Project: Vortex Ring – Introduction and Theory

Introduction

Now that I have finally wrapped up EOGee/EOGlass I can focus on my next project. I decided to do something with magnetics because I wanted to build a little more applied intuition and understanding of magnetic sensors and actuators. My original plan was to investigate building my own electro-permanent magnets, because I can think of some interesting applications for a switchable magnet. However in the process of my research I came up with a new idea for a wearable communication technology.

Human Body Communication (HBC) is a catch-all term for communication methods that use the human body as a communication channel. This means that the signals are contained within the human body and do not travel through a wire or through the air. This is potentially useful in wearable devices that may need to communicate with each other, for example a smart-watch can communicate with a heart rate monitor on the user’s chest, or an accelerometer on their leg, or even a medical device like pacemaker or cochlea implant. In such a network, all devices can communicate with a central hub (e.g. smart-watch) that then communicates to the user’s phone or other device to deliver the data to the user. Advantages of this approach potentially include reduced power consumption (due to the body’s higher channel gain compared to air), reduced network congestion (as each human will constitute a separate network rather than all sharing the air), as well as increased security and/or privacy (since the signals are constrained to the user’s body).

There are two broad classes of HBC – galvanic (where current is used to transmit information) and capacitive coupling (where voltage is used to transmit information). These are described in the paper A Review on Human Body Communication: Signal Propagation Model, Communication Performance, and Experimental Issues by Zhao et al.

Galvanic and Capacitive Coupling Human Body Communication

Typically both galvanic and capacitive coupling HBC is achieved using two electrodes. In galvanic HBC, both electrodes are in contact with the user and are used to drive a small current into the user’s body. In capacitive coupling HBC, one electrode is in contact with the user while the other is intended to capacitively couple to earth ground in order to create a voltage potential between the user’s body and earth ground. These electrodes come with challenges when creating a device for long time use. One challenge is how to make reliable contact to the user’s body without creating discomfort. Another challenge is corrosion of the electrodes when in contact with the user for a long time.

Vortex” is a new approach to Human Body Communication with the focus on enabling communication between the user’s devices and a secondary external device. Vortex is most closely related to galvanic HBC and uses magnetic fields to sense and induce currents in the user’s body. Unlike traditional HBC, however, it does not require electrodes to be in contact with the user as communication is achieved by generating a magnetic field around the user’s finger which can be achieved with no contact to the user. Specifically, Vortex is targeted at smart-ring devices where a current can be induced or sensed within the finger when a user is interacting with an external interface, such as a fixed button or touch-screen device. The ring form-factor lends itself to this approach due to the alignment between the toroidal shape of the ring and the circular flow of the magnetic field around the finger that is induced by a current.

Vortex’s high spacial precision and security could enable a single tap to select an item, identify the user and complete the payment transaction

Many of the key applications of Vortex would be in places where NFC is used today. These applications may include mobile payment by transmitting payment details to a payment terminal, user authentication by transmitting secret keys to an electronic door lock or bank system, and peer-to-peer information sharing by touching another person’s finger. While NFC may be capable of these interactions today, Vortex has a number of advantages.

  1. A more natural, touch-based interaction with the external device
  2. Increased security as the signal is constrained to the user’s finger
  3. Higher spacial precision allowing the user to select from multiple targets

While today not many people wear smart-rings, they are likely to become more prevalent as mobile computing shifts from handheld devices (like phones) to head-mounted devices (like AR glasses). In such a scenario, there is a need for a new method of creating ad-hoc communications with external devices where NFC would be used today.

Physics

Electromagnetics

As discussed in a previous article a coil can be used to detect a current via the voltage generated on the coil as per Faraday’s law. In order to boost the signal we can use a ring of high magnetic permeability material to increase the magnetic flux flowing around the current. We can also boost the signal by adding more turns on the coil.

In this application, the current is generated by driving our touch target with an AC voltage relative to earth ground. When the user touches the touch target a large capacitance, Cf, is created between the finger and the touch target. Because the human body is typically well coupled to earth ground via capacitance Cb, a current can flow through the finger, through the ring, and back to earth ground. The ring is made of a high magnetic permeability material such as ferrite resulting in a large alternating magnetic flux around the finger. This flux can then be detected as a voltage on our coil. As long as the magnetic permeability of the ring is sufficiently large the signal will be irrespective of the fit of the ring, allowing it to be as loose or tight as the user finds comfortable.

Drawing of the finger touching the touch target forcing a current to flow, inducing a voltage on our coil

Equations

We can formalise the above concept with concrete equations.

First we find the current flowing through the finger, If:

Where f is the frequency of the driven signal, Vdrive is the magnitude of the driven signal and Cf is capacitance between the finger and the touch target. Here we are assuming that the capacitance from the body to earth ground, Cb, is much larger than Cf and can therefore be ignored.

We can then calculate the magnitude of the magnetic field around the finger, inside the ring, H:

Here we define le to be the effective magnetic length of the ring. This is typically specified by ferrite core manufacturers but can be approximated as 2πr where r is the radius of the ring.

We can then calculate the magnetic flux density inside the ring, B:

Where µr is the relative permeability of the ring material and µ0 is the permeability of free space.

We can then calculate the magnetic flux intersecting the coil, Φ:

Where A is the effective area of the ring, which is typically specified by the ferrite core manufacturers but can also just be approximated as the cross-sectional area of the ring.

Finally we can calculate the voltage generated across the coil, V:

Where N is the number of turns in the coil.

Modelling

In reality, this setup is practically identical to a transformer and the equations governing a transformer. We can therefore model the scenario as a transformer in any typical SPICE program.

Spice model capturing the behaviour of Vortex

As becomes apparent, there is an associated inductance with the finger and the coil which is not taken into account in the above equations.

Parameter Optimisation in the Presence of Parasitic Capacitance

From there equations above, it appears that we can increase our voltage by adding more turns on our coil (increasing N) or by increasing the drive frequency (increasing f), however in reality there comes a point where adding more turns or increasing the frequency results in no increase in our signal.

This is due to the parasitic capacitance, Cp, that will always be present on the coil. As a result we form an LC circuit which has a resonance at a certain frequency. At frequencies above this resonance value, the signal observed at the output will level off due to the low impedance path to ground provided by the parasitic capacitance. This resonant frequency will decrease as the number of turns on our coil increases, due to the increasing inductance of the coil.

Vortex SPICE model with parasitic capacitance Cp
AC Sweep of the drive voltage

Our simulation results are plotted above and shows that initially the voltage increases with frequency as predicted by our equation. However once we hit resonance we see a spike in the voltage. Above this value the output voltage levels off and stays constant. In order for our equation to be valid we want to stay below the resonant frequency. It could be argued that we should target the resonant frequency in order to maximise our signal, however if we were to do that then our voltage signal would become very dependent on frequency and any mismatch between the TX and RX frequencies could result in large voltage variation resulting in inconsistent performance. Therefore it is best to target a frequency below resonance.

The equation for this resonant frequency is defined as fr:

Where L is equal to the inductance of our coil which can be calculated as so:

Finally, if we assume that we want to operate at a frequency that is 𝑥 times lower than the resonant frequency (we call this the “resonance safety factor”, fr = 𝑥f), then we can put this all together to get a final equation for our voltage:

This equation is intentionally broken down into the multiplication of three fractions. The first fraction represents the parameters of the driving circuit, including the frequency, drive voltage, capacitance to the finger and the resonance safety factor. The second fraction represents the parameters of the ring including the effective area, effective magnetic length and the magnetic permeability. Finally we have the term due to the parasitic capacitance at the output.

It is interesting to observe that the number of turns on our coil, N, is no longer present in the equation. This is because the number of turns is already constrained by the other variables in our system. We can calculate the optimal number of turns N with the following equation:

Design Process

With the equations defined above we can finally understand how the parameters of our design will impact the signal at the output and therefore choose our parameters to create an optimal design.

  1. The overall design is likely to be driven by the desired aesthetic design of the ring and this will define the area, A, and the effective magnetic length, le. These values will need to be chosen to make the ring comfortable to wear. To boost the signal we want to minimise the inner radius and maximise the outer radius as well as the thickness of the ring but this would lead to a very bulky ring that might not fit on the finger.
  2. Next, the material of the ring is selected to maximise the magnetic permeability, µrµ0. This is limited by the available materials, as well as any other properties that might need to be balanced such as density, strength, cost, manufacturability etc.
  3. We then can select our operating frequency, f, based on available components for generating the signal as well as demodulating the signal. We will likely need to trade off power consumption with frequency which would be critical in a space constrained device such as a ring.
  4. We then select our resonance safety factor. This is likely to depend on the exact parameters of the circuit and will require circuit modelling to define, however needs to be large enough to ensure that over all frequency drift and component tolerance we never operate near to resonance.
  5. The coupling capacitance between the finger and touch target, Cf, is defined by the geometry and materials of the touch target and of the finger. This is likely to depend on use case and aesthetic choices. A larger target will provide a larger capacitance up to a point. A thinner dielectric will also result in a larger capacitance.
  6. The drive voltage can be selected in combination with the coupling capacitance to ensure safe operation as well as acceptable power consumption.
  7. Finally the parasitic capacitance of our coil, Cp, can be estimated. The parasitic capacitance should be minimised where possible, for example by selecting components with low input capacitance.
  8. We can now calculate our voltage signal magnitude using the equation above
  9. Finally we calculate the required number of turns on the coil in order to achieve the desired operating point

Summary

So far we have defined the operating principle of Vortex, as well as deriving the governing equations. This has allowed us to create a process to optimise the design parameters. In the next post we will use this process to create and test the proof of concept.

It is also worth noting that we have only discussed the case where the ring is receiving data, rather than transmitting data. It is fairly clear to see from the circuit diagram that the whole principle can be performed in reverse, where the coil is driven in order to induce a current in the finger, since transformers operate in both directions, however the optimisation may be slightly different.

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