IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL 45, NO 7, JULY 1998
`
`867
`
`A Study of Printed Spiral Coils for Neuroprosthetic
`Transcranial Telemetry Applications
`
`Maulik R. Shah, Richard P. Phillips, and Richard A. Normann,* Member, IEEE
`
`Abstract— We have explored the use of printed spiral coils
`(PSC’s) for neuroprosthetic transcranial telemetry applications.
`We fabricated two-dimensional PSC’s on a thin (25 m) poly-
`imide substrate using copper (35 m) as a conducting material.
`All the coils had a fixed inner diameter of 1.0 cm. We fabricated
`two sets of coils. One set of coils consisted of 2- to 5-turn
`circular and square spiral coils and had different trace widths
`(WW ), different spacings (S) between adjacent traces, and different
`outer diameters. The other set of coils consisted of 5-turn circular
`spiral coils and had fixed inner and outer diameters but different
`sRs and
`pRp)
`W to SS ratios. We measured loss resistances (
`and quality factors (Q) of these coils at different resonating
`frequencies in the range of 5–40 MHz. Over this frequency range,
`we observed that for fixed inner and outer diameters, the coil
`with the largest WW achieved the lowest Rs and the highest
`pRp and Q. These electrical properties and the fact that these
`coils can conform to the complex convoluted cortical surface
`suggest that a PSC [15] can provide a viable alternative to a
`conventional wire-wound coil for neuroprosthetic transcranial
`telemetry applications.
`
`losses, neuroprosthesis,
`Index Terms— Coil efficiency, coil
`printed spiral coil, transcranial telemetry system.
`
`I. INTRODUCTION
`
`individual electrodes and inject a safe level of current through
`them in order to elicit a pattern of phosphenes [15]. Further,
`in order to access the implanted electrodes and the associated
`electronics, and to provide the required level of current for the
`electrical stimulation of the visual cortex, a suitable interfacing
`link (the link that connects the external power supply and
`the external electronics to the implanted visual prosthesis) is
`required.
`In the previous designs of prototype visual prostheses, two
`types of interfacing links were implemented [2], [7]. These
`interfacing links were a telemetry system implemented by
`Brindley and his research group [2], and a multiple-lead wire-
`percutaneous connector system implemented by Dobelle et al.
`[7]. There are distinct advantages associated with the lead
`wire-percutaneous connector system: 100% efficient power
`transfer (providing for a long life of external batteries), wide
`bandwidth for data transfer, and no need for electronic circuitry
`to be attached with the implanted electrodes. However, the
`lead wire-percutaneous connector that breaches the skin and
`the skull, increases the chances of infection. As the lead wires
`are fastened to both the connector and the array, there is
`an increased chance of lead wire failure due to motion of
`the brain with respect to the cranium. This relative motion
`can cause forces on the array due to its being tethered
`to the connector, which increases the chance of lead wire
`failure and/or displacement of the implanted array. Further,
`patients are unlikely to accept a skull mounted connector for
`a chronic application. Considering these issues for a cortical
`neuroprosthesis (such as a visual prosthesis), a transcranial
`telemetry system across a closed scalp may offer advantages
`over a lead wire-percutaneous system. By eliminating a direct
`connection between internal and external components of the
`neuroprosthesis, the telemetry system substantially reduces
`the likelihood of infection and the consequences of tethering
`forces. However, the design of such a telemetry system offers
`more challenges than a lead wire-percutaneous connector
`system. Further, the use of implanted electronics mandates
`the use of hermetic sealing of the prosthesis to protect the
`circuitry from the corrosive environment of the cerebral spinal
`fluid. Considering these issues, we are beginning to implement
`a transcranial telemetry system to be used in the design of
`the visual prosthesis. The schematic diagram of the telemetry
`system, its associated components, and its integration with the
`electrode array and the demultiplexing chip are shown in Fig. 1
`[19].
`Designs of transcutaneous/transcranial telemetry systems for
`various neuroprosthetic applications have been reported in
`0018–9294/98$10 00 ª
`
`RESEARCHERS have demonstrated that by electrically
`
`stimulating the visual cortex of blind volunteer, spots of
`light (termed phosphenes) could be evoked where a sighted
`individual would normally have his/her visual field [2], [7].
`If patterns of electrically evoked phosphenes can be sys-
`tematically organized to convey useful spatial information,
`then a functional visual prosthesis could become a reality.
`These considerations, coupled with recent advances in the
`fields of silicon micromachining and microelectronics, have
`caused researchers to reexamine the possibility of developing
`a cortically based visual prosthesis for the blind. It is likely
`that silicon-based electrode arrays will become an integral
`part of such a visual prosthesis for accessing neurons of
`the visual cortex [20]. We have developed such an electrode
`array, fabricated on a 4.2 mm 4.2 mm monolithic silicon
`substrate and containing 100 microneedles that project out of
`the substrate [14]. An advanced, silicon-based demultiplexing
`scheme has also been designed to select each of the 100
`
`Manuscript received January 4, 1995; revised January 14, 1998 Asterisk
`indicates corresponding author
`M R Shah is with the Department of Bioengineering, The University of
`Utah, Salt Lake City, UT 84112 USA
`R P Phillips is with Link Research, Salt Lake City, UT 84111 USA
`*R A Normann is with the Department of Bioengineering, The University
`of Utah, Salt Lake City, UT 84112 USA (e-mail: normann@m cc utah edu)
`Publisher Item Identifier S 0018-9294(98)04381-X
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`1998 IEEE
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`SAMSUNG EXHIBIT 1014
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`

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`868
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`IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL 45, NO 7, JULY 1998
`
`Fig 2 A 5-turn circular spiral coil (W = S = 313 m) fabricated on a
`flexible and biocompatible polyimide substrate
`
`appropriate to the skin depth at the frequency at which the
`) and the inner
`coil is operated [4], [25]. The trace width (
`trace spacing (
`) can be optimized to reduce the effect of
`proximity that could result due to the influence of current
`in the adjacent traces of the coil [4]. Further, the substrate
`upon which the coil is fabricated could provide an excellent
`insulating and encapsulating layer and could be used to mount
`discrete microelectronic components and provide interconnect
`traces for the electrode array and the demultiplexing chip.
`These aspects prompted us to fabricate and study the electrical
`properties of PSC’s that could be useful in our neuroprosthetic
`transcranial telemetry application.
`Researchers have described the electrical properties of cylin-
`drical, closely packed wire-wound coils in the frequency range
`of 0.2–20 MHz, as well as the dependence of series (
`)
`and parallel (
`) loss resistances of such coils on resonating
`frequency and the number of turns in the coils [8]. Others
`have reported on electrical properties of printed thin film
`coils (fabricated on glass and ceramic substrates) designed
`to be operated in the frequency range of 100 MHz–1 GHz
`for nonbiological applications [4]. In this reported study, the
`optimum quality factor (
`) (for a coil with an outer diameter
`of 0.25 cm) was obtained when the
`equaled to the
`. Since
`no data were provided on the electrical properties of PSC’s
`in the frequency range of 1–100 MHz, our study focused on
`the frequency range judged most appropriate for a transcranial
`telemetry application.
`We fabricated PSC’s on a thin, conformable, and biocom-
`patible (polyimide) substrate using copper as a conducting
`material (Fig. 2). We fabricated two sets of coils. One set
`of coils consisted of 2- to 5-turn circular and square spiral
`coils and had a variety of
`,
`, and outer diameters. The
`other set of coils were 5-turn circular spiral coils with fixed
`inner and outer diameters and different
`to
`ratios (
`to
`ratios ranging from
`to
`). We studied
`electrical properties of these PSC’s in the frequency range
`of 5–40 MHz. Over this frequency range, we observed that
`for fixed inner and outer diameters, the coil with the largest
`achieved the lowest
`and the highest
`and
`. These
`electrical properties and the fact that these coils are very thin
`and can conform to the complex convoluted cortical surface
`suggest that a PSC coil can provide a viable alternative to a
`
`Fig 1 Different components of the visual prosthesis and the telemetry
`system An external
`transmitting coil will send power and data to the
`implantable receiving coil The receiving coil will provide power and data to
`the demultiplexing chip and the electrodes The component interconnection is
`made clear in the side view of the prosthesis, which shows the demultiplexing
`chip [built into a very large scale integration (VLSI) chip] connected to the
`electrode array in the plane of the receiving coil The top view of the prosthesis
`shows the geometrical layout of the PSC and its interconnection with the
`electrode array and the demultiplexing chip
`
`the literature [2], [5], [8], [9], [13], [18], [21], [27]. Recent
`advances in silicon micromachining and silicon microelec-
`tronics [very large scale integration (VLSI) technology] have
`also enabled researchers to develop miniature neuroprosthetic
`devices that contain RF telemetry systems [16], [19], [26].
`Despite the design variations in these telemetry systems,
`most use a multiple-turn, three-dimensional (3-D), wire-wound
`receiving coil as an internal component of the neuroprosthesis.
`In a conventional wire-wound coil, different turns of the
`coil are stacked one upon another to achieve a multiple-
`turn coil with a “doughnut geometry.” If such 3-D coils are
`to be used in a visual prosthesis application, they may not
`be able to conform to the convoluted surface of the cortex.
`The thickness of the wire-wound coil can be substantially
`reduced by orienting successive turns of the coil in a spiral
`geometry [two-dimensional (2-D)] rather than the doughnut
`configuration (3-D). Conformability of a wire-wound coil
`could be achieved by bonding a very thin wire in a spiral
`configuration to a thin and flexible substrate. These issues sug-
`gest that a thin, conformable, and biocompatible coil could be
`fabricated using simple photolithographic and microfabrication
`techniques. Further, as such a printed spiral coil (PSC) would
`be produced using standard photolithographic techniques, the
`geometric features of the coil can be precisely specified to
`address issues such as the skin and proximity effect on coil
`efficiency. The issue of skin effect (at high frequency) can
`be addressed by adjusting the thickness of the coil to be
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`

`SHAH et al : PRINTED SPIRAL COILS FOR NEUROPROSTHETIC TRANSCRANIAL TELEMETRY APPLICATIONS
`
`869
`
`TABLE I
`COIL DIMENSIONS OF DIFFERENT CIRCULAR AND SQUARE SPIRAL
`COILS WITH FIXED INNER AND VARIABLE OUTER DIAMETERS
`
`conventional wire-wound coil for neuroprosthetic transcranial
`telemetry applications.
`
`II. MATERIALS AND METHODS
`
`A. Coil Materials and Fabrication
`Polyimide was chosen as the substrate of the PSC’s de-
`scribed herein because of its demonstrated biocompatibility
`and because it has been widely used as an insulating material
`in a variety of neuroprosthetic applications [12], [17], [22].
`Copper was selected as the model material because of its high
`conductivity and its commercial availability. However, since
`copper is not a biocompatible material, copper coils should
`be avoided in systems intended for chronic implantation. All
`our coils were fabricated from a commercially available cured
`polyimide ( Kapton)-based copper foil (Rogers Corporation,
`Chandler, AZ) using photolithographic techniques. The overall
`thickness of the PSC was approximately 90 m, the thickness
`of copper was 35 m, and the thickness of polyimide was 25
`m. The remaining thickness was due to the adhesive between
`polyimide and copper.
`As the PSC was intended to be used along with the
`silicon-based Utah Intracortical Electrode Array [14], the inner
`diameter of all the PSC’s was chosen to be 1.0 cm, a size
`large enough to contain the demultiplexing chip, the electrode
`array (on the back side), and a few discrete microelectronic
`components in the center of the coil (see Fig. 1). We fabricated
`two sets of coils. In one set of the coils, the outer diameter
`of the PSC was variable and was dependent on the number of
`turns and
`and
`of the coils. These coils were a set of 16
`circular spiral PSC’s and also a set of 16 square spiral PSC’s
`with the number of turns varying from 2–5 having different
`and
`. We fabricated these coils in order to explore the
`electrical properties of PSC’s and specifically to study the
`effect of coil geometry, operating frequency, number of turns,
`, and
`on the coil efficiency. Table I shows the dimensions
`of square and circular spiral coils.
`The other set of coils were 5-turn circular spiral coils with
`fixed inner and outer diameters, but with a variety of
`to
`ratios (
`). These coils were fabricated such that the
`
`center to center inner and outer diameters of all the coils
`were 1.0 and 1.625 cm, respectively. In between the outer
`and inner perimeters of the coil, a variety of 5-turn coils
`were fabricated such that the sum of
`and
`remained
`approximately constant. However, individual values of
`and
`varied from coil to coil providing different
`to
`ratios
`for the coils (see Table II). Further, depending on the width
`(
`) associated with an individual coil (in this set of coils),
`the minimum and maximum inner and outer diameters varied
`approximately by 5% from the center to center inner and outer
`diameters of all the coils. We fabricated these coils in order
`to study the possible proximity effect due to different
`to
`ratio (
`) as reflected in coil efficiency. Table II shows the
`values of
`,
`, and
`to
`ratios of these 5-turn circular
`spiral coils.
`
`B. Analysis of Electrical Properties of Coils
`In a telemetry system, the transmitting and receiving coils
`are inductively coupled to each other in order to transfer the
`required power and data from the transmitter to the receiver
`(see Fig. 1). In order to deliver the required level of power
`and data from the transmitter to the receiver efficiently, in
`most of the cases, the transmitting and the receiving coils
`operate at a particular frequency (most commonly the coil
`is operated at the resonant frequency determined by the coil
`and a parallel capacitor). The circuit in which the coil and a
`capacitor are connected to each other such that they resonate at
`a particular frequency is called a resonant circuit (also called
`a resonant tank circuit). There are two main configurations of
`the resonant circuits. One configuration is the series resonant
`circuit in which the coil is resonated by connecting a capacitor
`in series with it, and in another configuration, known as a
`parallel resonant circuit, the coil is resonated by connecting a
`capacitor in parallel with it. The losses associated with the
`resonant circuit are divided into coil losses and capacitive
`losses. However, using capacitors that have negligible losses,
`the resonant tank losses can be attributed to the coil losses.
`The coil, acting as an inductor in either the series or parallel
`resonant tank circuit, has an intrinsic dc resistance associated
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`Page 3 of 10
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`

`

`870
`
`IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL 45, NO 7, JULY 1998
`
`TABLE II
`COIL DIMENSIONS FOR THE 5-TURN CIRCULAR SPIRAL COILS WITH FIXED
`INNER AND OUTER DIAMERERS AND DIFFERENT W TO S RATIOS
`
`with it. This dc loss resistance of the coil mainly depends on
`the nature of the conducting material used in the fabrication
`of the coil, the length of the coil and the cross-sectional area
`of the coil. When the coil is operated at a high frequency, the
`losses associated with the coil are commonly represented by
`the series resistance of the coil (
`), represented in series with
`the coil. However, in some cases, the losses associated with
`the coil,
`, are represented by a parallel loss resistance,
`.
`This ac resistance,
`of the coil, depends on several factors
`such as the frequency at which the coil is being operated, the
`skin effect, the proximity effect, and eddy current effects due
`to metallic objects around the coil.
`The quality factor (
`) of a coil is defined as how much
`energy it can store (in a coil inductor) versus how much energy
`it dissipates (by a series loss resistance,
`). The relationship
`between the coil
`, coil inductance (
`), and
`is defined as
`
`(1)
`
`The representation of
`is one way to describe
`in terms of
`the quality of the coil. Another way is to represent coil losses
`is by a parallel loss resistance (
`) that is represented as being
`in parallel with the coil. The relationship between the coil
`,
`coil inductance (
`), and the parallel loss resistance (
`) is
`defined as
`
`(2)
`
`Further, the relationship between
`is defined as
`and
`and can be further simplified as
`], for
`. Thus, in order to
`[or
`characterize the coil
`one should know coil inductance, coil
`operating frequency, and either its series loss resistance (
`)
`or its parallel loss resistance
`.
`We estimated coil inductances using appropriate equations
`described in the literature [1], [4], [6], [11]. To validate the
`calculated values, coil inductances were measured using two
`different methods. The first method involved making a parallel
`tuned tank with a PSC and a capacitor of a known value
`and connecting that parallel tank in series with a resistor. A
`sinusoidal voltage was applied to the circuit from a variable
`frequency generator and the waveforms across the tank and
`tank plus the resistor were monitored with an oscilloscope. By
`bringing both the waveforms into phase, we could determine
`
`the resonant frequency of the tank. From the value of resonant
`frequency, the inductance of the PSC was then calculated.
`The second technique involved the use of an HP 4194A
`impedance/gain-phase analyzer. The calculated values of coil
`inductances differed from the measured values by no more
`than 10%–15% for all PSC’s.
`We measured the dc resistances of all PSC’s with an
`LCR (inductance/capacitance/resistance) meter. Values of both
`the theoretically calculated and the measured dc resistances
`of PSC’s were in close agreement. We also measured loss
`resistances
`and
`of all
`these coils at different res-
`onating frequencies (the coils were resonated using different
`values of capacitance connected in parallel with the coil)
`in the frequency range of 5–40 MHz using the HP 4194A
`impedance/gain-phase analyzer. As the goal of the experiment
`was to achieve the greatest
`for a given coil, from the
`coils described herein, we characterized coils by calculating
`coil
`, using the relation between
`,
`, and
`:
`is the
`, where
`is the coil inductance,
`is the series
`is the parallel loss resistance.
`
`resonating frequency,
`loss resistance, and
`
`III. RESULTS
`The electrical properties of the PSC’s were measured in
`an unloaded, parallel tuned tank model made from a parallel
`connection of the PSC and a capacitor. Since the capacitors
`were selected such that they had negligible losses, all tank
`circuit losses were attributed to coil losses and represented
`either by
`or
`. The parallel tank model was chosen
`so that direct comparison could be made between the
`of
`the tank (
`of the coil) and the load (computed from the
`power requirement of the electrode array) that will be placed in
`parallel with the parallel tuned tank. For an efficient telemetry
`system, most of the power that is received at the receiver tank
`should be delivered to the load, which can be achieved by
`making
`of the parallel tuned receiver tank relatively high
`compared to the actual load (at resonance the receiver tank
`appears simply as a resistor). Thus, the goal of our study was
`to determine if a PSC could be fabricated that has a value of
`substantially greater than the anticipated load resistance
`and that the PSC could provide the required value of
`.
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`SHAH et al : PRINTED SPIRAL COILS FOR NEUROPROSTHETIC TRANSCRANIAL TELEMETRY APPLICATIONS
`
`871
`
`The frequency dependence of series loss resistance (Rs), parallel
`Fig 3
`loss resistance (Rp), and quality factor (Q) of a 5-turn circular spiral coil
`(W = S = 313 m) at different resonating frequencies
`
`To investigate the frequency dependence of loss resistance
`of PSC’s, we measured values of
`,
`, and
`for our sets
`of 16 circular spiral PSC’s, 16 square spiral PSC’s (with four
`different values of
`and
`and four different numbers of
`turns), and 5-turn circular spiral coils with fixed inner and
`outer diameters having different
`to
`ratios. These tests
`were conducted at various resonating frequencies (by creating
`a parallel tank using each PSC and resonating it at a particular
`frequency with an appropriate value of a capacitor), ranging
`from 5–40 MHz. The results, as shown in Fig. 3, show that
`and
`have a square root dependence (
`) on
`the operating frequency. This has also been widely reported
`in the literature for other types of coils [4], [8], [25]. Since
`the relation between
`and
`can be approximated as
`, if the frequency dependence of
`is
`substituted in the relation,
`it
`is obvious that
`has the
`frequency dependence of the order of
`. The
`dependence of frequency on the
`, and
`,
`of a 5-turn
`circular spiral coil (
`313 m) is shown in Fig. 3. A
`similar dependence was found for the coils with 2–4 turns.
`The representation of the tuned tank losses (coil losses) by
`a parallel loss resistance (
`) is one way to model the tank.
`A functionally identical model of tuned tank losses (the most
`common representation) is to represent the loss resistance of
`the coil as a series loss resistance
`. A plot of values of
`of PSC’s with
`313 m and different number of
`turns (Fig. 4) illustrates the effect of resonating frequency and
`number of turns on the coil losses.
`These results are similar to the results described in the
`literature for other types of coils [4], [8]. The coil losses
`increase with an increase in the number of turns and the
`operating resonant frequency. As it is convenient to replace
`of the coil by
`, similar PSC’s were used to measure
`values of
`at different resonating frequencies. Fig. 5 shows
`a comparison between the values of
`of the PSC’s (with
`313 m) having different numbers of turns, with the
`increasing as either the number of turns or the resonating
`frequency (or both) increases. Although this effect is similar to
`
`Fig 4 Values of series loss resistance (Rs) of 2- to 5-turn circular spiral
`coils (W = S = 313 m) at different resonating frequencies
`
`Fig 5 Values of parallel loss resistance (Rp) of 2- to 5-turn circular spiral
`coils (W = S = 313 m) at different resonating frequencies
`
`(Fig. 4), the frequency dependence
`the results shown for
`than for
`. This behavior has also been
`is greater for
`described by others for conventional wire-wound coils [8].
`Since the frequency and number of turns of the coil have
`effects on coil losses that are similar to those seen in the
`conventional wire-wound coils, coil geometry is an important
`parameter in the design of the spiral configuration of the
`for 5-turn circular PSC’s with dif-
`printed coils. Values of
`ferent
`and , measured at different resonating frequencies,
`are shown in Fig. 6. As the width of the coil increases,
`of
`the coil decreases. The coil with the biggest
`achieved the
`smallest
`. This was also found to be true for any number
`of turns in the coil [2–4 in our case].
`Values of
`for 5-turn circular PSC’s with different
`and
`, measured at different resonating frequencies, are also
`shown in Fig. 7. The PSC with
`313 m achieved
`the highest
`at each resonating frequency (the PSC’s have
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`872
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`IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL 45, NO 7, JULY 1998
`
`Fig 6 Values of series loss resistance (Rs) of 5-turn circular spiral coils
`with different W and S at different resonating frequencies
`
`Fig 7 Values of parallel loss resistance (Rp) of 5-turn circular spiral coils
`with different W and S at different resonating frequencies
`
`and ). This was
`different outer diameters due to different
`also found true for all other coils with different numbers of
`turns (2–4). This is because
`is inversely proportional to
`.
`The coil with a larger
`has a smaller
`(see Fig. 6). As
`is related to
`by the relation,
`, a coil
`with a larger
`(smaller
`) has a higher
`. The coil with
`250 m,
`313 m had only a small change in
`compared to the coil with
`250 m,
`375 m. As
`was the same in these two coils, the small change in
`was
`due to the change in inductance resulting from the different
`and the different outer diameter.
`Since losses in the PSC’s are reflected in coil
`, the results
`shown in Fig. 7 can be represented in terms of
`. These results
`are shown in Fig. 8, which show values of
`for 5-turn circular
`PSC’s with different
`and
`. A PSC with
`313
`m achieved the highest
`at all resonating frequencies. This
`was because the
`associated with the coil with
`
`Fig 8 Values of quality factor (Q) of 5-turn circular spiral coils with
`different W and S at different resonating frequencies
`
`313 m was minimum. Further, as shown in Fig. 8, a change
`in width of the coil from 163 to 313 m, resulted the change
`in
`by approximately 50% at 20 MHz. Further, the coils that
`had identical
`, the coil with
`250 m and
`375
`m and the coil with
`250 m and
`313 m, had a
`small change in
`caused by a change in
`of the coil.
`The above described coils (Figs. 3–8) had a fixed inner
`diameter and variable outer diameters. In these coils, the outer
`diameter was dependent on
`,
`, and the number of turns in
`the coil. However, in the design of a cortical neuroprosthetic
`device where miniaturization is an important issue, there is a
`restricted space available for the receiving coil. This constrains
`the size of the receiving coil and thus defines the inner and
`outer diameters of the coil. In between these inner and outer
`diameters of the coil, a certain number of turns can be provided
`by three different approaches: by making
`less than
`,
`equal to , and
`greater than . In order to study the effect of
`various
`to
`ratios on coil
`, we fabricated a set of 5-turn
`circular spiral coils that had fixed inner and outer diameters of
`1.0 and 1.625 cm, respectively. Further, by keeping the sum of
`and
`approximately constant, various
`to
`ratios were
`obtained. We studied the effect of various
`to
`ratios on
`,
`, and
`of these coils at different resonating frequencies in
`the range of 5–40 MHz. The results of these coils at 21 MHz
`are shown in Fig. 9.
`The top part of Fig. 9 shows the values of
`for these coils
`for different
`decreases
`to
`ratios. As shown in Fig. 9,
`as the
`to
`ratio of the coil increases. This is due mainly
`to the larger
`associated with the coil. This is similar to
`what has been shown in Figs. 6–8. The remaining parts of
`Fig. 9 show the results in terms of
`and
`. As
`and
`are related to
`such that any decrement in
`is reflected
`as an increment in both
`and
`, the coils with
`. Finally,
`achieved greater
`and
`than coils with
`the coil that had the biggest
`1.94), in the set of
`(
`all these coils, represented the lowest
`and the highest
`of
`,
`, and
`and
`. Finally, at 21 MHz, the values of
`the circular spiral coil with
`to
`ratio of 1.94 were 0.985
`, 4.774 k , and 69.6, respectively.
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`Page 6 of 10
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`SHAH et al : PRINTED SPIRAL COILS FOR NEUROPROSTHETIC TRANSCRANIAL TELEMETRY APPLICATIONS
`
`873
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`(a)
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`(b)
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`(c)
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`Fig 9 Values of (a) Rs, (b) Rp, and (c) Q of 5-turn circular spiral coils with fixed inner and outer diameters and different W to S (W=S) ratios
`
`IV. DISCUSSION
`
`For the visual prosthesis under development at the Uni-
`versity of Utah, we needed “surface mount space” in the
`center of the PSC for mounting the electrode array and the de-
`multiplexing chip, as well as various discrete microelectronic
`components. Surrounding this required “surface mount space,”
`we placed coils with 2–5 turns of either square or circular
`spirals. Because a circle has the minimum circumference for
`a given spacing between the inner edges of the coil, a square
`spiral geometry provides more area in the center of the coil
`and more inductance compared to a circular spiral coil of the
`similar dimensions. For similar numbers of turns, frequencies,
`
`dimensions, the dependence of coil losses (and
`and
`and
`) of square spiral PSC’s were similar to those measured
`for the circular spiral PSC’s. However, the consequences of
`misalignment between transmitting and receiving coils are
`greater for square spiral coils than for circular spiral coils
`(personal observations). Thus it would be preferable to use
`circular spiral coils rather than square spiral coils for a
`neuroprosthetic transcranial telemetry system.
`
`A. Coil Electrical Properties
`The PSC’s that we have built achieved electrical properties
`similar to other coils that have been described in the literature.
`A previous study on the coil losses of resonant wire-wound
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`Page 7 of 10
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`

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`874
`
`IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL 45, NO 7, JULY 1998
`
`of circular wire-wound coils
`coils demonstrated that the
`changes by a factor of 1.5 for every doubling of the resonating
`frequency [8]. However, this compares only the relative values
`of coil losses at different resonating frequencies. In order to
`compare the efficiencies of wire-wound coils and PSC’s, we
`have normalized the series loss resistance (ac resistance) of
`both the types of coils (measured at 30 MHz for PSC’s and
`extrapolated to 30 MHz for wire-wound coils) to their dc
`resistances. The ratio (
`to
`) for PSC’s was approxi-
`mately four times smaller than their wire-wound counterparts
`described in the literature [8]. This suggests that our coils are
`less lossy than the wire-wound coils because the increase of
`coil resistance from its dc value to ac value (at a particular
`frequency) was smaller in our coils than the wire-wound
`coils.
`The qualities of PSC’s have been the subject of one other
`study in which the printed thin film coils were fabricated on
`ceramic and glass substrates [4]. This study focused on the
`electrical properties of printed thin film coils in the frequency
`range of 100 MHz to 1 GHz for nonbiological applications.
`The coils differed from our PSC’s in terms of size, substrate
`material, substrate thickness, frequency of operation, and the
`model of the coil circuit (resonated tank in our case, self-
`resonated tank in their case). An empirical relationship was
`derived in the previous study that allows the determination of
`the series loss resistance,
`, of any coil (with any dimension)
`at any frequency [4]. However, a constant that was used in
`the empirical relationship was derived to fit the data that were
`taken for their printed thin film coils in the frequency range of
`100 MHz to 1 GHz. We calculated values of
`for our PSC’s
`based on this relationship in order to compare the results. The
`predicted frequency dependence of our PSC’s agreed with the
`measured values. However, the absolute values of
`for our
`PSC’s agreed only roughly with this empirical relationship.
`We do not have any solid reasons to explain this, however
`we can only speculate that the constant that was calculated
`in order to fit the data taken for the printed thin film coils
`operated in the frequency range of 100 MHz to 1 GHz, did
`not fit well with the values of loss resistances of our PSC’s.
`Further, for our PSC’s in the frequency range of 5 to 40 MHz,
`we could not find the effect of proximity that was described
`for the printed thin film coils by others [8]. We could not
`find any optimum
`ratio, instead we found a dominating
`effect on the coil losses for the our PSC’s: the greater
`is the width (
`) of the coil, the greater is the coil
`(see
`Fig. 9).
`
`B. Mutual Inductance Between Spiral Coils
`
`Because we have developed a PSC with a 2-D geometry
`in order to reduce the height of the coil, we are forced to
`use a spiral configuration of the coil
`to achieve multiple
`numbers of turns. Since we are proposing the use of a PSC
`for telemetry applications,
`the mutual
`inductance between
`two circular spiral PSC’s (transmitting and receiving coils)
`should be calculated. The calculation of the mutual inductance
`between two circular coils is described in the literature [18].
`Similar analysis can be done between two circular spiral coils.
`
`However, because the radius of the spiral coi