Optimization of Data Coils in a Multiband Wireless Link for Neuroprosthetic Implantable Devices

Abstract

We have presented the design methodology along with detailed simulation and measurement results for optimizing a multiband transcutaneous wireless link for high-performance implantable neuroprosthetic devices. We have utilized three individual carrier signals and coil/antenna pairs for power transmission, forward data transmission from outside into the body, and back telemetry in the opposite direction. Power is transmitted at 13.56 MHz through a pair of printed spiral coils (PSCs) facing each other. Two different designs have been evaluated for forward data coils, both of which help to minimize power carrier interference in the received data carrier. One is a pair of perpendicular coils that are wound across the diameter of the power PSCs. The other design is a pair of planar figure-8 coils that are in the same plane as the power PSCs. We have compared the robustness of each design against horizontal misalignments and rotations in different directions. Simulation and measurements are also conducted on a miniature spiral antenna, designed to operate with impulse-radio ultra-wideband (IR-UWB) circuitry for back telemetry.

I. Introduction

WIRELESS operation of implantable microelectronic devices (IMD) is necessary in clinical neuroprostheses to reduce the risk of infection and patient discomfort, which may result from transcutaneous wires breaching the skin. This requirement, however, adds to the complexity of the system and may form a bottleneck in the design of high-performance IMDs that are being developed for new applications, such as retinal implants and cortical brain-machine interfaces (BMI). Even though the transmission range of these wireless links is limited to 5 ~ 20 mm across the skin, the medium (tissue) and extreme size constraints may require the adoption of nontraditional design criteria. For example, cochlear implants need to be placed inside the 3- to 6-mm-thick temporal bone near the ears [1], and invasive BMIs are being developed for the 1- to 3-mm epidural spacing between the outer surface of the brain and the skull [2]. Moreover, the retinal implants are expected to be placed inside the eyeball through a 5-mm incision [3], [4].

The wireless link is expected to perform three functions as follows.

1. Power transmission: Design and optimization of efficient inductive power transmission links with filament coils have been studied over the last decades [5]–[9]. Nonetheless, the geometry of the coils used in the next generation of low-power IMDs is more likely to be planar and lithographically defined, to allow fabrication through micromachining technology [10]. Therefore, we devised an iterative design methodology to find key geometric parameters of the planar spiral coils (PSC) and maximize their power transmission efficiency in [11].

2. Forward data transmission: Prostheses that substitute for sensory modalities, such as vision, need large volumes of data to simultaneously stimulate a large number of sites at high rates [12]. Thus, wideband wireless data transmission from outside into the body (downlink) is needed. Due to conflicting requirements between power and data links, we have utilized a separate pair of coils for data transmission [13]. In this paper, we consider two types of data coils. First, there are a pair of vertical coils wound across the diameter of the power PSCs, whose symmetry and orthogonal magnetic-field orientation will minimize the power carrier interference. Second, a pair of planar figure-8 coils, in which the electromotive force (EMF) induced from the power carrier in one loop, opposes the same in the other loop [14]. Hence, the total electromotive-force (emf) interference from the power carrier can be very small when the two coils are properly aligned.

3. Back telemetry: Recording the neural response to stimulation in neuroprostheses and closing the control feedback loops in the BMIs require a wideband back telemetry link (uplink). Passive back telemetry, used in radio-frequency identification (RFID), does not provide enough bandwidth for this application [15], or requires strong coupling between coils [16]. Therefore, we chose impulse-radio ultra-wideband (IR-UWB) for this purpose, which can provide wide bandwidth with simple and low-power transmitters [17]. We have included a pair of planar spiral UWB antennas in our multiband wireless link. However, we have not yet optimized it at this stage.

Fig. 1 shows the block diagram of a high-performance neuroprosthetic device, which has wireless neural recording and stimulation capabilities, with emphasis on the proposed multiband wireless link. The upper, middle, and lower rows in this diagram are responsible for power, forward data, and back telemetry functions, respectively. L₁ is the external power PSC that is attached to the skin from outside of the body and L₂ is the internal PSC that is implanted under the skin flap. L₃ and L₄ are the forward data coils. The back telemetry link utilizes miniature UWB antennas A₁ and A₂.

Fig. 1.

Block diagram of the multiband wireless link and its associated blocks in a high-performance implantable neuroprosthetic device [20].

In Section II, we construct a theoretical foundation for data coils. The design procedure and optimization of the multiband wireless link components are discussed in Section III. The theory and design of the power PSCs have already been covered in [11] and [18]. Section IV is dedicated to simulation and measurement results, followed by concluding remarks.

II. Theoretical Calculations for Data Coils

A. Vertical Data Coil

The geometry and orientation of the forward data coils are key issues because the power carrier amplitude can be up to two orders of magnitude larger than the data carrier, and can easily dwarf the data carrier particularly on the receiver side. A coaxial approach has been proposed, in which data coils are placed in the center of the power coils in the same plane [19]. This approach provides good coupling between data coils (k₃₄ in Fig. 1). However, L₁ ~ L₄ all share the same flux linkage, resulting in a strong cross coupling between these coils, which can lead to saturation of the data receiver by strong power carrier interference. Although a high-pass filter on the receiver side can reduce the power carrier interference up to a certain extent, in our experience, the power carrier is so strong that only a high-order filter with large area and power costs might be effective. Even then, the inband harmonic components of the power carrier cannot be neglected. Hence, unless the interference between the power and data carriers is adequately attenuated on both sides, demodulation of the received data carrier and correct detection of the data bits would be difficult.

To solve this problem, we proposed using orthogonal coils by winding the data coils across the diameter of the power PSCs, as shown in Fig. 2 [13]. In this method, due to symmetry and orthogonality of the coils’ geometries, the magnetic flux generated by the power PSCs does not pass through data coils and their undesired cross coupling factors (k₁₄, k₁₃, k₂₃, and k₂₄) can theoretically be close to zero when the coils are perfectly aligned. The data coils, however, can maintain a small but adequate direct coupling k₃₄ as they are parallel with long conductors.

Fig. 2.

(a) Rendering of the power and forward data transmission coils, showing their important geometrical parameters. (b) Receiver data and power coils fabricated on a four-layer printed-circuit board (FR4) [20].

One should note that unlike power PSCs, which need strong coupling (k₁₂) to efficiently supply the IMD, here we only need to maintain k₃₄ in the same range or slightly higher than the undesired couplings. Since the forward data link operates at a different frequency band, the receiver L₄C_P4 tank helps with amplifying the received data carrier and filtering out the undesired power carrier interference [13]. In the following text, we have constructed a theoretical foundation to optimize the geometries of the vertical data coils.

In Fig. 2, the height (h_d), width (w_d), and length (l_d) of each rectangular vertical data coil depend on the thickness of the power PSC substrate, number of turns of data coil (N_d), and the diameter of the power PSC, respectively. w_d also depends on the diameter of the chosen wire (Dia) and their spacing. Using these geometrical parameters in tabular self inductance formulation in [5], we calculated L₃ and L₄ (see the Appendix).

The coupling coefficient between a pair of coils is defined as

$$k_{34}=M_{34}/\sqrt{L_3{L}_4}$$ (1)

where M₃₄ is the mutual inductance between L₃ and L₄. Fig. 3 shows the cross section of the rectangular solenoid-shaped data coils. We showed in [13] that vertical data coils are quite robust against misalignments along the Y-axis (see Fig. 2), and sensitive to misalignments along the X-axis. Therefore, to derive M₃₄ equations, we not only considered the coils relative distance D, but also their X-axis misalignment X. The original equations for the mutual inductance from [5] were based on circular solenoids. We used the rectangular coil height (h_d) instead of the circular solenoid diameter. We also replaced the area of the circular solenoid by the rectangular solenoid area (l_d × h_d). Our simulation and measurement results showed that these approximations are valid for l_d/h_d < 20. Detailed equations for calculating M₃₄ from data coil geometries are included in the Appendix.

Fig. 3.

Cross-sectional view of a pair of coupled solenoid inductors [5].

B. Figure-8 Data Coils

Our second design for the data coils is based on the planar figure-8 geometry, shown in Fig. 4(a). This type of coil is often used in transcranial magnetic stimulation (TMS) [21]. The direction of windings in each loop of the coil is chosen so that when the coil is exposed to an external field symmetrical to both loops, induced currents will cancel each other out [22]. Therefore, even when they are in the same plane as the power PSCs, figure-8 coils can attenuate the power interference. Moreover, the mutual coupling M between two figure-8 data coils is larger than that between vertical coils because these coils are facing each other. We dedicated two out of four metal layers in the printed-circuit board (PCB) implementation of the multiband link to the figure-8 data coils with N_d3 = N_d4 = 2 [see Fig. 4(b)]. We made L₄ as large as the IMD size allowed (i.e., filling the same area as L₂). Geometry, line width, and substrate thickness affect the self inductance and the mutual coupling of the figure-8 coils. Since closed-form equations for figure-8 coils are quite complicated, we used a commercial field solver, HFSS (Ansoft, Pittsburgh, PA), to model these parameters.

Fig. 4.

(a) Planar figure-8 coil layout. (b) Exploded view of the UWB antenna stacked on top of the power PSC and figure-8 data coil in a four-layer PCB to form the implantable side of the multiband wireless link (10 × 10 × 1.5 mm³).

III. Multiband Wireless Link Design Procedure

A. Printed Spiral Power Coils

Theoretical analysis, modeling, and experimental validation of an iterative design procedure for the power PSCs based on a set of constraints imposed by the fabrication process and medical application can be found in [11]. We combined the theoretical foundation of optimal power transmission in inductive links with simple models that calculate M in a pair of PSCs, their quality factors (Q), and parasitic components. The result was an iterative PSC design methodology that starts with a set of realistic design constraints imposed by the application and PSC fabrication process, and ends with the optimal PSC geometries for maximum power efficiency.

Table I summarizes the constraints that we have considered in the design of the prototype power transmission PSCs for an exemplar visual prosthesis application, using 1-oz copper on FR4 substrate in a standard PCB fabrication process. We executed the iterative procedure for f_P = 13.56 MHz in the industrial scientific medical (ISM) band and nominal coupling distance of D = 10 mm. Even though 13.56 MHz is on the high end of the frequencies that have been traditionally adopted for inductive power transmission to implantable devices, it is still within the range in which the specific absorption rate (SAR) in the tissue is quite low compared to the thermal power dissipation in the coils [24]–[27]. On the other hand, it provides high-Q for L₁ and L₂, which is a key factor in improving the power transmission efficiency [28]. It also allows us to take advantage of the existing radio-frequency identification (RFID) technology. Table II depicts the optimized geometries for L₁ and L₂.

TABLE I.

Design Constrains Imposed by the Application and Fabrication Process

Parameter	Symbol	Design Value
Implanted PSC outer side	do2	10 mm
PSCs relative nominal distance	D	10 mm
Power carrier frequency	fP	13.56 MHz
Secondary nominal loading	Rl	500 Ω
Conductor thickness	tc	38 μm
PCB substrate thickness	ts	1.5 mm
PCB substrate dielectric constant	εrs	FR4, 4.4

TABLE II.

Optimized Power PSC Geometries and Specifications

Parameter	L1	L2	Parameter	L1	L2
do (mm)	79	10	w (μm)	5500	290
di (mm)	11.2	2.96	s (μm)	150	150
ϕ (fill factor)	0.751	0.543	L (μH)	1.22	0.49
n (turns)	6	8	Q	102	36
Frequency (MHz)	13.56
k12	0.036
Efficiency (%)	56.65 (with perfect alignment)

^*Derived from using Table I in the iterative procedure explained in [11].

B. Vertical Data Coils

Optimal forward data coil geometries depend on the choice of the forward data carrier frequency. In this prototype, we chose a phase-coherent frequency-shift-keyed (pcFSK) carrier at f_FD1 = 25 and f_FD0 = 50 MHz based on the method described in [23]. Fig. 2(a) shows the main geometrical parameters of the data coils (l_d, w_d, h_d, n_d). In order to reduce thickness and the skin effect, we chose the thinnest multistrand Litz wires that we could find for winding the vertical data coils (MWS Wire Industries, Westlake Village, CA). This wire had a diameter of Dia₄ = 100 μm, including insulation, which contained seven insulated strands of AWG-48 wires (diameter ~ 30.5 μm).

Fig. 5 summarizes our three-step design procedure for vertical data coils. To maximize k₃₄, we would like l_d4 to be as long as possible. Therefore, the first constraint is imposed by the size of the IMD, which is basically the size of L₂ [11]. Using Table II, l_d4 = d_o2 + 2Dia₄ = 10.2 mm. The height of L₄ (i.e., h_d4) is dictated by the IMD thickness with 2Dia₄ which is 1.7 mm in this case. Increasing n_d3 and n_d4 improves k₃₄ at the expense of decreasing the data coils’ self resonant frequency (SRF) and increasing undesired k₁₄ and k₂₃. SRF is defined as

Fig. 5.

Design procedure for the optimal design of the vertical data coils.

$$\text{SRF}=1/2\pi \sqrt{\text{LC}},$$ (2)

where L is the coil’s self-inductance and C is its parasitic capacitance. The closer the SRF gets to the carrier frequency, the smaller the size of the added parallel or series capacitance needs to be with the data coil inductor (C_p4 and C_s3). Therefore, it becomes more difficult to tune the LC resonance frequency right at the desired carrier frequency because we have little control over C. Hence, as a rule of thumb, we try to keep SRF at least twice the carrier frequency, which means C ≤ C_p4/3. SRF should not be too high either. In order to increase SRF, one has to reduce n_d3 and n_d4 at the cost of reducing k₃₄.

Considering the aforementioned discussion, in our example, we would like to choose n_d3 and n_d4 so that SRF_3,4 ≥ 100 MHz. Even though there are closed-form equations for the SRF of solenoid air-core inductors [29]; in this case, L₃ and L₄ are wound around L₁and L₂, respectively, which degrade the accuracy of these equations. Hence, in Fig. 6, we used HFSS to simulate the relationship between SRF and n_d4 for a single-strand rectangular coil with l_d4 = 10.2 mm, h_d4 = 1.7 mm, w_d4 = 1 mm, and Dia₄ = 100 μm. It can be seen that for n_d4 = 6, SRF₄ = 96.3 MHz. Measurements with the 7-strand Litz wire and same dimensions resulted in SRF₄ = 98.8 MHz.

Fig. 6.

Self-resonance frequency versus number of turns for the vertical data coils.

In the second step, since dimensions of L₁ and L₄ as well as their relative distance D are known, we can simulate k₁₄ using the field solver to determine the power carrier interference. D in this case is considered the distance between the closest conductors in L₁ and L₄. Our simulation with HFSS resulted in k₁₄ = 9.1 × 10⁻⁵ at 25 MHz, which is the minimum value for k₁₄ when the coils are perfectly aligned. However, since the interference can be through multiple paths, the best alignment can be found by shifting L₄ horizontally about 0.5 mm in each direction from the center of the power coil until minimum power interference from f_P is achieved. In the next step, we would like to design L₃ so that k₃₄ is at least one order of magnitude larger than k₁₄.

l_d3 (length of L₃) plays an important role in k₃₄ value. A short l_d3 turns L₃ into a solenoid with concentrated magnetic field but smaller cross section. If l_d3 is too long, on the other hand, L₃ turns into a series of infinite parallel conductors with respect to L₄ with lower mutual coupling. Hence, there is an optimal length for l_d3. To demonstrate the effect of l_d3 on k₃₄, we simulated k₃₄ between L₄ (from step 1) and an n₃ = 3-, 5-, and 10-turn L₃, while sweeping l_d3 from 10 ~ 70 mm. Once again, D = 10 mm, and h_d3 was set to 2.2 mm (PCB thickness with 2Dia₃), where Dia₃ = 350 μm which is a reasonable thickness (we will discuss it latter). The results in Fig. 7 show that l_d3 = 30 mm is the optimal length for L₃ in these conditions.

Fig. 7.

Vertical data coils direct coupling as a function of the length of L₃ when the coils are 10 mm apart.

Dia₃ and n_d3 are the other parameters that need to be determined in this step, which have direct relationships with k₃₄. From the previous step, l_d3/h_d3 ≈ 17.6 < 20. Hence, the models and equations discussed in Section II are valid. Using (3)–(5) in the Appendix, we have created Fig. 8 in MATLAB by sweeping Dia₃ and n_d3 from 0 to 0.5 mm and 0 to 10 turns, respectively. Despite their positive effect on k₃₄, increasing Dia₃ will add to the thickness of the external coil/antenna complex, and increasing n_d3 will reduce SRF₃. To wind L₃, we decided to use Litz wires with Dia₃ = 350 μm, made of seven insulated AWG-36 strands (diameter ~ 127 μm). This type of wire, indicated by a dashed line in Fig. 8, adds ~ 700 μm to the 1.5-mm-thick L₁, which is reasonable for outside the body.

Fig. 8.

Effects of varying the number of turns and the wire diameter of the external data coil (L₃) on data coils direct coupling, k₃₄.

To find the proper n_d3, we simulated SRF₃ with all the known geometrical parameters of L₃, while sweeping n_d3 from 1 to 10. It can be seen in Fig. 6 that n_d3 = 5 would be the best choice, resulting in SRF₃ = 128.8 MHz. This point has been shown by a red dot in Fig. 8, corresponding to k₃₄ = 0.00246, which is 27 times larger than simulated k₁₄. This concludes with the optimal vertical data coils design, whose specifications are summarized in Table III for D = 10 mm.

TABLE III.

Optimized Vertical Data Coil Characteristics

Parameter	L3	L4
Type of Litz wire	7 × AWG-36	7 × AWG-48
Wire Diameter (μm)	350	100
Number of Turns	5	6
Length (mm)	30	10.2
Width (mm)	2.0	1.0
Height (mm)	2.2	1.7
Inductance (μH)*	0.3081	0.5972
SRF (MHz)*	128.8	98.8
Cs3 and Cp4 (pF)	58.46	27.9
Q @ 50 MHz*	50.2	20.2
k34*	0.0022

^*Simulated in the HFSS.

C. Figure-8 Data Coils

Fig. 4(a) shows the figure-8 data coil (L₄) geometry. Note that the two loops are laid out symmetrically with opposite winding directions. Similar to the vertical data coils, the largest possible area for L₄ is dictated by the IMD size, which is the size of L₂ (d_o4 = 10 mm). We chose the line width for L₄ to be 200 μm, slightly larger than the minimum widths possible in our PCB fabrication process. Layers 2 and 3 of a four-layer FR4 PCB are dedicated to the implantable figure-8 data coil, which are spaced at 0.8 mm [see Fig. 4(b)]. The simulated SRF₄ with the aforementioned dimensions was 256 MHz.

To find the best size for L₃, we learned from [15] that the optimal radius of a 1-turn circular loop for maximum coupling with another loop that has a radius of R at distance D is ~ D√2, when R is small. Since D = R =10 mm in our design, we chose the size of L₃ to be 32 × 32 mm², which is slightly larger than the optimal size to account for the width of the planar conductors. The line width affects not only the parasitic resistance but also SRF₃. We chose a line width of 2 mm on a 2-layer 1.5-mm-thick PCB, and achieved SRF₃ = 138 MHz in simulations. Specifications of our figure-8 data coil designs are summarized in Table IV.

TABLE IV.

Optimized Figure-8 Data Coil Characteristics

Parameter	L3	L4
Line width (mm)	2	0.2
Size (mm2)	32 × 32	10 × 10
Number of turns	2	2
Inductance (μH)*	0.1306	0.3338
SRF (MHz)*	138	256
Cs3 and Cp4 (pF)	137.9	52.80
Q @ 50 MHz*	46.4	38.8
k34*	0.011

^*Simulated in the HFSS.

D. UWB Antenna

Wideband antennas are often composed of several resonant frequencies [30]. To cover the lower bands, a long antenna is needed to be efficient for long wavelengths. However, with the limited space available in the implant, another choice could be to use a high dielectric substrate to create lower resonant frequencies at shorter wavelengths. Unfortunately, a 10 × 10 mm² lossy FR4 substrate is not a suitable choice for either one of the aforementioned solutions. Therefore, we do not expect a great performance from our antenna pair A₁and A₂ in Fig. 1. Fortunately, that is not a major issue because of the proximity of the two antennas across the skin. In order to reduce the size, spiral antennas can be used [31], [32]. Even then, dedicating only one metal layer for this antenna is not enough to create a low resonance frequency. Thus, we took advantage of the power coil as the ground plane to create another radiation path and lower the resonance frequency of the antenna further.

A₂ consists of seven turns of planar copper with the line width of 400 μm and line spacing of 200 μm on the backside of L₂. The feedpoint of this 10 mm in diameter UWB antenna is at the center. A key advantage of this planar design is that it can be batch fabricated on a thin organic substrate with minimum volume overhead in an actual IMD. However, we still need to improve the design of this antenna based on its specific conditions inside the body [33], [34]. Fig. 4(b) shows an exploded view of the entire multiband coil-antenna complex on a four-layer PCB. A₁ is not under a strict size constraint, and can be an elliptical dipole antenna, filling the area on the back of L₁. The operating principle between A₁ and A₂ is considered near-field coupling (5 ~ 20 mm). However, the short-range impulse radio UWB communication, which we will utilize for back telemetry [35], is much less susceptible to misalignments compared to the forward data coils.

IV. Measurement and Simulation Results

The measurement setup is shown in Fig. 9. We connected the coils under test to a 4-GHz vector network analyzer (R&S ZVB4) in pairs to measure their S-parameters. S-parameters were then converted to Z-parameters to calculate the quality factors and mutual inductances [36]. We finally used (1) and equations in [11] to calculate the coupling coefficients and efficiency, respectively. Since optimal d_o1 > l₃ (see Tables II and III), in order to wind L₃ we had to create a pair of holes in L₁ PCB and pass the Litz wire through them (see Fig. 9 inset). More detail on the power efficiency setup can be found in [11].

Fig. 9.

Setup for direct- and cross-coupling measurements. Inset: the relative position of the external power (L₁) and vertical data coils (L₃) with respect to implantable coils (L₂ and L₄), which are also shown separately in Fig. 2(b).

A. Power Coils Efficiency

Fig. 10 shows the measured efficiency of the power PSCs in Table II versus coils relative distance D at 13.56 MHz, and compares it with HFSS simulations and calculations based on the models we constructed in [11]. The calculated, simulated, and measured results are in good agreement. The small discrepancies of the calculated values result from the fact that the equations in [11] were mainly for circular coils and we empirically adjusted them for the rectangular-shaped PSCs by adding a simple coefficient. Furthermore, we did not take into account the effects of eddy currents in those equations.

Fig. 10.

Calculated, simulated, and measured efficiency variations with coils relative distance D for power PSCs in Table II at 13.56 MHz [11].

B. Data Coils Linear Misalignments

One of the key issues in forward data transmission using a multiband wireless link is its robustness against misalignments. Here, because we have previously shown that these coils are robust against misalignments along the Y-axis [13], we focus on misalignment along the X-axis [see Fig. 2(a)]. Fig. 11(a) shows the result of k₁₄ and k₃₄ variations at D = 10 mm when vertical data coils in Section III-B are misaligned up to 10 mm along the X-axis. It can be seen that the desired k₃₄ appears well above the undesired interference from power PSCs (k₁₄) in perfect alignment (ΔX = 0 mm) and k₃₄ > k₁₄ for ΔX < 2.5 mm. Therefore, we can conclude that this design can generally withstand misalignments of up to 2.5 mm for the 10 × 10 mm² implant (~25% of the implant size).

Fig. 11.

(a) Calculation (see Appendix), simulation, and measurement of vertical data coils’ direct coupling (k₃₄) and cross coupling with power PSCs (k₁₄) versus misalignment along the X-axis (see Fig. 2(a)). (b) Simulation and measurement of figure-8 data coils’k₃₄ and k₁₄ versus misalignment along the X-axis [see Fig. 8(b)]. The coils’ relative distance is maintained at D = 10 mm.

A similar set of experiments was conducted with figure-8 data coils of Section III-C, and the results in Fig. 11(b) show that k₁₄ and k₃₄ of figure-8 coils are stronger than k₁₄ and k₃₄ of the vertical data coils when the coils are perfectly aligned. In this design, however, k₃₄ > k₁₄ for ΔX < 8 mm. Thus, we can conclude that this design can withstand misalignments of up to 8 mm for the 10 × 10 mm² implant (~80% of the implant size).

C. Data Coil Rotations

Due to coils’ proximity, even small rotations affect their coupling coefficients considerably. In this section, simulations and measurements of the vertical and figure-8 data coils’ k₃₄ versus the rotation angle are shown in Fig. 12(a) and (b) based on the Cartesian coordinates shown in Figs. 2(a) and 4(b), respectively. In these measurements, L₄ is held stationary and L₃ is rotated pivotal to X-, Y-, and Z-axes, while the center-to-center spacing between the coils is maintained at D = 10 mm.

Fig. 12.

(a) Simulation and measurement results of the vertical data coils direct coupling (k₃₄) versus rotation angle of L₃ pivotal to the X-, Y-, and Z-axes, while maintaining a center-to-center spacing of D = 10 mm. (b) Similar simulation and measurement results for figure-8 data coils.

According to Fig. 12(a), the rotations along X- and Y-axes actually increase k₃₄ in the vertical data coils. In figure-8 coils, however, all rotations result in k₃₄ reductions. Nevertheless, without considering the changes in k₁₄, we cannot draw any conclusions about the effects of rotations. k₁₄ was too small to be shown in the same scale as k₃₄. Hence, we considered k₃₄/k₁₄ as a figure of merit (FoM) to compare the data coil designs.

D. Comparison of Data Coils

Fig. 13(a) and (b) shows k₃₄/k₁₄ versus linear misalignments and rotations, respectively. The level at which k₃₄/k₁₄ = 1 is a good measure for indicating how much misalignment or rotation can be handled by each coil design. Fig. 13(a) shows that when the coils are perfectly aligned, the vertical data coils are in a stronger position. However, they are affected by X-axis misalignment more rapidly than figure-8 coils. According to Fig. 13(b), vertical data coils are more robust against rotations pivotal to X- and Z-axes compared to figure-8 coils. In rotations larger than 10° pivotal to the Y-axis, however, figure-8 coils are stronger, because this type of rotation affects the orthogonal advantage of the vertical data coils and increases their exposure to power PSCs magnetic flux [see Fig. 2(a)].

Fig. 13.

(a) Comparing the k₃₄/k₁₄ ratio between vertical and figure-8 data coils versus linear misalignment along the X-axis. (b) Comparing k₃₄/k₁₄ be-tween vertical and figure-8 coils versus rotations. The coils’ relative distance is kept at D = 10 mm.

E. Power PSC and Data Coils Cross Coupling

So far, we have only considered the interference from the power carrier onto the received data carrier directly through k₁₄. By inspecting Fig. 1, however, one can see that there are two other possible paths for this interference. One is the coupling from L₁ onto L₂ (the power link) and then from L₂ onto L₄. This can be represented by k₁₂ × k₂₄. The other is from L₁ onto L₃ and then from L₃ onto L₄ (the forward data link), which can be represented by k₁₃ × k₃₄. Between these two, we expect k₁₂ × k₂₄ > k₁₃ × k₃₄ because of the strong coupling between L₁ and L₂ (k₁₂). To understand the significance of these undesired coupling paths, particularly when the coils are misaligned, we have compared all three paths versus X-axis misalignments in Fig. 14 through simulation and measurements. Fig. 14(a) shows that in vertical data coils, even though k₁₂ × k₂₄ and k₁₃ × k₃₄ are comparable to k₁₄ in perfect alignment (k₁₄ = 3.9 × 10⁻⁵ versus k₁₂ × k₂₄ = 1.1 × 10⁻⁵), they remain at about two orders of magnitude below k₃₄, while k₁₄ grows rapidly as a result of X-axis misalignment [compared with Fig. 11(a)]. Therefore, we do not need to be concerned about these indirect interference paths in vertical data coils.

Fig. 14.

(a) Calculation (see Appendix), simulation, and measurement of the effect of misalignment along the X-axis on indirect coupling paths in vertical data coils [see Fig. 2(a)]. (b) Effect of misalignment along the X-axis on indirect coupling paths in figure-8 data coils [see Fig. 4(b)]. The coils’ relative distance is maintained at D = 10 mm.

Fig. 14(b) shows the same comparison for figure-8 data coils. In this case, k₁₃ × k₃₄ is very small and can be ignored. However, k₁₄ and k₁₂ × k₂₄ are close in perfect alignment (k₁₄ = 6.8 × 10⁻⁴ versus k₁₂ × k₂₄ = 4.0 × 10⁻⁴), and k₁₂ × k₂₄ remains smaller but comparable to k₁₄. One possible way of taking advantage of k₁₂ × k₂₄ is to make sure that its sign is opposite that of k₁₄. This is possible with the proper selection of the direction of windings in L₁ and L₂. This leads to the power carrier interference through k₁₂ × k₂₄ to be out of phase with the main source of interference through k₁₄ and slightly weakens it.

F. UWB Antennas

Antennas are typically characterized by their radiation pattern, directivity, efficiency, gain, and bandwidth, and all of these characteristics are affected by their environment [33], [34]. However, in this work, we only measured the S₁₁, the return loss, in the air to observe the radiation bandwidth. Fig. 15 shows the simulation and measurement results for the S₁₁ of the planar spiral UWB antenna A₂, stacked on top of the power PSC and figure-8 data coils in a 4-layer PCB as shown in Fig. 4(b). It can be seen that the UWB antenna has a radiation bandwidth from 2.5 to 5 GHz with S₁₁ < −10 dB, which is expected to be sufficient for transmitting tens of megabits per second of recorded data across a short distance (5 ~ 20 mm) by using the IR-UWB technique [37].

Fig. 15.

Simulation and measurement of S₁₁ with and without the vertical data coil for the UWB spiral antenna, A₂, that is implemented on the same PCB as L₂ and figure-8 L₄, as shown in Fig. 4(b).

Fig. 15 also shows the S₁₁ when we added the vertical data coil to the Fig. 4(b) combination, as seen in Fig. 2(b). The vertical data coil affected the frequency response of the antenna, and the 2.5 ~ 5 GHz window was no longer available. Therefore, the spiral UWB antenna design needs to be modified if it is intended to be used with vertical data coils. It should also be noted that at high frequencies, electromagnetic power absorption in the tissue increases the antenna losses, and true evaluation of these antenna designs should be done in saline or appropriate tissue simulants [38], [39]. Therefore, more work is needed to develop IR-UWB antennas that are optimized specifically for the ground-plane geometry (PSC), the choice of data coils, and the surrounding environment.

V. Conclusion

We have presented a novel method for the design and optimization of a multiband wireless link that has a dedicated carrier signal and a coil/antenna pair for every major function that is expected from the wireless link across the skin barrier in a high-performance implantable neuroprosthetic device, such as a visual prosthesis or BMI. Previously, we had described the optimization of the PSC geometries for efficient power transmission based on the application and fabrication process in an iterative design procedure [11]. Here, we have used a pair of PSCs, optimized in the air at 13.56 MHz, as the foundation for design and optimization of two types of coils for forward data transmission, vertical coils, and figure-8 coils.

Considering that the power carrier of the external transmitter can be up to two orders of magnitude larger than the data carrier, minimization of the power carrier interference on the implanted receiver data coil is of utmost importance. Vertical coils take advantage of the fact that orthogonal coils that are symmetrical ideally have no cross coupling. Figure-8 coils, on the other hand, take advantage of their differential windings to attenuate the effects of any common-mode external electromagnetic field. A detailed comparison between the vertical and figure-8 coils revealed that the former leads to lower interference when coils are perfectly aligned, while the latter is more robust against linear misalignments. With respect to rotations, the results are mixed. Therefore, similar to many other engineering designs, the choice of data coil geometry will depend on the intended application. If the coils’ relative positions are going to be stable, such as BMIs, then vertical coils would be better. However, if the coils are expected to move with respect to one another, such as visual prostheses, then Figure-8 coils can result in a more robust system.

Most of the calculations, simulations, and measurement results were in close agreement within the range of parameters needed for neuroprosthetic applications. One major deviation from practical conditions, however, was air as the surrounding medium around the coils, as opposed to neural tissue. The tissue volume conductor will increase the coils’ parasitic capacitance and decrease their SRF and quality factors. Therefore, the optimal number of turns and size of the coils are expected to be reduced, particularly for external coils, as we have shown for power PSCs in [18]. On the other hand, since the permeability of tissue is close to that of the air, the difference between k in air and tissue environments will be small. Therefore, the same design criteria that are proposed here will be applicable in the tissue environment.

We are going to use micromachining (MEMS) technology with smaller feature size on high dielectric substrates in order to further shrink the volume of the implantable multiband coil/antenna complex from the present 0.15 cc, and conduct measurements in the real tissue environment.

Biographies

Uei-Ming Jow: (S’07) received the B.E. degree in electrical engineering from Tatung University, Taipei, Taiwan, in 1999, the M.S. degree in electronic engineering from the National Taiwan University of Science and Technology, Taipei, in 2001, and is currently pursuing the Ph.D. in electrical and computer engineering at the Georgia Institute of Technology, Atlanta.

From 2001 to 2006, he joined the Industrial Technology Research Institute, Hsinchu, Taiwan, and was an RF Engineer with the Electronics Research and Service Organization. He was involved in the analysis of electromagnetic compatibility for the high-speed digital circuit as well as the embedded radio-frequency circuit packaging technology. His main research interests are neural engineering, bionic systems, integrated analog circuit design, and wireless-implantable biomedical systems.

Maysam Ghovanloo: (S’00–M’04–SM’10) was born in 1973 in Tehran, Iran. He received the B.S. degree in electrical engineering from the University of Tehran, Tehran, Iran, in 1994, the M.S. degree in biomedical engineering from the Amirkabir University of Technology, Tehran, in 1997, and the M.S. and Ph.D. degrees in electrical engineering from the University of Michigan, Ann Arbor, in 2003 and 2004, respectively.

From 2004 to 2007, he was an Assistant Professor in the Department of Electrical and Computer Engineering, North Carolina State University, Raleigh. In 2007, he joined the faculty of Georgia Institute of Technology, Atlanta, where he is currently an Assistant Professor and the Founding Director of the Georgia Tech (GT) Bionics Laboratory in the School of Electrical and Computer Engineering. He has authored or coauthored more than 70 conference and journal publications. Dr. Ghovanloo is an Associate Editor of the IEEE Transactions on Circuits and Systems, Part II: Express Briefs.

Dr. Ghovanloo is the recipient of a CAREER award from the National Science Foundation in 2010. He also received awards in the 40th and 41st Design Automation Conference (DAC)/International Solid-State Circuits Conference Student Design Contest in 2003 and 2004, respectively. He has organized several special sessions and was a member of technical review committees for major conferences in the areas of circuits, systems, sensors, and biomedical engineering. He is a member of the Tau Beta Pi, the Sigma Xi, and the IEEE Solid-State Circuits Society, the IEEE Circuits and Systems Society, and the IEEE Engineering in Medicine and Biology Society.

Appendix

Rectangular coils’ self inductance L was calculated from the following equation by substituting data coil geometries in centimeters [5]

$$\begin{array}{l}L=0.008N_d^2\frac{l_d{h}_d}{w_d}\\ \times \{\frac{1}{2}\frac{w_d}{h_d}{sinh}^{-1}\frac{l_d}{w_d}+\frac{1}{2}\frac{w_d}{l_d}{sinh}^{-1}\frac{h_d}{w_d}-\frac{1}{2}\left(1-\frac{h_d^2}{w_d^2}\right)\\ \times \frac{w_d}{l_d}{sinh}^{-1}\frac{l_d}{w_d\sqrt{1+h_d^2/w_d^2}}-\frac{1}{2}\left(1-\frac{l_d^2}{w_d^2}\right)\frac{w_d}{l_d}\\ \times {sinh}^{-1}\frac{h_d}{w_d\sqrt{1+l_d^2/w_d^2}}-\frac{1}{2}\frac{h_d}{w_d}{sinh}^{-1}\frac{l_d}{h_d}-\frac{1}{2}\\ \times \frac{l_d}{w_d}{sinh}^{-1}\frac{h_d}{l_d}+\left(\frac{\pi }{2}-{tan}^{-1}\frac{l_d{h}_d}{w_d^2\sqrt{1+g^2/w_d^2}}\right)\\ +\frac{1}{3}\frac{w_d^2}{l_d{h}_d}[\sqrt{1+\frac{g^2}{w_d^2}}\left(1-\frac{1}{2}\frac{g^2}{w_d^2}\right)+1-\sqrt{1+\frac{l_d^2}{w_d^2}}\\ \times \left(1-\frac{1}{2}\frac{l_d^2}{w_d^2}\right)-\sqrt{1+\frac{h_d^2}{w_d^2}}\left(1-\frac{1}{2}\frac{h_d^2}{w_d^2}\right)]\\ +\frac{1}{6}\frac{w_d}{l_d{h}_d}\frac{g^3-l_d^3-h_d^3}{w_d^2}\}\end{array}$$ (3)

in μH, where $g^2=l_d^2+w_d^2$.

Mutual inductance between a pair of rectangular solenoids was calculated by making adjustments in the circular solenoid equations from [5]

$$M=0.001(A_3)(A_4)\frac{N_3}{W_{d3}}·\frac{N_4}{W_{d4}}·\left[\frac{Z_1}{r_1}-\frac{Z_2}{r_2}-\frac{Z_3}{r_3}+\frac{Z_4}{r_4}\right]$$ (4)

where

$$\begin{array}{l}{A}_3=(l_{d3}·h_{d3}),A_4=(l_{d4}·h_{d4}),\text{and}\\ Z_m=T_2{t}_2-\frac{1}{4}\frac{h_{d3}^2}{r_m^2}\left(T_4{t}_2+\frac{h_{d4}^2}{h_{d3}^2}{T}_2{t}_4\right)P_2({\mu }_m)+\frac{1}{8}\frac{h_{d3}^4}{r_m^4}\\ \times \left(T_6{t}_2+3\frac{h_{d4}^2}{h_{d3}^2}{T}_4{t}_4+\frac{h_{d4}^4}{h_{d3}^4}{T}_2{t}_6\right)P_4({\mu }_m)-\frac{5}{64}\frac{h_{d3}^6}{r_m^6}\\ \times \left(T_8{t}_2+6\frac{h_{d4}^2}{h_{d3}^2}{T}_6{t}_4+6\frac{h_{d4}^4}{h_{d3}^4}{T}_4{t}_6+\frac{h_{d4}^6}{h_{d3}^6}{T}_2{t}_8\right)P_6({\mu }_m)\\ +\frac{7}{128}\frac{h_{d3}^8}{r_m^8}(T_{10}{t}_2+10\frac{h_{d4}^2}{h_{d3}^2}{T}_8{t}_4+20\frac{h_{d4}^4}{h_{d3}^4}{T}_6{t}_6\\ +10\frac{h_{d4}^6}{h_{d3}^6}{T}_4{t}_8+\frac{h_{d4}^8}{h_{d3}^8}{T}_2{t}_{10})P_8({\mu }_m)+\dots \end{array}$$

in microHenries. The four radii vectors r_m (m = 1 to 4), depend on the four distances d_m given by

$$\begin{array}{l}{r}_m=\sqrt{d_m^2+{(D+h_{d3}/2+h_{d4}/2)}^2},\\ d_1=X-\left(\frac{W_{d4}+W_{d3}}{2}\right),d_2=X+\left(\frac{W_{d4}-W_{d3}}{2}\right),\\ d_3=X+\left(\frac{W_{d3}-W_{d4}}{2}\right),d_4=X+\left(\frac{W_{d3}+W_{d4}}{2}\right).\end{array}$$

μ_m = d_m/r_m, and P_2n(μ_m) (n is a positive integer) are known as zonal harmonics, given by [5]

$$P_{2n}({\mu }_m)=\frac{(2·2n-1)(2·2n-3)\dots 1}{(2n)!}\times \left[{\mu }_m^{2n}-\frac{2n(2n-1)}{2(2·2n-1)}{\mu }_m^{2n-2}+\frac{2n(2n-1)(2n-2)(2n-3)}{2·4(2·2n-1)(2·2n-3)}{\mu }_m^{2n-4}-\dots \right].$$ (5)

T₂ and t₂ are a function of ${\mathit{Dia}}_3^2/{(h_{d3}/2)}^2$ and ${\mathit{Dia}}_4^2/{(h_{d4}/2)}^2$, respectively, and the same is true for T₄ and t₄, T₆ and t₆, so on and so forth. The coefficients t₂, t₄, t₆,… or T₂, T₄, T₆,… are functions of the ratio τ of the height of the coil (h_d) and its mean wire diameter (Dia).

• For the external coil, $\text{L}3(T_n){\tau }_{ex}^2={\mathit{Dia}}_3^2/{(h_{d3}/2)}^2$.

• For internal coil, $\text{L}4(t_n){\tau }_{in}^2={\mathit{Dia}}_4^2/{(h_{d4}/2)}^2$

  $$T_n\text{or}{t}_n=1+\frac{n(n-1)}{3!}\frac{{\tau }^2}{2^2}+\frac{n(n-1)(n-3)}{5!}\frac{{\tau }^4}{2^4}+\dots +\frac{n(n-1)(n-3)\dots [n-(n-1)]}{(n+1)!}\frac{{\tau }^n}{2^n}.$$

Finally, by substituting L and M from the aforementioned equations in (1), k₃₄ can be found.