Backward wave tubes

Usually a traveling wave tube means a forward wave tube. In the vacuum tube, the electron beam and forward waves interact with each other. There is a vacuum tube in which the electron beam interacts with backward waves. This type of tube is termed the backward wave tube. The backward wave tube is inherently highly regenerative (built-in positive feedback) therefore, it is usually an oscillator. Such an oscillator is termed a backward wave oscillator (BWO). The BWO has a traveling wave structure inside, but usually it is not called a traveling wave tube. Details of a BWO are presented in Chap. 6.4.3. The oscillation frequency of a BWO is dominated by the electron speed, which is determined by the anode voltage. Therefore, a BWO is a microwave frequency voltage controlled oscillator (VCO). 

Backward wave tube A backward wave traveling wave tube the microwave input is located in proximity to the collector and the microwave output is located in proximity to the electron gun. The direction of traveling microwave and direction of electron motion in the beam are opposite to one another. 

A family of vacuum-tube MMW sources is based on the propagation of an electron beam through a so-called slow-wave or periodic structure. Radiation propagates on the slow-wave structure at the speed of the electron beam, allowing the beam and radiation field to interact. Devices in this category are the traveling-wave tube (TWT), the backward-wave oscillator (BWO) and the extended interaction oscillator (EIO) klystron. TWTs are characterized by wide bandwidths and intermediate power output. These devices operate well at frequencies up to 100 GHz. BWOs, so called because the radiation within the vacuum tube travels in a direction opposite to that of the electron beam, have very wide bandwidths and low output powers. These sources operate at frequencies up to 1.3 THz and are extensively used in THZ spectroscopic applications [10] [11] [12]. The EIO is a high-power, narrow band tube that has an output power of 1 kW at 95 GHz and about 100 W at 230 GHz. It is available in both oscillator and amplifier, CW and pulsed versions. This source has been extensively used in MMW radar applications with some success [13]. 

Figure 11.12 Two tube model with terminations at the glottis and lips. This system has three reflection coefficients. In the middle we have r the only real reflection coefficient, whose value is given by the area Equation 11.15. The lips and glottis reflection coefficients are artificial values designed to ensure there are some losses from the system. Note that there is no backwards wave entering at the lips, and no forwards wave (save the source) entering at the glottis.

Of particular importance is the fact that the boundary condition is completely described by the reflection coefficient, which is governed entirely by the areas of the tubes the speed-of-sound and density terms have been eliminated. We shall see that reflection coefficients are a simple and usefiil way to define the characteristics between two tubes and we will henceforth use them instead of tube areas. Using reflection coefficients, we can find expressions that relate the forward wave or the backward wave in one tube to the forward and negative waves in the other tube ... 

Backward wave oscillators (BWO) A microwave oscillator tube that is based on a backward wave interaction. 

Helical beam tube A backward wave amplifier based on interaction between a forward helical electron beam launched into a waveguide and backward traveling microwave in the waveguide. 

Microwave spectroscopy uses tunable coherent sources of radiation such as microwave synthetizers, solid state oscillators (Gunn diodes) or electronic tubes (klystrons). These oscillators can be operated in their fundamental mode (up to 120 GHz) but harmonic generation is commonly realized with frequency multipliers up to 500 GHz, and has been used to reach 1 THz on occasions. Backward wave oscillators are available up to 1.2 THz in their fundamental mode. Figures 1 and 2 show typical rotational spectra recorded with this type of sources. Different techniques can be used to work in the THz region ... 

Figure 11.8 A uniform tube with forwards travelling wave, +, and backwards travelling wave u...

This equation is interesting in that it shows the make up of the forward travelling wave in tube As we would expect, this is partly made up of the forward travelling wave from tube k and partly from some of the backward travelling wave being reflected at the junction. The coefficient of in Equation 11.14 is the amount of that is transmitted into the next tube, k+, and is termed the transmission coefficient. The coefficient of j is the amount of that is reflected... 

The effect of a sound source in the middle of the vocal tract is to split the source such that some sound travels backwards towards the glottis while the remainder travels forwards towards the lips. The vocal tract is thus effectively split into a backward and forward cavity. The forward cavity acts a tube resonator, similar to the case of vowels but with fewer poles as the cavity is considerably shorter. The backwards cavity also acts as a further resonator. The backwards travelling source will be reflected by the changes in cross sectional area in the back cavity and at the glottis, creating a forward travelling wave which will pass through the constriction. Hence the back cavity has an important role in the determination of the eventual sound. This back cavity acts as a side resonator, just as with the oral cavity in the case of nasals. The effect is to trap sound and create antiresonances. Hence the back cavity should be modelled with zeros as well as poles in its transfer function. 

We start the LSF analysis by constructing two new transfer functions for the lossless tube. We do this by adding a new additional tube at the glottis, which reflects the backwards travelling wave (whose escape would otherwise cause the loss) into the tube again. As explained in Section 11.3.3, this can be achieved by either having a completely closed or completely open termination. In the closed case, the impedance is infinite, which can be modelled by a reflection coeflBcient value 1, by contrast the open case can be modelled by a coefficient value -1. 

Figure 11.9 Behaviour of forward and backward traveUing waves at a tube junction.

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