*4.4. Cycle Resolved Pressure Assessment*

Figure **??** shows cycle resolved raw data from a single cycle from the SOP with a set pressure of the DWPG of 30.7 kPa; Figure **??**a displays the measured beat frequency, *f*(*t*), Figure **??**b shows the changes in cavity mode numbers, Δ*qi*(*t*), and Figure **??**c illustrates the calculated shift of the unwrapped beat frequency Δ*fUW*(*t*). This shows that although mode jumps are seen as steps in the beat frequency in Figure **??**a, when the measured shifts in cavity mode numbers displayed in Figure **??**b is taken into account, the unwrapped beat frequency illustrated in Figure **??**c is a continuous function. The gas modulation had a cycle time of 200 s, distributed over a filled and an evacuated measurement cavity cycle, both lasting 100 s (denoted *tI* and *tI I* in Figure **??**, respectively).

The filled measurement cavity cycle was initiated at 0 s by the closing of valve *VS*.2 and an opening of valve *VS*.1, which results in a fast increase of the pressure. The MFC was then filling the system (resulting in a constant increase of the pressure) for a time of 20 s (referred to as *tf* in Figure **??**), until the set pressure was reached.

After the set pressure was reached, the piston in the DWPG was floating, which resulted in a stabilization of the pressure at a constant pressure for 80 s (denoted *ts* in Figure **??**, given by *tI* − *tf*). The filled measurement cavity assessment, *fUW*(*n*, *t*), was measured during the last 20 s of this period.

Thereafter, valve 1 was closed and valve 2 was opened, which resulted in a fast decrease in pressure (an increase in the unwrapped beat frequency). Both cavities were then evacuated for 100 s. The empty measurement cavity assessment, *fUW*(*n* = 1, *t*), was measured during the last 20 s of this period. After this, the cycle was repeated.

These signals were then converted into pressure by Equations (2)–(4) and (**??**). Figure **??** shows the cycle resolved pressure calculated by these means from the *fUW*(*t*) data displayed in Figure **??**. Note that the data in Figure **??** include several mode jumps during the filling (*tf*) and the emptying stages that produced short "sparks" in the unwrapped pressure. Since the evaluation procedure did not use data points during the these stages (i.e., when the mode hops take place), they did not affect the final assessments.

**Figure 5.** The time evolution of (**a**) the raw beat frequency [*f*(*t*)]; (**b**) the evaluated shift in mode number (Δ*q*1(*t*) and Δ*q*2(*t*)); and (**c**) the corresponding unwrapped beat frequency (*fUW*(*t*)) from the SOP over a 200 s long modulation cycle. For descriptions of the various time intervals of the modulation cycle, see the caption of Figure **??**.

**Figure 6.** The time evolution of the pressure assessed in the SOP during the 200 s long gas modulation cycle displayed in Figure **??**, *P*(*t*). *tI* represents the time of filling and *tI I* the time of evacuation during the modulation cycle, here set to 100 and 100 s, respectively. *tf* is the time at which the MFC was re-filling the DWPG, and *ts* is the time during which the DWPG was stabilizing the pressure (i.e., when the piston was floating).
