Introduction

The problem of phase synchronization in microwave oscillators has been of interest for decades (Schamiloglu, 2012). Creation of coherent high-frequency radiation sources offers great opportunities for the development of modern microwave technology. It allows to carry out the coherent spatial summation of radiated power and to provide the coherent signal accumulation mode in the near- and far-field radar systems. In turn, this can significantly increase the capabilities of receiving and transmitting devices (e.g. noise-to-signal ratio). The use of coherent microwave pulse oscillators will significantly improve the location range resolution. Furthermore, these capabilities allow developing active phased arrays modules.

The analysis of the excitation of microwave oscillations conventionally assumes the decisive role of noise in phase setting, resulting in randomness of the phase (Holliday, 1970). The phase stabilization of microwave oscillators is generally attained by using injection locking and phase locking providing strong electrodynamic feedback between oscillators (Pikovsky et al, 2010). The possibility of obtaining coherent oscillations from electrodynamically independent Gunn oscillators remained undiscovered for a long time. However, one more way has been discovered - to use a modulating voltage pulse (Vvedensky et al, 1975; Vvedensky et al, 1985). Vvedensky with co-authors explain the observed phase stabilization effect by a current spike which arises in the resonator of a Gunn oscillator and sets the initial phase (“shock” excitation). It has been emphasized that a reliable phase stabilization requires a rather short modulating pulse rise time (of about the oscillation period).

Based on the hypothetical possibility of synchronizing an oscillator without feedback, in our later experimental papers dealing with two electrodynamically independent nanosecond X-band Gunn oscillators producing ~ 30 W of microwave power (Gubanov et al, 2010; Konev et al, 2011), we observed phase stabilization and synchronization when the oscillators were excited from a common modulator with the modulating pulse rise time much longer than the oscillation period. The minimum standard deviation of the phase difference between the oscillator signals was ~ 2 ps at a modulating pulse rise time of 6.5 ns (Konev et al, 2013).

These observations have been explained by means of a computer simulation and additional experiments. The results obtained suggest that the phase stabilization of a Gunn oscillator by a modulating voltage pulse, U_GD(t), is governed by the intrinsic properties of the Gunn diode semiconductor. Specifically, the microwave oscillation phase is stabilized, once the semiconductor starts operating in a mode of negative differential resistance and a first high-field domain appears. This corresponds to a threshold voltage U_GD = U_th reached at some point of the modulating pulse leading edge. The discovered effect was rather unexpected for us because we failed to find similar interpretation in the previous investigations.

Theoretical results

The initial experimental work led us to the idea that widely used electrotechnical computational methods (for example, the technique of replacing a semiconductor Gunn diode with an equivalent RCL circuit) are not sufficiently informative for studying the phase stability of a device. So we proposed theoretical studying of electronic processes in Gunn diodes to be based on a numerical simulation of the active layer of the Gunn diode semiconductor crystal in a non-stationary model. All proposed simulations have been carried out using the nonlinear local field model (McCumber & Chynoweth, 1966; Kroemer, 1966). The semiconductor structure of the Gunn diode is considered to be a GaAs one-dimensional crystal with two ohmic contacts at the opposite faces. Its microscopic structure in calculations is given by simplified quasihomogeneous doping profile containing localized inhomogeneity, the so-called "notch" (Figure 1).

In most computations, the quasihomogeneous semiconductor was assumed to have a donor concentration of 10¹⁵ cm^–3. The semiconductor layer diameter and length were 300 $\mathrm{\mu }$m and 12.5 $\mathrm{\mu }$m, respectively. A high field domain was formed due to the existence of a 0.6 $\mathrm{\mu }$m long region of lower donor concentration (0.9·10¹⁵ cm^–3) located 0.6 $\mathrm{\mu }$m away from the cathode ("notch" region). To describe the relation between the electron velocity and the electric field strength, a well-known approximation (McCumber & Chynoweth, 1966) was used with the electron mobility taken equal to 8000 cm²/(V·s) and the saturation drift velocity of carriers at high field (4000 V/cm) equal to 10⁷ cm/s. The diffusion coefficient was taken constant and equal to 200 cm²/s.

Figure 1
Simplified active layer quasihomogeneous doping profile n₀(x) of the Gunn diode semiconductor

Two important cases of connecting Gunn diodes were considered. In the first case, a simulation was performed for the simplest Gunn oscillator circuit consisting of a Gunn diode, a modulator, and a current-limiting resistor (R = 1 $\mathrm{\Omega }$) connected in series (Kozhevnikov et al, 2013).

In the other case, the Gunn oscillator equivalent circuit (with parameters R₁ = 1 $\mathrm{\Omega }$, L₁ = 0.5 nH, C₁ = 0.5 pF, L₂ = 1.2 nH, C₂ = 1.2 pF, R₂ = 0.5 $\mathrm{\Omega }$, L₃ = 0.5 nH) contained a resonator (Figure 2) to take into account the effect of the electric field on the processes occurring in the semiconductor layer (Konev et al, 2013). The units of this circuit and its parameters were specified to match the design of the oscillator used in our experiments (Gubanov et al, 2011) and so that sinusoidal microwave oscillations with a carrier frequency of 10 GHz were excited at the load R₂ simulating the output waveguide. The voltage pulse generated by the modulator had a trapezoidal shape and its instability was simulated by variations in the rise time t_e and the amplitude U₀. These variations produced phase deviations in the microwave pulse. For instance, for the circuit with resistive load, the variation ∆t_e = ± 0.05 ns about an average value of 1 ns gave a current phase deviation ∆t_ph equal to ± 0.016 ns (Figure 3a). For the circuit with a resonator under the same conditions, the ∆t_ph was ± 0.022 ns (Figure 3b).

Figure 2
Equivalent circuit simulating a Gunn oscillator in a resonator

Figure 3
Time dependences of the Gunn diode current at voltage pulse rise times t_e of 0.95 (1), 1 (2), and 1.05 ns (3) for the single-layer structure (a) in the circuit with resistive load and (b) at the load R₂ in the equivalent circuit, U₀ = 20 V.

The simulation has also shown that $\text{∆}$t_ph did not increase on increasing t_e at a fixed U₀ and ∆t_e ≠ 0, whereas an increase in t_e at a fixed ∆t_e = 0 and ∆U₀ ≠ 0 gave an increase in ∆tph. This means that the modulating pulse amplitude noise is the main reason of the oscillator phase instability increase caused by the pulse leading edge rise.

For the circuit with a resonator, the effect of phase stabilization was observed in the background of “shock” excitation in the oscillatory circuit, as demonstrated in Figure 3c. As it was shown (Konev et al, 2013), the only microwave oscillations appeared due to “shock” excitation observed both in the simulation and in the experiment could be considered as some appreciable “noise”. The calculations show that in all studied cases, the oscillation amplitude of the Gunn diode current is about 1 A even in the first period when U_GD exceeds U_th, and this amplitude is noticeably higher than the above mentioned “noise” amplitude (Figure 3b). As a result, the observed phase deviation is defined by the instability of the modulating pulse rise time and amplitude, and the Gunn diode itself provides a stable phase during the excitation of the oscillatory process.

Experimental results

The experimental work was aimed to investigate the possibility of creating synchronized Gunn diodes oscillators. It includes several series of experiments. Most of experimental setups were carried out on nanosecond Gunn oscillators with one and two series-connected 3А762‑type Gunn diodes. The use of two diodes implied, along with phase measurements, a study of the possibility for power enhancement. The oscillators were tuned to a carrier frequency of 10 GHz.

The first group of experiments have been conducted in order to measure the phase delay standard deviation with respect to the modulator pulse rise time (in Figure 4). The measurements were performed with a LeCroy WaveMaster 830Zi oscilloscope. The “delay” function was used to measure the standard deviations σ_t1 and σ_t2 of phase delay with respect to a certain time point during the modulating pulse rise U_DG(t) for one and two series-connected Gunn diodes, respectively. The measuring channel for the modulating pulse had a working bandwidth of 1 GHz and each of those for the microwave signal had a working bandwidth of 13 GHz. The oscilloscope trigger voltage was ~ 500 mV.

Figure 4
Measuring circuit for the standard deviation of phase delay

Figure 5
a) Oscillograms of the modulating pulse and (b) set of 2500 superimposed oscillograms of the modulating pulse and the microwave signal at different voltage rise times.

The minimum standard deviations were σ_t1 = 2.1 ps and σ_t2 = 0.8 ps after excluding the oscilloscope jitter. The peak power with one and two diodes was ~ 30 and ~ 60 W, respectively. The much lower value of σ_t2 compared with σ_t1 suggests that the semiconductor structure has a stabilizing effect on the microwave oscillation phase.

In the experiments, we studied the influence of the voltage pulse rise time (rate of voltage rise dU_GD/dt) on σ_t1. For this purpose, chip inductors L of 8.2 and 82 nH were connected in series with a Gunn diode between the modulator and the oscillator resonance chamber. Figure 5a and Figure 5b show the waveforms of the voltage pulse (1–3) and the microwave signal (4–6) for L = 0 nH (traces 1, 4), L = 8.2 nH (traces 2, 5), and L = 82 nH (traces 3, 6).

In the first case, the minimum standard deviation σ_t1 was 2.1 ps; in the second case, it was 14.5 ps; and in the third case, the phase becomes unstable. The voltage rise times shown in Figure 5a are as follows: $\text{τ}$ ₁ = 4 ns, $\text{τ}$ ₂ = 7.2 ns, $\text{τ}$ ₃ = 16.4 ns. This dependence of σ_t1 on the voltage rise time is explained by the fact that the phase deviation ∆t_ph increases with increasing t_e due to some instability of the voltage pulse amplitude, as found in the simulation.

In the second experiment (Figure 6), we studied the phase synchronization of two oscillators with a peak power of 30 W which were connected in parallel and excited concurrently by a common modulator via strip lines of a geometric length of 120 cm (insulator – fiber glass laminate). This excluded the oscillators coupling via the modulator. Measurements were performed by a special procedure (Konev et al, 2011).

The modulating pulse rise time was 6.4 ns. Figure 7 shows the synchronized oscillograms of microwave signals 1 and 2 for these two oscillators. The oscillograms demonstrate that the microwave oscillation arising on time interval 4 due to the transition of the Gunn diode semiconductor structures to the mode of negative differential resistance is independent of the oscillations appeared within time interval 3 due to the “shock” excitation of the oscillatory circuit. It is seen that signal 2 (green) displays some phase failure.

Nevertheless, after several periods, signal phases 1 and 2 are aligned. On alternately switching off one of the Gunn oscillators, the oscillograms remained unchanged. Thus, a crosstalk-induced synchronization was excluded. The oscillations remained cophased during the whole microwave pulse with a full width at a half maximum of 16 ns.

Figure 6
Experimental measuring circuit for the syncronization of two independent Gunn oscillators

Figure 7
Set of 2500 superimposed oscillograms of two Gunn oscillators

As the measured deviation value was 2.1 ps, so it fits the phase stability criterion for the development of antenna active phased arrays. It was also established that the serial connection of two identical Gunn diodes led to a significant reduction of the standard deviation value as compared to the same value for a single diode. Both of these favorable factors prompted another experimental study of the antenna system wave field (Kozhevnikov et al, 2015). Its visual scheme is shown in Figure 8. The antenna system consists of two synchronized nanosecond X-band Gunn oscillators GO₁ and GO₂ connected to rectangular horns 8 via attenuators 2 and a phase shifter 3. The Gunn oscillators were fed from a single voltage source 1 through strip lines. The horn antennas 8 were arranged in parallel to each other at a distance a = 14 cm between them.

Figure 8
Experimental setup of a wave field measurement of an antenna system

Figure 9
Far-field measurement results:

1, 2 – radiation pattern of each horn excited by an independent Gunn oscillator;

3 – microwave oscillations superposition of two horn antennas powered by a single standard oscillator with 500 us pulse duration;

4 – microwave oscillations superposition of two synchronized nanosecond Gunn oscillators

The receiving antenna 5 was connected to the waveguide semiconductor detector 6 through an adjustable attenuator 2. The detected signal was recorded with the Tektronix-5401 real-time oscilloscope 7 with 1 GHz operating band. The coherent summation of the wave field patterns from two horn antennas powered by a single standard oscillator with a 500 us pulse duration, and powered by two synchronized nanosecond Gunn oscillators is shown in Figure 9.

Conclusions

The studies show that the microwave oscillation phase in the Gunn oscillators is stabilized in an instant when the Gunn diode semiconductor structure passes to the mode of negative differential resistance. In the experiments, we did not find the influence of noises that can perceptibly affect the phase. Appreciable oscillations were only those arising due to the pulse excitation of the oscillator resonance system. Once the threshold voltage is reached and the first high field domain is formed, the current amplitude through the Gunn diode structure increases in a time of about the oscillation period, reaching a near-stationary value which is much higher than the noise and “shock” excitation values. Thus, the oscillation phase of the Gunn oscillators with a microwave power of several tens of watt (e.g., those based on 3А762 diodes), can be stable even at much longer modulating pulse rise time compared to the microwave oscillation period.

The discovered effect and the phase instability measurements results suggest prerequisites for the development of phased arrays. It requires a simple phase synchronization mechanism with only the voltage pulse of common modulator or several synchronized modulators that produce a repeatable modulating pulse without strict limitations on its rise time.

Acknowledgments

The authors thank Dr. Herbert Krömer (Nobel Prize winner, IEEE Fellow) and Valery S. Syuvatkin for their help and fruitful discussion on the problem of phase synchronization phenomenon. Also, the authors express their sincere gratitude to doctors and nurses around the world who fight against COVID-19 infection, not sparing their health and lives for the benefit of all mankind.

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Author notes

Vasily.Y.Kozhevnikov@ieee.org

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FIELD: Microwave Electronics

ARTICLE TYPE: Review paper

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