Water, dielectric in a resonant circuit

Refer to the image below on right side, showing the conical section of a bottle neck, filled with beverage when passing thru a bridge.  In the following we are naming High Frequency bridge a sensor presenting two metal plates directed toward the liquid in the neck of the bottle.  These metal plates are the equivalent of the capacitor plates seen here.  Capacitor made of metallic material and wired to an high frequency generator by mean of metallic wires.   All metallic parts have their own induction and capacity, depending by pure geometric factors and by constants.   The system is connected to an High Frequency Generator, part of the High Frequency Fill Level electronic inspection, whose carrier is tuned at ~21 MHz.    

When the Generator is powered, the:

  • induction of all of the metallic parts lying in the the electromagnetic field, implies inductive reactance;
  • capacity of the metal plates lying in the electromagnetic field, implies capacitive reactance;
  • resistance of the metallic parts lying in the electromagnetic field to transfer active power, implies what is commonly named an ohmmic resistance.

We are then in front of a resonant circuit whose impedance Z is the vectorial sum of these components. The length, section, shape and kind of metal wires are constant, then the inductive reactance is also constant.  On the opposite it is variable the Capacity, because of the reasons yet analysed here.  As an example, introducing water in the neck, at a reference temperature of 20 ºC, it is felt a huge increase (80.1 times) of the dielectric permittivity ε with respect to the value present in a vacuum (no water), and a nearly neglibile for the magnetic permeability μ.  

That, implying changes on the capacitive reactance and, as a consequence, changes of the total impedance of the resonant circuit, say the impedance presented by the entire system:

  • liquid beverage + gas, in the bottle neck;
  • humidity between the bottle neck and the metal plates in the bridge, where Generator's radio-frequency (RF) is applied;
  • HF fill level inspection bridge electronic circuit own impedance to the frequency of the Generator;
  • metal masses around the bottle;

to the movement of the electrons of the Generator.   

 High Frequency Fill level Inspection for still beverages, inspected at 50000 bottles-per-hour

The Environment around the HF fill level inspection is part of its measurements

 The total impedance of the resonant circuit, say the impedance presented by the entire system, includes all metal masses around the bottle neck where the electromagnetic field reach its maximum intensity. No generator at all is connected to the permanent magnet visible in the figure. The orientation of the iron threads along the magnet magnetic field lines of force, illustrates visually the relevance of the Environment for the measurements

The contribution to the total impedance of the metal masses around the bottle cannot be ignored, because the conveyor:

  • and the side guides defining bottles’ passage thru the bridge, are massive metal objects (commonly grounded for safety reasons);
  • can be interested to the transient passage of parasitic currents, originating e.g. by several other conditions of the machinery around the Electronic Inspector.   

 A common copper multithreaded cable of this kind is the best way to immunize the HF fill level inspection circuit by the dagnine effects (e.g. false rejects) of the changes in the geometry of the metal masses around the bottle passage

It is always necessary to provide an excellent (Radio Frequency grade) connection of the HF bridge to the conveyor.   Also, it has to be cared that the bottles’ passage side guides' inner metal parts are connected the same way to the conveyor.  Wherever a doubt exists, it is necessary to add multi-wire copper cables, to reduce the impedance.  And this last is the keyword: a common multimeter, powered by a 3 VDC battery, cannot test in high frequency the impedance of such a circuit.   It can only measure the ohmic resistance component of the impedance complex vector. More, a measurement instrument for impedances is not something commonly available into Bottling Factories.  

That’s why having a doubt, it is better to add copper meshes.   A common copper cable is thinked to handle, virtually without impedance, frequencies like 50 or 60 Hz.   But here they have to be grounded components whose frequency is 21 MHz, where skin effect shows itself in such a way that the current only flows in a thin external layer of each copper individual wire.   The impedance of the same copper conductor at 50 Hz is completely different than at  21 MHz: negligible in the first case and very high in the second.   Conveyor has to be perfectly balanced, on both axes X and Y, all around the inspection bridge.   

As seen with more detail elsewhere in these pages, the exposure of clustered water molecules to high frequency electromagnetic fields, like the commonly used whose frequency ~ 21 MHz, implies a transient reorientation of part of the clusters, caused by the cyclically changing polarity of the field, a phenomenon named dielectric relaxation.  

The coloured graphic on right side shows the frequency spectrum of the dielectric permittivity and details its character for the frequency of 21 MHz.  But, there is more than that: also the transient reorientation of part of the clusters and individual molecules, participates in the changes affecting the impedance of the resonant circuit. Red and blue colour curves represent respectively the real and the imaginary parts of the complex vector permittivity:   

  • real part related to the energy stored within the medium,
  • imaginary part related to the dissipation of energy within the medium.   

Changing the amount of water in the neck shall imply a net change on the current absorbed by the Generator, because of the change on the impedance of the entire circuit, caused by the change of permittivity of the Capacitor.

Frequency spectrum of the complex dielectric permittivity ε.  Water dipolar bonds relaxation evidenced by yellow colour at the frequency of 21 MHz adopted by electronic inspectors’ HF filling level check.  The red and blue curves represent the real and imaginary components of the complex vector permittivity

Electromagnetic Field used as a Fill Level 

Measurement Instrument

The animation below, shows a hypothetical mechanical device that separates electric charge to produce an electric dipole. Initially, we have a negative and positive charge on top of each other. There is no net charge and no electric field anywhere in space.  Each charge is connected to a rod, and the rods are pulled apart. As the rods are pulled apart to their maximum extent, the charges are separated slightly. 

  A hypothetical mechanical device that separates electric charge to produce an electric dipole. Initially, we have a negative and positive charge on top of each other. There is no net charge and no electric field anywhere in space.  Each charge is connected to a rod, and the rods are pulled apart. As the rods are pulled apart to their maximum extent, the charges are separated slightly.  This separation generates the electric field (animation abridged by TEAL/Studio Physics project, Massachusetts Institute of Technology)

This separation takes place over a time T, after which the charges remain a fixed distance apart.  This separation generates electric field. Initally we see a pulse of radiation of radial extent cT that propagates outward at its own speed, the speed of light naturally. Once that pulse disappears, we have left the classice static electric dipole field.  In evidence the phases of radiation, radiation reversing and radiation by a quarter-wave cutted antenna.  

The complexity of action of the real fill level measurement instrument, the electromagnetic field, is hinted by the following video:

Ambient conditions

As yet seen elsewhere in the fine detail, the high frequency fill level inspection is sensible to the changes on ambient conditions, namely:

  • ambient humidity;
  • beverage temperature.

There is an additional contribution to the dielectric permittivity ε also by the humidity in the air interposed between the Capacitor and the bottle neck filled with water.   This is attacked with systems trying to compensate it.  Then, to reduce this dagnine dependance hinting to false rejects, some Vendors equip the high frequency fill level inspection with a system recontrolling automatically the amount of humidity in the air,  each one time at least 0.5 m of conveyor passes without containers, say when only the air can be measured.   These results are later subtracted by the measurements of the containers, ameliorating the estimation of the amount of liquid in the neck.   One of the Vendors’ devices  keeps in memory the ambient conditions of last 72 hours of production.  To measure the intensity of the electric current crossing a circuit when there are no bottles, does not provide any information about the Temperature of the Beverage in the bottle.   Thus, the high frequency fill level inspection remain exposed to massive false rejects because of this variable.

Fill level Inspection

HF fill level bridge has to be perfectly centered on the avg. passage line of the containers. “Perfectly” means maximum error 1 mm.  This restriction is another hint on the random measurement of the HF fill level check.   An inspection window, whose extension is optimal when being ≈60 % of the diameter of the liquid column in the container, has its centre after a certain distance to the prior trigger.   As an example, in the Figure on right side the inspection window is displayed by mean of a couple of blue vertical segments, where the peak value for the red-colour curve shall be considered the variable’s measurement.  The variable is measured into evaluation windows

Containers' height compensation

An (optional) further linearization is offered by some Vendors: it is considered the fact that containers’ height is not identical, something much more true when speaking of PET bottles, inflated at different temperature conditions.   As a matter of fact, we are measuring in an indirect way the height of a column of water which lies in a bottle, then the bottle does matter.   Height compensation circuit and algorithm allow to linearize the filling level measurement, reducing the fluctuations due to this factor, ameliorating the filling measurement.


The final step is the comparison of the linearized  measurement with a sensitivity parameter set during inspector commissioning.   The container shall be considered underfilled (defective) when the measurement is lower than sensitivity threshold.   Both sensitivity threshold and measurement, are expressed by mean of  adimensional units in the scale of the digitizer circuit processing the analog values incoming by the HF resonant circuit.

                                                                                                            Copyright Graphene Limited 2013-2019