Introduction

The vacuum is needed in a MWT to prevent the electrons emitted from the cathode (electron emitter) from colliding with the atoms thereby losing their energy before crossing or passing through the anode of the tube. Besides, the vacuum prevents ionization inside the tube caused by electrons colliding with atoms that produces positive ions, which can strike the cathode and damage it. A high order of vacuum prevents high power tubes from high voltage breakdown and arcing. The vacuum in MWTs depending on their applications (chapter 2) is created in the range of high vacuum (10⁻⁵–10⁻⁷ Torr) to ultra high vacuum (<10⁻⁷ Torr) (where 1 Torr = 1.333 22 millibar = 1 mm Hg = 133 Pascal).

The factors responsible for setting a high-frequency limit of electron tubes are mainly (i) power loss due to skin effect (ii) I² R loss caused by the capacitor charging currents, (iii) radiation losses, (iii) issues related to the thermal management of tiny tubes, (iv) interelectrode capacitance and lead inductance effects, (v) finite transit time of electron flight between electrodes and (vi) constancy of gain-bandwidth product [2–5].

Highly conducting materials should be used to make the tube parts to reduce power loss caused by the skin effect. I² R loss caused by the capacitor charging currents and associated losses can be reduced by reducing the interelectrode capacitances and by increasing the number of shunt paths along which the charging current flows. At high frequencies when the dimensions of the tube become comparable with wavelengths, electromagnetic waves may radiate out from the tube (interaction structure). In order to reduce such radiation losses the spacing between the electrodes needs to be reduced to the order of 1/100 of wavelengths, although at the cost of RF resistance of the conductors. Shielding the tube using a highly conducting shield is very effective in reducing radiation losses. At high frequencies, when the tube uses tiny parts, thermal management should be performed to cool the parts [4].

At high frequencies, the interelectrode capacitances and lead inductances of the tube become comparable with the capacitance and inductance, respectively, of the circuit connected to the tube, a resonant circuit for example, the dimensions of which are reduced at high frequencies [1, 2]. Thus, at such high frequencies, the reactance of the grid and cathode lead each increase and the reactance of the interelectrode capacitance between the grid and the cathode and that between the grid and the plate (anode) each decrease. Also, there can be a resonance between the lead inductance and the interelectrode capacitance of the tube at such frequencies. These high-frequency effects have been studied by the equivalent-circuit representation of an electron tube. For instance, a triode can be replaced by a constant source of current ${g}_{m}{e}_{g}$ between the anode (plate) and the cathode, in parallel with the plate resistance ${r}_{p}$. Here, ${g}_{m}$ is the transconductance of the tube and ${e}_{g}$ the incremental grid-cathode voltage ${E}_{gk}$. We can find the input resistance ${R}_{g}$ of the triode by analyzing the equivalent circuit of the triode connected to a load impedance ${Z}_{l}$. For this purpose, we can consider the effect of only the cathode lead inductance ${L}_{k}$ and ignore the effect of the grid lead inductance. We can also make the approximation that the potential across the cathode lead inductance is much less than ${E}_{gk}$ and ${r}_{p}\gt \,\gt {Z}_{l}+j\omega {L}_{k}$. The grid-cathode capacitance ${C}_{gk}$ can also be taken much larger than the grid-plate capacitance. Thus, such equivalent circuit analysis leads to the following expression for the input resistance ${R}_{g}$ of the triode:

$$\begin{eqnarray}&&{R}_{g}\cong \frac{1}{{\omega }^{2}{g}_{m}{L}_{k}{C}_{gk}}.\end{eqnarray} \tag{ 1.1 }$$

We can then appreciate from (1.1) that when the effect of the cathode lead inductance is much more significant than that of the grid lead inductance, the input resistance ${R}_{g}$ of the triode is inversely proportional to the square of the operating frequency. Therefore, at high frequencies, energy is drawn from the signal source because of the coupling between the grid and cathode circuits caused by the cathode lead inductance [4].

Similarly, we can easily obtain the following approximate expression for the input admittance ${Y}_{g}$ if we set ${L}_{k}=0$ and consider only the effect of ${L}_{g}\ne 0$ [4]:

$$\begin{eqnarray}&&{Y}_{g}\cong \frac{j\omega {C}_{gk}}{1-{\omega }^{2}{L}_{g}{C}_{gk}}\,({L}_{k}=0,\,{L}_{g}\ne 0).\end{eqnarray} \tag{ 1.2 }$$

Interestingly, it follows from (1.2) that at the frequency $\omega =1/{({L}_{g}{C}_{gk})}^{1/2}$, ${Y}_{g}\to \infty$, which corresponds to the occurrence of the resonance of the input circuit caused by the grid lead inductance ${L}_{g}$ coupled to the grid-to-cathode capacitance ${C}_{gk}$. In other words, at this frequency of resonance, the signal input to the triode is short-circuited thereby making the input fail to cause any effect in the plate circuit [3]. The physical dimensions of the tube should be therefore reduced to minimize the effect of the electrode lead inductances and interelectrode capacitances. The reduction of these tube inductances and capacitances will also increase the maximum resonance frequency of a resonator circuit connected to the tube.

Furthermore, at high frequencies, the transit time of the electrons between the cathode and grid becomes comparable with the time period of the modulating electric field in the cathode-grid space. As a result, the field may reverse its phase before electrons traverse this space, thereby causing the electrons to oscillate between the cathode and the grid or return to the cathode. The phenomenon can be easily understood considering the flight of an electron carrying a negative charge accelerated between a large, planar electrode to another similar electrode at a higher potential and studying the induced charges on these two electrodes while the electron is in transit between these electrodes. During the flight of the electron, the positive charge induced on the approaching electrode increases with time and that on the receding electrode decreases at the same time such that the sum of the two induced charges at any instant of time is equal to the magnitude of the electron charge. We can find the induced charge on the approaching electrode at any instant of time by equating the work done in transferring the induced charge to the approaching electrode, raised to a given potential with respect to the receding electrode, to the work done by the electron to move through a distance from the receding electrode at that instant of time. The induced charge so found becomes directly proportional to the distance of the electron from the receding electrode at that instant and, consequently, the induced current obtained by differentiating the induced charge with respect to time becomes proportional to the electron velocity at that instant. However, this electron velocity varies linearly with time since the electron has a constant acceleration, subject to the constant electric field between the electrodes. As a result, the induced current, which is proportional to the electron velocity, also varies linearly with time. Corresponding to this induced current, there will be a current flowing in the external circuit connected to the triode while the electron is in flight between the electrodes, contrary to the notion that some might have that the current would flow when the electron strikes the positive electrode and completes the path through the external circuit. The current ceasing to flow as the electron strikes the positive electrode is essentially a triangular pulse. For an electron beam, the total induced current is the addition of such triangular pulses of current associated with the motion of all the electrons in flight between the electrodes.

Interestingly, current may even be induced in an electrode to which no flows of electrons are collected (for instance, the grid of a triode), if the number or velocity of electrons approaching the grid is greater than the number or velocity of electrons receding from it or vice versa depending on the grid bias voltage. From the concept of the induced current due to a finite transit time of electrons between the electrodes developed here, it can be appreciated by simple analytical reasoning that the grid conductance ${G}_{g}$ is jointly proportional to the square of signal frequency $f$ and the transit time $\tau$ of electrons in the tube [2–5]:

$$\begin{eqnarray}&&{G}_{g}=C{g}_{m}{\tau }^{2}{f}^{2}.\end{eqnarray} \tag{ 1.3 }$$

A finite value ${G}_{g}$, due to the transit-time effect given by (1.3), is responsible for the power loss to the grid. The grid power loss can be reduced by increasing the plate voltage to reduce the value of $\tau$, however, at the cost of the plate dissipation and/or by decreasing the interelectrode spacing, which, however, causes an undesirable increase of the interelectrode capacitance. This calls for the simultaneous decrease of the interelectrode spacing and electrode areas to avoid an increase of capacitance with allowable plate dissipation.

The gain-bandwidth product limitation of an electron tube can be appreciated by studying the output of an electron tube in the form of a tuned resonator circuit comprising a tuning inductance $L$ for the stray capacitance $C$ of the tube. With the increase of the operating frequency, in the limit, the terminating leads form a short loop or a quarter-wave line terminated within the tube by the interelectrode capacitances [2–5]. The circuit analysis of such a tuned amplifier replacing the electron tube by a constant current source, supplying a current ${g}_{m}{e}_{g}$, in parallel with the plate resistance ${r}_{p}$, yields the following expression for the gain-bandwidth product in terms of the transconductance ${g}_{m}$ of the tube and the stray capacitance $C$:

$$\begin{eqnarray}&&\mathrm{gain}\text{-}\mathrm{bandwidth}\,{\rm{product}}=\frac{{g}_{m}}{C}.\end{eqnarray} \tag{ 1.4 }$$

It follows from (1.4) that the gain-bandwidth product of an electron tube amplifier is a constant, being independent of the operating frequency and depending only on ${g}_{m}$ and $C$ of the tube, suggesting that the gain of the amplifier can be increased only at the cost of its gain [4].

The lead inductance and interelectrode capacitance effects, as well as the transit-time effect, which limit the high-frequency performance of electron tubes, have been alleviated in tubes such as the acorn, doorknob and lighthouse tubes [2, 10]. The physical dimensions of these tubes are reduced in the same proportion as the high-frequency limiting effects are reduced without reducing the amplification capability of the tube. Although the operating frequencies of these tubes can be increased to UHF, the reduction of their size entails the reduction of their power handling capability as well. (The acorn tube is so named due to its glass cap resembling the cap of an acorn and the doorknob tube is an enlarged version of the acorn tube that enables the former to deliver higher power than the latter.) The limiting factor of this tube is the power dissipating ability of the grid in the proximity of the cathode [2]. The grid and plate of some of the acorn and doorknob tubes are each provided with two leads so that, if required, a section of parallel-wire line may be connected between each pair of grid and plate leads. Such an arrangement makes it possible to make the lead impedance high, for instance, if a quarter-wave is connected to the lead and is short-circuited at its load end [2]. The lighthouse tube has a planar construction—made of the cathode, grid and plate discs—to reduce interelectrode capacitance and lead inductance, which makes it resemble a lighthouse tower. The interelectrode distances of the tube are made a fraction of a mm and the terminals are made of flat discs welded to the end faces of glass cylinders; the edges of these discs projecting outside the vacuum tube envelope so that they could be connected to sections of coaxial lines of an oscillatory system [2]. The resonant circuit load of the lighthouse tube is constructed as the integral part of the tube (unlike the acorn and doorknob tubes) so that the undesirable effects of the lead inductance and interelectrode capacitance resulting from the tube and the resonant circuit load of the tube being separate units could be alleviated.

The adverse effect of electron transit time in conventional electron tubes, such as the triode, which imparts a finite value of the grid conductance responsible for the power loss to the grid of the tube, can be used to advantage in MWTs. Thus, the concept of the induced current in an electrode of such a tube when the number or velocity of electrons approaching the electrode is different from the number or velocity of electrons receding from it can be used in a MWT such as the multi-cavity klystron. However, as the operating frequency is increased to the millimeter-wave regime, the sizes of the interaction structures of conventional MWTs need to be reduced limiting the device RF output powers. This has led to the development of fast-wave MWTs such as the gyrotron, which can deliver high powers even in the millimeter-wave regime since the sizes of the interaction structures of these devices do not reduce as much as those of conventional MWTs. Further, with the advent of vacuum microelectronic technology, the high-frequency capability of MWTs has been extended to the terahertz regime.

MWTs continue to be important despite competitive incursion from solid-state devices (SSDs) (figure 1.2). MWTs enjoy superiority over their solid-state counterparts with respect to having a lesser heat generated due to collision in the bulk of the device, a higher breakdown limit on maximum electric field inside the device, a smaller base-plate size (determined by the cooling efficiency), higher peak pulsed-power operability, ultra-bandwidth (three-plus octave) performance above a gigahertz, and so on (table 1.2). Further, unlike SSDs, MWTs—being fabricated out of metals and ceramics—are inherently hardened against radiation and fairly resistant to temperature and mechanical extremes (table 1.2). In fact, attempts were made to replace space-TWTs with SSDs, however, with limited success in view of the required $\sim 5\times {10}^{6}$ h MTBF (mean time between failures) in satellite qualified devices. Thus, although SSDs were tried in satellite communication systems during the last decade of the 20th century, for instance, replacing ∼50% TWTs with SSDs in 1995, such replacements declined beyond 1998 to only ∼10% making space TWTs more relevant than their SSD counterparts.

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The book is divided into two volumes comprising of ten chapters. Chapters 1 through 5 are contained in volume 1, and chapters 6 through 10 in volume 2. The present introductory chapter has presented the historical timeline of the development of MWTs (chapter 1, volume 1). Moreover, in this chapter, the order of vacuum required in conventional electron tubes and the high frequency limitations of these tubes have been discussed. How the development of tiny electron tubes and then the advent of transit-time tubes alleviated the high-frequency limitation of conventional electron tubes have also been discussed. An explanation for the sustenance of MWTs despite competitive incursions from solid-state devices has also been given. In the subsequent chapters, the classification and applications of MWTs and trends in their research and development (chapter 2, volume 1), the enabling concepts involved in understanding the principles of MWTs (chapter 3, volume 1), and the formation, confinement and collection of an electron beam in MWTs (chapter 4, volume 1) have been discussed. We have also analytically appreciated the various aspects of beam-absent and beam-present slow-wave and fast-wave interaction structures—the former typically with respect to a helical slow-wave structure and disc-loaded cylindrical waveguide, respectively, and the latter typically with reference to the conventional TWT and the gyro-TWT, respectively (chapter 5, volume 1). A qualitative description has been presented for conventional and familiar microwave tubes, namely, TWTs, klystrons including multi-cavity and multi-beam klystrons, klystron variants, which include reflex klystron, inductive output tube, extended interaction klystron (EIK), extended interaction oscillator (EIO) and twystron, and also crossed-field tubes, namely, magnetron, crossed-field amplifier (CFA) and carcinotron (chapter 6, volume 2). Fast-wave tubes have also received attention encompassing the gyrotron, gyro-backward-wave oscillator, gyro-klystron, gyro-travelling-wave tube, cyclotron auto-resonance maser (CARM), slow-wave cyclotron amplifier (SWCA), hybrid gyro-tubes and peniotron (chapter 7, volume 2). The book has further brought within its purview vacuum microelectronic, plasma-filled and high power microwave (HPM) tubes (chapter 8, volume 2). Handy information about the frequency and power ranges of common microwave tubes has also been given (chapter 9, volume 2) though more such information has been provided at relevant places in the rest of the book as and where necessary. An epilogue at the end summarizes the authors' attempt to elucidate the various aspects of the basics of, and trends in, high power microwave tubes (chapter 10, volume 2).