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Implementing Voltage Controlled Current Source in Electromagnetic Full-Wave Simulation Using the FDTD Method Khaled Elmahgoub and Atef Z

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Implementing Voltage Controlled Current Source in Electromagnetic Full-Wave Simulation Using the FDTD Method Khaled Elmahgoub and Atef Z Implementing Voltage Controlled Current Source in Electromagnetic Full-Wave Simulation using the FDTD Method Khaled ElMahgoub and Atef Z. Elsherbeni Center of Applied Electromagnetic System Research (CAESR), Department of Electrical Engineering, The University of Mississippi, University, Mississippi, USA. [email protected] and [email protected] Abstract — The implementation of a voltage controlled FDTD is introduced with efficient use of both memory and current source (VCCS) in full-wave electromagnetic simulation computational time. This new approach can be used to analyze using finite-difference time-domain (FDTD) is introduced. The VCCS is used to model a metal oxide semiconductor field effect circuits including VCCS or circuits include devices such as transistor (MOSFET) commonly used in microwave circuits. This MOSFETs and BJTs using their equivalent circuit models. To new approach is verified with several numerical examples the best of the authors’ knowledge, the implementation of including circuits with VCCS and MOSFET. Good agreement is dependent sources using FDTD has not been adequately obtained when the results are compared with those based on addressed before. In addition, in most of the previous work the analytical solution and PSpice. implementation of nonlinear devices such as transistors has Index Terms — Finite-difference time-domain, dependent been handled using FDTD-SPICE models or by importing the sources, voltage controlled current source, MOSFET. S-parameters from another technique to the FDTD simulation [2]-[7]. In this work the implementation of the VCCS in I. INTRODUCTION FDTD will be used to simulate a MOSFET with its equivalent The finite-difference time-domain (FDTD) method has gained model without the use of external tools, the entire simulation great popularity as a tool used for electromagnetic can be done using the FDTD. The paper is organized as simulations. Although it is based on a time-domain solution, it follows: In Section II, the new VCCS implementation provides a wideband frequency-domain response using time- approach is described and the FDTD equations are derived. In domain to frequency-domain transformation. It can easily Section III, numerical examples to prove the validity of the handle composite geometries consisting of different types of new approach are presented, including a simple resistive materials. In addition, it can be easily implemented using circuit with a single VCCS and a MOSFET circuit. The parallel computational algorithms. These features of FDTD numerical results show good agreement with the analytical have made it one of the most attractive techniques in results or numerical results obtained from PSpice [8]. In computational electromagnetics for many applications [1]. Section IV, conclusions are provided. One of the strengths of the FDTD method, is that it can be used to implement lumped linear and nonlinear elements such II. THE NEW APPROACH as resistors, inductors, capacitors, diodes, etc. In addition, it In this section the new approach is described and the FDTD can be used to implement independent sources such as hard updating equations are derived. In general, every VCCS is and soft current and voltage sources. FDTD is used widely in connected between two nodes and its value is controlled by simulating microwave circuits such as amplifiers, active the voltage between two other nodes. To drive the FDTD filters, etc. These circuits usually consist of nonlinear updating equations for a VCCS let's consider a simple circuit components as well as the linear components. Most of the as the one shown in Fig.1. As shown in the figure all the nodes nonlinear elements such as transistors are modeled using can be normally updated using lumped elements FDTD dependent sources. A dependent source is a source that implementation except for the dependent source which needs generates a voltage or current whose value depends on another special handling. voltage or current in the circuit. There are in general four The updating equation of the electric field of node (i+1, j, k) different types of dependent sources as follows: voltage must be derived taking into consideration the dependent controlled current source (VCCS), current controlled current source which is controlled by the value of the voltage between source (CCCS), voltage controlled voltage source (VCVS) and nodes (i+2, j, k) and (i+2, j, k+1). current controlled voltage source (CCVS). Dependent current To update the electric field at node (i+1, j, k), the Jiz should sources appear in most of the three and four terminal be calculated as follows (assuming the VCCS is in z- semiconductor devices, such as bipolar junction transistor direction): 1 n+ (BJT) and metal oxide field effect transistor (MOSFET), most 1 n+ Ii2 (1,,)+− jkXV of the equivalent circuit models for such devices includes a Ji2 (1,,)+= jk iz =1 , (1) VCCS. In this paper implementation of the VCCS using iz ΔΔxy ΔΔ xy 978-1-4673-1088-8/12/$31.00 ©2012 IEEE components if the dependent source is in x- or y-directions. This FDTD approach could be summarized as follows: 1- Update magnetic field components at time instant (n+0.5) Δt. 2- Update electric field components at time instant (n+1) Δt, taking into account the independent sources and lumped elements. 3- Update electric field components at time instant (n+1) Δt, taking into account the dependent sources if any as described. Fig. 1. A simple resistive circuit with both dependent and 4- Apply the boundary conditions. independent sources. 5- Increment the time step, nÆ n+1. 6- Repeat steps 1 to 5. where X is the control factor and the value of V1 can be calculated as follows: III. NUMERICAL RESULTS −Δz + VEijkEijk=+++⎡⎤nn1 ()()2, , 2, , . (2) In this section, numerical results generated using the new 1 ⎣⎦zz 2 approach are presented. The FDTD code was developed in Substitute (2) in (1), yields MATLAB [9] and run on a computer with an Intel Core i7 1 n+ ΔzX + CPU Q720, 1.6 GHz with 6 GB RAM. These results J2 ( i+= 1,,) jk Enn1 ()() i +2,, jk ++ E i 2,, jk . iz ⎣⎦⎡⎤z z demonstrate the validity of the new approach for analyzing 2ΔΔxy circuits with dependent VCCS in FDTD. The first example is (3) a simple resistive circuit containing VCCS. The second The updating equation for node (i+1, j, k) can be written as example is a MOSFET circuit analyzed using the equivalent follows: circuit model of the MOSFET. The results are compared with ∂ ∂ ∂ E 1 ⎡⎤H y H e z =−−−x σ EJ. (4) those obtained from analytical and PSpice solutions for the ∂∂∂ε ⎢⎥zz iz first and second examples, respectively. txyz ⎣⎦ Using the discretization and rearranging (4), and using the A. Test Case 1 (Simple Resistive Circuit with VCCS) coefficient convention used in [1] equation (4) can be The new approach is used to analyze the circuit shown in Fig. rewritten as follows: 1. The voltage source V(t) is implemented using sinusoidal + Enn1 ()()() i+=+1, jk , C i1, jk , E i + 1, jk , wave form with amplitude of 5 volts and frequency of 5 GHz, zezez the X factor is equal to 0.01. The main goal is to implement 11 ⎡⎤nn++ the circuit with its VCCS using the new approach and ++C() i1,, jk H22() i + 1,, jk − H() i ,, jk calculate the value of the voltage V . The FDTD grid cell size ezhy ⎢⎥y y 1 ⎣⎦is ∆x = ∆y = ∆z = 0.25 mm, the circuit is simulated with 3×1×2 in x, y and z-directions respectively as shown in Fig. 1, 11(5) ⎡⎤nn++ 3000 time steps are used. Convolutional perfect matched layer ++C() i1, jk , H22() i +1, jk , − H() i +−1, j 1, k ezhx ⎢⎥x x (CPML) is used as the absorbing boundaries of the ⎣⎦computational domain as implemented in [1] with 5 cells air + buffer in every direction. The results are compared with ++C()()() i1, jk , ⎡⎤ Enn1 i +++2, jk , E i2, jk , , ezvccs ⎣⎦z z analytical results in Fig. 2. The analytical solution is based on where mesh analysis method and it was found that for X = 0.01, V1 V(t)/6. From Fig. 2 good agreement between analytical ⎡⎤21,,εσ()()ijktijk+−Δ+e 1,, solutions and results generated by the new approach can be ()+=⎣⎦zz Cieze 1, jk , noticed. The computational time is 0.75 minute and the ⎡⎤21,,εσ()()ijktijk++Δ+e 1,, memory usage is 320KB. ⎣⎦zz 2Δt ()+= B. Test Case 2 (MOSFET Circuit) Ciezhy 1, jk , Δ++Δ+xijktijk⎡⎤21,,εσ()()e 1,, ⎣⎦zz This approach is also used to analyze the MOSFET circuit −Δ2 t shown in Fig. 3. It consists of IRF150 N-MOS transistor and ()+= Ciezhx 1, jk , three resistor and two sinusoidal sources V1 and V2, the Δ++Δ+yijktijk⎡⎤21,,εσ()()e 1,, ⎣⎦zz voltage source V1 is a sinusoidal voltage source with −ΔtzX Δ frequency of 9 MHz and amplitude of 0.8V, while the voltage ()+= Cijkezvccs 1, , . source V2 is a sinusoidal voltage source with frequency of 9 ΔΔxyijktijk⎡⎤21,,εσ()() + +Δe + 1,, MHz and amplitude of 1.6 Volts. The MOSFET will be ⎣⎦zz Using (5) the updating equation of the electric field implemented in the FDTD using the equivalent circuit model associated with a VCCS can be easily implemented in FDTD. shown in Fig. 4. The values of the equivalent circuit Similarly, the procedure can be used for different electric field parameters according to [7] are as follows: Cgd = 0.06pF, Cgs = 978-1-4673-1088-8/12/$31.00 ©2012 IEEE 0.96pF, Cds = 0.26pF, gm =10 mS and Rds = 197 Ω. The FDTD grid cell size is ∆x = ∆y = ∆z = 0.25 mm, the circuit is simulated with 5×1×2 in x, y and z-directions respectively, 1000 time steps are used, CPML is used as the absorbing boundaries of the computational domain with 5 cells air buffer in every direction.
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