rk for action ak results in a strengthening (weakening) of the propensity qk for ak. 31 MRE = Modified Roth-Erev RL 1. Initialize action propensities to an initial propensity value. 2. Generate choice probabilities for all actions using current propensities. 3. Choose an action according to the current choice probability distribution. 4. Update propensities for all actions using the reward for the last chosen action. 5. Repeat from step 2. 32 MRE Updating of Action Propensities Parameters: qj(0) Initial propensity Experimentation Recency (forgetting) Variables: aj Current action choice qj Propensity for action aj ak Last action chosen rk Reward for action ak t Current time step N Number of actions Xxxx Ej( ,N,k,t) xxxx Xxx ,N,k,t) Ej(Xxx xxx xxx 33 From Propensities to Probabilities for MRE pj(t) = Probability of choosing action j at time t N = Number of available actions at each time t 34 Sample Table of Experimental Results 35 Summary of Policy-Relevant DA Findings Market Efficiency: Generally high when traders use MRE (Modified Roth-Erev) reinforcement learning but not when traders use GA (genetic algorithm) social mimicry (type of learning can matter). Structural Market Power: Microstructure of the DA market is strongly predictive for the relative market power of traders (rule details matter). Strategic Market Power: Traders are not able to change their relative market power through learning (importance of countervailing power). 36 Application 2: An ACE Bilateral Trade Hash-and-Beans Economy B1 B2 B3 H2 H1 H3 H4 ManySeller Posted Bean Auction N(0) Bean Firms SOB2 SOB3 SOB1 SOH1 SOH2 J(0) Hash Firms ManySeller Posted Hash Auction Supply Offers SO=(q,p) SOH3 SOH4 DivB Consumer-Shareholders k=1, ,K(0) DivH 37 Dynamic Flow of ACE H&B Economy World Constructed. World configures Markets, Firms, Consumers and starts the clock. Firms receive time signal and post quantities/prices in H & B markets Consumers receive time signal and begin price discovery process Firms-consumers match, trade, calculate profits/utilities & update wealth levels Firms update their exp s & prod/price strategies 38 Dynamic Flow of Activity for H & B Firms Each firm f starts out (T=0) with money Mf(0) and a production capacity Capf(0) Firm f s fixed cost FCf(T) in each T 0 is proportional to its current capacity Capf(T) At beginning of each T 0, firm f selects a supply offer = (production level, unit price) At end of T 0, firm f is solvent if it has NetWorth(T) = [Profit(T)+Mf(T)+ValCapf(T)] > 0 (T) If solvent, firm f allocates its profits (+ or -) between Mf , CAPf, and dividend payments. 39 Dynamic Flow of Activity for Consumer-Shareholders Each consumer k starts out (T=0) with a lifetime money endowment profile ( Mkyouth , Mkmiddle , Mkold ) In each T 0, consumer k s utility is measured by Uk(T)=(hash(T) - hk*) k (beans(T) - bk*)[1- k] (T) In each T 0, consumer k seeks to secure maximum utility by searching for beans and hash to buy at lowest possible prices. At end of each T 0, consumer k dies unless consumption meets subsistence needs (bk*, hk*). 40 Experimental Design Treatment Factors Initial size of consumer sector [ K(0) ] Initial concentration [ N(0), J(0), Cap(0) values ] Firm learning (supply offers & profit allocations) Firm cost functions Firm initial money holdings [ Mf(0) ] Firm rationing protocols (for excess demand) Consumer price discovery processes Consumer money endowment profiles/TMax (rich, poor, , , life cycle u-shape) Consumer preferences ( values) Consumer subsistence needs (b*,h*) 41 The Computational World Public Access: // Public Methods The World Event Schedule, i.e., a system clock that permits inhabitants to time and synchronize activities (e.g., opening/closing of H & B markets); Protocols governing firm collusion; Protocols governing firm insolvency; Methods for receiving data; Methods for retrieving World data. Private Access: // Private Methods Methods for gathering, storing, and sending data; // Private Data World attributes (e.g., spatial configuration); World inhabitants (H & B markets, firms, consumers); World inhabitants methods and data. 42 A Computational Market Public Access: // Public Methods getWorldEventSchedule(clock time); Protocols governing the public posting of supply offers; Protocols governing matching, trades, and settlements; Methods for receiving data; Methods for retrieving Market data. Private Access: // Private Methods Methods for gathering, storing, and sending data. // Private Data Data recorded about firms (e.g., sales); Data recorded about consumers (e.g., purchases); Address book (communication links). 43 A Computational Consumer Public Access: // Public Methods getWorldEventSchedule(clock time); getWorldProtocols (stock share ownership); getMarketProtocols (price discovery process, trade process); Methods for receiving data; Methods for retrieving stored Consumer data. Private Access: // Private Methods Methods for gathering, storing, and sending data; Method for determining my budget constraint; Method for searching for lowest prices. // Private Data Data about me (history, utility function, current wealth, ); Data about external world (posted supply offers, ); Address book (communication links). 44 Public Access: A Computational Firm // Public Methods getWorldEventSchedule(clock time); getWorldProtocols (collusion, insolvency); getMarketProtocols (posting, matching, trade, settlement); Methods for receiving data; Methods for retrieving Firm data. Private Access: // Private Methods Methods for gathering, storing, and sending data; Methods for calculating expected & actual profit outcomes; Method for allocating my profits to my shareholders; Method for updating my supply offers (LEARNING). // Private Data Data about me (history, profit function, current wealth, ); Data about external world (rivals supply offers, ); 45 Address book (communication links). Interesting Issues for Exploration Initial conditions carrying capacity? (Survival of firms/consumers in long run) Initial conditions market clearing? (Walrasian equilibrium benchmark) Initial conditions market efficiency? (Walrasian equilibrium benchmark) Standard concentration measures at T=0 good predictors of long-run market power? Importance of learning vs. market structure for market performance? (Gode/Sunder, JPE, 1993) 46 ACE Hash-and-Beans Economy: Comp Lab Implementation Christopher Cook and Leigh Tesfatsion, AgentBased Computational Laboratories for the Experimental Study of Complex Economic Systems, Working Paper, ISU Department of Economics, in progress. Computational laboratory under construction for the ACE Hash-and-Beans Economy Programming language C#/.Net (all WinDesktops) Under development for Econ 308 (ACE course) www.econ.iastate.edu/classes/econ308/tesfatsion/ 47 ACE Hash & Beans Economy: Comp Lab Main Screen 48 Potential Disadvantages of ACE for Dynamic Market Modeling Intensive experimentation is often needed (fine sweeps of parameter ranges to attain robust findings) (strong path dependence possible) Multi-peaked rather than central-tendency outcome distributions can arise Can be difficult to ensure platform robustness (i.e., results that are independent of the hardware and/or software implementation of a model) of existing comp labs requires good programming knowledge) Effort needed to gain computer modeling skills can be significant (creative computer modeling as opposed to use 49 Potential Advantages of ACE for Dynamic Market Modeling Permits systematic experimental study of empirical regularities, economic institutions, and dynamic behaviors of complex market processes . Facilitates creative experimentation with realistically modeled market processes: - Using ACE comp labs, researchers/students can evaluate interesting conjectures of their own devising, with immediate feedback and no original programming required - Modular form of ACE software permits relatively easy modification/extension of features. 50

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AttributionsPart1student.ppt
Path: Iowa State >> PSYCH >> 380 Fall, 2008
Description: Welcome to Social Cognition Psychology 380 Professor: Dr. Stephanie Madon Syllabus Required Textbooks: 1) Pennington, D. (2000). Social cognition. London: Routledge. 2) Nelson, T. D. (2002). The psychology of prejudice. Boston, MA: Allyn & Bacon....
AttributionsPart2student9.pdf
Path: Iowa State >> PSYCH >> 380 Fall, 2008
Description: Lecture Outline Attributions Part 2 1) Mini-Theories of the Attribution Process Theory of Nave Psychology Corespondent Inference Theory Covariation Model Theory of Emotional Lability Self-Perception Theory Attribution Theory No unifying theory of at...
AttributionsPart2student4.pdf
Path: Iowa State >> PSYCH >> 380 Fall, 2008
Description: Lecture Outline Attributions Part 2 1) Mini-Theories of the Attribution Process Theory of Nave Psychology Corespondent Inference Theory Covariation Model Theory of Emotional Lability Self-Perception Theory Attribution Theory No unifying theory of at...
Heuristicsstudent6.pdf
Path: Iowa State >> PSYCH >> 380 Fall, 2008
Description: Lecture Outline Heuristics Heuristics and Social Influence Types of heuristics Stereotypes as base rates Dilution Effect Other cognitive errors Heuristics Definition: Rules or principles that allow people to make social inferences rapidly and with r...
ErrorBiasstudent.ppt
Path: Iowa State >> PSYCH >> 380 Fall, 2008
Description: Lecture Outline: Error & Bias 1. Bem vs. Festinger revisited Post-identification feedback effect 2. Attributional Biases Fundamental Attribution Error Actor Observer Effect Self-Serving Bias Ultimate Attribution Error False Consensus Effect 3. Indivi...
ErrorBiasstudent1.pdf
Path: Iowa State >> PSYCH >> 380 Fall, 2008
Description: Lecture Outline: Error & Bias 1. Bem vs. Festinger revisited Post-identification feedback effect 2. Attributional Biases Fundamental Attribution Error Actor Observer Effect Self-Serving Bias Ultimate Attribution Error False Consensus Effect 3. Indivi...
AttributionsPart2student6.pdf
Path: Iowa State >> PSYCH >> 380 Fall, 2008
Description: Lecture Outline Attributions Part 2 1) Mini-Theories of the Attribution Process Theory of Nave Psychology Corespondent Inference Theory Covariation Model Theory of Emotional Lability Self-Perception Theory Attribution Theory No unifying theory of at...
Heuristicsstudent1.pdf
Path: Iowa State >> PSYCH >> 380 Fall, 2008
Description: Lecture Outline Heuristics Heuristics and Social Influence Types of heuristics Stereotypes as base rates Dilution Effect Other cognitive errors Heuristics Definition: Rules or principles that allow people to make social inferences rapidly and with r...
Psych422 F2006\422 syllabus F2006 8-21-06.doc
Path: Iowa State >> PSYCH >> 401 Fall, 2008
Description: Psychology 422 Counseling Theories and Techniques (Fall 2006) Contact Information: Course time: 11:00-12:15 Tues/Thurs Instructor: Phone: Office Hours: Homepage: Course TA: Meifen Wei, Ph.D. (515) 294-7534 Course location: Office #: Email: W 262 Lago...
Psych422 F2005\Revised Course Outline.doc
Path: Iowa State >> PSYCH >> 401 Fall, 2008
Description: Revised Course Outline: 8 9 10 11 12 13 14 15 16 Date 10/11 10/20 10/25 11/03 11/08 11/17 11/22 12/1 12/06 & 12/08 Topic -Gestalt Therapy -Existential Therapy Cognitive-Behavioral theorie...
Divapl1.pdf
Path: Iowa State >> E E >> 311 Fall, 2008
Description: ...
Phase-speed-L1.pdf
Path: Iowa State >> E E >> 314x Fall, 2008
Description: Waves: definitions, discussion, and basics Here is a short summary of the ideas of waves and definitions Basic definitions related to waves Period: T in Seconds (sec) T is the shortest time for the wave to repeat. The time for one oscillation Wavele...
Lecture3-19-07.pdf
Path: Iowa State >> E E >> 314x Fall, 2008
Description: ...
Lect3-5-07.pdf
Path: Iowa State >> E E >> 314x Fall, 2008
Description: ...
Scales and decibel scales.pdf
Path: Iowa State >> E E >> 314x Fall, 2008
Description: Notes for EE418x Project: High Speed Systems Engineering CISE-EAI Last Modified: 9/06 Scales and decibel scales Prepared for EE 418x Fall 2006 The issues of scaling, in physical sciences is an issue that is more or less learned based on experience. ...
lect3-26-07.pdf
Path: Iowa State >> E E >> 314x Fall, 2008
Description: ...
Concept-sheets.doc
Path: Iowa State >> E E >> 314x Fall, 2008
Description: The concept Sheet Definitions, concepts, and what we know Last updated 1/25/07 Period: T in Seconds (sec) T is the shortest time for the wave to repeat. The time for one oscillation Wavelength: in meters (m) is the shortest distance for a wave to ...
chap8a.pdf
Path: Iowa State >> E E >> 330 Fall, 2008
Description: ...
chap4a.pdf
Path: Iowa State >> E E >> 330 Fall, 2008
Description: ...
post_layout_simulations.pdf
Path: Iowa State >> E E >> 330 Fall, 2008
Description: Performing post-layout simulations Parasitic capacitances and resistances in the layout can strongly affect the performance of a design. To evaluate the effects of parasitics and to gain a higher degree of confidence that a layout will result in a ch...
chap2b.pdf
Path: Iowa State >> E E >> 330 Fall, 2008
Description: ...
chap2a.pdf
Path: Iowa State >> E E >> 330 Fall, 2008
Description: ...
EE434_Exam2_Fall2003.pdf
Path: Iowa State >> E E >> 330 Fall, 2008
Description: EE 434 Exam 2 Fall 2003 Name_ _ _ _ _ _ _ _ _ _ _ _ _ _ Instructions. Students may bring 4 pages of notes to this exam. There are 9 questions. The first 8 are worth 2 points each and question 9 is worth 4 points. There are 6 problems. Solve any 5 o...
EE434_FinalExam_Fall2003.pdf
Path: Iowa State >> E E >> 330 Fall, 2008
Description: Page 1 of 9 EE 434 FINAL EXAM Fall 2003 Name _ Instructions. You may bring up to 6 sheets of notes to this exam which is comprised of 6 problems and 8 questions. The weight for each question is 2 points and for each problem is 14 points. Please solv...
chap4b.pdf
Path: Iowa State >> E E >> 330 Fall, 2008
Description: ...
chap9b.pdf
Path: Iowa State >> E E >> 330 Fall, 2008
Description: ...
chap5.pdf
Path: Iowa State >> E E >> 330 Fall, 2008
Description: ...
chap7c.pdf
Path: Iowa State >> E E >> 330 Fall, 2008
Description: ...
smithchart-paper.pdf
Path: Iowa State >> E E >> 418 Fall, 2008
Description: antennas tx/rx Impedance matching and the Smith chart The fundamentals. Tried and true, the Smith chart is still the basic tool for determining transmission line impedances. designer has to be familiar with the multiple data inputs that need to be e...
smithchart-paper.pdf
Path: Iowa State >> E E >> 418x Fall, 2008
Description: antennas tx/rx Impedance matching and the Smith chart The fundamentals. Tried and true, the Smith chart is still the basic tool for determining transmission line impedances. designer has to be familiar with the multiple data inputs that need to be e...
T-line-example.pdf
Path: Iowa State >> E E >> 418 Fall, 2008
Description: ...

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