Mode Stirrer

This section, in the form of an example, discusses a relatively complex situation when

• a high-ripple rectified signal is used for powering the magnetron, and

• the applicator (e.g., a heating cavity) comprises a mode stirrer.

The example illustrates how to properly set up the signal sampling parameters for autotuning purposes.

The appropriate sampling mode to handle the situation is Rectified.

First, an inspection of the signal waveform should be performed. In principle, this can be done using a microwave detector and an oscilloscope. Nevertheless, Homer in Rectified mode and with transmission of individual samples is even better suited for this purpose. First, select the Rectified sampling mode, then activate Free Run and the transmission of individual samples. Then start measurement and experiment with sampling parameters to arrive at a meaningful, if jittery, display. To steady the display, disable Free Run. The displays may now look like Fig. 28. In this example, this was achieved with sampling time T_s = 1 s and sample count Ns = 3001 (resulting in sampling rate fs = 3 kHz). The horizontal axis is the sample sequential number (proportional to time). Two samples are separated by Dt_s = 1/3000 Hz = 1/3 ms.

Fig. 28.  Waveforms of incident power (green), reflected power (black), and reflection coefficient modulus (red). The x-axis is the sample sequential number.

The slowest periodicity (T₁) the traces exhibit corresponds to about 900 points, i.e., T₁ = 300 ms. The repetition rate is f₁ = 1/T₁ = 3.333 Hz. The origin of these slow oscillations is the mode stirrer rotation.

Rule 1: To arrive at proper mean values, the sampling time T_s should be an integral multiple of the longest periodicity.

In our example, the longest period is T₁, hence T_s = 300 ms, or 600 ms, or 900 ms, etc.

Fig. 29.  Zoomed waveforms of the incident power (green) and the reflected power (black). The red dots show the actual samples.

The traces also exhibit a fine structure (Fig. 29). It is visible after zooming (to zoom, click on the display window, uncheck Automatic and set Xmin, Xmax). The fastest period (T₂) in our case corresponds to about 10 points (the red dots), i.e., T₂ = 3.333 ms. The repetition rate is f₂ = 1/T₂ = 300 Hz. The origin of these oscillations is the three-phase full-wave rectification of the up-transformed power line voltage with frequency f_p = 50 Hz. A 50-Hz periodicity is also discernible in Fig. 29 (six fast ripples).

For proper sampling, there is an additional rule, concerning the sample count n₂ per the fastest ripple period.

Rule 2: The fastest variations must be well covered by sampling (e.g., n₂ = 10 points/period).

Combining Rule 1 and Rule 2 leads to the sample count

In our example, the shortest period T₂ = 3.333 ms is sampled at 10 points, as shown by the red dots in Fig. 29. Choosing the sampling time T_s = T₁ = 300 ms calls for the sampling count

N_s = 10 points ´ 300 ms /3.333 ms + 1 = 901 points.

The sampling rate is then

In Rectified mode, the sampling time T_s is not defined directly but in terms of the number N_p of the ripple periods constituting T_s. To obtain the desired T_s, set N_p to

In our example N_p = 0.3 s ´ 300 Hz = 90.

Since, as seen in Fig. 28, all samples are valid (the incident power never drops close to zero):

• It is best to switch Free Run on (to also handle very low-ripple signals).

• You can set the Acceptance level L_acc = 0. However, to handle cases where ripple goes as low as zero (like one-phase half-wave rectification), a better choice is to set a small but nonzero Acceptance level, e.g., L_acc = 10% or 20%. Then meaningless reflection coefficients resulting from noise (when signal level is near-zero) will be disregarded.

There are additional important rules in the Mode Stirrer situation:

Rule 3: For tuning, averaged reflection coefficient must be used. This is automatically taken care of when selecting Rectified or Pulsed modes of sampling.

Rule 4: The mean reflected power should not be computed from the mean incident power and the mean reflection coefficient but as the average of the reflected powers for individual samples. This is again automatically taken care of when using Rectified or Pulsed modes of sampling.

Application of Rule 3 is illustrated in Fig. 30, showing trajectories of reflection coefficient. The red trace is a reflection coefficient before tuning (tuning stubs completely withdrawn). The oscillations along a deformed circle are caused by the mode stirrer. When tuning based on the mean value is activated, the locus moves closer to the center (blue trace). No individual point is perfectly matched and the size of the pattern has slightly increased, yet this is the a uch better situation. The trace is optically not centered: this is because the samples spacing may be denser in certain locus portions, as the detail on the right reveals. Thus, the “center of mass” of the trace is offset from an intuitive center.

The importance of Rule 4 is also evident from Fig. 30. It shows that while the mean value of the complex reflection coefficient in tuned state is practically zero, the mean magnitude M of the reflection coefficient is approximately M = 0.07 (the “radius” of the blue trace). Consequently, the mean reflected power, which is proportional to M², is about 0.5% of the incident power. Using the zero mean reflection coefficient for the computation would incorrectly result in zero reflected power.

This is the reason why, for instance, the CW sampling mode, albeit configured to take samples exactly as in the Pulsed mode, would deliver a false (i.e., nearly zero) mean reflected power.

Fig. 30.  Left: Reflection coefficient locus before tuning (red) and after tuning using mean value (blue). Right: A portion of the blue trace zoomed.

Appropriate settings for the Mode Stirrer situation in our example are summarized in the following table:

Sampling method (Waveform)	Rectified
Free Run	TRUE
Triggering level	(Irrelevant)
Ripple frequency (fr)	300 Hz
Number of ripple periods (Np)	90
Sampling time (Ts)	300 ms: Computed by Homer as Np/fr
Sample count (Ns)	901: This results in 10 samples per a ripple period
Sampling rate (fs)	3 kHz: Computed by Homer
Acceptance level (Lacc)	0 to 20%
Frequency counting time (Tc)	Arbitrary, e.g., 20 ms (if the power never drops to zero)

If the microwave power ripple drops close to zero during some intervals, false frequency readings may be experienced in the case of Free Run, which may result in incorrect reflection coefficient and power outputs. If triggering for some reason does not help, one can disable the counter and set an appropriate Substitute Frequency in the Homer menu.