# Design of the Radio Frequency Section of a Ka-Band Multiple Beam Ladder-Type Extended Interaction Klystron

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## Abstract

**:**

## 1. Introduction

## 2. Design Approach

_{mm}of TE

_{mn}or TM

_{mn}mode of a resonator with sides a and b. Light velocity in free space is represented by c. The relative permeability and permittivity of the medium are represented by µ

_{r}and ε

_{r}. It may be noted that TM mode has been considered where the electric field inside the gaps does not vary much in the beam propagation direction. For efficient RF amplification in the extended interaction cavity, different configurations of the operating mode are possible. Among these modes, the 2π mode of operation has been focused on because this mode generally provides maximum coupling between the RF signal and beam. The pitch length (p) and gap length (G) of the EIK cavities can be obtained using the Floquet theorem of periodicity. Phase velocity v

_{p}of the space harmonics is presented by

_{e}= Beam propagation constant. Considering length of the pitch as p and 2π mode of operation, one may have

_{0}before entering the input cavity is called DC electrons velocity (U

_{0}) in m/s

^{−19}C and m = mass of electron = 9.109 × 10

^{−31}kg. Angular frequency (ω) may be determined using the relation

_{p}), the electrons would continue to oscillate. The frequency at which they would oscillate is the electron plasma frequency (ω

_{p}).

_{0}= 8.854 × 10

^{−12}farad/m and (e/m) = 1.758 × 10

^{11}C/kg. The equation shows that the plasma frequency is a function of the density of electron beam and DC velocity of the electrons. The reduced plasma frequency ω

_{q}is given by the expression

_{B}is the Brillouin field value in Gauss, I

_{b}is beam current in Amperes, V

_{b}is the beam voltage in volts, and r

_{b}is the beam radius in meters.

## 3. Simulation Results

#### 3.1. Design of the Intermediate Cavity

#### 3.2. Design of the Input/Output Cavities

_{e}) of about 38, dictated by the coupling of the cavity with the waveguide.

#### 3.3. Design of the RF Section

_{h}) and lower (f

_{l}) −3 dB frequency points are found to be f

_{h}= 28.66 GHz and f

_{l}= 28.15 GHz. Therefore, the −3 dB bandwidth of the device can be calculated as 510 MHz. Similarly, the −1 dB bandwidth of the device comes out to be 180 MHz. The operating bandwidth of the device can be further increased by employing the stagger tuning of the intermediate cavities, i.e., tuning each individual cavity at slightly different frequencies.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Electric field distribution of the 2π mode (cut-plane view) for the intermediate cavities with CST.

**Figure 4.**Magnetic field distribution of the 2π mode (cut-plane view) for the intermediate cavities with CST.

**Figure 5.**Electric field and magnetic field distribution of the intermediate cavities with HFSS. (

**a**) E-field distribution; (

**b**) M-field distribution.

**Figure 7.**Electric field distribution of the 2π mode (cut-plane view) for the input and output cavities with CST.

**Figure 8.**Magnetic field distribution of the 2π mode (cut-plane view) for the input and output cavities with CST.

**Figure 9.**Electric field distribution and magnetic field distribution of the input and output cavities with HFSS; (

**a**) E-field distribution; (

**b**) M-field distribution.

**Figure 10.**RF cavity considered for simulation: ladder-type multibeam EIK input/output cavities with port.

Parameter | Specifications |
---|---|

Operating Frequency | 28.5 GHz |

Bandwidth | 500 MHz (min) |

Beam Voltage | 4 kV |

Beam Current | 0.196 A |

No. of beams | 4 |

Parameter | Value (mm) |
---|---|

X | 5.8 |

Y | 7.96 |

Z | 4.83 |

H | 5.5 |

D | 0.36 |

GAP | 0.27 |

P | 1.14 |

Parameters | Values from CST | Values from HFSS |
---|---|---|

Resonant Frequency (GHz) | 28.53 | 28.52 |

Q | 720 | 708 |

R (MΩ) | 35.07 | 35.09 |

R/Q | 48.7 | 49.56 |

Parameters | Value (mm) |
---|---|

X | 5.5 |

Y | 9.9 |

Z | 4.83 |

H | 5.1 |

D | 0.36 |

GAP | 0.27 |

P | 1.14 |

A | 5.5 |

B | 2.5 |

h | 1 |

Parameters | Values from CST | Values from HFSS |
---|---|---|

Resonant Frequency (GHz) | 28.53 | 28.52 |

Q | 720 | 702 |

R (MΩ) | 31.85 | 34.04 |

R/Q | 44.2 | 48.5 |

SIGNAL | Port-1 | Port-2 |
---|---|---|

Amplitude (sqrt(W)) | 2.0 | 19.39 |

Peak Power (W) | 4.00 | 375.97 |

RMS Power (W) | 2.0 | 187.98 |

Beam Voltage (kV) | 4.00 | |

Beam Current (A) | 0.196 | |

Gain in Db | 19.73 | |

Bandwidth (−3 dB) | 510 MHz | |

Bandwidth (−1 dB) | 180 MHz | |

Efficiency in % | 23.98% |

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**MDPI and ACS Style**

Maity, S.; Kumar, M.S.; Koley, C.; Pal, D.; Bandyopadhyay, A.K.
Design of the Radio Frequency Section of a Ka-Band Multiple Beam Ladder-Type Extended Interaction Klystron. *Electronics* **2022**, *11*, 3781.
https://doi.org/10.3390/electronics11223781

**AMA Style**

Maity S, Kumar MS, Koley C, Pal D, Bandyopadhyay AK.
Design of the Radio Frequency Section of a Ka-Band Multiple Beam Ladder-Type Extended Interaction Klystron. *Electronics*. 2022; 11(22):3781.
https://doi.org/10.3390/electronics11223781

**Chicago/Turabian Style**

Maity, Santigopal, Madutha Santosh Kumar, Chaitali Koley, Debashish Pal, and Ayan Kumar Bandyopadhyay.
2022. "Design of the Radio Frequency Section of a Ka-Band Multiple Beam Ladder-Type Extended Interaction Klystron" *Electronics* 11, no. 22: 3781.
https://doi.org/10.3390/electronics11223781