Measuring Liquids & Semi-Solids: The Open-Ended Coaxial Probe Method

If you are consulting for the biomedical, agricultural, or chemical industries, the standard rules of RF material characterization no longer apply. You cannot machine a block of human tissue, nor can you pour liquid solvents into an open waveguide without ruining your equipment. The industry standard solution for liquids, gels, and semi-solids is the Open-Ended Coaxial Probe.

The Physics of the Fringing Field

The hardware setup is deceptively simple: a rigid, highly polished coaxial line that has been cut completely flat at the end. Unlike an airline or waveguide where the RF wave propagates through the sample, the probe relies on an evanescent "fringing" field.

When the RF signal reaches the flat, open end of the probe, the Electric (E) field arches out from the inner conductor to the outer conductor, creating a small electromagnetic "bubble" at the tip. When you press this flat face against a semi-solid or submerge it in a liquid, the material interacts with that fringing field.

The mathematical extraction utilizes an Aperture Admittance Model. The VNA measures the phase and magnitude of the reflection coefficient (S11). The software then maps that reflection to an equivalent circuit—composed of the fringing capacitance radiating into the material (C₀) and the internal fringing capacitance within the probe's own dielectric (C_f)—to calculate the complex permittivity.

Setup and Calibration Pitfalls

Because you are measuring microscopic changes in fringing capacitance based entirely on a 1-port reflection measurement, your margin for error is razor-thin.

• The 3-Standard Calibration: Standard SOLT calibration at the end of your test cable is insufficient. You must calibrate at the exact aperture of the probe. This requires three known states: Air (Open), a highly conductive shorting block pressed firmly against the tip (Short), and a well-documented Reference Liquid.
• The Temperature Trap: Deionized (DI) water is the most common reference liquid. However, water's permittivity is highly sensitive to temperature (e.g., ε' is ~80 at 20°C but drops to ~78 at 25°C). If your DI water is sitting at 23°C in the lab, but your software's calibration model assumes exactly 20°C, your entire baseline is corrupted. Always use a calibrated digital thermometer in your reference liquid.

Mechanical Errors at the Bench

The physical interaction between the probe tip and the material under test (MUT) is where most engineers fail.

• Beware the Bubbles: The biggest enemy of the coaxial probe is trapped air. Air has a dielectric constant of 1.0. If a microscopic air bubble gets trapped against the flat face of the inner conductor while submerged, the E-field will interact primarily with the air, not the liquid. When submerging the probe, always insert it at a slight angle to allow bubbles to roll off the face.
• The Infinite Sample Assumption: The mathematical model assumes the material is a "semi-infinite medium." This means the sample must be thick enough that the fringing field completely dissipates before hitting the bottom or sides of your beaker. As a rule of thumb, ensure you have at least 5 mm to 10 mm of pure material in all directions extending from the probe tip. If the E-field hits the glass bottom of your container, your data will skew.
• Tissue Compression: When testing biological samples (like muscle tissue or synthetic phantoms), pressing the probe down too hard is a critical error. Excessive pressure squeezes water out of the local cellular structure right at the interface, fundamentally altering the local permittivity you are trying to measure. Use a micrometer stand to gently lower the probe until it makes uniform, uncompressed contact.