1. The Physics of Reflection: Dielectric Constant ($\epsilon_r$)

Radar level measurement technology (whether FMCW or Pulse) relies entirely on the principle of electromagnetic reflection. When the radar microwave pulse hits the surface of a medium, a portion of the energy is reflected back to the antenna, and the rest penetrates into the medium. The ratio of reflected energy depends fundamentally on the change in impedance between the vapor space (usually $\epsilon_r \approx 1$) and the liquid product.

This relationship is governed by the Reflection Coefficient ($\Gamma$), which is derived from the Dielectric Constant ($\epsilon_r$) of the medium:

• Conductive / Polar Liquids (Water, Acids, Bases): These have high dielectric constants ($\epsilon_r > 20$). Water has an $\epsilon_r \approx 80$. Substituting this into the formula gives a very high reflection coefficient. Almost all the radar energy bounces back. This makes water-based applications the easiest for radar, offering strong, distinct echo peaks even at long ranges (30m+).
• Hydrocarbons / Non-Polar Liquids (Oil, Diesel, LPG, Solvents): These present the greatest challenge. Typical hydrocarbons have $\epsilon_r$ values between 1.4 and 3.0.
  • Example ($\epsilon_r = 2.0$): $\Gamma = (\sqrt{2}-1)/(\sqrt{2}+1) \approx 0.17$. The Power Reflection is $\Gamma^2 \approx 0.03$, meaning only 3% of the signal is reflected, while 97% penetrates the liquid.

Engineering Implication: For low dielectric fluids ($\epsilon_r < 2.0$), the surface return is extremely weak. If the tank has a flat metallic bottom, the radar may see through the liquid and track the bottom echo instead, reporting a "Tank Empty" status when full. Solution: Use a **Stilling Well (Standpipe)** or **Bypass Chamber**. The metal tube concentrates the radar energy, preventing beam spread and significantly boosting the signal return.

2. Frequency Selection: 6 GHz vs 26 GHz vs 80 GHz

Choosing the right radar frequency is a trade-off between beam focus, condensation immunity, and foam penetration.

A. 6 GHz (C-Band) - The Legacy Workhorse

• Pros: Long wavelength (~50mm). Excellent at penetrating heavy foam, condensation, and turbulent surfaces. Ideally suited for dirty process tanks with agitators where coating on the antenna is likely.
• Cons: Very wide beam angle (20°-30°). Requires large antennas (6-8") to get a decent signal. Prone to false echoes in narrow tanks.

B. 26 GHz (K-Band) - The Standard

• Pros: Good balance. Wavelength (~11mm) allows for smaller antennas (3-4") with decent beam angles (~10°). Standard for water treatment and general chemical storage.
• Cons: Can struggle with very thick, dense foam.

C. 80 GHz (W-Band) - The Precision Expert

• Pros: Tiny wavelength (~3mm). Allows for extremely focused beams (3°-4°) using small 3" lenses. This "Laser-like" focus avoids internal tank obstructions like heating coils, ladders, and agitators. Excellent for tall, narrow silos (up to 100m).
• Cons: The short wavelength is easily scattered by condensation droplets on the lens. Modern 80 GHz radars require optimized lens shapes (convex) and algorithms to ignore near-zone condensation noise.

3. Beam Geometry & Installation Rules

The "Beam Angle" quoted in datasheets is usually the -3dB point (half-power beam width). However, microwave energy exists outside this cone. To avoid false echoes, engineers must calculate the Beam Footprint.

The Footprint Formula: The diameter ($W$) of the beam at a specific distance ($H$) is calculated as:

Installation Guideline:

1. Distance from Wall: Mount the sensor at least 1/6th of the tank diameter from the wall, but never less than 200mm. Ideally, the calculated beam radius ($W/2$) at the bottom of the tank should not touch the tank wall.
2. Nozzle Height: Unlike Ultrasonic sensors, Radar sensors can "see" out of nozzles better, but the nozzle must not be too tall or narrow. If the nozzle creates a "tunnel" that encroaches on the beam expansion, it will create "nozzle ringing" noise. Rule of Thumb: The nozzle diameter should be greater than the antenna diameter, and the nozzle height should create no more than a few degrees of obstruction.
3. Polarization: Radar waves are polarized. If measuring near a tank wall or obstruction, rotate the housing. This changes the polarization axis. Often, rotating the device by 90° can reduce the false echo amplitude from a nearby ladder or pipe by 10-20 dB.

4. Measuring Solids (Powders, Granules)

Solids measurement presents unique challenges compared to liquids:

• Angle of Repose: Solids do not form a flat surface; they form a cone during filling and an inverted cone during emptying. The radar signal hits this sloped surface and scatters away from the antenna rather than reflecting directly back. Solution: Use an aiming gimbal to point the radar at the surface, or use 80 GHz radar which catches the diffuse scatter better.
• Dust: While radar penetrates dust better than ultrasonic, extremely dense dust clouds (like in cement silos) can attenuate high-frequency signals. 26 GHz is often preferred over 80 GHz for extreme dust density.
• Pull-Forces: In tall silos, the forces on the antenna/cable from shifting solids can be massive. Non-contact radar is preferred over Guided Wave Radar (GWR) to avoid cable breakage.