PHASE MODULATION OF THE MAGNETRON
5.1.4 Effect of the anode current level
Figure 5.9 shows this transient response for differing anode currents of 317 mA, 265 mA and 210 mA.
138
325mA 257mA 335mA
355mA
175mA 245mA
275mA
280mA
210mA 150mA 245mA
230mA
(a) 317 mA (b) 265 mA (c) 210 mA
Figure 5.9 Phase modulation with different anode currents,
Heater Power 33W, Injection Level -29dbc
A heater power of 33W is used again because the effect of 50 Hz and 100 Hz ripples becomes very large on the injection locked magnetron phase at higher heater power. It was not possible to obtain stable phase shift keying for anode currents below 200 mA. In
139 this region the pushing curve has a high gradient hence the frequency modulation for our level of anode current ripple (~|13%) was very large.
For low anode currents, the oscillation amplitude of the phase is somewhat higher when the injection phase is advanced compared with when the injection phase is retarded.
5.2 Phase Modulation with Un-matched Load
When the magnetron output is loaded and a certain amount of power is reflected back, it is observed that the transient behaviour of the magnetron RF output varies depending upon the phase angle of the reflected power. Some dependency of dθ/dt and VRF(t) on the load (G+jB) is obvious from equations (5.4) and (5.7). Experimental results in this regard are shown in Figure 5.10 where 10% of the output power is reflected back into the magnetron with differing reflection angles set apart by 30o steps (appropriate for
encompassing the complete load dependent behaviour).
The top of each plot is labelled with reflection angles with respect to the magnetron’s plane of reference (where the magnetron efficiency is at its maximum). As described in Chapter2, the magnetron is maximally efficient at the reflection angle about 135o w.r.t.
waveguide launcher. Hence 0.1∠0o on top of Figure 5.10a represents 10% reflection from the stub tuner at 135o w.r.t. to the waveguide launcher. The heater is kept at 44W
and results were recorded for two different anode currents near to 340mA and 270mA. An injection level of -29 dBc has been used for all the plots in Figure 5.10. These plots
140 are 180o phase shifted compared with the plots in the previous section in order to obtain a
good coverage of the DC coupled anode current and the magnetron output phase at the
same time.
The load effect on the phase modulation of the driven magnetron can be divided into
three categories, in-phase reflection, quadrature phase reflection and out of phase reflection. When part of the magnetron output is reflected in phase or within +/- 30o of
this region, the peak-to-peak oscillation in the anode current is considerably less, about half as much, compared with the case when the load is matched. Also the overshoot in the
magnetron output phase response is relatively small.
As the phase of the reflected signal becomes in quadrature with the magnetron plane of
reference, the level of the anode current oscillation increases and keeps increasing until it reaches the out of phase reflection region, as shown in Figures 5.10c and 5.10d. A very interesting thing to notice in the phase quadrature zone is that the response tends to
become quite symmetric for phase retard and phase advance when the anode current is low. The phase of the reflected wave has an effect on the net field in the anode cavities and hence on the relative movement of the charge spokes (w.r.t. the RF peak). It is also interesting that the oscillations in the anode current and more prominently in the magnetron phase take longer to decay for low anode currents. For higher anode currents
i.e. when the spokes experience higher Retarding field (spoke near the middle of the cavity and α is minimal) the magnetron phase response still remains asymmetric for phase retard and advance just like when the load is matched.
141 The level of oscillation in the anode current is the highest when the reflected signal is nearly out of phase (close to 180o w.r.t. magnetron’s plane of reflection), a bit more than
when the load is matched. For the reflection angles 0.1∠150oand 0.1∠−150o Figures 5.10f and 5.10h show that we have very large oscillation of the anode current. This anode
current oscillation becomes so large at the reflection angle 0.1∠180othat the corresponding shift in the natural frequency of the magnetron is beyond the lock in range of the Injection level (-29dBc) and destabilises the Digital frequency control on the magnetron, hence the Injection + FLL system stops working altogether. This effect of
extremely large overshoot in the anode current is more pronounced at lower anode currents where the pushing curves slope is greater. It is represented as ‘No Result’ in Figure 5.10g. Interestingly we do not see a large overshoot in the magnetron phase
response in the region of anti-phase reflection (reflection angles 0.1∠150oto0.1∠−150o), albeit large anode oscillations
From Figures 2.4 and 2.5 we see that the pushing curves have a significant frequency shift as the phase of reflected power is varied close to quadrature. This dependency could be relevant to explaining some aspects the oscillatory response.
142
o
0 1 .
0 ∠ w.r.t.. magnetron plane of reference (135o w.r.t. Waveguide Launcher )
(a) 339mA 265mA
o
30 1 .
0 ∠ w.r.t.. magnetron plane of reference (105o w.r.t. Waveguide Launcher )
(b) 335mA 268mA
o
60 1 .
0 ∠ w.r.t.. magnetron plane of reference (75o w.r.t. Waveguide Launcher )
(c) 342mA 267mA
Figure 5.10 Effect of unmatched load on Phase modulation of the injection locked
143
o
90 1 .
0 ∠ w.r.t.. magnetron plane of reference (45o w.r.t. Waveguide Launcher )
(d) 342mA 265mA
o
120 1 .
0 ∠ w.r.t.. magnetron plane of reference (15o w.r.t. Waveguide Launcher )
(e) 338mA 267mA
o
150 1 .
0 ∠ w.r.t.. magnetron plane of reference (-15o w.r.t. Waveguide Launcher )
(f) 335mA 276mA
Figure 5.10 Effect of unmatched load on Phase modulation of the injection locked
144
o
180 1 .
0 ∠ w.r.t.. magnetron plane of reference (-45o w.r.t. Waveguide Launcher)
(g) Injection+ FLL stops working at this load
o
150 1
.
0 ∠− w.r.t.. magnetron plane of reference (-75o w.r.t. Waveguide Launcher)
(h) 335mA 280mA
o
120 1
.
0 ∠− w.r.t.. magnetron plane of reference (-105o w.r.t. Waveguide Launcher)
(i) 339mA 275mA
Figure 5.10 Effect of unmatched load on Phase modulation of the injection locked
magnetron (Continued)
145
o
90 1 .
0 ∠− w.r.t.. magnetron plane of reference (-135o w.r.t. Waveguide Launcher)
(j) 336mA 265mA
o
60 1 .
0 ∠− w.r.t.. magnetron plane of reference (-165o w.r.t. Waveguide Launcher)
(k) 348mA 270mA
o
30 1 .
0 ∠− w.r.t.. magnetron plane of reference (165o w.r.t. Waveguide Launcher)
(m)342mA 270mA
Figure 5.10 Effect of unmatched load on Phase modulation of the injection locked
146 Digital frequency control on the magnetron through the power supply does not have an effect on the second order response of the driven magnetron phase as the loop bandwidth
is very small (a few KHz) and it cannot contribute to the large sub-microsecond phase transitions. It only kicks in when the anode current (hence the natural frequency of the magnetron) shifts by a large amount and it is beyond the lock-in range of the injection
signal power. This is explained earlier in this chapter for Figure 5.10g.
Results presented in this chapter add a new dimension towards understanding the behaviour of an injection locked magnetron. Although not fully understood and explained
yet, they can be used to develop a complete model for the dynamic behaviour of the magnetron when driven by an external injection source. We have seen that the phase of the magnetron output follows the phase of the injection signal and the rate of change of
phase mainly depends upon the heater power, injection level and the anode current. This feature can be used for many applications such as fixed power long distance data transmission and phase stable RF sources by correcting the effect of the power supply
ripple and other inputs on the magnetron output phase via the injection phase. The latter is discussed in detail in the next chapter.
145