Modeling and Experiments of an Injection-Locked Magnetron With Various Load Reflection Levels

In this article, we investigate the performance of an injection-locked 5.8-GHz continuous-wave magnetron with various load reflection levels. The load reflection is introduced to an equivalent magnetron model to theoretically evaluate the system performance. The effects of different load reflection levels on the magnetron’s output are numerically analyzed. Experiments are performed while the load reflection is varied using an E-H tuner between a magnetron and a circulator. A narrower locking bandwidth is observed under constant injection power with increasing load reflection. The proper-mismatched system suppresses its sideband energy, thereby reducing phase noise. The experimental features qualitatively validate the theoretical analyses results. The investigation results also provide guidance for advanced applications in communication and high-energy physics based on injection-locked magnetrons.

💡 Research Summary

This paper investigates how varying load reflection affects the performance of a 5.8 GHz continuous‑wave magnetron that is operated under injection‑locking. The authors first develop an analytical model that incorporates the load reflection coefficient (|Γ|) into an equivalent circuit representation of the magnetron and into a three‑port scattering matrix that includes the circulator used for injection. In the equivalent circuit, the magnetron is approximated by a parallel RLC resonator; the load is expressed as a complex conductance + susceptance (G + jB). When the load is mismatched, the effective conductance becomes G̃ = 1 − 2|Γ|/(1 + |Γ|), which introduces a scaling factor k = 1 − 2|Γ|/(1 + |Γ|). This factor simultaneously scales the output RF voltage (Ṽ_RF0 = V_RF0/k) and the external quality factor (Q̃_ext = Q_ext/k).

The injection ratio ρ̃, which determines the locking condition, is derived from the scattering matrix. It depends on the original injection ratio ρ, the scaling factor k, the magnitude of the reflection coefficient, and two phase‑related parameters α = 1 − |Γ|² and β = cos χ₃ (χ₃ is the circulator port phase difference). By substituting ρ̃ into Adler’s classic locking‑bandwidth condition and introducing γ = cos χ₁ as an auxiliary variable, the authors obtain a cubic equation whose real root yields the modified locking bandwidth. The final closed‑form expression (Eq. 22) shows that the bandwidth shrinks dramatically as |Γ| increases because k and α both decrease, while the term involving β and ρ moderates the effect.

Phase‑noise analysis follows a similar approach. The free‑running magnetron’s spectral width is Δf_b = f_c/Q_L. With a mismatched load, the width becomes Δf̃_b = f_c/(η̃_c Q̃_ext), where η̃_c = G̃/(G̃ + Q̃_ext/Q₀). The phase‑noise power spectral density (PSD) retains the 1/f² dependence but is attenuated under injection locking according to Eq. (27), which includes the modified injection ratio |ρ̃| and the effective 3‑dB bandwidth ω₃dB = ω₀/(2Q̃_ext).

To validate the theory, the authors built an experimental setup using a Panasonic M5802‑KRSC1 magnetron, a high‑power solid‑state amplifier, a circulator, and an E‑H tuner (EMH‑6H) placed between the magnetron and the circulator. The tuner allows systematic adjustment of the reflection coefficient from 0.06 to 0.98, which is measured with a vector network analyzer. Two output‑power levels (≈370 W and 180 W) are examined.

Measurements confirm the model’s predictions. When |Γ| is close to zero (near perfect match), the observed locking bandwidth agrees with Adler’s formula. As |Γ| rises to 0.4, the bandwidth drops by 26 %–75 % depending on the injection ratio (ρ = 0.05–0.20). Phase‑noise measurements show that a moderate mismatch (|Γ| ≈ 0.05–0.5) suppresses noise by roughly 6 dB in the low‑offset region, while a strong mismatch (|Γ| > 0.7) actually degrades the noise floor by up to 20 dB. Increasing the injection ratio to ρ = 0.15 further improves noise suppression, especially at higher offset frequencies (≈1 MHz).

The discussion highlights a trade‑off: a slight load mismatch can be beneficial because it absorbs sideband energy and reduces phase noise, yet excessive mismatch reduces the external quality factor, weakens RF power conversion, and narrows the locking range. The authors suggest keeping |Γ| in the 0.1–0.4 range for optimal performance in applications such as wireless power transmission, phased‑array radars, and high‑energy‑physics accelerators that rely on injection‑locked magnetrons.

In conclusion, the paper contributes (1) a rigorous analytical framework that embeds load reflection into the magnetron’s equivalent circuit and scattering matrix, (2) a modified locking‑bandwidth formula that extends Adler’s condition, and (3) experimental verification that validates the theory and provides practical design guidelines for high‑power, injection‑locked magnetron systems.