Theoretical Research on a D-Band Traveling Wave Extended Interaction Amplifier

I.   Introduction

Millimeter wave and terahertz radiation sources are finding increasing use in radar imaging, communications, medical imaging, biological research, and materials scanning [1]–[4]. Due to their high gain and wide bandwidth, vacuum electron devices are finding new traction in the development of a new generation of millimeter wave and terahertz radiation sources [5], [6].

At present, traveling wave tubes (TWTs) and extended interaction klystrons (EIKs) are two of the most commonly used vacuum electronic millimeter wave and terahertz radiation sources [7]. Both types of devices have superior performance in many aspects, however a number of technical challenges still exist. Specifically, TWTs have, comparatively, very wide bandwidths [8], [9], but their attenuation of high frequency signals increases noticeably when the operating frequency reaches terahertz band. As a result, numerous periods are needed to achieve the required high gains. In the terahertz band, the transverse dimensions of incumbent devices are typically of the order of hundreds of μm and the overall longitudinal dimensions are relatively much larger, conventional millimeter-wave and terahertz TWTs are extremely difficult, time consuming and costly to fabricate and implement. EIKs have higher gain at a same unit length, but the bandwidth is limited by the characteristics of the input and output cavities. In recent years, a variety of research institutions have made considerable progress in the development of EIKs [10]–[12]. And the Canadian CPI Company has developed and manufactured a series of millimeter-wave and terahertz EIKs. Some of the EIKs reach a relative bandwidth of 1% at Ka-band and lower frequencies, but the typical relative bandwidth of the EIKs is basically in the range of 0.1%–0.3% at W-band and above frequencies. Besides, some multi-mode EIKs have a relative bandwidth approaching 2%, but the multi-mode phenomenon results in lower signal purity, compared with single-mode EIKs [13]. In general, although notable progress has been made, bandwidth limitation at high frequency remains the most crucial technological challenge in the development of EIKs.

For the development of high-gain, yet compact millimeter wave and terahertz radiation sources, a traveling-wave extended interaction amplifier (TWEIA) is proposed in this paper. Folded waveguide structure is adopted as the input and output circuits to effectively expand the modulation bandwidth, and unequal-length slots cavities are adopted as the intermediate circuit to increase the gain.

II.   Design and Simulation

A relative bandwidth of 1% in the D-band is sufficient for many applications [1]–[3]. The design is therefore targeted to achieve such a bandwidth within three cavities, so that the longitudinal length of the beam-wave interaction circuit could be shorter. Specifically, the beam-wave interaction circuit proposed in this paper consists of two commonly applied structures: the folded waveguide slow wave structure and unequal-length slots extended interaction cavities, as shown in Figure 1. Both the left and right sections consist of folded waveguide, which operate as the input and output of the circuit, respectively. At the end of the input section, an attenuator is attached to absorb reflected signals.

Figure  1.  Schematic of the beam-wave interaction circuit.

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The input and output sections both operate in traveling wave mode, while the intermediate cavities operate in $\pi$-mode. The high coupling impedance, diverse central frequencies and the frequency-selective characteristics of the cavities allow the electron beam, which is preliminary modulated in the input section, to interact efficiently with the signal. It should be ensured that the operating bands of the folded waveguide structures and the cavities partially overlap, so that the beam-wave interactions occur throughout all structures. Therefore, matching the beam-wave interaction frequencies and the synchronization conditions of the two mentioned structures is of central importance.

The single-period structure of the folded waveguide is shown in the inset of Figure 2, and the structural parameters are noted as follows: waveguide port length $a$, waveguide port width $b$, electron beam channel diameter $h$ and the length of the period $P$. The engineered values of these parameters are shown in Table 1, to ensure a central operating frequency of 140 GHz, which is in accordance with the overall design requirement in the D-band. The dispersion curve can be determined by modifying the phase shift on the periodic boundaries. As shown in Figure 2, the ordinate of the intersection of the 21.5 kV beam-line and the dispersion curve is approximately 140 GHz, indicating that the electron beam accelerated by this voltage can interact adequately with the operating mode near this frequency.

Figure  2.  Dispersion curve and the operating beam line of the periodic SWS (The inset: 3D model of the folded waveguide).

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Table  1.  Folded waveguide geometric parameters

Parameters	Value (mm)		Parameters	Value (mm)
a	1.17		h	0.30
b	0.20		P	0.80

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The simulation is carried out under the conductivity $\sigma=2.5\times10^7\ {\rm S/m}$, and the results of the S-parameters are shown in Figure 3. The $S_{11}$ of the developed folded waveguide is less than 0.06 when the frequency is between 139 GHz and 141 GHz, which meets the transmission requirements in the operating bandwidth.

Figure  3.  Scatter parameters of the folded waveguide (The inset: 3D model of the folded waveguide structure).

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The structure of the extended interaction cavities is shown in Figure 4. The adjacent slots in the cavities have different width and are named as long-slots and short-slots, respectively. The slots are placed alternately along the longitudinal direction, and their widths are defined as $g_{x1}$ and $g_{x2}$, while the ratio of $g_{x1}$ and $g_{x2}$ is defined as $\alpha = g_{x1}/g_{x2}$.

Figure  4.  Schematic diagram of the unequal-length slots cavity. (a) 3D model; (b) top cross-section.

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Parameters of the cavities such as coupling coefficient $M$, characteristic impedance $R/Q$, operating voltage $V$, and operating frequency $f$ are all important in the design and optimization.

Coupling coefficient and characteristic impedance are defined by (1) and (2) [14], where $E_z$, $W_s$, ${\beta}_e$ and $\omega$ are the axial electric field intensity, total stored energy, wave constant and angular frequency, respectively. On this basis, the effective characteristic impedance $(R/Q) ·M^2$, which describes the strength of the electromagnetic field coupling with the electron beam, is calculated. Considering that the $\pi$-mode has higher coupling coefficient and effective characteristic impedance [15], and the frequency spacing ${\Delta}f$ between the $\pi$-mode and the nearest competitive mode is wider, the $\pi$-mode is set as the operating mode.

Figure 5(a) shows the change of frequency spacing $\Delta f$ and effective characteristic impedance $(R/Q) ·M^2$ when $\alpha$ is varied. $\Delta f$ increases significantly after a slight decrease, with a minimum at $\alpha$= 1.03; $(R/Q)·M^2$ first increases and reaches a peak at $\alpha$= 1.18, then decreases slowly, indicating the interaction between the electron beam and the signal is the most effective when $\alpha= 1.18$. However, the reduction of the effective characteristic impedance is not appreciable when $1.18\leq\alpha\leq1.39$, so $\alpha$ in this range is acceptable when designing the extended interaction cavities. Figure 5(b) shows the influence of the length of the cavity gaps, denoted as $g_z$, on the effective characteristic impedance $(R/Q) ·M^2$ and coupling coefficient $M$. $(R/Q) ·M^2$ increases gradually slower when 0.14 ${\mathrm{mm}}\leq g_z\leq 0.15\; {\mathrm{mm}}$. Taking the trend of $M$ shown in Figure 5(b) into account, the selected value of $g_z$ is from 0.13 mm to 0.14 mm, which lies within machinable tolerances. The preliminary structural parameters of the intermediate extended interaction cavities are listed in Table 1.

Figure  5.  Influence of (a) $\alpha$ on effective characteristic impedance $(R/Q) ·M^2$ and frequency spacing $\Delta$f, and (b) $g_z$ on effective characteristic impedance $(R/Q) ·M^2$ and coupling coefficient $M$.

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As mentioned above, the interaction circuit should be compact and has a certain bandwidth and gain. Therefore, it would be more appropriate for the circuit to be composed of three idler cavities. Since the length of the period, denoted as $P$, is the key structural parameter that influences the central frequency [16], it is possible to obtain three cavities with diverse operating frequencies by varying $P$ alone. The optimal values of $P$ and other structure parameters of the cavities are listed in Table 2, and the corresponding unloaded quality factor $Q_0$ and other high frequency characteristics of the cavities are listed in Table 3, which also shows the maximum frequency interval of the cavities is 1.19 GHz.

Table  2.  Geometric parameters of the cavities

Parameter	Value (mm)		Parameter	Value (mm)
$g_z$	0.14		$P_1$	0.60
$g_{x1}$	0.94		$P_2$	0.58
$g_{x2}$	1.18		$P_3$	0.56

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Table  3.  Characteristic parameters of the cavities

Parameter	Cavity 1	Cavity 2	Cavity 3
$f$ (GHz)	140.95	141.73	142.14
$M$	0.612	0.632	0.626
$(R/Q)M^2$ ($\Omega$)	43.75	46.01	41.16
$Q_0$	369.37	366.68	352.33

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The beam-wave interaction circuit, as illustrated in Figure 1, is composed of the two structures mentioned above. The input and output structures of the TWEIA consist of 10 folded waveguide periods each. The lengths of the drift tubes along the electron propagation direction are 0.80 mm, 2.40 mm, 1.20 mm and 0.60 mm, respectively. PIC simulations are carried out under an operating voltage of 21.5 kV, 0.3 A beam current and 5 mW input power, the conductivity is set to $\sigma = 2.5\times 10^7$ S/m The results show that the maximum output power reaches 351 W at 139.7 GHz, as shown in Figures 6–8, with a gain of 48.4 dB and a relative 3-dB bandwidth over of 1%, from 139.22 GHz to 140.64 GHz.

Figure  6.  Output power signal as a function of time when the frequency of the input signal is 139.7 GHz (The inset: frequency spectrum of the output signal).

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Figure  7.  (a) Beam bunching simulation result; (b) Phase-space diagram (when the output power is stable and the frequency of the input signal is 139.7 GHz).

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Figure 6 shows the output power signal corresponding to the input signal of 139.7 GHz. The spectrum of the output signal is shown in the inset of Figure 6, which shows the frequency purity of the output signal at 139.7 GHz, identical to the frequency of the input signal. And Figure 7 shows the beam bunching within the structure and the electron phase space diagram when the output signal is stable.

Figure  8.  Output power and gain versus frequency.

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By altering the frequency of the input signal, the impact on the frequency, output power and gain are as shown in Figure 8. The curves are typically M-shaped, and the extreme points lie at 139.7 GHz, 139.9 GHz and 140.5 GHz, respectively. From the curves in Figure 8, it can be calculated that the 3-dB bandwidth reaches 1.42 GHz (139.22–140.64 GHz).

III.   Conclusion

A high gain and compact millimeter wave and terahertz radiation source amplifier is developed in this paper. Folded waveguide structures and unequal-length slots extended interaction cavities have been optimized allowing for the design of a compact beam-wave interaction circuit of a D-band TWEIA. The maximum output power of the circuit is 351 W, while only 5 mW of input power is required. With a maximum gain of 48.4 dB and a relative 3-dB bandwidth of over 1%. The bandwidth could be further extended by adding more intermediate cavities with different operating frequencies to the beam-wave interaction circuit. The developed beam-wave interaction circuit of this D-band TWEIA benefits from a shortening to 26 mm in length compared with conventional TWTs, making the electro-optical and magnetic systems considerably easier to be implemented.