FDTD is a numerical method that uses the second-order central-difference method to discrete the Maxwell¡¦s equations in differential form, and positioning electromagnetic field in space grids and time grids. It is applied to analyze many electromagnetic problems in time domain. In this report the FDTD method is extended to include lumped-elements (as resistor, inductor, capacity),and nonlinear elements(as diode, transistor) to combine the circuit elements and electromagnetic fields, it¡¦s so called LE-FDTD algorithm. The first, we will introduce the theory derivations and simulate some circuit structures in 2D, and then in order to simulate the real circuits, we will extend this algorithm in 3D to make full-wave analysis.

For the advanced high speed digital circuits with faster edge rate, smaller packaged size, and higher layout density, crosstalk becomes one of the serious problems for good signal integrity (SI) in the circuits. Accurate extraction of the equivalent model of the general three conductors transmission lines structure can help us understand the behavior of the crosstalk phenomenon. Based on combining the Layer Peeling Technique (LPT) and Finite-Difference Time-Domain (FDTD) numerical approach, both the impedance profile and the equivalent lumped model of the three-conductors transmission lines are theoretically obtained. The equivalent model can easily incorporate into SPICE program. The transient behavior of the these extracted model is compared with the experienced results measured by Time-domain Reflectometry (TDR). The agreement is good.

Because SAW filters are small, high reliability, and it cannot be easily integrated with silicon substrate, they have become one of the most popular communication passive components recently. As the working frequency becomes higher, SAW filters are more sensitive to electromagnetic interference introduced by the package. Discrepancy in performance between design and measurement can be large if the packing effects are not considered. In this thesis, we make use of Finite Difference Time Domain method (FDTD) and develop a procedure combining High Frequency Structure Simulator (HFSS) with ADS software to simulate electromagnetic effect of a packaged SAW Filter. This is a full-wave method that integrates electromagnetic wave and acoustic wave. Measurement is also carried out to verify the simulated results. Preliminary results show that this method that we provide can predict frequency response in package effectively. Our Prediction can save factory design time and production cost.

FDTD is an electromagnetic field computation method with the ability of considering circuit elements. Traditional lump element method is insufficient for simulating circuit. In this thesis, we use equivalent source method to combine non-linear circuit elements like active devices into the FDTD simulation. The advantages of this is powerful and time-saving. The accuracy of this method is checked of transmission line driving by CMOS circuits. By employing this method, we find that it will increase EMI phenomenon by strengthening current of driving load, and the load of coupling line will affect noise due to impedance mismatch.

The FDTD method is a numerical method that uses the second-order central-difference method to discrete the Maxwell¡¦s equations in differential form, and positioning electromagnetic field in space grids and time grids. It is applied to analyze many electromagnetic problems in time domain. In the thesis, we applied FDTD methods to solve EMC/EMI problems like the interference to a mixer from an antenna, and the packaging effects to a small signal microwave amplifier and so on. Therefore, we applied equivalent current source approach to simulate each microwave elements at first. And, we extend the approach to field of EMC/EMI. researching the advantages of FDTD methods in Full-Wave analysis.

The finite-Difference Time Domain method (FDTD) is to derive the discrete form of the Maxwell¡¦s equations by second-order central difference with the electromagnetic distribution of the Yee space lattice, and computes the value of the electric field and magnetic field in the simulation space by using leapfrog for time derivatives. This method is also different with the frequency domain method which needs to analyze its value individually (ex. Finite Element method). The frequency domain method needs to take a long time for analyzing the response on each spectrum point when the bandwidth is very wide. The advantage of time domain analysis is to obtain the complete frequency response from the simulation value through Fourier Transform method. It¡¦s impossible to combine the electromagnetic analysis with the lumped circuit simulation in current simulation CAD. Thereby the performance of the simulation result and the practical implementation always occurs error because of the lake of the consideration. The FDTD method is the full-wave algorithm which can also simulate the lump element, nonlinear element or active element in simulation space by linking to SPICE or S-parameter. The purpose of this thesis is to develop the method for simulating microwave circuit, and to verify the credibility between the equivalent source method and the S-parameter method in FDTD by the simulation of active antenna and low-noise amplifier.

The finite-Difference Time Domain method (FDTD) derives the discrete form of the Maxwell¡¦s equations with second-order central difference with the electromagnetic distribution of the Yee space lattice, and computes the value of the electric field and magnetic field in the simulation space using leapfrog for time derivatives. This method is different from the frequency domain method which needs to analyze its value individually (ex. Finite Element method). The frequency domain method needs to take a long time for analyzing the response on each spectrum point when the bandwidth is very wide. The advantage of time domain analysis is to obtain the complete frequency response from the simulation value through Fourier Transform method. It¡¦s difficult to combine the electromagnetic analysis with the lumped circuit simulation in current simulation CAD. Thereby the performance of the simulation result and the practical implementation always causes error. The FDTD method is the full-wave algorithm which can also simulate the lump element, nonlinear element or active element in simulation space by linking to SPICE or S-parameter. In this dissertation, an efficient scheme for processing arbitrary one-port devices in the finite-difference time-domain (FDTD) method is proposed. Generally speaking, methods invoking analytic pre-processing of the device¡¦s V-I relations (admittance or impedance) are computationally more efficient than methods employing numerical procedure to iteratively process the device at each time step. The accuracy of the proposed method is verified by comparison with results from the equivalent current-source method and is numerically stable.

The Speedy Delivery (SD) waveform does not undergo dispersion in transmission lines. The waveform was first introduced by Dr. Robert Flake in US Patent 6,441,695 B1 issued on August 27, 2002. Use of the SD waveform allows for high precision time domain measurements on transmission lines. High precision time domain reflectometry (TDR) and time domain transmission (TDT) measurements are described. An example measurement is presented. The design of the experimental apparatus is detailed. Voltage bias adjustments are made during measurements to increase the repeatability. Voltage bias adjustments are examined in detail. Efforts to produce short terminated measurements with high precision are included. A technique for performing TDR measurements with highly attenuated signals is presented with results. / text

Time Domain Reflectometer (TDR) measures the electrical length of a cable from the applied end to the location of an impedance change. An impedance change causes a portion of the applied signal to reflect back based on the value of its reflection coefficient. The time of flight (TOF) between the applied and reflected wave is computed and multiplied with previously determined signal propagation velocity to determine the location of the impedance change. We intentionally open terminate the output end of the cable which makes the reflection coefficient be maximum (=1) to measure its electrical length. Conventional TDRs designed for testing integrity of long cables use various closed pulse shaped test signals i.e. the half sine wave and the Gaussian pulse, that disperse (change shape) and change velocity while propagation along the cable. Quoting Dr. Leon Brillouin’s comments on electromagnetic energy propagation [10], “in a vacuum, all waves (e.g. frequencies) propagate at the same velocity, hence withoutdistortion, whereas in a dispersive lossy media, except for an infinitely long sinusoidal waveform, distortion will occur due to frequency dependent velocity.” This signal distortion generally degrades the accuracy of the measurement of the signal’s TOF. We discuss here an Enhanced Resolution Time Domain Reflectometer (e-TDR). The enhanced resolution is due to a newly discovered signal called SPEEDY DELIVERY (SD) by Dr. Robert Flake at The University of Texas at Austin (US PATENT 6,441,695 B1 issued in August 27, 2002). This SD signal has a propagation velocity that is a programmable constant and this signal preserves its shape during propagation through dispersive lossy media (DLM). This signal behavior allows us to use ‘e-TDR’ in applications where remotely located signals need to be synchronized or asynchronized precisely. Potential applications include signal based synchronization of devices like sensors connected in a network. Since the cable carrying data from sensors at discrete and remote locations to a collecting center have different electrical lengths, it is necessary to precisely offset the timestamp of the incoming signal from these sensors to allow accurate data fusion. Our prototype is capable of synchronizing signals 1,200 ft (~ 400 m) apart with sub-nanosecond resolution. / text

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