Effect of the Beam Perveance on the Nonlinear Performance

electron beam and the helix, affecting the non-linear properties of the TWT. The most effective beam parameter to influence the beam-wave synchronism, and therefore the nonlinear properties, is the beam voltage or gun perveance [6,7]. This section will refer to the perveance instead of the voltage since this is specified by the geometry of the electron gun and is therefore more appropriate from the design perspective.

Figures 3.27 and 3.28 show results when the micro-perveance is increased from

higher beam perveance, the AM/AM curves are flatter in overdrive, indicating that the power in the circuit is maintained better beyond saturation, and not lost to the beam. Here, the condition for maximum AM/AM linearity occurs with an increased pitch of 0.81mm. This lies closer to the maximum efficiency condition, thus providing increased output RF power (2dB below the highest that can be achieved). The non-

linear phase shift at this optimum AM/AM condition however is increased (from 5° to

16°), as shown in fig. 3.27b.

Fig. 3.27 Output power and phase versus Fig. 3.28 Output power and phase versus helix pitch for different drive levels with helix pitch for different drive levels with

(a) (a)

(b) (b)

a 0.287µPerv (6KV) beam a 0.355µPerv (5.5KV) beam

When a higher gun perveance of 0.355µPerv is used, as in fig. 3.28a, the optimum

amplitude linearity occurs with a reduced pitch of 0.755mm. The difference between the conditions of optimum linearity and efficiency is therefore reduced further, but the trade-off again is increased phase nonlinearity.

3.5 Conclusions

In this chapter, research has been carried out on how the fundamental parameters of a helix TWT affect its nonlinear performance. The transfer curves of each design were generated, since these determine the nonlinear performance of any quasi-memoryless power amplifier. The carrier-to-intermodulation ratio was also computed.

The initial criterion (in Section 3.2) was to ensure beam-wave synchronism. It was found that the space-charge waves is particularly sensitive to voltage adjustment, while the forward wave is very sensitive to the helix pitch. Therefore any variation of the beam voltage required a pitch adjustment to re-align the forward wave to intersect with the slow space-charge wave.

Basically, the aim is to maximise the operating efficiency at a backed-off power level that gives an acceptable level of carrier-to-IM ratio. The results from this section have found that the basic parameters resulting in an optimum backed-off operating efficiency with C/I3=-21dBc is as follows: -

1. A 6.2KV(or a 0.244µPerv) beam with DC Power of 800W

2. A corresponding helix radius of 0.778mm and a pitch of p=0.902mm to ensure βo = β-

3. A beam filling factor of 0.6

4. The tape width (within the realistic range 0.4<δ/p<0.6) has a negligible effect

on the nonlinear performance.

The design strategy for this case is favourable where broadband is essential; this is shown by the consistency of the results across the bandwidth. The condition where the beam-wave synchronism applies may not include the optimum linearity condition In Section 3.4, the work involved adjusting one design parameter at a time in order to determine the design which corresponds to the most favorable conditions. The helix pitch and beam perveance are the two most effective design parameters for controlling

the forward wave on the helix and the slow space-charge wave respectively. The results reveal how these parameters affect the efficiency and linearity of a helix TWT. Towards power saturation, the non-linearity in the TWT causes a substantial amount of peak RF beam current to be lost at that frequency. It is also shown how the amplitude and phase curves vary across the range of helix pitches as power saturation is approached. The nonlinear TWT processes result in (1) an increased helix pitch for optimum electron bunch intensity and (2) a reduced pitch for maximum conversion efficiency. The results also reveal that the helix design corresponding to the minimum phase shift is independent of drive power up to power saturation.

A major goal in the design of high power TWT amplifying systems is achieving maximum efficiency for an acceptable linearity. This chapter concludes a number of trade-offs: if the helix pitch is designed to correspond to optimum AM/AM linearity, then increasing the beam perveance increases the output power, at the expense of increased phase conversion. If a helix pitch corresponding to optimum AM/PM linearity is selected however, then the output power remains constant at 49dBm as the beam perveance increases, but at the expense of AM/AM linearity.

Single, un-severed uniform structures are not used in practice, because the saturated output gain is at such a level that is too high for stable operation. The design of a practical helix TWT will therefore be covered in Chapter 6. This Chapter however, has explored how the fundamental parameters affect its nonlinearity in a uniform structure. The results provides a basis on which to fully optimise the design of a helix by identifying the design parameters which correspond to the desirable high linearity and high efficiency required in modern communications systems. The work has also contributed to our understanding on the development of nonlinearity in helix TWTs across a range of helix and beam designs. Further research in the next chapter will attempt to uncover the fundamental mechanisms that produce nonlinearity in a TWT.

References

[1] S. F. Paik, “Design Formulas for Helix Dispersion Shaping”, IEEE Trans. on Electron Devices, Vol. ED-16, p.1010, 1969.

[2] A. S. Gilmour, Jr, "Principles of Travelling Wave Tubes", Artech House Inc., p. 259, 1994.

[3] R. O. Jenkins and R. G. Carter, “Optimisation of the Transfer Curves of Multi- Carrier Power Amplifiers for Low Intermodulation Distortion”, in Proc. EPSRC- PREP 2001, April 9-11, 2001.

[4] R. O. Jenkins and R. G. Carter, “High Linearity Broad-band TWT Amplifiers for Satellite Communications Systems”, MRG/2000/1: Report One, Lancaster University, January 2001.

[5] V. Strivastava et. al., “Design of Helix Slow-wave Structures for High Efficiency TWTs”, IEEE Trans. on Electron Devices, Vol. 47, No. 12, December 2000.

[6] R. O. Jenkins and R. G. Carter, “Effect of the Beam Parameters on the Non-linear Performance in Helix TWTs”, in Proc. Conf. Intl. Vacuum Electronics, Monterey, USA, April 2002.

[7] R. O. Jenkins and R. G. Carter, “Design of Helix TWTs for Optimum Linearity”,

Chapter Four: The Development of

Non-Linearity in Helix TWTs

4.1 Introduction

Nonlinearity is a phenomenon that exists in all power amplifiers. Intermodulation distortion, which arises as a result of this, can result in severe degradation of the amplifier’s performance. Since the nonlinear performance of a quasi-memoryless power amplifier can be determined by its AM/AM and AM/PM transfer curves [1], it can be separated into two types: phase and amplitude nonlinearity.

Amplitude nonlinearity occurs whenever there is a limiting of RF power generation at the operating frequency. This power becomes distributed across discrete frequency values. For a single carrier, regrowth occurs at multiple frequencies of the carrier (as harmonics), for a multicarrier signal regrowth also occurs at frequencies spaced by the difference between the carrier frequencies. Across the complete range of helix pitches, the power transfer characteristics are never completely linear i.e. there is always some degree of curvature from a slope of 45° to 0° (saturation point). Therefore, the helix TWT is never a completely linear device: there is always some generation of harmonics and IM products (for multi-tone signals).

Whenever there is a phase delay in the output RF signal, the spectral regrowth of the output signal is increased. Phase delay has traditionally been known to develop naturally from the deceleration of the beam as RF energy is transferred to the circuit [2]. The relationship between the beam velocity and the resulting phase conversion in the helix will be investigated in Section 4.4.4. However, it was shown in Chapter 3.4 that, for a certain helix pitch, a condition occurs where there is a phase shift transition between positive and negative. At this point, the phase shift is zero. It was also shown in fig 3.26 that the helix pitch for minimum phase lag corresponds roughly to a high intensity of electron beam bunching. The manner in which electrons are formed and captured and decelerated by the RF electric field is fundamental to the overall nonlinear performance of the helix TWT. All of this is covered in Section 4.4. which

uses Applegate diagrams to compare results (simulated from the Large-Signal Model) that correspond to conditions of interest e.g. minimum phase lag and high efficiency. This chapter will first introduce the basic models of nonlinearity in TWTs and SSPAs.