**3.1. Model of an infinite homogeneous lossy plane surface**

The propagation mechanisms of an electric doublet near a dissipative infinite homogenous plane has been investigated in [8]. These results provide a description of the electric field components as a function of the given geometry. Therefore the absolute value of the electric field *E* can be calculated depending on the dipole current distribution **i**, its effective height *h*, the frequency *f* , the complex dielectric parameters of the media *ε* and a tangential to the surface defined distance *d*, see Figure 4.

**Figure 4.** Principle geometry of the on-body scenario.

Included in this theory is the separation of the total electric field in its space and surface wave. As defined by Figure 4 the space wave consists of the wave components which propagates along the direct path *d* and the ground reflected path *d*ref. A surface wave component which is excited by the dissipative nature of the tissue is guided by the air-media boundary. It only contributes to the related electromagnetic field if the antenna is located in close proximity to the surface. This means that the effective antenna high *h* is typically lower than a few wave lengths. Otherwise, this wave component is negligibly small compared to the space wave. The electric field of any observation point *P* along a parallel surface path at the effective antenna high *h* can be described by Norton's formulation *N* as follows:

$$E \propto \frac{U\_{\rm n}}{d} N \left( \mathbf{i}\_{\rm v,h}, d, h, f, \underline{\mathbf{e}} \right), \tag{8}$$

where the normalization value *U*n depends on the antenna excitation. The term *N* is a function of the current distribution of the source **i**v,h, the distance *d*, the frequency *f* and the complex tissue permittivity *ε*. The absolute value of the electric field is given by the superposition of the space wave *E*sp and surface wave *E*sw as follows:

$$E(d) = E\_{\rm sp} + E\_{\rm SW} \tag{9}$$

where *E* is given by

6 Will-be-set-by-IN-TECH

As shown in [1], boundaries between high water content tissues (muscle tissue) and air filled regions (paranasal sinus, frontal sinus) or low water content tissues (fat tissue, bone tissue) lead to various electromagnetic interactions which reduce the accuracy of the approach presented above. The average attenuation of the electromagnetic field may still be characterized by the proposed model but especially with respect to time domain analysis the multi path behavior of these structures leads to insufficient results. Moreover, the specific anatomical location of the RF application may have a strong influence on the corresponding radiation characteristic of the antenna which cannot be adequately described by a homogeneous tissue model. Despite this fact the generality of the approach enables an extension of the theory by including anatomic realistic human models in the antenna design process to derive the resulting radiation characteristic. In this case the corresponding far field distance has to be enlarged related to the anatomical structure but the average description of

Encouraged by [7], the didactic first step to deduce a de-embedding for a wide class of on-body applications is the deduction of an adequate far field propagation model of a

The propagation mechanisms of an electric doublet near a dissipative infinite homogenous plane has been investigated in [8]. These results provide a description of the electric field components as a function of the given geometry. Therefore the absolute value of the electric field *E* can be calculated depending on the dipole current distribution **i**, its effective height *h*, the frequency *f* , the complex dielectric parameters of the media *ε* and a tangential to the

Included in this theory is the separation of the total electric field in its space and surface wave. As defined by Figure 4 the space wave consists of the wave components which propagates along the direct path *d* and the ground reflected path *d*ref. A surface wave component which is excited by the dissipative nature of the tissue is guided by the air-media boundary. It only contributes to the related electromagnetic field if the antenna is located in close proximity to the surface. This means that the effective antenna high *h* is typically lower than a few wave lengths. Otherwise, this wave component is negligibly small compared to the space wave. The

the far field may still be given by the proposed homogeneous model.

**3. Antenna de-embedding for on-body applications**

**3.1. Model of an infinite homogeneous lossy plane surface**

radiating source near a planar tissue like surface.

surface defined distance *d*, see Figure 4.

**Figure 4.** Principle geometry of the on-body scenario.

*2.1.2. Limitations of the in-body model*

$$E(d) \propto \frac{\mathcal{U}\_n}{d} \left[ \underbrace{e^{j\frac{2\pi d}{\lambda}}}\_{\text{direct wave}} + \underbrace{\mathcal{R}\_{\text{v,h}}\cos^3(\psi)}\_{\text{ground-reflected wave}} + \underbrace{\left(1 - \mathcal{R}\_{\text{v,h}}\right)F\_{\text{v,h}}\cos^2(\psi)}\_{\text{surface wave}} \right]. \tag{10}$$

In equation 10, *λ* denotes the free space wave length, *R*v,h the plane-wave reflection coefficient of the ground, *F*v,h the surface-wave attenuation function and *dref* the reflected path at angle *ψ*. Both, the reflection and the attenuation functions depend on the current distribution of the antenna and are given by [9] for vertical and horizontal antenna orientations. The related far field solution is valid for sufficient great distances *d* and depends in first place on the mathematical description of the surface-wave attenuation function. If an adequate description can be assumed the minimal valid distance, referred by Norton in [8], has to be greater than one free space wave length. An additional limitation is the assumption of locally plane waves for the derivation of the reflection coefficient of the ground. Under the assumption that the surface acts as a perfect mirror the electrical antenna size may be enlarged by the mirror image. Analog to equation 2 the far field distance *d*ff is defined by:

$$d\_{\rm ff} = \frac{2D\_{\rm max,eff}^2}{\lambda} \,\tag{11}$$

where the modified maximum antenna dimension is denoted by *D*max,eff. For an adequate derivation of the far field distance the quantity *D*max,eff has to be chosen appropriate under the aspect that the enlargement of the antenna by the ground acts primarily in normal direction to the surface. For distances greater than the minimum far field distance, given by equation 11, the formulation of equation 10 enables the definition of the directivity for on-body scenarios. Analog to equation 3 the directivity *D* is defined by the normalization of the power density to the far field model:

$$D = \frac{|\mathcal{S}|}{|\mathcal{S}\_{\text{Norton}}|}. \tag{12}$$

The related electromagnetic field is in general a superposition of TE-, TM- and TEM-wave components and therefore a function of the parameters given in equation 8. Despite this fact, the TEM-wave component contributes the most significant part to the power flux density. Even if a strong surface wave is excited, the resulting TM-wave component is comparatively

#### 8 Will-be-set-by-IN-TECH 160 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Antennas and Propagation for On-, Off- and In-Body Communications <sup>9</sup>

low. This fact enables a simple approximation of the power density by the given expression of electric field:

$$D \approx \frac{|E|^2}{\left|E\_{\text{Norton}}\right|^2} = \frac{|E|^2}{\left|\frac{\underline{\underline{\underline{\underline{\underline{\underline{\underline{\underline{\alpha}}}}}}}}{r}N\right|^2}}.\tag{13}$$

**i**v,h *f* = 3.1 GHz *f* = 6.85 GHz *f* = 10.6 GHz

Antennas and Propagation for On-, Off - and In-Body Communications 161

h 0.13 0.28 0.43

h 6.64 3.15 3.48

h 1.34 1.23 0.47

<sup>h</sup> 10.3 · <sup>10</sup>−<sup>4</sup> 1.8 · <sup>10</sup>−<sup>4</sup> 3.4 · <sup>10</sup>−<sup>5</sup>

*d*ff[m] v 0.16 0.35 0.54

Δ*S*[%] v 10.38 4.83 5.56

*D*[lin] v 1.37 1.07 0.99

eff[m2] <sup>v</sup> 8.7 · <sup>10</sup>−<sup>4</sup> 1.7 · <sup>10</sup>−<sup>4</sup> 4.4 · <sup>10</sup>−<sup>5</sup>

**Table 2.** Calculated on-body antenna parameters of the UWB teardrop antenna. The quantities Δ*S*, *G*

eff are calculated for the maximum far field distance of the considered frequency range with

directivity of the evaluated antennas decreases with increased frequencies. This behavior implies a reduced excitation of surface waves in the upper UWB frequency range due to the greater effective height of the antenna. Note, the derived gain is not directly comparable to the free space or in-body values. Due to the dependency of the channel model to the antenna polarization even the vertical and horizontal quantities are incomparable to each other. Despite this restriction the formulation of the directivity defines a quantity which enables an adequate discussion of various on-body antenna types and to enhance the corresponding

**Figure 5.** Distance to the antenna where the surface wave exceeds the space wave as function of the frequency and tissue parameters of a vertical polarization; First row: The effective antenna height is set to a quarter wave length of the respective frequency; Second row: Effective antenna height is set to a quarter wave length at *f* = 3.1 GHz; Green square marker: Fat tissue; Red round marker: Muscle tissue. Figure 5 shows an analysis of the effective antenna height in relation to the surface wave excitation. It discusses the distance *d*s where the surface wave exceeds the space wave as

*A*'

*d*ff,v = 0.54 m and *d*ff,h = 0.43 m.

and *A*'

design process.

Considering the free space and in-body definition of the directivity it is consistent to define the normalization value *U*n related to a isotropic source which is modified by the function *N*:

$$D = \frac{\left|E\right|^2}{\frac{\eta\_0 P\_{\text{rad}}}{4\pi d^2} \left|N\right|^2}. \tag{14}$$

Due to the fact that the effective area of an antenna is defined for the condition in which the antenna receives a locally plane electromagnetic wave [10] the received power of an antenna inserted in the far field of the transmitting on-body antenna cannot be calculated directly by equation 6. Nevertheless, as shown by a preceding study, see [11], even for body worn antennas a derivation of the received power as a function of the incident power density is possible. The results imply a nearly constant ratio between the received power *P*out and the incident power density *S* if the corresponding antennas are farther than the minimum far field distance apart. The constant ratio *A*' eff can be calculated by

$$A\_{\rm eff}^{'} = \frac{|P\_{\rm out}|}{|S|}. \tag{15}$$

Note, that the ratio defined by equation 15 is a function of the parameters given above and is therefore limited in its applicability to the specific setup. Apart from these aspects the equation enables the opportunity to calculate the received power as a function of arbitrary far field distances.

### *3.1.1. Validation of the on-body model on the example of an UWB teardrop antenna*

The verification of the suggested model has been done for a vertically and horizontally orientated UWB teardrop antenna for the frequency range defined by [3]. The effective height of the antenna has been set to a quarter free space wave length at *f* = 3.1 GHz to avoid intersections between the antenna and the tissue medium. In contrast to the in-body design an encapsulation of the radiating antenna elements is not necessary to obtain an adequate matching of the antenna. The key parameters of the antenna geometry are set to *lz* = 39 mm and *lx* = 18.5 mm, see Figure 2, to achieve a return loss below 10 dB for the desired frequency range. The tissue properties have been set to muscle tissue, given by [5], and analog to [7] the geometry has been numerically calculated by the FDTD method presented in [6]. The minimum far field distance *d*ff has been calculated along equation 11 and is shown in Table 2 for a vertical and horizontal orientated teardrop antenna.

Table 2 also shows the quantities *D* and *A*' eff which are calculated for the minimum far field distance *d*ff,v = 0.54 m and *d*ff,h = 0.43 m. Analog to the in-body scenario the quality of the suggested model has been verified by the absolute difference Δ*S* defined by equation 7. The absolute difference shows a sufficient applicability of the suggested on-body model. In contradiction to the in-body scenario it describes a non monotone behavior for the target frequencies due to the inverse frequency dependence of the reflection coefficient of the ground and the surface-wave attenuation function defined by equation 10. As shown in Table 2, the


8 Will-be-set-by-IN-TECH

low. This fact enables a simple approximation of the power density by the given expression

Considering the free space and in-body definition of the directivity it is consistent to define the normalization value *U*n related to a isotropic source which is modified by the function *N*:

> *η*0*P*rad <sup>4</sup>*πd*<sup>2</sup> |*N*|

Due to the fact that the effective area of an antenna is defined for the condition in which the antenna receives a locally plane electromagnetic wave [10] the received power of an antenna inserted in the far field of the transmitting on-body antenna cannot be calculated directly by equation 6. Nevertheless, as shown by a preceding study, see [11], even for body worn antennas a derivation of the received power as a function of the incident power density is possible. The results imply a nearly constant ratio between the received power *P*out and the incident power density *S* if the corresponding antennas are farther than the minimum far field

eff can be calculated by

eff <sup>=</sup> <sup>|</sup>*P*out<sup>|</sup>

Note, that the ratio defined by equation 15 is a function of the parameters given above and is therefore limited in its applicability to the specific setup. Apart from these aspects the equation enables the opportunity to calculate the received power as a function of arbitrary far

The verification of the suggested model has been done for a vertically and horizontally orientated UWB teardrop antenna for the frequency range defined by [3]. The effective height of the antenna has been set to a quarter free space wave length at *f* = 3.1 GHz to avoid intersections between the antenna and the tissue medium. In contrast to the in-body design an encapsulation of the radiating antenna elements is not necessary to obtain an adequate matching of the antenna. The key parameters of the antenna geometry are set to *lz* = 39 mm and *lx* = 18.5 mm, see Figure 2, to achieve a return loss below 10 dB for the desired frequency range. The tissue properties have been set to muscle tissue, given by [5], and analog to [7] the geometry has been numerically calculated by the FDTD method presented in [6]. The minimum far field distance *d*ff has been calculated along equation 11 and is shown in Table 2

distance *d*ff,v = 0.54 m and *d*ff,h = 0.43 m. Analog to the in-body scenario the quality of the suggested model has been verified by the absolute difference Δ*S* defined by equation 7. The absolute difference shows a sufficient applicability of the suggested on-body model. In contradiction to the in-body scenario it describes a non monotone behavior for the target frequencies due to the inverse frequency dependence of the reflection coefficient of the ground and the surface-wave attenuation function defined by equation 10. As shown in Table 2, the

*A*�

*3.1.1. Validation of the on-body model on the example of an UWB teardrop antenna*

for a vertical and horizontal orientated teardrop antenna.

Table 2 also shows the quantities *D* and *A*'

*<sup>D</sup>* <sup>=</sup> <sup>|</sup>*E*<sup>|</sup>

<sup>2</sup> <sup>=</sup> <sup>|</sup>*E*<sup>|</sup>

2

 *U*<sup>n</sup> *<sup>r</sup> N* 

2

<sup>2</sup> . (13)

<sup>2</sup> . (14)

<sup>|</sup>*S*<sup>|</sup> . (15)

eff which are calculated for the minimum far field

2


*<sup>D</sup>* <sup>≈</sup> <sup>|</sup>*E*<sup>|</sup>

of electric field:

field distances.

distance apart. The constant ratio *A*'

**Table 2.** Calculated on-body antenna parameters of the UWB teardrop antenna. The quantities Δ*S*, *G* and *A*' eff are calculated for the maximum far field distance of the considered frequency range with *d*ff,v = 0.54 m and *d*ff,h = 0.43 m.

directivity of the evaluated antennas decreases with increased frequencies. This behavior implies a reduced excitation of surface waves in the upper UWB frequency range due to the greater effective height of the antenna. Note, the derived gain is not directly comparable to the free space or in-body values. Due to the dependency of the channel model to the antenna polarization even the vertical and horizontal quantities are incomparable to each other. Despite this restriction the formulation of the directivity defines a quantity which enables an adequate discussion of various on-body antenna types and to enhance the corresponding design process.

**Figure 5.** Distance to the antenna where the surface wave exceeds the space wave as function of the frequency and tissue parameters of a vertical polarization; First row: The effective antenna height is set to a quarter wave length of the respective frequency; Second row: Effective antenna height is set to a quarter wave length at *f* = 3.1 GHz; Green square marker: Fat tissue; Red round marker: Muscle tissue.

Figure 5 shows an analysis of the effective antenna height in relation to the surface wave excitation. It discusses the distance *d*s where the surface wave exceeds the space wave as

#### 10 Will-be-set-by-IN-TECH 162 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Antennas and Propagation for On-, Off- and In-Body Communications <sup>11</sup>

function of the tissue parameters. The first row shows the intersect point for effective antenna heights of a quarter wave length of the respective frequency. The second row shows the intersection point for a fixed effective antenna height which has been set to a quarter wave length of the lower UWB edge frequency (*f* = 3.1 GHz). The comparison of the results shows that with increasing frequency even at distances greater than 10 m the surface wave component is lower than the corresponding space wave. This fact implies a relatively weak far field and causes a reduction of the directivity at high frequencies. With respect to the design of future UWB on-body antennas this circumstance has to be considered. Additional investigations have also shown that vertical polarized antennas excite a much more dominant surface wave than equivalent horizontal orientated antenna configurations, see [7]. These results are in accordance to the theory given by [8] and should be considered to optimize UWB applications for given propagation scenarios.

As shown in Figure 6 the modified model is capable to give an adequate description of the detailed voxel simulation. In future approaches this fact can be used to enhance the presented on-body far field model by a modification of the surface-wave attenuation function *F*v,h, see equation 10, by an adaption of the numeric distance as function of the surface impedance [13]. An additional effect, which is not included in the model presented, is the propagation in shadowed regions of the human body. While locally small shadowed regions are still covered by the model, large shadowed regions seem not to be described by this theory [7]. Nevertheless, these aspects have also been discussed in the last century with respects to the wave propagation above a spherical earth [9] and may also be transferred to the field of body

Antennas and Propagation for On-, Off - and In-Body Communications 163

The study has shown that an antenna de-embedding for in- and on-body applications can be realized by the derivation of corresponding far field models with reasonable accuracy for practical applications. Related to this theory, quantities as the directivity and the effective antenna area have been defined to derive good approximations of propagation models. Especially for on-body applications the suggested model gives a detailed insight by the

Moreover, the presented theory enables the calculation of average path gain models of arbitrary antennas which can be reduced to a source of vertical and horizontal orientated current distributions. By this, the numerical calculation space can be reduced to the minimum far field distance of the corresponding model. Additionally, an insulated UWB tear drop antenna design has been presented for in-body communication applications to give an adequate validation example. For the on-body scenario the UWB teardrop antenna has been

In future studies the in-body approach has to be modified to a multipath channel model to include additional propagation effects like surface waves. In addition, the on-body model has to be extended to give a wider applicability with respects to the complex structure of the human body. Moreover, the effective antenna area for on-body applications has to be described as function of the given model. With these improvements a structured combination of the on-, off- and in-body scenarios seems realizable to develop an optimized antenna theory

[1] Grimm, M. & Manteuffel, D. (2011). Characterization of electromagnetic propagation effects in the human head and its application to Deep Brain Implants, *IEEE-APS Topical Conference on Antennas and Propagation in Wireless Communications (APWC)*, pp. 674-677,

[2] Balanis, C. A. (2005). *Antenna Theory*, John Wiley & Sons., ISBN 978-0-4716-6782-X

separation of the electromagnetic field in its space and surface wave components.

centric communications.

modified and also been discussed.

for body centric communications.

Markus Grimm and Dirk Manteuffel

ISBN 978-1-4577-0046-0

**Author details**

**5. References**

*University of Kiel, Germany*

**4. Conclusion**

### *3.1.2. Limitations of the on-body model*

The validation of the suggested model with respect to the anatomical structure of the human body, with its numerous tissue types and curved surfaces, is done by a path gain calculation of a complete human body voxel model. Basis for this derivation is the numerical IT'IS virtual family Duke model [12]. The selected scenario consists of a transmitting antenna TX which is located at the right shoulder front. The corresponding receiver RX is shifted along the front side of the trunk above the right leg to the right foot. Figure 6 shows the path gain along the chosen path *d*. In addition, the path gain of the suggested on-body model has been calculated for homogeneous muscle and fat tissues. As seen in Figure 6, the calculated path gain of the voxel model lies between the graphs of the theoretical models.

**Figure 6.** Path gain of the Duke voxel model in comparison to the homogeneous model of fat and muscle; Additional included is a numerical validation graph of a layered model analog to [7].

Analog to [7] a numerical model of a layered plane surface has been implemented to realize a more realistic representation of the human tissue structure. The suggested simulation model consists of 2 mm skin and 5 mm fat tissues which are positioned on an infinite muscle tissue. As shown in Figure 6 the modified model is capable to give an adequate description of the detailed voxel simulation. In future approaches this fact can be used to enhance the presented on-body far field model by a modification of the surface-wave attenuation function *F*v,h, see equation 10, by an adaption of the numeric distance as function of the surface impedance [13].

An additional effect, which is not included in the model presented, is the propagation in shadowed regions of the human body. While locally small shadowed regions are still covered by the model, large shadowed regions seem not to be described by this theory [7]. Nevertheless, these aspects have also been discussed in the last century with respects to the wave propagation above a spherical earth [9] and may also be transferred to the field of body centric communications.
