**4.1 Brief description**

232 Modern Telemetry

Fig. 10. Antenna impedance in homogeneous human models

Fig. 11. Antenna impedance in heterogeneous human models

A global study of the impedance characteristics shows that the sensitivity of the antenna to the human tissues results in a shift of the resonant mode. As the MICS band is in the vicinity of this resonant frequency characterized by fast impedance variation, the shift of 50 MHz in frequency involves a huge shift in impedance levels (see Fig. 10 and Fig. 11); hence, while the values of real part of impedance in heterogeneous models are between 39 and 51 Ω, those in the homogeneous models are between 185 and 260 Ω. Similar discrepancies can be seen on imaginary part of impedance. These impedance random shifts are too significant to In general, the power consumption of radio communication modules is dominated by the power consumption of the power amplifier during the transmitting path and by the power consumption of the low noise amplifier during the receiving path. Since antenna impedance calibration procedure is done during the transmitting mode, in order to achieve low power antenna impedance tuning unit, it is necessary to reduce strongly the time required for the calibration.

Therefore, we propose an innovative single step antenna tuning unit concept which basic topology is illustrated in Fig. 12. A generic detector made of capacitor *Cdet*, which advantageously replaces the usual bulky coupler, is inserted between the power module and the tunable matching network. The sensed signal *v1* and *v2* are attenuated for linearity issue, down converted to a lower intermediate frequency and analyzed by a processor. As described by the flow chart in Fig. 13, the processor exploits the magnitude and the phase of the sensed signals *v1* and *v2* to first calculate the impedance *Z1* and/or *Z2* located in the left and the right port of the detector, respectively. Finally, the extraction of the antenna input impedance exploits the well known deembedding techniques to calculate *ZAnt* from *Z1* or *Z2*. The obtained antenna input impedance value is used to directly calculate the parameters of the matching network that reach the proper state of the system at a selected frequency.

Fig. 12. Description of the proposed antenna tuning unit

An Efficient Adaptive Antenna-Impedance

matching networks.

impedance matching process.

the sensitivity of the detection.

matches a load resistance *RL* to a source resistance *RS* is

Fig. 15. Source equivalent resistance in the presence of Cdet

**4.2.1 Sensing module** 

*Cdet* becomes

Tuning Unit Designed for Wireless Pacemaker Telemetry 235

The benefit of the proposed architecture is that the down conversion module and the baseband processor used for the design of the antenna tuning unit, as illustrated in Fig. 12 are already included into the MICS band transceiver [22]. Only minor extra hardware is therefore added for its implementation: a sensing module, an attenuator and tunable

In addition to the TX tunable matching network, we insert a RX tunable matching network between the antenna and the front-end receiver in order to maximize the sensitivity of the receiver regardless of the value of the antenna impedance. Since the matching algorithm is able to match the extracted antenna impedance to the optimal impedance of the power amplifier, it is obviously possible to use the same program to match the antenna impedance to the input impedance of the low noise amplifier (LNA) optimizing the sensitivity of the receiver. This is to our knowledge the first antenna impedance tuning unit able to calibrate both the transmitter and the receiver in a same

The sensing module made of a transmit capacitor *Cdet* is inserted between the power amplifier and the TX tunable matching network. A capacitor is easy to integrate and its high quality factor advantageously limits the loss generated due to the sensing operation. However, the value of the capacitor *Cdet* needs to be chosen carefully. To set the value of *Cdet*, we analyze the impact of *Cdet* on the degradation of the network transformation ratio and on

As demonstrated in [26], the associated transformation quality factor *Q* of a network that

In the presence of the capacitor *Cdet*, the expression of the equivalent source resistance is

The associated transformation quality factor *Q* of the network topology in the presence of

*<sup>R</sup> <sup>Q</sup> <sup>R</sup>* = − if *R R S L* <sup>≥</sup> (1)

*<sup>R</sup> <sup>Q</sup> <sup>R</sup>* = − if *R R S L* <sup>≤</sup> (2)

1 *<sup>S</sup> L*

1 *<sup>L</sup> S*

obtained exploiting the network series parallel transformation in Fig. 15.

Fig. 13. Flow chart of the antenna tuning unit process

The success of the calibration with arbitrary source and load impedances is achieved with a single iteration. Since iteration is avoided, the matching time is strongly reduced by more than several hundred times compared to iterative optimization method to achieve high speed and low power consumption solution.

#### **4.2 Proposed architecture and analysis**

Here, we integrate the antenna tuning unit topology presented in Fig. 12 into the architecture of the MICS frequency band transceiver as illustrated in Fig. 14.

Fig. 14. Integration of the ATU into the architecture of the proposed MICS transceiver

The benefit of the proposed architecture is that the down conversion module and the baseband processor used for the design of the antenna tuning unit, as illustrated in Fig. 12 are already included into the MICS band transceiver [22]. Only minor extra hardware is therefore added for its implementation: a sensing module, an attenuator and tunable matching networks.

In addition to the TX tunable matching network, we insert a RX tunable matching network between the antenna and the front-end receiver in order to maximize the sensitivity of the receiver regardless of the value of the antenna impedance. Since the matching algorithm is able to match the extracted antenna impedance to the optimal impedance of the power amplifier, it is obviously possible to use the same program to match the antenna impedance to the input impedance of the low noise amplifier (LNA) optimizing the sensitivity of the receiver. This is to our knowledge the first antenna impedance tuning unit able to calibrate both the transmitter and the receiver in a same impedance matching process.

#### **4.2.1 Sensing module**

234 Modern Telemetry

The success of the calibration with arbitrary source and load impedances is achieved with a single iteration. Since iteration is avoided, the matching time is strongly reduced by more than several hundred times compared to iterative optimization method to achieve high

Here, we integrate the antenna tuning unit topology presented in Fig. 12 into the

Fig. 14. Integration of the ATU into the architecture of the proposed MICS transceiver

architecture of the MICS frequency band transceiver as illustrated in Fig. 14.

Fig. 13. Flow chart of the antenna tuning unit process

speed and low power consumption solution.

**4.2 Proposed architecture and analysis** 

The sensing module made of a transmit capacitor *Cdet* is inserted between the power amplifier and the TX tunable matching network. A capacitor is easy to integrate and its high quality factor advantageously limits the loss generated due to the sensing operation. However, the value of the capacitor *Cdet* needs to be chosen carefully. To set the value of *Cdet*, we analyze the impact of *Cdet* on the degradation of the network transformation ratio and on the sensitivity of the detection.

As demonstrated in [26], the associated transformation quality factor *Q* of a network that matches a load resistance *RL* to a source resistance *RS* is

$$Q = \sqrt{\frac{R\_S}{R\_L} - 1} \qquad \qquad \text{if } R\_S \ge R\_L \tag{1}$$

$$Q = \sqrt{\frac{R\_L}{R\_S} - 1} \qquad \qquad \text{if } R\_S \le R\_L \tag{2}$$

In the presence of the capacitor *Cdet*, the expression of the equivalent source resistance is obtained exploiting the network series parallel transformation in Fig. 15.

Fig. 15. Source equivalent resistance in the presence of Cdet

The associated transformation quality factor *Q* of the network topology in the presence of *Cdet* becomes

An Efficient Adaptive Antenna-Impedance

**4.2.2 Attenuator** 

in Fig. 17.

range of the system as

Fig. 17. Dynamic range of the down conversion module

Fig. 18. Proposed capacitive attenuator

Tuning Unit Designed for Wireless Pacemaker Telemetry 237

An attenuator is inserted between the detection capacitor *Cdet* and the down conversion module for linearity issue. Indeed, the magnitude of the signals *v1* and *v2* at the output of the power amplifier stage is large, whereas the input linearity of down conversion module made of mixer and channel filter is in general small. To avoid corruption of the wanted signals from undesirable harmonics generation, magnitude and phase errors due to AM/AM and AM/PM conversions in such nonlinear system, the attenuation value must be set so as to adapt *v1* and *v2* to the dynamic range of the down conversion module as shown

The 1-dB compression dynamic range DR1-dB of the down conversion module is the difference between the input 1-dB compression point *ICP1* and the sensitivity *Smin* of the donw conversion module. A back off is added to preserve the magnitude and phase integrity of the signals from AM/AM and AM/PM distortions. We obtain the dynamic

min *DR ICP S Back off* = −− 1 (5)

$$Q = \sqrt{\frac{R\_S \left(1 + \frac{1}{\left(C\_{\text{det}} \, R\_S \, a\_0\right)^2}\right)}{R\_L}} - 1 \qquad\qquad\text{if } R\_S \left(1 + \frac{1}{\left(C\_{\text{det}} \, R\_S \, a\_0\right)^2}\right) \ge R\_L\tag{3}$$

$$Q = \sqrt{\frac{R\_L}{R\_S \left(1 + \frac{1}{\left(C\_{\text{det}} \, R\_S \, a\_0\right)^2}\right)}} - 1 \qquad \text{if } R\_S \left(1 + \frac{1}{\left(C\_{\text{det}} \, R\_S \, a\_0\right)^2}\right) \le R\_L \tag{4}$$

As demonstrated in [26], an increase of the transformation quality factor Q in (3) reduces the efficiency of a lossy matching network, whereas a decrease of Q in (4) offers a better efficiency. In order to limit the impact of *Cdet* on the raise of Q in (3) and therefore on the degradation of the matching network efficiency, it is mandatory to set the *Cdet* value greater than ( ) <sup>0</sup> 1 / *RS*ω.

Moreover, as shown in Fig. 16, the sensing sensitivity depends on the value of *Cdet*. In Fig. 16 (a), the range variation of the ratio *v2/v1* is limited and centered around 1 and 0 for a strong and small value of *Cdet*, respectively. An example of wide range variation of the ratio *v2/v1* that provides a good sensitivity of the impedance sensing operation is illustrated in Fig. 16 (b) where *Cdet* is equal to ( ) <sup>0</sup> 1 / *RS*ω.

Fig. 16. Range variation of v2/v1 function of Cdet value plotted in polar domain for Re(Z2) ∈ [10, 300] and Im(Z2) ∈ [-100, 100]

A tradeoff between the sensitivity of the impedance sensing and the degradation of the association transformation quality factor, that could reduce lossy matching network efficiency, gives the expression of *Cdet* as follow

$$C\_{\text{det}} = \frac{2}{R\_{\text{S}} \, a\_0} \tag{3}$$

In this condition, neglecting the loss in capacitors and for RS=100Ω , RL=50Ω and QL=50, a well matched single stage matching network will achieve a power efficiency [27] (η ≈ −1 / *Q QL* ) of 98% and 97.55% without and with *Cdet*, respectively. As the same, for RS=50Ω, RL=100Ω and QL=50, the power efficiency is this time improved from 98% to 98.45%.

#### **4.2.2 Attenuator**

236 Modern Telemetry

( )<sup>2</sup> det 0 <sup>1</sup> if 1 *S L S R R C R*

( )<sup>2</sup> det 0 <sup>1</sup> if 1 *S L S R R C R*

 + ≤ 

 + ≥ 

ω

ω

(3)

(4)

1

1

As demonstrated in [26], an increase of the transformation quality factor Q in (3) reduces the efficiency of a lossy matching network, whereas a decrease of Q in (4) offers a better efficiency. In order to limit the impact of *Cdet* on the raise of Q in (3) and therefore on the degradation of the matching network efficiency, it is mandatory to set the *Cdet* value greater

Moreover, as shown in Fig. 16, the sensing sensitivity depends on the value of *Cdet*. In Fig. 16 (a), the range variation of the ratio *v2/v1* is limited and centered around 1 and 0 for a strong and small value of *Cdet*, respectively. An example of wide range variation of the ratio *v2/v1* that provides a good sensitivity of the impedance sensing operation is illustrated in Fig. 16

Fig. 16. Range variation of v2/v1 function of Cdet value plotted in polar domain for

det

*C*

matched single stage matching network will achieve a power efficiency [27] (

QL=50, the power efficiency is this time improved from 98% to 98.45%.

A tradeoff between the sensitivity of the impedance sensing and the degradation of the association transformation quality factor, that could reduce lossy matching network

> *R* ω

In this condition, neglecting the loss in capacitors and for RS=100Ω , RL=50Ω and QL=50, a well

98% and 97.55% without and with *Cdet*, respectively. As the same, for RS=50Ω, RL=100Ω and

0 2 *S*

<sup>=</sup> (3)

η

≈ −1 / *Q QL* ) of

( )<sup>2</sup> det 0

*L*

<sup>1</sup> <sup>1</sup> *L*

= − + 

*C R*

 + = −

*S*

( )<sup>2</sup> det 0

*C R*

ω.

*S*

ω

ω

<sup>1</sup> <sup>1</sup>

*S*

*<sup>Q</sup> <sup>R</sup>*

*S*

*R*

than ( ) <sup>0</sup> 1 / *RS*

ω.

(b) where *Cdet* is equal to ( ) <sup>0</sup> 1 / *RS*

Re(Z2) ∈ [10, 300] and Im(Z2) ∈ [-100, 100]

efficiency, gives the expression of *Cdet* as follow

*<sup>R</sup> <sup>Q</sup>*

*R*

An attenuator is inserted between the detection capacitor *Cdet* and the down conversion module for linearity issue. Indeed, the magnitude of the signals *v1* and *v2* at the output of the power amplifier stage is large, whereas the input linearity of down conversion module made of mixer and channel filter is in general small. To avoid corruption of the wanted signals from undesirable harmonics generation, magnitude and phase errors due to AM/AM and AM/PM conversions in such nonlinear system, the attenuation value must be set so as to adapt *v1* and *v2* to the dynamic range of the down conversion module as shown in Fig. 17.

The 1-dB compression dynamic range DR1-dB of the down conversion module is the difference between the input 1-dB compression point *ICP1* and the sensitivity *Smin* of the donw conversion module. A back off is added to preserve the magnitude and phase integrity of the signals from AM/AM and AM/PM distortions. We obtain the dynamic range of the system as

$$DR = ICP1 - S\_{\text{min}} - Back\,\text{off} \tag{5}$$

Fig. 17. Dynamic range of the down conversion module

Fig. 18. Proposed capacitive attenuator

An Efficient Adaptive Antenna-Impedance

and load impedances.

smaller than

Tuning Unit Designed for Wireless Pacemaker Telemetry 239

To facilitate the design of the inductance *L* value, we study the network in a real source and load impedance domain instead of complex source and load topology. A network transformation is computed and we obtain the matching network in Fig. 21 with real source

The expression of the real source *RPS* and real load *RPL* are given by (6) and (7), respectively. The normalized real load impedance range varies from min(*rPL*) and max(*rPL*) as reported

frequency of the elements, the forbidden circle where load impedance can not be matched to

*<sup>L</sup> <sup>D</sup> R* ω<sup>=</sup>

2

min min *PL PL*

*PS R*

( )

*PS*

*<sup>R</sup>* = = (9)

*<sup>R</sup>* <sup>=</sup> (10)

*PS*

Since *rPL* should be outside the forbidden circle, the forbidden circle diameter should be

( ) ( ) max

As a consequence, the value of the inductance L should be smaller than the inductance

max *PS* min *PL*

The architecture of the processor is illustrated in Fig. 22. It analyses the magnitude/phase information of the down converted signals *v1\_IF*, *v2\_IF* to extract the antenna input impedance *ZAnt* used to calculate the proper state of the system. We detail in this section the steps of the algorithm that contribute to reach the goals. The impedances *Z1* and/or *Z2* are first

ω

*R R*

the source impedance has a diameter *D* function of the inductance *L* and given by

*D r*

*L*

( ) <sup>2</sup> 1 *RR Q PS S S* = + where *Q XR S SS* = − (6)

( ) <sup>2</sup> 1 *RR Q PL L L* = + where *Q XR L LL* = − (7)

, and neglecting the self resonant

(8)

ω

Fig. 21. Transformed matching network with real source and load impedances

on the Smith charts in Fig. 20 by the blue bold lines.

As demonstrated in [27], at a given angular frequency

maximum value *Lmax* which expression is

**4.3 Matching processor algorithm** 

We basically implement a capacitive voltage divider as represented in Fig. 18 dedicated to the attenuation of *v1* and *v2*. The value of the input capacitance *C1,att* is small enough to achieve good isolation, whereas the value of the shunted capacitor *C2,att* is strong and chosen to set the desired attenuation. *C3,att* is also small value capacitor and added to limit the impact the output load impedance on the attenuation.

#### **4.2.3 Tunable matching network**

The tunable matching network is needed for its ability to adapt a great number of load impedances or any change of load impedance to the source impedance. Single stage matching network ability to cover a wide range of impedance is relatively limited [28]. We prefer a generic low pass π matching network with complex load and source impedances as shown in Fig. 19. It is made of one fixed inductor and two variable capacitors made of diode varactors or bank of switched capacitors.

Fig. 19. Matching network with complex source and load impedances

As illustrated in Fig. 20, the ability of the network to match a load impedance range to the source impedance is strongly dependent on the inductance *L* value. Indeed, any normalized complex conjugate load impedance located in the dotted area can be matched to the source whereas any normalized impedance located in the forbidden region can not be adapted. As an example, let consider the poorly designed inductance *L* scenario in Fig. 20 (a). A part of the load impedance range, represented by the semicircular shape, is located in the forbidden region. To achieve the well-designed topology in Fig. 20 (b), the value of L must be set carefully.

Fig. 20. Example of dynamic range of the impedance tuner (a) poorly inductance *L* designed scenario (b) well inductance *L* designed scenario

We basically implement a capacitive voltage divider as represented in Fig. 18 dedicated to the attenuation of *v1* and *v2*. The value of the input capacitance *C1,att* is small enough to achieve good isolation, whereas the value of the shunted capacitor *C2,att* is strong and chosen to set the desired attenuation. *C3,att* is also small value capacitor and added to limit the

The tunable matching network is needed for its ability to adapt a great number of load impedances or any change of load impedance to the source impedance. Single stage matching network ability to cover a wide range of impedance is relatively limited [28]. We prefer a generic low pass π matching network with complex load and source impedances as shown in Fig. 19. It is made of one fixed inductor and two variable capacitors made of diode

As illustrated in Fig. 20, the ability of the network to match a load impedance range to the source impedance is strongly dependent on the inductance *L* value. Indeed, any normalized complex conjugate load impedance located in the dotted area can be matched to the source whereas any normalized impedance located in the forbidden region can not be adapted. As an example, let consider the poorly designed inductance *L* scenario in Fig. 20 (a). A part of the load impedance range, represented by the semicircular shape, is located in the forbidden region. To

Fig. 20. Example of dynamic range of the impedance tuner (a) poorly inductance *L* designed

scenario (b) well inductance *L* designed scenario

achieve the well-designed topology in Fig. 20 (b), the value of L must be set carefully.

impact the output load impedance on the attenuation.

Fig. 19. Matching network with complex source and load impedances

**4.2.3 Tunable matching network** 

varactors or bank of switched capacitors.

To facilitate the design of the inductance *L* value, we study the network in a real source and load impedance domain instead of complex source and load topology. A network transformation is computed and we obtain the matching network in Fig. 21 with real source and load impedances.

Fig. 21. Transformed matching network with real source and load impedances

The expression of the real source *RPS* and real load *RPL* are given by (6) and (7), respectively. The normalized real load impedance range varies from min(*rPL*) and max(*rPL*) as reported on the Smith charts in Fig. 20 by the blue bold lines.

$$R\_{PS} = R\_S \left(1 + Q\_S^2\right) \qquad \text{where} \quad Q\_S = -X\_S/R\_S \tag{6}$$

$$R\_{PL} = R\_L \left(1 + Q\_L^2\right) \quad \text{where} \ Q\_L = -X\_L / R\_L \tag{7}$$

As demonstrated in [27], at a given angular frequency ω, and neglecting the self resonant frequency of the elements, the forbidden circle where load impedance can not be matched to the source impedance has a diameter *D* function of the inductance *L* and given by

$$D = \left(\frac{L\alpha}{R\_{PS}}\right)^2\tag{8}$$

Since *rPL* should be outside the forbidden circle, the forbidden circle diameter should be smaller than

$$D\_{\text{max}} = \min\left(r\_{PL}\right) = \frac{\min\left(R\_{PL}\right)}{R\_{PS}}\tag{9}$$

As a consequence, the value of the inductance L should be smaller than the inductance maximum value *Lmax* which expression is

$$L\_{\text{max}} = \frac{R\_{PS}}{\alpha \nu} \sqrt{\frac{\min\left(R\_{PL}\right)}{R\_{PS}}} \tag{10}$$

#### **4.3 Matching processor algorithm**

The architecture of the processor is illustrated in Fig. 22. It analyses the magnitude/phase information of the down converted signals *v1\_IF*, *v2\_IF* to extract the antenna input impedance *ZAnt* used to calculate the proper state of the system. We detail in this section the steps of the algorithm that contribute to reach the goals. The impedances *Z1* and/or *Z2* are first

An Efficient Adaptive Antenna-Impedance

where,

and,

where,

and,

where,

and,

detection capacitor *Cdet* in the time domain as

*K*

σ

The impedance *Z1* at the left port of the detector *Cdet* is

1

ω

= ×=

Tuning Unit Designed for Wireless Pacemaker Telemetry 241

2 \_ ( ) <sup>2</sup> ( ) 2 2 cos with *IF IF v t B t B KA* = − ω

From (11) (12) (13) and (14), we obtain the analytical expression for the voltage *vC* across the

det 1 2 () () () ( ) <sup>0</sup> cos *Cv t vt vt R t* =−= −

=− +

arctan

1 1

*v B <sup>Z</sup>*

( ) ( ) ( ) ( ) 2 2 1 2 2 <sup>1</sup> *R BB B* cos sin

> ( ) ( )

α

α

cos

( ) ( ) <sup>1</sup> arg

*<sup>C</sup>* cos sin

π = − σ

( ) ( ) <sup>2</sup> arg

( ) ( ) ( ) ( )

π

αα

2 <sup>2</sup> 2 2 det 0 1 2 <sup>2</sup> cos sin

− +

=+− α σ

α

2 1 2

*B B B*

<sup>=</sup> <sup>−</sup>

1 1 <sup>1</sup> 2 2 det 0 det det 0 1 2 <sup>2</sup>

> ( ) <sup>1</sup> arg <sup>2</sup> *Z*

Similarly, we obtain the impedance *Z2* at the right port of the detection capacitor *Cdet* as

*C BB B*

( ) <sup>2</sup> arg <sup>2</sup> *Z*

It is interesting to note that the impedances *Z1* and *Z2* at the ports of the detector are extracted with simplicity only from the magnitude *B1*, *B2* and phase shift α of (*v1\_IF*, *v2\_IF*). The extraction of the antenna input impedance exploits the de-embedding techniques to

2 2

*<sup>B</sup> <sup>Z</sup>*

ω

=

*jC v C BB B*

ω

sin

ω

 σ

 α

*j Z Z Ze* <sup>×</sup> = × , (18)

αα

*j Z Z Ze* <sup>×</sup> = × , (21)

. (20)

. (23)

( ) ( ) ( ) ( )

− +

 α

= × (14)

, (15)

(16)

, (19)

, (22)

. (17)

calculated and de-embedded to extract the antenna input impedance *ZAnt*. A novel matching network design algorithm presented in [27] is finally run to adapt the antenna input impedance to the front-end power module (power amplifier and low noise amplifier).

Fig. 22. Architecture of the ATU processor

#### **4.3.1 Impedance calculation**

Let consider the expression of *v1(t)* and *v2(t)* on the left and right terminals of *Cdet* as

$$v\_1(t) = A\_1 \cos\left(a\_0 \, t\right) \tag{11}$$

$$v\_2(t) = A\_2 \cos\left(\alpha\_0 \, t + \alpha\right) \tag{12}$$

where ω*<sup>0</sup>* is the angular carrier frequency, *A1* and *A2* are the magnitude of *v1* and *v2* respectively and α the phase shift.

The expression of the down converted signals *v1\_IF(t)* and *v2\_IF(t)* are

$$\left(\upsilon\_{1\\_IF}\left(t\right) = B\_1 \cos\left(\alpha \rho\_{\text{IF}}\left(t\right)\right)\right.\quad\text{with}\quad B\_1 = K \times A\_1\tag{13}$$

$$v\_{2\\_IF}(t) = B\_2 \cos\left(\alpha\_{\text{IF}} \ t - \alpha\right) \quad \text{with} \quad B\_2 = K \times A\_2 \tag{14}$$

From (11) (12) (13) and (14), we obtain the analytical expression for the voltage *vC* across the detection capacitor *Cdet* in the time domain as

$$v\_{\mathcal{C}\det}(t) = v\_1(t) - v\_2(t) = R\cos\left(a\_0\,t - \sigma\right),\tag{15}$$

where,

240 Modern Telemetry

calculated and de-embedded to extract the antenna input impedance *ZAnt*. A novel matching network design algorithm presented in [27] is finally run to adapt the antenna input impedance to the front-end power module (power amplifier and low noise amplifier).

Fig. 22. Architecture of the ATU processor

Let consider the expression of *v1(t)* and *v2(t)* on the left and right terminals of *Cdet* as

The expression of the down converted signals *v1\_IF(t)* and *v2\_IF(t)* are

*vt A t* 1 10 ( ) = cos ( )

*vt A t* 2 20 ( ) = + cos ( ) ω

1\_ ( ) <sup>1</sup> ( ) 1 1 cos with *IF IF v t B t B KA* = ω

ω

*<sup>0</sup>* is the angular carrier frequency, *A1* and *A2* are the magnitude of *v1* and *v2*

 α

(11)

(12)

= × (13)

**4.3.1 Impedance calculation**

respectively and α the phase shift.

where

ω

$$R = \frac{1}{K} \sqrt{\left(B\_1 - B\_2 \cos\left(\alpha\right)\right)^2 + \left(B\_2 \sin\left(\alpha\right)\right)^2} \tag{16}$$

and,

$$\sigma = \arctan\left(\frac{B\_2 \sin(\alpha)}{B\_1 - B\_2 \cos(\alpha)}\right). \tag{17}$$

The impedance *Z1* at the left port of the detector *Cdet* is

$$Z\_1 = \left| Z\_1 \right| \times e^{j \times \left( \arg \left( Z\_1 \right) \right)},\tag{18}$$

where,

$$|Z\_1| = \left| \frac{1}{jC\_{\text{det}}a\_0} \right| \times \left| \frac{v\_1}{v\_{\text{C det}}} \right| = \frac{B\_1}{C\_{\text{det}}a\_0\sqrt{\left(B\_1 - B\_2\cos(\alpha)\right)^2 + \left(B\_2\sin(\alpha)\right)^2}},\tag{19}$$

and,

$$\arg\left(Z\_1\right) = \sigma - \frac{\pi}{2} \,. \tag{20}$$

Similarly, we obtain the impedance *Z2* at the right port of the detection capacitor *Cdet* as

$$Z\_2 = |Z\_2| \times e^{j \times \left(\arg(Z\_2)\right)},\tag{21}$$

where,

$$\left| Z\_{2} \right| = \frac{B\_{2}}{C\_{\text{det}} \, a\_{0} \sqrt{\left(B\_{1} - B\_{2} \cos \left(\alpha \right)\right)^{2} + \left(B\_{2} \sin \left(\alpha \right)\right)^{2}}},\tag{22}$$

and,

$$\arg\left(Z\_2\right) = \alpha + \sigma - \frac{\pi}{2} \,. \tag{23}$$

It is interesting to note that the impedances *Z1* and *Z2* at the ports of the detector are extracted with simplicity only from the magnitude *B1*, *B2* and phase shift α of (*v1\_IF*, *v2\_IF*). The extraction of the antenna input impedance exploits the de-embedding techniques to

An Efficient Adaptive Antenna-Impedance

the microcontroller for impedance matching consideration.

Fig. 24. ATU prototype including the pacemaker antenna

Pacemaker antenna ATU demonstrator

calculation and the excecution of the matching network design algorithm.

(a)

Fig. 25. Measured reflection coefficient (a) before the calibration process (a) after the

proposed single step calibration

Tuning Unit Designed for Wireless Pacemaker Telemetry 243

The demonstrator was made using a Flame Retardant 4 substrate (FR4) with a relative permittivity of 4.6, a dielectric loss tangent of 0.02 and a layer's thickness of 360 μm. The tunability of the low pass π matching network is realized by varactors which control voltages are decided by the microcontroller ADUC7026 from Analog Device. It is an ARM7TDMI based controller with a CPU that clocks up at 40MIPS. The signal carrier frequency is 403 MHz down converted to 256 kHz intermediate frequency and analyzed by

Fig. 25 shows two experimental reflection coefficient measurements. The first one plotted in Fig. 25 (a) was done before the calibration process in the presence of a detuned tunable lowpass π matching network. The second one illustrated in Fig. 25 (b) highlights a postcalibration reflection coefficient result up to -30 dB at the desired frequency of 403 MHz. As represented in Fig. 26, the proposed antenna tuning unit demonstrator spends no more than 900μs to realise the overall calibration process, including the data acquisition, the impedance

(b)

Processor

calculate *ZAnt* from *Z1* or *Z2*. For better results, input parasitic capacitance from the attenuator could be taken into account during the process.

#### **4.3.2 Matching network design**

The matching design algorithm exploits a novel method for synthesizing an automatic matching network summarized in Fig. 23 and previously presented in [27] in order to match the antenna input impedance *ZAnt* to the optimal impedance of the power amplifier *Zopt* and to the input impedance of the low noise amplifier. This method transforms the load and source complex impedances to real source and load impedances for simplicity. The parameters of the networks that achieve the proper state of the system are calculated exploiting the Smith chart in a novel way achieving the process with simple analytical expressions. By reducing the complexity of the algorithm, we reduce the number of instructions, the time required to calculate the optimal configuration of the tunable matching networks and the power consumption of the antenna impedance calibration unit.

Fig. 23. Matching network design methodology presented in [27]

#### **4.4 Results**

A first experimental set-up of the antenna impedance tuning unit operating at the MICS 402- 405 MHz frequency band was fabricated [29] as illustrated in Fig. 24. It includes the MICS frequency band demonstrator with only the TX low pass π tunable matching network, a microcontroller board and a pacemaker antenna immersed into a homogeneous human model liquid described in section III whose permittivity εr and conductivity σ are 56.2 and 0.95 S/m, respectively.

calculate *ZAnt* from *Z1* or *Z2*. For better results, input parasitic capacitance from the

The matching design algorithm exploits a novel method for synthesizing an automatic matching network summarized in Fig. 23 and previously presented in [27] in order to match the antenna input impedance *ZAnt* to the optimal impedance of the power amplifier *Zopt* and to the input impedance of the low noise amplifier. This method transforms the load and source complex impedances to real source and load impedances for simplicity. The parameters of the networks that achieve the proper state of the system are calculated exploiting the Smith chart in a novel way achieving the process with simple analytical expressions. By reducing the complexity of the algorithm, we reduce the number of instructions, the time required to calculate the optimal configuration of the tunable matching networks and the power consumption of the antenna impedance calibration

attenuator could be taken into account during the process.

Fig. 23. Matching network design methodology presented in [27]

A first experimental set-up of the antenna impedance tuning unit operating at the MICS 402- 405 MHz frequency band was fabricated [29] as illustrated in Fig. 24. It includes the MICS frequency band demonstrator with only the TX low pass π tunable matching network, a microcontroller board and a pacemaker antenna immersed into a homogeneous human model liquid described in section III whose permittivity εr and conductivity σ are 56.2 and

**4.3.2 Matching network design** 

unit.

**4.4 Results** 

0.95 S/m, respectively.

The demonstrator was made using a Flame Retardant 4 substrate (FR4) with a relative permittivity of 4.6, a dielectric loss tangent of 0.02 and a layer's thickness of 360 μm. The tunability of the low pass π matching network is realized by varactors which control voltages are decided by the microcontroller ADUC7026 from Analog Device. It is an ARM7TDMI based controller with a CPU that clocks up at 40MIPS. The signal carrier frequency is 403 MHz down converted to 256 kHz intermediate frequency and analyzed by the microcontroller for impedance matching consideration.

Fig. 24. ATU prototype including the pacemaker antenna

Fig. 25 shows two experimental reflection coefficient measurements. The first one plotted in Fig. 25 (a) was done before the calibration process in the presence of a detuned tunable lowpass π matching network. The second one illustrated in Fig. 25 (b) highlights a postcalibration reflection coefficient result up to -30 dB at the desired frequency of 403 MHz. As represented in Fig. 26, the proposed antenna tuning unit demonstrator spends no more than 900μs to realise the overall calibration process, including the data acquisition, the impedance calculation and the excecution of the matching network design algorithm.

Fig. 25. Measured reflection coefficient (a) before the calibration process (a) after the proposed single step calibration

An Efficient Adaptive Antenna-Impedance

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Fig. 26. Time Antenna calibration
