Table 1 Design parameters for the UroSleeve with the integrated antenna and pressure sensor as well as the external reader antenna used – σ: internal residual stress, E: Young’s modulus, ν: Poisson’s ratio, ε: dielectric permittivity R: DC resistance, L: inductance, f_r: reflectance peak of the external reader antenna

Parameter	Size [µm]	Relevant parameters
Tesla-valve enabled touch mode capacitive pressure sensor
Sensor chip
Width	870
Length	3200
Substrate thickness	500
Sensor membrane		σ 26 MPa
Radius	250
Au thickness	2.85^a	E 78 GPa, ν 0.44
Ti adhesion layer thickness	0.02	E 116 GPa, ν 0.32
Parylene C thickness	4.6	E 2.76 GPa, ν 0.40
Sensor gap (before deflection)	2.8
Sensor dielectric
Sensor dielectric Si₃N₄ thickness	0.275	ε 9.7^b
Tesla-valve channels		4 Channels/Cavity
Overall length	178
Overall width	420
Channel entrance width	10
UroSleeve 9 loop spiral antenna		R 1.4 ohm, L: 1.97 µH @ 15.1 MHz, f_r 18.1 MHz
Length	50,000
Outer spiral width	8270
Inner spiral width	2110
Cu Line width	200
Cu Line thickness	70
Polyimide substrate thickness	25
Assembled bend curvature^c	2790
External reader 10 loop inductor		R 0.1 ohm, 4.5 µH @ 16.7 MHz, f_r 28.5 MHz
Overall length	50,000
Overall width	8000
Wire thickness	510.6	24-gauge magnetic wire

^aThe fabricated sensor had a 2.85-µm thickness based on FEM simulation to place the sensor in touch mode when the sensor cavity is under vacuum
^bThe constant was experimentally measured using the capacitance and the known surface area of characterization structures
^cThe curvature is based on the assembly of a 6-Fr double-J ureteral stent

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