Wireless energy transfer is often used in industrial applications to power actors or sensors, for example in rotating applications as replacement for mechanical slip rings. In addition to the energy transfer, we have developed inductively coupled data transfer systems to expand the range of possible applications. The data transfer is accomplished by using loosely coupled coils on both sides of the power transfer system. In pure energy transfer systems, resonant coupling is used, meaning that the power transfer coils are both tuned to a common frequency to compensate the relatively small coupling factor between power transmitter and receiver and to achieve an impedance matching between both sides by compensating the inductive component of the transfer coils. In this case, capacitors can be connected in series or in parallel to the coils, leading to a sharp, narrow band resonance peak in the transfer function. In inductively coupled data transfer systems, this approach is often not useful because not just a pure sine wave has to be transferred but more likely a signal of a certain bandwidth. In one of our applications, a 100

For passive, lossless circuits, Foster's theorem states that the reactance increases monotonically with frequency. Subsequently, the inductive part of a circuit can just be exactly compensated with a capacitance for one single frequency. In contrast, active circuits like a negative impedance converter (NIC) can be used to achieve a non-Foster behaviour, for example a negative inductance can be realized. In theory, an inductance in series or parallel to a negative inductance of the same magnitude would be cancelled out for every frequency applied. For low power level applications like active receiving antennas, this approach has already been successfully used in the past to achieve improved matching of simple antenna structures over a comparably large bandwidth.

We make use of non-Foster circuits, namely negative impedance converters, to compensate the inductive part of two loosely coupled inductors to achieve smaller transfer losses and better impedance matching, which should lead to a decreased transfer signal loss and higher signal to noise ratio. The results of this paper serve as a basis for this development. So far, we achieved almost complete cancellation of the reactive part introduced by the loosely coupled data transfer inductors. Unfortunately, the circuits active device used to form the negative impedance converter introduced a highly resistive element, greatly increasing the signal transfer losses. Nevertheless, the theory of loosely coupled inductors is shown in a compact form and a strategy to cancel the reactive part is presented. Simulations and measurements of a transfer system are carried out, both showing good agreement regarding the reactance cancellation. Based on this, optimised implementations will be developed in the future.

Besides pure wireless inductive power transfer, additional simultaneous data transfer is an important research topic in recent years. One of the most challenging aspects of this combination, besides possible interference between energy and data signal, is the contrary demand regarding the respective transfer channel. For an energy carrier, power loss must be minimised to achieve a reasonable efficiency while just a small bandwidth is needed because the energy is transferred as pure sine wave (or as a rectangular signal whereby just the fundamental is actually transferred). In contrast, data transmission's efficiency is always connected to bandwidth, which in turn dictates the amount of data transferable per time unit. Dependent on the intended application, different implementations have been reported in literature which can be categorized in two main groups based on the inductor arrangement used.

A single pair of inductors can be used to transfer both, energy and data at the same time. In

An additional approach to increase the usable bandwidth is presented in

The second category of simultaneous energy and data transfer is based on the usage of separate inductors for the energy and data channel, thus making it possible to optimize both based on their specific requirements. Again, biomedical implants are the main research area. In

Our work presented in this paper also uses a pair of loosely coupled (non-resonant) inductors transfer high-speed data bi-directionally in the vicinity of a commercially available inductive energy transfer system from a project partner, transferring up to 60

The part marked as “1” is the energy transfer coil, consisting of several loops of litz wire inside a ferrite core. The same coil is used on the receiving side, forming an almost closed magnetic circuit due to the ferrite cores. The system is used in industrial machines to power sensors and actors on a rotating shaft at constant distance. Due to the magnetic circuit formed by the ferrite cores, the rotation does not affect the magnetic coupling of the power transfer coils.

Contactless inductive power and data transfer system.

The parts marked as “2” are two data transfer coils, in this case simple wire loops, one for each direction of data transfer and again the same implementation being present at the energy receiving side, forming the data transfer channels for a full-duplex system. As these coils are formed by concentric loops with just a small gap, the rotation does just slightly affect the coupling factor between both sides. Anyway, the possibility for higher coupling factor variation due to the rotation and increased transfer distances will be addressed in Sect.

As the data coils are just loosely coupled, dependent on the transfer distance, the signal loss is in the range of 10 to 15

In the following chapters, we will examine the possibility to increase the data signal transfer distance by cancellation of the self-inductances of the data coils using non-Foster elements, namely negative inductors and thus reducing the path loss.

Foster's theorem

In contrast, networks not obeying Eq. (

Reactance over frequency for Foster

An important result of Foster's reactance theorem can be found in impedance transformation networks. Let's consider an arbitrary, passive load impedance

For simplicity, we further assume that the load's reactance is purely capacitive, so

To overcome the limitations, non-Foster elements can be used, as they are able to compensate the load's reactance with the corresponding negated reactance. The usability of this approach has been shown in

To achieve a non-Foster behaviour, at least one of the prerequisites of Foster's reactance theorem – losslessness and passivity – must be violated. In

A more common implementation of non-Foster elements is by using active elements like transistors or op amps forming a negative impedance converter (NIC), being able to negate a conventional. In for example

Using op amps as an NIC significantly reduces the count of circuit elements, omits the complexity of transistor biasing and simplifies circuit analysis. Such circuits are presented in

The basic circuit of an op amp based NIC is shown in Fig.

Negative Impedance converter.

As we will be using cascade matrices (or

Loosely coupled inductors.

As described in the introduction, the data transfer path in our systems is formed by loosely coupled inductors. A very basic, idealised equivalent circuit of such a transfer channel is shown in Fig.

To be able to describe the transfer behaviour mathematically, we use the equivalent

Equivalent

By using

An additional aspect to keep in mind is the increased complexity when dealing with non-constant transfer distances, thus variable coupling factor. Without further proof, it should be clear that the dependency between coil spacing and magnetic coupling is strongly non-linear. Additionally, the impedance transformations presented before are square-law dependent on the coupling factor, resulting in a broad range of possible input impedances for different transfer distances. As the inductive power and data transfer systems we focus on are, besides rotational motion, static, further investigations are out of the scope of this work. Nevertheless, the attempt to compensate the inductive part of the input impedance by use of Non-Foster elements is still applicable, especially as we have seen that the main reactive part of the input impedance is formed by the self inductance of the source side coil.

Simulation model.

Assuming that we compensate the self inductances in Eq. (

Simulation model.

One method of compensating the self inductances is the use of series or parallel capacitors, leading to loosely coupled resonating circuits as used for example in wireless energy transfer systems

As a second method, non-Foster elements, namely negative inductors in series with the self inductances of the transfer system could be used. For ideal negative inductances, a frequency independent compensation of the coupled coils' reactance can be achieved. In this case, the input impedance would be exactly described by Eq. (

To verify the cancellation of the input reactance, we use a system as shown in Fig.

Starting at the load resistance

It is worth noting that all considerations so far were made under the assumption of ideal coupled inductors and especially ideal negative impedance converters. The following sections show that mainly the non-idealities of the op amps used as negative impedance converters lead to significant deviations from the ideal case.

To verify the reactance cancellation approach described before, a schematic

The inductances

For comparison, the

Looking at the

As we have simulated the system using measured data of the coupled coils and an ideal implementation of the negative impedance converters, the results presented so far have shown the maximally achievable system performance regarding reactance cancellation.

The system described before has been built using the op amp OPA684 by Texas Instruments in the NIC circuit, promising a high open-loop gain and bandwidth as needed for the NIC to work correctly. As a first step, the input impedances of the NIC circuits connected to the coupling coils have been measured. For comparison, Fig.

The plot shows the expected non-Foster behaviour, namely the negative (almost) linear slope of a negative inductor. As next step, the compensation inductances have been added to the NIC circuit. The measured input reactance of both ports is shown in Fig.

Measured

Consequently, the setup shows the expected behaviour regarding the cancellation of the coupling coils' self-inductance.

In contrast, regarding the transformation of the load resistance, the setup shows a non-ideal behaviour as can be seen from Fig.

As this is just the value of the feedback resistors of our circuit, it can be concluded, that the parameters of the op amp like open loop gain and bandwidth are possibly too low. Followingly, the circuit adds a real component as described in

It was tried to achieve the same behaviour in simulation by degrading the gain and bandwidth of the op amps, but without being able to fully depict the measurement results. A simulation model of the op amp used exists but just as spice model which cannot be used in an s-parameter simulation. Additionally, the frequency behaviour and roll-off of the gain cannot be portrayed in the simulation, just a constant, frequency independent value. Further investigations are needed to find the cause, possibly parasitic effects not directly covered by the simulation parameters.

To be able to compare the system's behaviour regarding the reactance cancellation, a post processing step has been made, substracting the
200

In conclusion, besides the offset in the real part, the principle of reactance cancellation works for loosely coupled inductors. More effort must be spend to improve the NIC circuits behaviour to finally be able to achieve an improved signal transfer and impedance matching over a certain bandwidth.

In this paper, a concept to compensate the reactive part of loosely coupled inductors used to transfer data has been presented. Negative impedance converter circuits have been used to successfully negate the coils' self-inductance and compensate it using additional series inductances. Further effort must be spend on the optimisation of the circuit to eliminate the additional resistive part introduced by the NICs in the measurements. By achieving this, inductive data links can be optimised regarding signal transfer loss and impedance matching. The transfer distance of the system presented in the introduction could be increased with sufficiently small bit error rate. As a new idea, in a certain frequency range, the matching achieved could be high enough to achieve bi-directional transfer using just one pair of coils by inserting (active) circulators to separate the two transfer directions.

Measurement data is available in the Supplement.

The supplement related to this article is available online at:

The main idea for this work was contributed by CS. He also did simulation, implementation and measurement tasks. MB and MC supported with fruitfull discussions and result interpretations. MB supported also with data post-processing and plotting.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Kleinheubacher Berichte 2018”. It is a result of the Kleinheubacher Tagung 2018, Miltenberg, Germany, 24–26 September 2018.

We thank IST – Ingenieurbüro für Sensortechnik GmbH for their support in this project.

This research has been supported by the Bundesministerium für Wirtschaft und Technologie (grant no. ZF4050305PRG).

This paper was edited by Jens Anders and reviewed by two anonymous referees.