Ballasting resistors

A second way to promote current sharing between emitters is to use a ballast resistor [28]. This resistor is in series with the CNTs and the voltage drop across it acts to share current between the emitters [29]. The idea is that some fraction of the total applied voltage between cathode and anode should be dropped across the ballast resistor, so that there is less across the emitter itself. Ballast resistors increase the emission site density [29]. It acts like negative feedback. 

There are two geometries for a ballast resistor, a thin film under the CNT (vertical resistor), or a thin film at the side of the CNT (horizontal resistor). Now, the local field for field emission from carbon is extremely high, 109 V/m, which may be 10 times larger than the breakdown field of many insulators. Given the dimensions of an emission system, it is likely that the thickness of any ballast resistor thin film will be smaller than that of the net cathode-anode distance. Thus, the applied field is likely to cause breakdown in any vertical ballast resistor design. Thus, horizontal ballast resistors are a safer option. However, they are more difficult to implement because they must be placed between each emitter and the current feed. 

A second structure to consider is a synthetic nanowall structure consisting of a closely packed forest of CNTs patterned into walls, on a square, hexagonal or triangular lattice (Fig. 13.6) [35]. These also allow for emission site redundancy. They have the added advantage that they can accommodate the lateral ballast resistor between a current source and the emitting walls. 

Fig. 13.6 (a) CNT array with lateral ballast resistors to the square grid, (b) honeycomb patterned mesh structure of CNT emitters (courtesy W. I. Milne). 

The field emission properties of carbon nanotube forests and single nanotubes are described. Controlled emission is possible for aligned CNT arrays where the spacing is twice the CNT height, as grown by plasma enhanced chemical vapor deposition. This leads to the maximum field enhancement factor. For random forests, the field enhancement obeys an exponential distribution, leading to a lower emission site density and imperfect current sharing. Ballast resistors can help alleviate this problem. Random nanocarbons perform less well than CNTs. Some applications are covered. Elec-... 

Vs - battery voltage, volt Rj = ballast resistor, ohm R = Strain gage resistance when relaxed, ohm... 

The two teems in the parentheses of this equation represent the potential in the unstrained condition (the right term) and in the strained condition (the left term). By setting the value of the ballast resistor Rj equal to the strain gage resistance R, a process that is often used in practice, the equation for the signal voltage becomes ... 

The frequency of the laser is measured relative to the deuterium n-2->4 transitions. These excitations are detected opto-galvanicallyEsi] in a simple circuit consisting of a regulated power supply, 10 ballast resistor, and a flowing gas Woods discharge tube operating at 0,4 torr of hydrogen and deuterium,... 

Figure 3.7 A simple arrangement for a hollow cathode discharge. The variable resistance provided by the ballast resistor limits the amount of current drawn and improves the stability of the discharge.

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