Patent Publication Number: US-10758152-B2

Title: Compensation and calibration for a low power bio-impedance measurement device

Description:
BACKGROUND 
     Technical Field 
     This application is directed to a bio-impedance measurement device that is calibrated to compensate the inaccuracies of the impedance measurements. 
     Description of the Related Art 
     Bio-impedance measurement has a wide range of applications. Bio-impedance may be used to determine the composition of a biological body. Bio-impedance may also be used to determine the cardiac output of the biological body and its breathing rate. An accurate bio-impedance measurement aids in accurately characterizing the conditions of the biological body. However, conventional bio-impedance measurement devices introduce errors that result in inaccurate bio-impedance measurements. 
     Wearable and portable devices have low power consumption requirements, such as the architectures described in U.S. Pat. Nos. 8,909,333 and 9,307,924 and U.S. Patent Application Publication Nos. 2013/0006136 and 2015/0051505. However, when working frequency is increased, the accuracy of these solutions is degraded. Therefore, for a multi-frequency (or high single frequency) device, novel architectural solutions are needed to enable high accuracy with low power consumption. It is desirable to compensate for the errors and inaccuracies introduced in the bio-impedance measurements made by a bio-impedance measurement device. 
     BRIEF SUMMARY 
     In an embodiment, an impedance measurement device includes memory configured to store a plurality of compensation parameters and a first detection channel configured to receive a first detection signal and compensate the first detection signal using a first compensation parameter of the plurality of compensation parameters. The impedance measurement device also includes a second detection channel configured to receive a second detection signal and a third detection signal and compensate the second and third detection signals using second and third compensation parameters of the plurality of compensation parameters and the compensated first detection signal. The impedance measurement device generates a first output signal representative of a first impedance measurement and a second output signal representative of a second impedance measurement based on the compensated first, second and third detection signals. 
     In an embodiment, the first and second detection channels are configured to compensate for a relative time quantization error introduced in a trigger signal used for sampling the first detection signal and the second and third detection signals. In an embodiment, compensating the first detection signal using the first compensation parameter includes scaling an amplitude and adjusting a phase of the first detection signal by the first compensation parameter. In an embodiment, the first compensation parameter is a complex value. In an embodiment, generating the first output signal includes demodulating the compensated first detection signal to produce a first demodulated signal, filtering the first demodulated signal and compensating the filtered first demodulated signal to produce the first output signal. 
     In an embodiment, compensating the second and the third detection signals using the second and the third compensation parameters includes determining a difference between the second and the third detection signals, compensating the difference between the second and the third detection signals by the second compensation parameter, determining a common mode voltage based on the compensated difference between the second and the third detection signals and the compensated first detection signal, compensating the common mode voltage by the third compensation parameter and reducing the scaled difference between the second and the third detection signals by the scaled common mode voltage. 
     In an embodiment, generating the second output signal includes demodulating the second and third detection signals, amplifying the difference between the second and the third detection signals to produce an amplified signal, filtering the amplified signal and compensating the filtered amplified signal to produce the second output signal. In an embodiment, the first detection channel includes a first demodulator and the first compensation parameter compensates for a gain of the first demodulator and an absolute time quantization error of the first demodulator. 
     In an embodiment, the second detection channel includes a second demodulator, a third demodulator and an amplifier and the second compensation parameter compensates for a gain of the second demodulator or the third demodulator and an absolute time quantization error of the second demodulator or the third demodulator and a gain of the amplifier. In an embodiment, the second detection channel is configured to use the third compensation parameter to compensate for a common mode rejection ratio of the second demodulator and the third demodulator. 
     In an embodiment, a method for calibrating an impedance measurement device includes setting a contact impedance of a plurality of probes of the impedance measurement device to a first impedance value and an impedance between two probes of the plurality of probes to a zero impedance value. In an embodiment, the method includes determining a first detection signal at an input of a first detection channel of the impedance measurement device and a first output signal at an output of the first detection channel. In an embodiment, the method includes determining a first compensation parameter based on the first detection signal and the first output signal. In an embodiment, the method includes detecting a second and a third detection signals at respective first and second inputs of a second detection channel of the impedance measurement device and a second output signal at an output of the second detection channel. 
     In an embodiment, the method includes compensating, in the first and second detection channels, for a relative time quantization error introduced in a trigger signal used for sampling the first, second and third detection signals. In an embodiment, the method includes setting a contact impedance of a plurality of probes of the impedance measurement device to a zero impedance value and an impedance between two probes of the plurality of probes to a second impedance value. In an embodiment, the method includes determining fourth and fifth detection signals at the respective first and second inputs of the second detection channel and a third output signal at the output of the second detection channel. In an embodiment, the method includes determining second and third compensation parameters based on the second, third, fourth and fifth detection signals and the second and third output signals. In an embodiment, the method includes causing the first, second and third compensation parameters to be stored in the impedance measurement device for compensating an impedance measurement to be made by the impedance measurement device. 
     In an embodiment, the method includes receiving a first detection signal, compensating the first detection signal using a first compensation parameter of the plurality of compensation parameters, receiving a second detection signal and a third detection signal, compensating the second and third detection signals using second and third compensation parameters of the plurality of compensation parameters and the compensated first detection signal and generating a first output signal representative of a first impedance measurement and a second output signal representative of a second impedance measurement based on the compensated first, second and third detection signals. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         FIG. 1  shows a bio-impedance measurement device in contact with a biological body. 
         FIG. 2  shows a block diagram of the measurement device. 
         FIG. 3  shows a schematic of a circuit that models capacitances at an input of the first and second detection channels of the measurement device. 
         FIGS. 4A and 4B  show a block diagram of a method for determining the compensation parameters of the measurement device. 
         FIG. 5  shows a block diagram of a method for measuring impedance. 
         FIG. 6  shows an example of a waveform generated by an accumulator. 
         FIG. 7  shows a calibration device coupled to the measurement device. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  shows a bio-impedance measurement device  100  in contact with a biological body  102 . The bio-impedance measurement device  100 , referred to hereinafter as the measurement device  100 , includes a plurality of electrodes  104   a - 104   d  (collectively referred to herein as electrodes  104 ), a current generator  106  and a voltage detector  108 . The current generator  106  is coupled to a first electrode  104   a  and a second electrode  104   b  of the plurality of electrodes  104 . The voltage detector  108  is coupled to a third electrode  104   c  and a fourth electrode  104   d  of the plurality of electrodes  104 . 
     The plurality of electrodes  104  make contact with the biological body  102 . For example, each electrode  104  may be positioned to be in contact with the skin or tissue of the biological body  102 . The measurement device  100  may be any device that measures the impedance (also known as the bio-impedance or bioelectrical impedance) of an object. Impedance is a measure of the opposition to current by the object. The impedance of the biological body  102  may be indicative of the composition of the biological body  102 . For example, the impedance of the biological body  102  may be used to determine an amount of water or liquids in the biological body, fat-free body mass, or body fat. The current generator  106  supplies current between the first and second electrodes  104   a ,  104   b . The voltage detector  108  measures the impedance across the third and fourth electrodes  104   c ,  104   d . Measuring the impedance may be based on a voltage detected at the third and fourth electrodes  104   c ,  104   d . As described herein, the measurement device  100  may also measure the impedance at the first and second electrodes  104   a ,  104   b  and utilize the measurement to improve impedance detection. 
     The measurement device  100  may be a wearable device. For example, the measurement device  100  may be part of a watch, an activity tracker, an armband, a chest band or a patch, among others. The measurement device  100  may be used to provide biometrics, for example, to a user. The biometrics may include body composition or fluid content among others. 
       FIG. 2  shows a block diagram of the measurement device  100 . The measurement device  100  includes the plurality of electrodes  104 , the current generator  106 , the voltage detector  108 , a controller  110  and a timer  112 . The voltage detector  108  includes a first detection channel  114  and a second detection channel  116 . The first detection channel  114  includes a first demodulator  118 , a first filter  120  and a first analog-to-digital converter (ADC)  122 . The second detection channel  116  includes a second demodulator  124 , a third demodulator  126 , and amplifier  128 , a second filter  130  and a second ADC  132 . The first and second filters  120 ,  130  may be low-pass filters. The current generator includes a waveform generator  134  and a voltage-to-current converter  136 . The measurement device  100  also includes memory  137 . It is noted that in an embodiment, the first and second ADCs  122 ,  132  may be integrated into the controller  110 . Furthermore, the controller  110  may perform the functions of the first and second ADCs  122 ,  132 . 
     The measurement device  100  reduces power consumption. In particular the use of the demodulators before the amplification in the channels  116 ,  114  enables the use of a narrower bandwidth amplifier. Thus reduces both power consumption and device cost. Furthermore, the detection channel  114  may use a voltage output of the voltage-to-current converter  136  to measure the impedance of the body (Z 0 ) plus the electrode-to-skin contact impedances. 
     The controller  110  sets the frequency for operating waveform generator  134  and the demodulators  118 ,  124 ,  126 . The controller  110  outputs a configuration signal indicating the frequency. The waveform generator  134  receives the configuration signal and generates a waveform having the frequency. The waveform may, for example, be a sine waveform among others. The waveform generator  134  outputs the waveform to the voltage-to-current converter  136 . 
     The waveform generator  134  outputs a synchronization signal to the timer  112 . The timer  112  receives the synchronization signal from the waveform generator  134  and also receives the configuration signal from the controller  110 . The timer  112  outputs a trigger signal  113  to the demodulators  118 ,  124 ,  126 . The demodulators  118 ,  124 ,  126  synchronously sample the detected voltage, based on the trigger signal, generating voltage signals proportional to the real and imaginary parts of the impedances. 
     The voltage-to-current converter  136  receives the waveform from the waveform generator  134 . The voltage-to-current converter  136  converts the waveform from a voltage signal to a current signal. The voltage-to-current converter  136  outputs of the current signal over the first electrode  104   a . The second electrode  104   b  may be connected to the ground. The current is supplied to the biological body  102  between the first and second electrodes  104   a ,  104   b.    
     The first detection channel  114  has an input coupled to the first electrode  104   a . The input may be a voltage signal generated by the voltage-to-current converter  136 . The voltage signal may be proportional to the voltage drop between the electrodes  104   a ,  104   b . The input signal is described in U.S Pat. No. 8,909,333. The second detection channel  116  has a first input coupled to the third electrode  104   c  and a second input coupled to the fourth electrode  104   d . The first detection channel  114  operates on an input received from the first electrode  104   a  and produces a first filtered signal  148  (V INJ.3 ). The second detection channel  116  operates on inputs received at the third and fourth electrodes  104   c ,  104   d . The second detection channel  116  produces a second filtered signal  160  (V 0.4 ). The first filtered signal  148  and the second filtered signal  160  are then used to determine a measurement of a contact impedance (Z E ) (denoted as contact impedance  140 ) and a measurement of the bio-impedance (Z 0 ) (denoted as bio-impedance  142 ) of the biological body  102  as described herein. The contact impedance  140  is the impedance made between one of the electrodes  104  and the biological body  102 . 
     In particular, the first demodulator  118  receives a first detection signal  144  that is output from the first electrode  104   a . The first demodulator  118  demodulates the first detection signal  114  based on the trigger signal  113  and outputs a first demodulated signal  146 . The first demodulated signal  146  is provided to the first filter  120 . The first filter  120  receives the first demodulated signal  146  and filters the demodulated signal  146 . The first filter  120  may low-pass filter the first demodulated signal  146 . The first filter  120  outputs a first filtered signal  148 . The first filtered signal  148  may be converted from analog to digital format by the first analog-to-digital converter  122 . 
     In the second detection channel  116 , the second demodulator  124  receives a second detection signal  150  that is output from the third electrode  104   c . The third demodulator  126  receives a third detection signal  152  that is output from the fourth electrode  104 d. The second demodulator  124  demodulates the second detection signal  150  based on a timing of the trigger signal  113 . The second demodulator  124  outputs a second demodulated signal  154 . The third demodulator  126  demodulates the third detection signal  152  based on a timing of the trigger signal  113 . The third demodulator  126  outputs a third demodulated signal  156 . 
     The amplifier  128  receives the second and third demodulated signals  154 ,  156 . The amplifier  128  compares the second and third demodulated signals  154 ,  156 . The amplifier  128  outputs an amplified signal  158  based on a difference between the third demodulated signal  156  and the second demodulated signal  154 . The second filter  130  receives the amplified signal  158 . The second filter  130  filters the amplified signal  158  to produce the second filtered signal  160 . The second filter  130  may be a low-pass filter and may remove, from the amplified signal  158 , frequency components that are higher than a threshold frequency. The second filtered signal  160  may be converted from analog format to digital format by the second analog-to-digital converter  132 . 
     The first filtered signal  148  and the second filtered signal  160  may then be used to determine the detected contact impedance  140  and the detected bio-impedance  142  as described herein. 
     The memory  137  is configured to store compensation parameters. The compensation parameters are used to compensate the output signals of the first and second ADCs  122 ,  132 . 
     The accuracy of measuring the bio-impedance  142  by the measurement device  100  is affected by several factors. The factors include an input parasitic impedance, e.g. a parasitic capacitance, to the demodulators and a gain accuracy of the demodulators  118 ,  124 ,  126 . The factors also include a common mode rejection ratio of the second and third demodulators  124 ,  126 . The factors affecting accuracy of the bio-impedance  142  measurement include the clock granularity of the trigger signal  113  and a delay associated with many blocks of the circuit, e.g. the trigger signal  113  the demodulators  118 ,  124 ,  126 , the voltage-to-current converter  136 , etc. Further, the accuracy of the waveform generator  134  also influences the accuracy of measuring the bio-impedance  142 . These error sources become especially critical when the power consumption is reduced. Low power consumption, i.e., requires the use of limited clock speed and of components with bandwidth as narrow as possible. Therefore, limited performances, like reduced CMRR, not negligible parasitic, lower clock granularity shall be expected, especially for high working frequency of the system. 
     As described herein, the measurement device  100  is calibrated to compensate for the factors that introduce inaccuracies in the bio-impedance measurement. After the measurement device is calibrated, the accuracy of the bio-impedance measurement is improved. The measurement device  100  may be calibrated during or after manufacture. The measurement device  100  may be configured to compensate for the sources of inaccuracy. When the measurement device  100  is used, the accuracy of bio-impedance measurement is improved as a result of the calibration and compensation of the sources of inaccuracy. 
     The measurement device  100  may be calibrated by applying a known contact impedance  140  and a known bio-impedance  142 . For example, the measurement device may be used to measure the known impedances  140 ,  142 . Thereafter, a plurality of compensation parameters may be obtained. The measurement device  100  may then be configured to compensate for the plurality of measured compensation parameters. Calibration may be performed during or after manufacture of the measurement device  100 . Parameter compensation may be performed while the measurement device  100  is being used, for example, by a user. 
       FIG. 3  shows a schematic of a circuit that models capacitances at inputs of the first and second detection channels  114 ,  116  of the measurement device  100 . The first detection channel  114  receives an injected voltage (V INJ,1 ). The second detection channel  116  receives a first voltage (V P1 ) and a second voltage (V  P2 ). The injected voltage is a voltage of a voltage injection node  202 . The first and second voltages are voltages of a first node  204  and a second node  206 , respectively. 
     A voltage source  208  has a cathode coupled to the voltage injection node  202  and an anode coupled to a ground node  210 . A first impedance, e.g. a capacitance  212  (denoted as C 1 ) may be coupled in series to the contact impedance  140  for safety reasons, preventing DC current to flow in the body. The first capacitance  212  and the contact impedance  140  are together coupled between the voltage injection node  202  and the first node  204 . 
     A second impedance, e.g. a second parasitic capacitance  214  (denoted as C s1 ) is coupled between the first node  204  and the ground node  210 . The bio-impedance  142  is coupled between the first and second nodes  204 ,  206 . A third impedance, e.g. a third parasitic capacitance  216  (denoted as C s2 ) is coupled between the second node  206  and the ground node  210 . The value of C s1  and C s2  may be determined, e.g., through datasheet of components, simulations or measurements. Another contact impedance  140  is coupled between the second node  206  and the ground node  210 . A current source  218  that provides an injected current (I INJ ) has an anode coupled to the contact impedance  140  and a cathode coupled to a virtual ground node  211 . The virtual ground node  211  may be a node that is kept to the same voltage as a ground node, but current cannot flow into the virtual ground node  211   
     The current generated by the current source  218  is partially absorbed by the capacitances  212 ,  214 ,  216 . Due to the capacitances  212 ,  214 ,  216 , the injection voltage (V INJ,1 ) received by the first detection channel  114  and the first voltage (V P1 ) and the second voltage (V P2 ) received by the second detection channel  116  are changed. 
     The injection voltage is a function of the bio-impedance  142 , contact impedance  140 , first, second and third capacitances  212 ,  214 ,  216  and injection current. The injection voltage may, therefore, be represented as:
 
 V   INJ,1   =f   1 ( Z   0   , Z   E   , C   s1   , C   s2   , C   1   , I   INJ )   Equation (1)
 
     Similarly, the first voltage and the second voltage are functions of the bio-impedance  142 , contact impedance  140 , first, second and third capacitances  212 ,  214 ,  216  and injection current. In addition, the difference between the first voltage and the second voltage is a function of the quantities and may be represented as:
 
 V   d,1   =V   P1   −V   P2   =f   2 ( Z   0   , Z   E   , C   s1   , C   s2   , C   1   , I   INJ )   Equation (2)
 
     The common mode voltage, which is the average of the first and second voltages, may be represented as: 
     
       
         
           
             
               
                 
                   
                     V 
                     CM 
                   
                   = 
                   
                     
                       
                         
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                             P 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
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                         + 
                         
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                             ⁢ 
                             2 
                           
                         
                       
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                         ⁡ 
                         
                           ( 
                           
                             
                               Z 
                               0 
                             
                             , 
                             
                               Z 
                               E 
                             
                             , 
                             
                               C 
                               
                                 s 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             , 
                             
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                                 s 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                             , 
                             
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                               1 
                             
                             , 
                             
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                           ) 
                         
                       
                       . 
                     
                   
                 
               
               
                 
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                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     3 
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     The bio-impedance  142  is function of the injection voltage  208 , the difference between the first voltage  204  and the second voltage  206 , the first, second and third capacitances  212 ,  214 ,  216  and injection current:
 
 Z   0   =f   4 ( V   d,1   , V   INJ,1   , C   s1   , C   s2   , C   7   , I   INJ )   (4a)
 
     The contact impedance  140  is function of the injection voltage  208  the difference between the first voltage  204  and the second voltage  206 , the first, second and third capacitances  212 ,  214 ,  216  and injection current:
 
 Z   E   =f   5 ( V   d,1   , V   INJ,1   , C   s1   , C   s2   , C   7   , I   INJ )   Equation (4b)
 
     Similarly, also the common mode voltage can be represented as a function of the injection voltage  208 , the difference between the first voltage  204  and the second voltage  206 , the first, second and third capacitances  212 ,  214 ,  216  and injection current:
 
 V   CM   =f   6 ( V   d,1   , V   INJ,1   , C   s1   , C   s2   , C   7   , I   INJ )   Equation (4c)
 
     Any skilled person can compute the expression of f 1 , f 2 , f 3 , f 4 , f 5  and f 6  from the analysis of the circuit in  FIG. 3 . 
     Referring back to  FIG. 2 , the first detection signal  144  (denoted as V INJ,1 ) received by the first demodulator  118  is the same as the injection voltage. The first demodulated signal  146  that is output by the first demodulator may be represented as:
 
 V   INJ,2   =G   D,I   V   INJ,1   e   jT     D,I      Equation (4d)
 
where G D,I  represents the gain of the first demodulator  118 , T D,I  represents a first time delay and j represents the unit imaginary number.
 
     The first filtered signal  148  may also be represented as: 
                                 V     INJ   ,   3       =     V     INJ   ,   2                     V     INJ   ,   3       =       (       G     D   ,   I       ⁢     e     j     T     D   ,   I             )     ⁢     V     INJ   ,   1                         V     INJ   ,   3       ⁢     =   def     ⁢       1     A   E       ⁢     V     INJ   ,   1           ,                 Equation   ⁢           ⁢     (   5   )                   
where A E  is a compensation parameter associated with the first detection channel  114 . It is noted that V INJ,3 =V INJ,2  is true in the passband of the filter  120 .
 
     In the second detection channel  116 , the difference between the second detection signal  150  and the third detection signal  152  is given by Equation (2). As described herein, the second and third demodulators  124 ,  126  respectively demodulate the second and third detection signals  150 ,  152  and output the second and third demodulated signals  154 ,  156 . The difference between the second and third demodulated signals  154 ,  156  is denoted herein as V d,2  and may be represented as:
 
 V   d,2   =G   D,0 ( V   d,1   +CMRR   FD   V   CM ) e   jT     D,0      Equation (6)
 
where G D,0  represents the gain of the second and third demodulators  124 ,  126 , CMRR FD  is the common mode rejection ratio of the of the second and third demodulators  124 ,  126 , V CM  is the common mode voltage described with reference to Equation (3) and T D,0  is a second time delay.
 
     The amplified signal  158  output by the amplifier  128  may be represented as:
 
V 0,3 =G A V d,2  
 
 V   0,3   G   A   G   D,0 ( V   d,1   +CMRR   FD   V   CM ) e   jT     D,0      Equation (7)
 
where G A  is the gain of the amplifier  158 .
 
     The second filtered signal  160  (V 0,4 ) output by the second filter  130  may be assumed to be the same as the amplified signal  158 . That is, V 0,4  may be set to V 0,3 . The second filtered signal  160  may be represented as:
 
 V   0,4   =G   A   G   D,0 ( V   d,1   +CMRR   FD   V   CM ) e   jT     D,0    
 
 V   0,4 =( V   d,1   +CMRR   FD   V   CM )( G   A   G   D,0   e   jT     D,0   )   Equation (8)
 
     The second part of Equation (8) may be defined to be a first compensation parameter of the second detection channel  116 . The first compensation parameter may be defined as: 
     
       
         
           
             
               
                 
                   
                     1 
                     
                       A 
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                     def 
                   
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                       ( 
                       
                         
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                           G 
                           
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                           e 
                           
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                     . 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     9 
                     ) 
                   
                 
               
             
           
         
       
     
     The common mode rejection ratio (CMRR FD ) may be defined as a second compensation parameter of the second detection channel  116 . Thus, the second filtered signal output by the second filter  130  may be represented as 
     
       
         
           
             
               
                 
                   
                     V 
                     
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                       , 
                       4 
                     
                   
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                               d 
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                               FD 
                             
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                       . 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
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                     ( 
                     10 
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       FIGS. 4A and 4B  show a block diagram of a method  400  for determining the compensation parameters of the measurement device  100 . The method  400  may be performed by a calibration device connected to the measurement device  100 . At step  402 , the calibration device sets the contact impedance  140  is to zero Ω and the bio-impedance to a fixed impedance. At step  404 , the calibration device sets the input frequency of the injection current at a frequency value. At step  406 , the calibration device determines second filtered signal  160  (denoted as {circumflex over (V)} dm1 ). The second filtered signal  160  is provided at the output of the second filter  130 . To determine the second filtered signal, the calibration device may be connected to an output of the second filter  130 . 
     At step  408 , the calibration device determines a first difference between the second detection signal  150  and the third detection signal  152 , for example using the Equation (2). The first difference is denoted herein as {circumflex over (V)} dt1 . The calibration device calculates the second and third detection signals  150 ,  152  (and their difference) using Equation (2). That is because the capacitances and the current are known, while the Z 0  and ZE are used for the calibration. 
     The calibration device then determines a first common mode voltage at step  410  (denoted herein as {circumflex over (V)} CM1 ). The calibration device may determine the first common mode voltage, for example, using Equation (3). 
     The method  400  proceeds to step  412 . At step  412 , the calibration device sets the bio-impedance  142  to zero Ω and the contact impedance  140  of electrodes  104  to a fixed impedance. At step  414 , the calibration device sets the input frequency of the injection current at a frequency value. At step  416 , the calibration device determines the second filtered signal  160  detected at zero Ω bio-impedance and a fixed contact impedance  140 . The second filtered signal  160  is denoted herein as {circumflex over (V)} dm2 . At step  418 , the calibration device determines a second difference between the second detection signal  150  and the third detection signal  152  detected at zero Ω bio-impedance and a fixed contact impedance  140 . The second difference between the second detection signal  150  and the third detection signal  152  is denoted herein as {circumflex over (V)} dt2 . The calibration device then determines a second common mode voltage (denoted as {circumflex over (V)} CM2 ) at step  420 . . 
     At step  422 , the calibration devices uses the second filtered signal  160  ({circumflex over (V)} dm1 ), the first difference signal ({circumflex over (V)} dt1 ) and the first common mode voltage ({circumflex over (V)} CM1 ) determined at the zero contact impedance and fixed bio-impedance as well as the second filtered signal  160  ({circumflex over (V)} dm2 ), the second difference signal ({circumflex over (V)} dt2 ) and the second common mode voltage ({circumflex over (V)} CM2 ) determined at the fixed contact impedance  140  and zero bio-impedance  142  to determine the first and second compensation parameters (A 0  and CMRR FD ) of the second detection channel. To determine the first and second compensation parameters, the calibration device uses Equation (10). In particular, when the contact impedance is zero and the bio-impedance is fixed to an impedance value, Equation (10) may be represented as:
 
 {circumflex over (V)}   dm1   A   0   ={circumflex over (V)}   dt1   +{circumflex over (V)}   CM1   CMRR   FD    Equation (11)
 
     When the contact impedance  140  is set to an impedance value and the bio-impedance is zero, Equation (10) may be represented as:
 
 {circumflex over (V)}   dm2   A   0   ={circumflex over (V)}   dt2   +{circumflex over (V)}   CM2   CMRR   FD    Equation (12)
 
     Having two unknowns, Equations (11) and (12) may be solved together to obtain the first and second compensation parameters. 
     After setting the injection frequency at step  414 , the calibration device determines the compensation parameter of the first detection channel. At step  424 , the calibration device determines the first detection signal  144  (denoted herein as {circumflex over (V)} INJ,t ), for example using Equation (1) . At step  426 , the calibration device determines the first filtered signal  148  that is output by the first filter  120  and denoted herein as {circumflex over (V)} INJ,m . At step  428 , the calibration device determines the compensation parameter (A E ) of the first detection channel based on the first detection signal  144  and the first filtered signal  148 . The calibration device may determine the compensation parameter (A E ) using Equation (5). In particular, the compensation parameter of the first detection channel may be determined as:
 
 {circumflex over (V)}   INJ,m   A   E   ={circumflex over (V)}   INJ,t    Equation (13)
 
     The calibration device, at step  430 , causes the compensation parameter of the first detection channel and the first and second compensation parameters of the second detection channel to be stored in the measurement device  100 . The procedure can be repeated for different frequencies. The measurement device  100  utilizes the compensation parameters as described herein to improve the obtained bio-impedance and contact impedance measurements. 
       FIG. 5  shows a block diagram of a method  500  for measuring impedance. The method  500  may be performed by the measurement device  100 . At step  502 , the measurement device  100  begins an impedance measurement. To perform the impedance measurement, the measurement device  100  may be connected to a biological body  102  as described with reference to  FIG. 1  herein, or through a different disposition of the 4 electrodes. 
     At step  504 , the measurement device  100  determines a difference between the second and third detection signals  150 ,  152 . The difference between the second and third detection signals  150 ,  152  is denoted herein as {circumflex over (V)} dm . At step  506 , the measurement device  100  determines the first detection signal  148  (denoted herein as {circumflex over (V)} INJ,m ). 
     At step  508 , the measurement device  100  compensates the first detection signal using the compensation parameter of the first detection channel. To compensate the first detection signal, the measurement device  100  may scale the first detection signal by the compensation parameter of the first detection channel as:
 
{circumflex over (V)} INJ,C ={circumflex over (V)} INJ,m   A   E    Equation (14)
 
     At step  510 , the measurement device  100  compensates the difference between the second and third detection signals using the first compensation parameter of the second detection channel. The measurement device  100  may compensate the difference between the second and third detection signals by scaling the difference by the first compensation parameter of the second detection channel as:
 
{circumflex over (V)} dC1 ={circumflex over (V)} dm A 0    Equation (15)
 
     At step  512 , the measurement device  100  determines the common mode voltage. The common mode voltage (denoted as {circumflex over (V)} CM ) may be obtained from Equation (4c) assuming V d,1 ≈{circumflex over (V)} d . At step  514 , the measurement device  100  compensates the difference between the second and third detection signals using the common mode voltage and the second compensation parameter of the second detection channel. The compensation performed at step  514  operates on the compensated difference performed at step  510 . In an embodiment, the accuracy of the determination of the common mode voltage at step  512  may be improved through iteration of steps  512  and  514 . 
     Compensating the difference between the second and third detection signals includes removing the contribution of common mode rejection from the difference between the second and third detection signals. The difference between the second and third detection signals may be compensated as:
 
{circumflex over (V)} dC2   ={circumflex over (V)}   dC1   −CMRR   FD   {circumflex over (V)}   CM    Equation (16)
 
     The measurement device  100 , at step  516 , determines the bio-impedance based at least in part on the compensated difference between the second and third detection signals and the compensated first detection signal. This may be done using Equation (4a). The measurement device  100 , at step  518 , determines the contact impedance based at least in part on the compensated difference between the second and third detection signals and the compensated first detection signal. This may be done using Equation (4b). 
     In an embodiment, the waveform generator  134  may be an accumulator register and may be incremented by a fixed value each clock cycle. When the incremented sum, exceeds a maximum value that may be stored in the register, the incremented sum wraps around (for example, as a result of a modulo operation). 
       FIG. 6  shows an example of a waveform generated by an accumulator. The accumulator generates a sawtooth-like envelope for sine wave peaks and valleys that is in effect a sum of a sine wave and a sawtooth. Following an envelope “tooth,” the accumulator output may be different from a previous cycle. Line  602  shows a first-order envelope of the accumulator output and line  604  shows a second-order envelope of the accumulator output. 
     The trigger signal  113  may follow the first-order envelope, the second-order envelope or an envelope of another order. If the frequency of all the resulting envelopes in the trigger signal  113  is large enough to be outside the acquisition signal bandwidth and filtered by the acquisition stage then the effect of the varying output of the accumulator is minimized. This may be taken into account before to set the frequency in the blocks  404 ,  414  ( FIGS. 4A and 4B ) and  502  ( FIG. 5 ). 
     The frequency of the injected current may be significantly smaller than the clock frequency of the trigger signal  113 . If the injected current frequency is not significantly smaller than the clock frequency of the trigger signal  113 , the sample and hold trigger time quantization of the demodulators  118 , 124 ,  126  may not be negligible. Consequently, the detection signals  114 ,  150 ,  152  may not be sampled by the respective demodulators  118 , 124 ,  126  at a precise phase (for example, 0° and 90° for phase-quadrature demodulation). The resulting absolute time quantization error that affects the sampling triggers is modeled as delays (taken into account in T D,I  and T D,0 ) herein. The absolute time quantization errors are compensated by A E  and A 0 . 
     Further, another error (relative error) may be introduced between consecutive triggers of the trigger signal (for example, the time difference between a 0° trigger and a 90° trigger). Geometrically, the relative error may be modeled as a projection on two non-orthogonal axes (the ideal phase-quadrature demodulation is a projection of a sine wave on two orthogonal axes). The angle of deviation from orthogonality may be compensated in each detection signal  148  and  160 . The compensation may be executed, immediately after the ADC conversion, in blocks  406 ,  416  and  426  ( FIGS. 4A and 4B ) and  504  and  506  ( FIG. 5 ). 
     In low-power application, a slow clock frequency is used and granularity may be poor. Further, contrary to the absolute time quantization error, which results in a delay and which is taken into account in the formulas above, the relative error parameter may not be a delay or a gain error. The relative error parameter may be compensated during operation (also during calibration) after ADC conversion. 
       FIG. 7  shows a calibration device  101  coupled to the measurement device  100 . The calibration device  101  is used for determining the compensation parameters as described herein. The calibration device  101  is connected to the outputs of the ADCs  122 ,  132  and receives the converted signals from the ADCs  122 ,  132 . The calibration device  101  is coupled to the controller  110 , whereby the calibration device  101  may instruct the controller  110  to perform a frequency sweep for the injection current. The calibration device  101  is coupled to the memory  137 . 
     The calibration device  101  may detect the converted filtered signals  148 ,  160  respectively output by the ADCs  122 ,  132 . The calibration device  101  may use the detected signals to determine the compensation parameters as described herein. 
     The calibration device  101  may store the compensation parameters in the memory  137  of the measurement device  100 . During use, the measurement device  100  may use the compensation parameters stored in the memory  137  to compensate for sources of error in the impedance measurements as described herein. 
     In an embodiment, the first detection channel  114  may be replicated. The detection channel replica may be configured to receive the third detection signal  152 , for example, in the event that the two contact impedances  140  described with reference to  FIG. 3  are different. 
     The various embodiments described above can be combined to provide further embodiments. These and other changes can be made to the embodiments in light of the above-detailed description. In general, in the following claims, the terms used should not be construed to limit the claims to the specific embodiments disclosed in the specification and the claims, but should be construed to include all possible embodiments along with the full scope of equivalents to which such claims are entitled. Accordingly, the claims are not limited by the disclosure.