Hysteresis

Only two of the three tuning stubs (1+2 or 2+3) are used at one time for matching any particular load reflection coefficient. Each pair covers a specific area in the Polar plot (Fig. 39). There is a boundary between these two sub-areas (the thick red line S1 in Fig. 39), where the central stub (Stub 2) is retracted and either Stub 1 or Stub 3 protrudes (up to the maximum). Slight variations of the load reflection coefficient across this boundary would cause stubs 1 and 3 to move up and down incessantly, without any useful effect. This is, for instance, the case of reflection coefficients (red dots) designated 1 and 2 in plot (a) and reflection coefficients 4 and 5 in plot (b). Because of this "stub swapping", the boundary can be aptly named a “discontinuous boundary”.

Another, slightly less critical, is the “continuous” boundary S2 (thick dark-blue line), where the central stub is inserted and stubs 1 and 3 swap smoothly through zero extension at S2 boundary. The two cases are illustrated in Fig. 40.

An additional inconvenience of stub swapping is that this “great reshuffling” may affect the dynamics and energy efficiency of the microwave process being monitored and controlled.

The concept of hysteresis aims to reduce the incidence of such stub swapping. To quantify hysteresis, the hysteresis distance r_H is introduced. It is the distance in the complex plane by which the load reflection coefficient G_L must intrude into the adjacent area for the system to swap the stubs. The downside is a somewhat greater mismatch, especially if r_H is set too high. In Fig. 39, the hysteresis area around S1 is bounded by the green line and around S2 by the grey line. In plot (a), the swapping does not occur when reflection coefficient variation is 1 ® 2 or u ® v but it occurs in cases 2 ® 3 or v ® w. In plot (b), the swapping will not occur in cases 4 ® 5 or x ® y but it occurs in cases 5 ® 6 or y ® z.

Fig. 39.  Stub swapping and hysteresis. Tolerance circle with radius r_T is also shown in (b).

Fig. 40.  Stub swapping across “discontinuous” boundary S1 (a, b, c), and across “continuous” boundary S2 (d, e, f).

If there is a gap between the two areas or if the areas overlap (Fig. 41), the “permissible distance of intrusion” r_H is measured from the decision curve running through the middle of the gap (or overlap). The gap/overlap can arise only at the discontinuous boundary S1 and its size is a function of the electrical distance of the stubs.

Fig. 41.  Gap between the matchable subareas (a) and their overlap (b). The decision curve (thick red line) runs in the middle of the gap/overlap.

The value of r_H is defined indirectly by the hysteresis angle j_H as follows from Fig. 39. If j_H is expressed in degrees, then hysteresis distance in milliunits is given approximately by

In Homer Autotuner Starting Parameters (Tun.cfg internal file), the hysteresis angle in degrees is defined by the line

HystDg=5        ;Hysteresis in degrees for stubs 1-3 swapping

The default value (5 degrees) yields r_H = 87 mU; other values (computed exactly) can be obtained from Fig. 42. Modifying the default hysteresis value without a good reason is not recommended.

The Autotune page of System Info window shows the hysteresis distance in parentheses.

Fig. 42.  Hysteresis distance r_H as a function of hysteresis angle j_H.

Note that Hysteresis is combined with Tolerance (a circle with radius r_T around the Target (usually zero) reflection coefficient (see Fig. 39b).

When reflection coefficient variations are confined to a relatively small cluster located exactly at one of the swap boundaries (like the reddish area in Fig. 43), the cluster can be moved off by inserting a waveguide section between the Tuner and the load. A waveguide with length 1/8 of the guide wavelength will rotate the load reflection coefficient by 90 degrees. For WR340 waveguide and 2.45 GHz, the required length is about 22 mm; for R-9 (WR-975) waveguide and 915 MHz, the length is about 55 mm.

Using solid-state generators with their exact frequency control, a similar effect can be achieved by changing the operating frequency. The needed frequency shift depends on the distance between the actual load (applicator) and the tuner.

Fig. 43.  Insertion of a waveguide section can move reflection coefficients off the critical area.