
Importance of RF cavities
RF / microwave cavities are of key interest for their use as oscillators, filters and also to expose devices to High Power Electro-Magnetics. One of the key parameter of a RF Cavity (RFC) is its quality factor Q linked to E-field strength that could be reached inside the RFC. However, as soon as a device is introduced inside, both resonant frequency and Q factor are modified. We show here how an optical E-field probe can be used to characterize a RFC while inducing almost no interference.
RF cavity
The schematic drawing of the 2.45-GHz RF cavity is shown below. To reduce the metallic absorption of the walls of the RF cavity, this latter one is silver-plated. When considering only metallic losses, i.e. when neglecting dielectric losses of the E-field probe tip and losses of the two cavity apertures used for the insertion of both coax input and E-field probe, the quality (Q) factor of the RF cavity is expected to have a value of the order of 7000.

Experimental setup for in situ Q factor assessment of the RF cavity
For the characterization of the 2.45-GHz RF cavity, both injected and reflected RF power are measured thanks to RF couplers. A 20-GHz Digital Sampling Oscilloscope (DSO) is used to record the vertical E-field component inside the RF cavity and it is triggered by a small part of the injected signal. For that purpose a longitudinal E-field probe eoProbeâ„¢ EL5-LK is used with an optoelectronic converter (OEC) eoSenseâ„¢ SHF to feed the probe. The Arbitrary Wave Generator (AWG) is followed by a high power amplifier able to deliver up to 50 dBm.

Assessment of the RF cavity inner power density
RF power inside the cavity is equal to product of cavity Q factor by injected RF power and divided by 4πL/λ where:
• L is the effective length of the RF cavity,
• λ is the considered wavelength.
Here we have L = 3λ/2. For a CW injected power of 1W, the steady state RF power inside the cavity could reach an order of magnitude of 370 W if both dielectric and cavity-apertures losses are negligible. Considering the cavity cross section at E-field probe position, this latter power of 370 W corresponds to a rough estimation of a 74 W/cm² power density at probe location.
Both to keep averaged power density below the E-field probe damage threshold (10 W/cm²) and to allow Q factor assessment of the RF cavity, measurements have to be carried out in pulse mode using gated-CW rectangular pulses. Using an optimized duty cycle, the averaged power density could be kept enough below E-field probe damage threshold and, moreover, both cavity filling and emptying times can be assessed.
Measurement of cavity Q factor
Emptying a RF cavity is ruled by an exponential decay of its inner power with a time constant given by Ï„ = Q / (Ï€ f) where f is the cavity resonant frequency.
The same expected time constant of 0.9 μs is governing the filling of the cavity.
A pulse duration of 10 μs has been chosen in order to be sure to reach the steady state of the cavity as 99.995% of cavity filling/emptying is obtained after a wait of 10 τ. For a single shot pulse, both injected signal and vertical E-field component inside the cavity have been recorded (see Fig. below).


An average over a few hundreds of rectangular pulses allow to drastically enhance the signal-to-noise ratio. A fit of the measured E-field strength during the cavity emptying by a function corresponding to a sine wave which magnitude is decreasing exponentially versus time leads to a very accurate assessment of the cavity Q factor. Indeed, we obtain Q = 3678.8 ± 0.7. The residue of the fit (difference from experimental data and fitting function) presents almost the same standard deviation than the noise one observed before of after the pulse with a Gaussian distribution, meaning that the fitting function perfectly fits the data. The very high value of the measured Q factor demonstrates the non-invasive behavior of the E-field probe and its compliance for in situ Q factor assessment of RF cavities. Moreover, the resonant frequency is only very slightly modified by E-field probe insertion.
As illustrated here, Kapteos E-field probe allows monitoring and fine adjustment of RF cavities through real-time assessment of their Q factor versus frequency or any tuning parameter like the penetration depth of the coax input in the present case.
To get a more complete review on this subject please refer to our application note on RF cavity characterization.
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