Nonlinear transmission lines, which define transmission lines periodically loaded with nonlinear devices such as varactors, diodes, and transistors, are modeled in the framework of finite-difference time-domain (FDTD) method. Originally, some root-finding routine is needed to evaluate the contributions of nonlinear device currents appropriately to the temporally advanced electrical fields. Arbitrary nonlinear transmission lines contain large amount of nonlinear devices; therefore, it costs too much time to complete calculations. To reduce the calculation time, we recently developed a simple model of diodes to eliminate root-finding routines in an FDTD solver. Approximating the diode current-voltage relation by a piecewise-linear function, an extended Ampere's law is solved in a closed form for the time-advanced electrical fields. In this paper, we newly develop an FDTD model of field-effect transistors (FETs), together with several numerical examples that demonstrate pulse-shortening phenomena in a traveling-wave FET.

The generation of a short electrical pulse with picosecond duration is one of the keys to producing a breakthrough in high-speed electronics. The applications of short pulses include measurement systems with picosecond temporal resolution, over-100-Gbit/s communication systems, and submillimeter-to-teraherz imaging systems [

In order to evaluate the above-mentioned results in monolithically integrated devices, we have to develop the models of nonlinear devices such as RTDs and FETs for use in a finite-difference time-domain (FDTD) electromagnetic solver [

Recently, we developed a concise model of nonlinear devices that contributes to eliminating the time-consuming root-finding procedures mentioned above. It approximates the voltage dependence of the device current by a piecewise-linear function and solves an extended Ampere’s law in a closed form. Actually, we successfully demonstrated an FDTD calculation of the pulse shortening in an RTD line [

When the conduction current density flowing in the device is denoted by

To solve (

By straightforward calculations, (

There are many different equivalent circuits of an FET, depending on the accuracy and the application to use. For clarity, we first consider the simplest representation: an FET is represented only by the drain-source current

At this point, we approximate the voltage dependence of

Next, we consider more practical FET models shown in Figure

FET model in FDTD. (a) The Statz model and (b) A triangulation of

To obtain a piecewise-linear function that approximates the device currents, we triangulate the

We again obtain the column vector

In the following, we demonstrate the pulse shortening in TWFETs by FDTD calculations. Although the line structure we set up is rather impractical, we successfully observed the shortening of the pulse traveling along a TWFET. It is observed, only when the nonlinear operations of a large amount of FETs are properly simulated. We thus believe that this example calculation clarifies the validity of our models. Before showing calculation results, we briefly review the mechanism of the pulse shortening in TWFETs.

Figure

Setup of TWFETs for shortening traveling pulses. (a) A representation of a TWFET, (b) the signal application to a TWFET and (c) the equivalent current-voltage relationship of an FET for a pulse traveling in the drain line.

When the TWFET succeeds in amplifying the unique mode, we can assume the simultaneous propagation of the leading edges of the gate and drain pulses. At this point, every FET operates as an electronic switch that is open for

Operation principle of pulse shortening in TWFETs.

Three-dimensional FDTD calculations were carried out for demonstrating nonlinear pulse propagation along a TWFET. The total number of cells was ^{2}, −1.0 V, and 2.0 V^{−1}, respectively. We ignore the influences caused by the gate-source current with the parasitic capacitors and resistors for clear observations of the nonlinear properties of a TWFET. We modeled

Setup of FDTD calculations. (a) The longitudinal and (b) the transverse structure of the calculated TWFET.

To obtain a rough estimation of the model TWFET, we carried out the quasi-TEM analysis [

Line parameters of test TWFET.

0.10 pF/mm | 0.73 nH/mm | ||

0.17 pF/mm | 0.70 nH/mm | ||

0.09 pF/mm | 0.42 nH/mm |

Wave propagation on test TWFET. The waveforms on the gate and drain lines are shown by the thin and thick curves, respectively. The black and red curves correspond to the quasi-TEM and FDTD calculations, respectively. (a) shows the input waveforms. Waveforms recorded at the

We demonstrated full-wave calculations that illustrate the pulse propagation characteristics of a TWFET. The pulse shortening in a TWFET was properly observed in the full-wave calculations. By using piecewise-linear modeling, FETs were characterized in FDTD without significant computational costs.