Chongyang Mao

Comparison of Nonuniform Transmission Lines With Gaussian and Exponential Impedance Profiles for

The circuit simulation of nonuniform transmission lines that were under consideration for the next generation of petawatt-class Z-pinch drivers was performed. It was confirmed that the power-transport efficiency of the designed radial transformer with an exponential impedance profile is higher than that with Gaussian profiles. Based on Fouriers theorem and the principle of superposition, it was found that there are considerable low-frequency components for the input voltage of a half-sine wave with an angular frequency of 14 Mrad/s. Compared with the exponential transformer, the Gaussian transformers amplify the low-frequency components to a lower extent, which makes the difference in power efficiency between the two types of transformers. The radial transformer also serves as a passive high-pass filter, and the Gaussian transformer may give better performance than the exponential transformer does if the signal transport rather than the power transport is concerned.

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The electromagnetic simulation of the monolithic radial transmission lines for future Z-pinch was performed. Focusing on the difference in the maximum transmitted power efficiency between the electromagnetic simulation and the circuit simulation, the monolithic radial transmission lines with different impedance profile (exponential, Gaussian, hyperbolic) were compared. The power efficiency for the exponential line is higher than that for the Gaussian lines and the hyperbolic line, which is similar to that from the circuit simulation. However, all the power efficiencies obtained with the electromagnetic simulation are about 15% lower than those obtained with the circuit simulation, indicating the existence of considerable non-TEM modes and a non-ignorable error in the circuit simulation based on the quasi-TEM mode approximation. In consideration of several monolithic radial transmission lines being stacked together and the flat electrodes required by the stacked lines, the hyperbolic line was compared with the exponential line with several wide radial slots cut on the flat electrodes. While the hyperbolic line has a little bit lower transmitted power efficiency than that of the exponential line, it is much easier in fabrication. For this reason, the hyperbolic line was recommended as the best choice.

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A mathematical expression of the output voltage from a nonuniform line was deduced by investigating the transient response of a cascaded multiple-section line to an input voltage of half-sine shape that is close to the wave shape of the pulse voltage for Z-pinch. The correctness of the mathematical expression was verified by comparing the result from the mathematical expression with that from circuit simulation using PSPICE code. The high-pass and pulse-compression characteristics of a nonuniform line were further clarified by the theoretical analysis of the analytical expressions.

Three-dimensional electromagnetic simulation of monolithic radial transmission lines for Z-pinch

A 21-channel quasi-square-wave nanosecond pulse generator was constructed. The generator consists of a high-voltage square-wave pulser and a channel divider. Using an electromagnetic relay as a switch and a 50-Ω polyethylene cable as a pulse forming line, the high-voltage pulser produces a 10-ns square-wave pulse of 1070 V. With a specially designed resistor-cable network, the channel divider divides the high-voltage square-wave pulse into 21 identical 10-ns quasi-square-wave pulses of 51 V, exactly equal to 1070 V/21. The generator can operate not only in a simultaneous mode but also in a delay mode if the cables in the channel divider are different in length.

Analytical Solution of Nonuniform Transmission Lines for Z-Pinch

A mathematical expression of the output voltage from a nonuniform transmission line with an arbitrary input pulse was deduced. The first arriving wave, peak power efficiency, and droop of the output voltage were further clarified using analytical method. The transmission characteristics of monolithic radial transmission lines (MRTLs) with different impedance profiles were investigated by 3-D electromagnetic (EM) simulation and it was found that the hyperbolic impedance profile is the best choice for future Z-pinch drivers. The results obtained from 3-D EM simulation are in good agreement with those obtained from the experiments on a scaled-down MRTL.

Note: A novel method for generating multichannel quasi-square-wave pulses

A mathematical expression of the output voltage from a nonuniform transmission line (NTL) with an arbitrary input pulse was deduced. Due to this mathematical expression, two transmission characteristics of NTLs with linear, exponential and Gaussian impedance profiles were further clarified. The first one is that the peak power efficiencies of NTLs with a half-sine input voltage are quantified as functions of Ψ (the ratio of the output impedance to the input impedance of the NTLs) and Γ (the ratio of the pulse width to the one-way transit time of the NTLs). The second one is that the top of an initially rectangle input voltage pulse falls at the terminal of the NTL and that the ratio of the droop to the top of the output voltage is also quantified as a function of Ψ and Γ.

Investigation of Monolithic Radial Transmission Lines for Z-Pinch

This paper presents the experimental results of a monolithic radial transmission line (MRTL) that may be used in pulsed power generators and microwave devices. The MRTL with a hyperbolic impedance profile is 508 mm in radius, corresponding to a one-way transit time of 15 ns for the electromagnetic wave. In the experiments, up to twenty identical voltage pulses, 10 ns in FWHM and 2 ns in rise-time, were fed into the MRTL through 20 input BNC connectors that are uniformly distributed along the outer circumference of the MRTL. It was found that the amplitude of the voltage from the output BNC connector located in the center of the MRTL is nearly proportional to the total number of the input branches. The effect of the failure modes on the output voltage was investigated. For the MRTL driven by 20 input branches, while the open-circuit or short-circuit even in one input branch considerably decreases the amplitude of the output voltage, the jitter shorter than 2 ns in 3 input branches makes no obvious effect on the output voltage.

Analysis of peak power efficiency and droop from a nonuniform transmission line

In the design of future Z-pinch driver, the monolithic radial transmission lines (MRTL) were used to combine the outputs of many pulse generators to Z-pinch load. In order to investigate the transmission characteristic of the MRTL with different impedance profiles, 3-dimensional electromagnetic simulation has been performed. From the results of 3-dimensional electromagnetic simulation, it was found that the maximum transmitted power efficiency of hyperbolic line is nearly same as that of exponential line. The hyperbolic line may be the best choice for Z-pinch, because it is much easier in fabrication than the exponential line.

Experiments of a monolithic radial transmission line

An experiment system of a scaled-down monolithic radial transmission line (MRTL) for future Z-pinch drivers was established to testify the validity of 3-D electromagnetic (EM) simulation. The MRTL had a hyperbolic impedance profile. Being immersed in deionized water, the MRTL was composed of two flat aluminum plates separated by a distance of 1 cm. The radius of both plates was 0.5 m, which corresponds to a one-way transit time of about 15 ns for the EM wave from the outer circumference to the center. As this was a linear system, the experiment could be performed at a low voltage. A high voltage pulse was divided into 21 low voltage pulses by a 1-way to 21-way convertor. 20 of the 21 pulses were fed into the MRTL by BNC connectors while the other one was connected to an oscilloscope. The input BNC connectors were uniformly distributed around and connected to the outer circumference of the MRTL. All input voltage pulses were same with each other, with a waveform of rectangle, about 2 ns in rise time, 10 ns in full width at half maximum (FWHM) and 30 V in amplitude. 20 paralleled resisters, each of which was 154 Ω in resistance, were put around the center to match the output impedance of the MRTL. The waveform of the output voltage on the load was measured and compared to the result from 3-D EM simulation of the same hyperbolic line. The two waveforms nearly superimposed onto each other, which validated the correctness of both the experimental method and 3-D EM simulation method.

Comparison between experiment and 3-dimentional electromagnetic simulation of monolithic radial transmission lines for Z-pinch

Recently, a number of architectures have been proposed for the design of future pulsed power Z-pinch drivers1. In the architectures nonuniform transmission lines were used to combine the outputs of several-hundred terawatt-level pulse generators to produce a petawatt-level pulse. In general, people obtained the output voltage from a nonuniform transmission line by considering the nonuniform line as a cascaded multiple-section line and then calculating it with the circuit simulation codes such as PSpice or TLCODE. We also treated the nonuniform line as a cascaded multiple-section line, but analyzed it with an analytical method. We found that a mathematical expression of the output voltage from a nonuniform line could be deduced if the impedance profile of the nonuniform line changes continuously and monotonically and each line section of the cascaded multiple-section line is short enough. The output voltage consists of one primary component called first arriving wave and numerous double-reflection components. In comparison with the input voltage wave, the first arriving wave is the same in wave shape and proportional to (Z out /Z in )1/2 in amplitude, where Z out and Z in are the output impedance and the input impedance of the nonuniform line, respectively. It was shown that the double reflection components not only lower the output voltage, but also compress the output voltage pulse. The waveform of the output voltage obtained using our mathematical expression is fully overlapping with that obtained from the circuit simulation using PSpice, which indicates that our mathematical expression is correct.