Mathematical Review and Circuit Analysis Software Development for Small-Signal Single-Stage Transistor Amplifier Using Hybrid Parameter

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1 American Journal of Quantum Cemistry and Molecular Spectroscopy 208; 2(): -8 ttp:// doi: 0.648/j.ajqcms Matematical Review and Circuit Analysis Software Development for Small-Signal Single-Stage Transistor Amplifier Using Hybrid Parameter Henry Erialuode Amenrior, *, Samuel Amanyo Amenrior 2 Department of Electrical/Electronic Engineering, Faculty of Engineering, Enugu State University of Science and Tecnology, Enugu, Nigeria 2 Department of Electrical/Electronic Engineering, Faculty of Engineering, Ambrose Alli University, Ekpoma, Nigeria address: * Corresponding autor To cite tis article: Henry Erialuode Amenrior, Samuel Amanyo Amenrior. Matematical Review and Circuit Analysis Software Development for Small- Signal Single-Stage Transistor Amplifier Using Hybrid Parameter. American Journal of Quantum Cemistry and Molecular Spectroscopy. Vol. 2, No., 208, pp. -8. doi: 0.648/j.ajqcms Received: July 30, 208; Accepted: August 0, 208; Publised: September 5, 208 Abstract: In tis paper, a matematical analysis of a Small-Signal Single-Stage Transistor Amplifier using Hybrid Parameter and te development of a software to aid tis analysis was carried out. Tis was borne out of te desire to be able to correctly and accurately analysis small signal transistors to get te required performance quantities tat can be used in te design of circuits. Also, te need to carry out tis analysis wit minimal error and time was of great motivation for tis development. Te metodology involved two aspects: te matematical review of te transistor amplifier and te Software development. In te matematical Analysis, matematical tools suc as matrix and determinant were used to analyze and evaluate te performance quantities namely te input resistance, te current and voltage gains; te output impedance and te power gain of te small-signal single-stage transistor using te generalized -parameter configuration equations in a two-port system. Also, te conversion of te generalized -parameter into te tree transistor configurations and te conversion from one configuration to anoter were obtained. Te software development was done in two stages wic are te Programming of te Analysis Metod and te Grapical User Interface (GUI) Development. Te Analysis Metod programming was done by te use of Visual Basic version 6 Programming Language troug te use of Object Oriented Programming designed wit a main program and subroutines namely te Matematical Analysis, te -parameter Conversion, te Circuit Diagram Simulation and te -parameter Equivalent Circuit. Tese Subroutines are called into te main program wenever needed. Te Grapical User Interface is a Menu based system for te administration of te Analysis Software Package. It was developed also by te use of Visual Basic version 6 Programming Language and Microsoft Access Office Te software development is resident in a PC wit a Windows Operating System. Te test results sow tat te matematical analysis was correctly done and te developed Software is very fast, efficient, accurate and reliable in analyzing small signal transistor amplifiers as designed. Keywords: Analysis, Transistor, Hybrid Parameter, Single-Stage Amplifier, Performance Quantities. Introduction Te efficiency and reliability of any uman activity depends on te ease wit wic te process can be carried out. Tis also applies to electronic circuit designs and analysis and indeed te analysis of a transistor amplifier. Te failure of transistor amplifiers is a common occurrence in electronic equipment and gadgets. Tese failures ave teir adverse effect in aving frequent down time of electronic system, tereby reducing production and profit of te establisment or te firm concerned due to unavailability of te equipment and gadgets concerned. Again, tere is te very costly risk of endangering te life of te user, and te people around im and even tose in te remote part were te effect of te system can be felt. As a result, some

2 2 Henry Erialuode Amenrior and Samuel Amanyo Amenrior: Matematical Review and Circuit Analysis Software Development for Small-Signal Single-Stage Transistor Amplifier Using Hybrid Parameter manufacturers of semiconductor devices suc as transistors usually advise tat safety sould be foremost in circuit designs, tat even wit maximum effort in producing semiconductor devices, failure may still occur and tese failures may cause personal injury, fire or property damage []. Tis situation is worrisome to every individual and stakeolders concerned. Tese failures and unreliability of transistor amplifiers are usually due to incorrect circuit analysis done manually and repeatedly, tereby making te analysis to be prone to undetectable errors. Tese errors manifest only wen te pysical models are built. Again, te repetitive nature and te long time spent on te analysis of one circuit makes it monotonous and causes fatigue. However, tere is te need to develop a process using computer tat is not prone to errors in transistor circuit analysis; not affected by fatigue and monotony; very fast and very efficient in operation. 2. Literature Review Te strengt of uman being is very feeble in consideration to oter mammals and universal forces. Similarly, most signals are usually weak for use in some applications. Sequel to tis, some researcers ave observed tat, tere is te need to advance devices tat can aggregate signal so tat very little pysical ability is required to execute various task and tese devices are referred to as amplifiers [2]. Signals and energies get fainted as tey move along teir transmission lines resulting from attenuation, interference, distortion, magnetic effect and oter penomena effects. One of suc amplifier for small signals are te transistors. Te performance and failure of most semiconductor devices like te transistor depends on te design and analysis of its configuration. Anant et al., in teir study recognized tat an isolator can fail due to ig voltage and current troug circuits or components integrated in it and an optocoupler, a semiconductor device was used in teir analysis [3]. Wu et al., observed tat catastropic failure mecanisms are closely associated wit semiconductor pysics and overstress working conditions. Tese failures are ard to anticipate and as a result may cause serious effect in te application of IGBJT in power electronic converters [4]. As appreciated by Mitsibusi Corporation, safety sould be foremost in circuit designs to ensure optimum performance []. Sequel to te above, scientists, stakeolders and many autors ave developed different ways to analyze te transistor amplifier over te years. Two main scools of tougt exist in prominence today in respect to te equivalent circuit to be substituted for te transistor namely te ybrid parameter model and te r e model. For some time, te industrial and educational institutions depended greatly on te ybrid parameters [5, 6]. Te ybrid parameter equivalent circuit continues to be very fasionable, noneteless te presence of an equivalent circuit obtained exactly from te operating conditions of te transistor te r e model [5]. Transistor ybrid parameters for a specific operating region ave continually been indicated by transistor manufacturers on teir dataseets. Te parameters of te model can be gotten exactly from te ybrid parameters in tis region. Neverteless, te ybrid equivalent circuit as a drawback of being limited to a distinct set of working situations for it to be seen to be accurate. Te parameter of te oter equivalent circuit can be gotten for any region of operation witin te active regions and are not restricted by te single set of parameters provided by te data seet. However, te r e model fails to account for te output impedance level of te device and te feedback effect from output to input. In addition, some autor ave opined tat r e model is te easiest to understand [7]. Electronic devices ave been variously analyzed using te two-port model. Lobna proposed a two port network tree impedance oscillators and analyzed all te attainable realizations using various arrangements. Tey studied te result of eac arrangement on te oscillation condition and te frequency of oscillation. Tey ten generate te transmission matrices for small-signal equivalent models of te BJT and MOS transistors [8]. Amed and Moammad modeled all te feasible four-impedance settings tat gives a good second-order two-stage Colpitts oscillator using twoport network transmission parameters and tey tested tese by te use of BJT and MOS transistors in an experimental case [9]. However, Amed addressed te task of Amed and Moammad above for BJT and MOS in favour of two-port network transmission parameters for general design equations not limited to matced devices [0]. In anoter study, Amed proposed two instances of two-port analysis namely, an elementary and te advanced; e derived te transmission matrices for small-signal equivalent models of te BJT and MOS transistors. He suggested tat is derived two-port network is especially good to employ in network analysis because te expression is only derived once and is independent of te complexity of any transistor, and it uses inter-network connectivity in wic network could be divided into series, parallel or cascade interconnects[]. Ankus et al., observed tat time and cost are involved during failure in fault isolation and tey terefore establised a igly integrated data network wit software analysis tool, te Synopsys Avalon to reduce te fault analysis time tat will elp in a better integrated circuit yield [2]. None of tese autors analyzed te equivalent circuit of a transistor using -parameters in matrix and determinant form. However, Ene attempted te analysis of te transistor using -parameter in matrix and determinant form, and tis could be andled by computer programs [3]. Yet, one of te researcers analyzed a small signal BJT amplifier using a software package suc as Pspice [5]. Te use of BASIC (Visual Basic) provides te opportunity for te user to define te scope and type of output for an analysis, wile Pspice is limited to a specific list of output qualities. 2.. A Transistor Te word transistor, is a combination two words: transfer and resistor, and it mean an effective resistance, or transresistance of a piece of component wen used as a

3 American Journal of Quantum Cemistry and Molecular Spectroscopy 208; 2(): -8 3 two-port, input/output device. A transistor is a tree-terminal piece of component tat gets its operation by using little amount of electric current or voltage to control great current [4]. A transistor is a tree-layer semiconductor device made up of eiter two N-type and one P-type layers of material or two P-type and one N-type layers of material. Te former is called an NPN transistor, wile te latter is called a PNP transistor. Bot are sown in Figure (a) and (b) respectively wit te proper D.C. basing. Te conventional representation of te transistor is as sown in Figure 2. It as tree terminals labeled E for emitter, B for base and C for te collector. Te emitter layer is eavily doped, te base is ligtly doped and te collector is only ligtly doped. Te outer layer as widts muc greater tan te sandwiced P- or N-type terminal material wit te ratio 0.50/ : [5]. (a) NPN Transistor (b) PNP Transistor Figure. Te tree layers of transistor and DC biasing. (a) NPN Transistor (b) PNP Transistor Figure 2. Conventional Representation Development of Transistor Te development of te transistor emanated from te vacuum tube diode tecnology and applications wic was launced in 904 by J. A. Fleming [5]. Tis application was used by Tomas Edison in te production of electric ligt bulb [5]. Tis discovery led to more researces by adding more control grid to te vacuum tube. As a result, Lee De Forest in 906, added a tird element called te control grid to te vacuum diode resulting in te first amplifier, te triode. In te early 930s te four-element tetrode and five-element pentode became popular in te tube industries [5]. Te amplifying action of te first transistor was successfully demonstrated at Bell Laboratories in Murray Hill, New Jersey in December 23, 947. Tree persons were credited wit te invention of te transistor namely William Sockley, Jon Bardeen and Walter Brattain. Sockley ad started working in 936 on te solid state pysics teory tat was te basis for te transistor [6]. Tis tree-terminal solid-state device as several advantages over te tubes namely, small size and ligt weigt; it ad no eat requirement or eat loss; it ad a very strong construction; it was more efficient as less power was absolved for its own operation; tere was no warm-up period required; and lower operating voltage was possible [5]. Wat appears to be te birt of modern transistor came in April 954 wen Adcock, Teal, and teir team used a ig purity silicon to fabricate an npn structure tat as an emitter region tat is carefully doped wit impurity to increase current gain and a base layer tickness of 25 micrometers made of p type material [7]. Also in 954, Texas Instruments of Dallas, Texas commenced te commercial manufacturing of junction transistors for use in small radios, wile in 960, Te Sony Company of Japan started te production of television sets from transistors after obtaining te rigt to produce transistors [6]. Te transistor is still undergoing canges and improvements in its operations and applications troug te efforts of researcers. Recently, Jose reported tat a group of scientists ad made a transistor tat is able to mimic some caracteristics of neurons, suc as counting, remembering and performing simple aritmetic operations [8]. At te moment, te potentiality of te transistor-type actions of ultracold atoms are being studied using various metods to

4 4 Henry Erialuode Amenrior and Samuel Amanyo Amenrior: Matematical Review and Circuit Analysis Software Development for Small-Signal Single-Stage Transistor Amplifier Using Hybrid Parameter acieve an atomtronic transistor [4]. 3. Metodology In tis section, te -parameters are used in analyzing a single stage transistor amplifier. Te performance quantities are calculated for te general representation. 3.. Analysis of te Single stage Amplifier Using te General H-Parameter Equivalent Circuit Te -parameter equivalent circuit of te transistor wit applied voltage source and series resistance at te input and output circuits using te transistor two-port system is used for tis matematical review. Tis is as sown in te general -parameter of Figure 3. From () and (5) i.e. We ave te following matrix Were! Wen 0 Figure 3. Transistor General H-Parameter Equivalent Circuit. Te five performance quantities to be calculated are:. Input resistance, 2. Voltage gain, 2. Current gain, 3. Output resistance, 5. Power gain, [9] Te generalized -parameter equations can be written as () [20] (2) Tis can be represented in matrix form as follows From te output circuit; Terefore (2) is equal to (3). Input resistance R i (3) (4) (5) But 0 2. Voltage Gain A v Wen V L 0 from () and (5) Voltage gain, 0 0

5 American Journal of Quantum Cemistry and Molecular Spectroscopy 208; 2(): Current Gain Ai In te output circuit of te Figure 3 wit V L 0, (3) becomes Also, from (4), 0 + % + % But output resistance 5. Power Gain A p + % + % Terefore, Tese performance quantities are as summarized in table Conversion of H-Parameters Output Resistance R o In te output circuit of Figure 3, wen V s 0 Terefore 0 % % (6) Also, () can be rewritten as equals to te above (6). Terefore, % % + Equation (2) remains uncanged Hence, te following equations, We ave 0 + % % 0 + % + % + % Transistor data seets generally specify te transistor in terms of its -parameters for common base configuration i.e. ib, fb, rb and ob. If we want to use te transistor in CE or CC configuration, we will ave to convert te given set of parameters into a set of CE or CC parameters. Approximate conversion formula are tabulated in te Table 2 below. Table. Performance quantities table. Performance Quantity Symbol Value Input Resistance R i + + Output Resistance R o + % + % Current Gain Voltage Gain Power Gain Number Parameter A i A v A p + + Table 2. Conversion of H-parameters. From CB to CE From CE to CB + + ( ) + ) ( + *) + *( From CE to CC ( 2,( ) -) + *),),) ( -( + *(,(,+ ) + *) 2 *( *) + *) *) *( + *( *+ + *) 22 -( -) + *) -) -( + *( -+ -) + *) 3.3. Analysis Software Package Development Te software aspect of tis work involves coding in Visual Basic Programming Language Version 6.0 (VB6) wit Microsoft Access application (MS Access office 2000) bot running in windows 98 operating system for te implementation of te various aspects of te analysis. Visual

6 6 Henry Erialuode Amenrior and Samuel Amanyo Amenrior: Matematical Review and Circuit Analysis Software Development for Small-Signal Single-Stage Transistor Amplifier Using Hybrid Parameter Basic is an efficient Object Oriented Programming Language wic permits modular programming and enances te development of subroutines. It is structured in a way tat it as a main program flow wic calls in any of te subroutines as need at a time. Tese subroutines are: te Matematical Analysis; te Amplifier Circuit diagram Simulation; te -parameter Equivalent Circuit and te - parameter Conversions. It as a developed user-friendly Grapical User Interface (GUI) for eac of te operation wic can be selected from te main program menu also a grapical user interface. Te flow cart for tis process is as sown in Figure 4. Figure 4. Te flow Cart of te Software Analysis. Wen te software starts, te main menu is opened in a grapical user interface were all te operations tat can be performed and Exit can be selected using teir various buttons. Eac selected operation executes te corresponding subroutine and prompt te user to provide te required data for te operation to be carried out. After te required data are provided and te "Compute button is clicked, te data will be processed and te results are displayed. In eac case, te results of -parameter values and tat of te matematical analysis wic are te performance quantities namely te input resistance, te output impedance, te current gain, te voltage and te power gain will always be displayed before proceeding to eiter te Amplifier Circuit diagram Simulation or te -parameter Equivalent Circuit. In te case of -parameter Conversions, te Common Emitter configuration values of te -parameter are supplied and te configuration to be converted to will be selected. Wen te Compute button is clicked, ten te conversion will be processed by te subroutine and te results displayed. To exit or close any of te submenu, te Quit button is clicked and to close te main menu, te Exit button is clicked. Te screensots of te Main Menu, te Matematical Analysis Submenu and tat of te -parameter conversion Submenu are sown in Figures 5-7.

7 American Journal of Quantum Cemistry and Molecular Spectroscopy 208; 2(): Test After te analysis and software development, real values were used to test te software to ascertain its suitability for tis analysis. Te problem used for tis analysis is as presented below. Problem: For te circuit in Figure 8, Q as te following values: fe 0, ie.6k, re 2x0-4, oe 20 UA/V. Determine te performance quantities. Figure 5. Snapsot of te Main Menu GUI. Figure 8. Sample Test Circuit. Te software used tese values entered and computed te performance quantities wit te results sown as follows. Input resistance R i 50 Figure 6. Snapsot of te Analysis Menu GUI. Voltage Gain A v Current Gain A i Output Resistance R o Power gain A p Te same values for common emitter transistor were used to stimulate te conversion by clicking CE to CB and te value displayed are as follows: ib 4.4; ib 0.883x -4 fb -0.99; ob 0.8 Te common emitter values were entered again and te simulation diagram as well as te -parameter equivalent circuits were displayed appropriately wit values. 5. Conclusion Figure 7. Snapsot of -parameter Conversion Menu GUI. Tis work as taken an in-dept look of te transistor performance quantities derivation using matematical tools. Te results of tis analysis are quantities tat can be computerized troug programming. Te review as expressed tese quantities in te simplest terms revealing te

8 8 Henry Erialuode Amenrior and Samuel Amanyo Amenrior: Matematical Review and Circuit Analysis Software Development for Small-Signal Single-Stage Transistor Amplifier Using Hybrid Parameter rudiments of te matematics and assumptions underlying te various processes and teir outcome. It as also presented an easy understanding of te inter-conversion between te tree configurations of te small-signal transistor - parameter using te generalized equivalent circuit. Te matematical analysis results suc as te performance quantities and te -parameter inter-conversions between configurations ave been successfully computerized. Te efficiency and reliability of a small signal transistor amplifier analysis can now be acieved troug te use of te circuit analysis package as developed in tis work. Most of te ordeals in analyzing small signal transistor amplifier circuits manually can be eliminated by te use of tis software analysis metod. Again, te unnecessary time wastage in manual analysis as now been eliminated as te software only needs input values to process witin some microseconds and produce te results of te analysis. Tis as gone a long way to reduce te tediousness of te calculations designers may need to contend wit during suc analysis. It also will elp in correct and error free analysis of Small signal transistor amplifier if te correct values are supplied. Tis will ensure tat failures and te accompanying risks and losses are greatly reduced in electronic equipment. Tis computer aided circuit analysis for transistor amplifier is terefore an indispensable tool for engineers, industrialists, scientists and educational institution. Hence, it is igly recommended tat stakeolders in tese fields sould be introduced to tis metod of analysis of amplifier for efficiency, speed, accuracy and ease of analysis. Tis is especially important in semiconductor circuitry design. Educational institutions will find te software package useful bot in learning and practice to facilitate students understanding of transistor circuit analysis and software development. References [] Mitsubisi Electric Corporation, Silicon RF Power MOS FET (Discrete) D6HHF, 208. [2] Carles H. Evans, Electronic Amplifier, Delmar Publisers, Albany, New York, 979. [3] Anant S. Kamat, Neeraj Bardwaj, Kannan Soundarapandian, Understanding failure modes in isolators, Texas Instruments Incorporated, 208. [4] Wu, R., Blaabjerg, F., Wang, H., Liserre, M., & Iannuzzo, F. (203), Catastropic Failure and Fault-Tolerant Design of IGBT Power Electronic Converters-An Overview, In Proceedings of te 39t Annual Conference of te IEEE Industrial Electronics Society, IECON, 203. (pp ). IEEE Press. DOI: 0.09/IECON [5] Robert B. and Louis N., Electronic Devices and Circuit Teory, Prentice-Hall International, Inc. USA, 996. [6] Al-Smadi, Prof. Adnan and Al-Zobi, Qassem, Derivations of te -Parameters for te BJT Amplifier Using its Caracteristics, 208. [7] Teraja A. K. and Teraja B. L., A textbook of Tecnology, S. Cad & Company Ltd, Raw Nagar, Nardet, 999. [8] Lobna A. Said, Amed G Radwan, A. H. Madian and A. M. Soliman, Two Port Network Analysis for tree impedance based Oscillators, Researc Gate, December 20. DOI: 0.09/ICM [9] Amed S. Elwakil and Muammad Ali Al- Radawi All possible second-order four- impedance two-stage Colpitts oscillators, Te Institution of Engineering and Tecnology Circuits, Devices & Systems, Vol. 5, Iss. 3, pp , 20. DOI: 0.049/iet- cds [0] Amed S. Elwakil Design of non- balanced cross-coupled oscillators wit no matcing Requirements, Te Institution of Engineering and Tecnology Circuits, Devices & Systems, Vol. 4, Iss. 5, pp , 200a. DOI: 0.049/ietcds [] Amed S. Elwakil, Motivating two-port network analysis troug elementary and advanced examples, International Journal of Electrical Engineering Education, 200b. [2] Ankus Oberai and Jiann-Siun Yuan, Efficient Fault Localization and Failure Analysis Tecniques for Improving IC Yield, February 208. [3] Ene I. I., Principles of Electronic Devices and circuits, Rojoint Communication Ltd, Enugu Nigeria, 999. [4] Set C. Caliga, Cameron J E, Alex A. Zozulya and Dana Z Anderson. Principles of an atomtronic transistor, New Journal of Pysics, , 206. Doi:0.088/ /8//0502. [5] David B Haviland, Te Transistor in a Century of Electronics, Available at: <ttps:// st ory/> [Accessed 29 August, 207] [6] Te History of te Transistor, San José State University, Silicon Valley, & Tornado Alley, USA. Available at: <ttp:// [Accessed 29 August, 207] [7] Micael Riordan, Te Lost History of te Transistor, Available at: <ttp://spectrum. ieee.org/tec-istory/siliconrevolution/te-lost- istory-of-te-transistor> [Accessed 29 August, 207]. [8] Jose Tadeu Arantes, Transistor tat mimics neurons developed, 207. Available at: <.ttp:// stormimics-neurons-ev.tml> [Accessed 29 August, 207] [9] Dr. U. Sezen and Dr. D. Gökcen, BJT Small- Signal Analysis, ELE230 Electronics, Hacettepe University, Apr [20] Electronic Devices and Circuits, EC 835, Jeppiaar Engineering College, Cennai, 208.