I-V characteristics of p-n junction diode
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This document discusses the I-V characteristics of a p-n junction diode. It derives equations for the current-voltage relationship under forward and reverse bias conditions. The derivation considers minority carrier diffusion currents and uses low-level injection approximations. It also examines the temperature dependence of the I-V characteristics and derives an equation showing the exponential relationship between current and temperature.
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Reflection and Transmission coefficients in transmission lineRCC Institute of Information Technology
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The document discusses transmission line impedance and input impedance. It defines characteristic impedance as the ratio of voltage to current waves travelling along a transmission line. It provides expressions for characteristic impedance in terms of line parameters R, L, G, C. It then derives expressions for input impedance of open circuit, short circuit, matched and mismatched lossless transmission lines. It shows that input impedance is capacitive for a short open circuit line and inductive for a short circuit line.
Distortionless Transmission Line
This document discusses transmission lines and the conditions required for distortionless transmission. It notes that losses in transmission lines can occur due to I2R loss, skin effect, and crystallization. Distortion can arise from amplitude distortion, attenuation distortion, and phase distortion. The conditions for distortionless transmission are that the attenuation constant must be zero and the phase velocity must be independent of frequency. This requires that the line's inductance and capacitance per unit length satisfy LG/RC=1/2. The document also examines propagation constants and phase velocity for lossless transmission lines. It provides examples of calculating phase velocity, propagation constant, and phase wavelength for given line parameters.
Quantum Hall Effect
The document summarizes a lecture on the quantum Hall effect. It defines the quantum Hall effect as a phenomenon where the resistance of a quantum well system is quantized under low temperature and high magnetic field conditions. It then provides calculations to show that the quantum Hall resistance is quantized and equal to h/q^2, where h is Planck's constant and q is the elementary charge. Finally, it discusses how the quantization occurs due to the formation of discrete energy levels called Landau levels in the presence of a magnetic field.
Telegrapher's Equation
This document discusses transmission lines and the Telegrapher's equation. It begins by introducing transmission lines and their parameters such as resistance, inductance, conductance and capacitance per unit length. It then derives the Telegrapher's equation that describes voltage and current on a transmission line. It shows how the equation can be used to find the propagation constant and solve for voltage and current as a function of position and time. It also discusses phase velocity and provides examples of calculating attenuation constant, phase constant, and phase velocity for different transmission line scenarios.
Dielectrics
This document discusses the topic of electrostatics and dielectrics in the Electromagnetic Theory course. It defines a dielectric as a material where charge displacement occurs in an external electric field rather than free motion of charges. Dielectrics are classified as polar or nonpolar depending on whether they have a permanent dipole moment. The types of polarization in dielectrics are electronic, orientation, and ionic polarization. Key concepts discussed include polarization density, polarization charge density, the relationship between polarization and electric field through susceptibility and relative permittivity, atomic polarizability, and the relationship between polarization and electric displacement. An example problem calculates the polarization given the electric displacement.
Capacitor
1) The document discusses different types of capacitors including parallel plate, cylindrical, and spherical capacitors. Equations for electrostatic potential and electric field are derived for each type.
2) Examples problems are worked out on determining the capacitance of a parallel plate capacitor when a dielectric slab is inserted, and the capacitance of a coaxial cylindrical capacitor with dielectrics of different permittivities in each region.
3) Key equations presented include the capacitance of parallel plate, cylindrical, and spherical capacitors in terms of their geometric parameters and dielectric properties.
Electrical Properties of Dipole
1) An electric dipole is formed when two equal but opposite charges are separated by an infinitesimal distance. The dipole moment is defined as the product of the charge magnitude and the distance between them.
2) The electrostatic potential and electric field due to a dipole can be expressed in terms of the dipole moment. The potential and field decrease with increasing distance from the dipole.
3) A torque is experienced by a dipole when placed in an external electric field, with the torque being proportional to the cross product of the dipole moment and the electric field.
Application of Gauss' Law
This document contains lecture notes on electrostatics and the application of Gauss' law from a course on electromagnetic theory taught by Arpan Deyasi. It defines line charge density, surface charge density, and volume charge density. It then uses Gauss' law to derive expressions for the electric field and potential due to different charge distributions, including line charges, surface charges on a ring and plane, and volume charges in a cylinder and sphere. Example problems are worked through applying Gauss' law to find electric fields and potentials for these various charge distributions.
Fundamentals of Gauss' Law
This document discusses Gauss's law and related electromagnetic theory concepts taught in a course. It provides:
1) An overview of Gauss's law, which states that the total outward electric flux through a closed surface is equal to the total charge enclosed divided by the permittivity of the medium.
2) Derivations and proofs of Gauss's law using calculus theorems like divergence theorem.
3) Applications of Gauss's law to problems involving charge distributions and electric field calculations.
4) Discussions of related concepts like Gauss's law in polarized media, current continuity equation, relaxation time, and Poisson's equation.
5) Example problems demonstrating the application of these electromagnetic theory principles.
Fundamentals of Coulomb's Law
This document discusses Coulomb's law and some key concepts in electrostatics, including:
- Coulomb's law describes the electrostatic force between two point charges, being directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
- The electric field intensity and electric flux density are introduced.
- Properties of the electric field such as it being irrotational are examined.
- The electrostatic potential is defined and its relationship to the electric field is explored.
Vector Integration
This document discusses vector calculus theorems including Stokes' theorem and the divergence theorem. Stokes' theorem relates the line integral of a vector field around a closed curve to the surface integral of the curl of the vector field over any surface bounded by the curve. The divergence theorem relates the volume integral of the divergence of a vector field over a volume to the surface integral of the vector field over the boundary surface of that volume. The document provides proofs of these theorems and examples of their applications to problems involving conservative vector fields and evaluating integrals.
Scalar and vector differentiation
This document discusses a course on electromagnetic theory taught by Arpan Deyasi. It covers topics related to vector differentiation, including the vector differential operator in Cartesian, cylindrical and spherical coordinates. It also covers differentiation of scalar functions, including calculating gradients, directional derivatives and finding normals to surfaces. Finally, it discusses differentiation of vector functions, specifically divergence, which represents the volume density of the net outward flux from a vector field.
Coordinate transformation
The document discusses various coordinate transformations between Cartesian, cylindrical, and spherical coordinate systems. It provides the transformation equations for scalar and vector variables between these coordinate systems. Examples are included to demonstrate transforming between Cartesian and cylindrical coordinates for points in both scalar and vector form. The key topics covered are the four types of coordinate transformations, the transformation equations, and examples to illustrate the transformations.
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一比一原版(爱大毕业证书)爱荷华大学毕业证如何办理
原版一模一样【微信：741003700 】【(爱大毕业证书)爱荷华大学毕业证成绩单】【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
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留信网认证的作用:
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3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
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办理(爱大毕业证书)爱荷华大学毕业证【微信：741003700 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理(爱大毕业证书)爱荷华大学毕业证【微信：741003700 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
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其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理(爱大毕业证书)爱荷华大学毕业证【微信：741003700 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
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一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
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1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
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办理(uoft毕业证书)加拿大多伦多大学毕业证【微信：741003700 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
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校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理(uoft毕业证书)加拿大多伦多大学毕业证【微信：741003700 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
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I-V characteristics of p-n junction diode
- 1. Course: Electronic Devices paper code: EC301 Course Coordinator: Arpan Deyasi Department of Electronics and Communication Engineering RCC Institute of Information Technology Kolkata, India 8/21/2020 1Arpan Deyasi, RCCIIT, India Topic: I-V characteristics of p-n Junction
- 2. EF EV EC EFI Vbi 8/21/2020 2Arpan Deyasi, RCCIIT, India I-V Characteristics of p-n junction Consider p-n junction under forward bias
- 3. I-V Characteristics of p-n junction 8/21/2020 3Arpan Deyasi, RCCIIT, India We consider p-n junction under external bias 0pJ = Under low level injection condition 0p z p dp qp E qD dz µ − =
- 4. 8/21/2020 4Arpan Deyasi, RCCIIT, India I-V Characteristics of p-n junction 1p z p D dp E p dzµ = T z V dp E p dz =
- 5. 8/21/2020 5Arpan Deyasi, RCCIIT, India I-V Characteristics of p-n junction TdV V dp dz p dz − = T dV dp V p − =
- 6. 8/21/2020 6Arpan Deyasi, RCCIIT, India I-V Characteristics of p-n junction pn0: concentration of holes under thermal equilibrium pn(0): concentration of holes at the beginning of n-side 0 (0) 0 n n pV T p dV dp V p − =∫ ∫
- 7. 8/21/2020 7Arpan Deyasi, RCCIIT, India 0(0) expn n T V p p V = I-V Characteristics of p-n junction 0 0(0) (0) exp 1n n n n T V p p p p V ′ = − = −
- 8. 8/21/2020 8Arpan Deyasi, RCCIIT, India I-V Characteristics of p-n junction Under low level injection condition, minority diffusion current due to holes crossing the junction at z = 0: (0) (0) p n pn p AqD p I L ′ = 0(0) exp 1p pn n p T AqD V I p L V −
- 9. 8/21/2020 9Arpan Deyasi, RCCIIT, India I-V Characteristics of p-n junction Under low level injection condition, minority diffusion current due to electrons crossing the junction at z = 0: 0(0) exp 1n np p n T AqD V I n L V −
- 10. 8/21/2020 10Arpan Deyasi, RCCIIT, India I-V Characteristics of p-n junction (0) (0)np pnI I I= +net current 0 0 exp 1 exp 1 n p n T p n p T AqD V I n L V AqD V p L V − + −
- 11. 8/21/2020 11Arpan Deyasi, RCCIIT, India I-V Characteristics of p-n junction 0 0 exp 1pn p n n p T AqDAqD V I n p L L V = + − 0 exp 1 T V I I V = −
- 12. 8/21/2020 Arpan Deyasi, RCCIIT, India 12 I-V Characteristics of p-n junction 0 exp 1 T V I I Vη − V I CASE I: for V = 0 0I =
- 13. 8/21/2020 13Arpan Deyasi, RCCIIT, India I-V Characteristics of p-n junction 0 exp 1 T V I I Vη − CASE II: for V small & V>0 exp 1 T T V V V Vη η = + 0 T V I I Vη = V I
- 14. 8/21/2020 14Arpan Deyasi, RCCIIT, India I-V Characteristics of p-n junction 0 exp 1 T V I I Vη − CASE III: for V large & V>0 2 exp 2T T V V V Vη η = 2 I V∝ V I
- 15. 8/21/2020 15Arpan Deyasi, RCCIIT, India I-V Characteristics of p-n junction 0 exp 1 T V I I Vη − V I CASE IV: for V small & V<0 exp 1 T T V V V Vη η = − 0 T V I I Vη = −
- 16. 8/21/2020 16Arpan Deyasi, RCCIIT, India I-V Characteristics of p-n junction 0 exp 1 T V I I Vη − V I CASE V: for V large & V<0 exp 0 T V Vη → 0I I= −
- 17. 8/21/2020 17Arpan Deyasi, RCCIIT, India Temperature Dependence of I-V Characteristics 0 0 0 pn p n n p AqDAqD I n p L L = + 0p Dn N= & 2 0 0 0p nn p n= 2 0 0n D n p N =
- 18. 8/21/2020 18Arpan Deyasi, RCCIIT, India Temperature Dependence of I-V Characteristics 2 0 0 0 pn n p D DD n I Aq n L L N = + 2 0 0 0 1 1pn n p D DD I Aqn L n L N = +
- 19. 8/21/2020 19Arpan Deyasi, RCCIIT, India Temperature Dependence of I-V Characteristics 2 3 0 exp GE n CT kT = − 3 0 1 1 exp pG n n A p D DE D I AqCT kT L N L N = − +
- 20. 8/21/2020 20Arpan Deyasi, RCCIIT, India Temperature Dependence of I-V Characteristics 3 0 1 exp GE I C T kT = − 0 1ln ln 3ln GE I C T kT = + −
- 21. 8/21/2020 Arpan Deyasi, RCCIIT, India 21 Temperature Dependence of I-V Characteristics 0 2 0 1 3 GdI E I dT T kT = + 0 2 0 3 GdI E dT dT I T kT = +
- 22. 8/21/2020 Arpan Deyasi, RCCIIT, India 22 Temperature Dependence of I-V Characteristics 0 0 3 GdI EdT dT I T kT T = + 0 0 3 GdI EdT I T kT = +
- 23. 8/21/2020 Arpan Deyasi, RCCIIT, India 23 Temperature Dependence of I-V Characteristics 0 0 3 .GdI EdT q I T q kT = + 0 0 3 G T dI VdT I T V = +