0 . 5 V Cardiac Sense Amplifier Realization Using Log-Domain Filtering

A novel configuration of a cardiac sense amplifier for pacemakers, realized using the concept of Log-Domain filtering, is introduced in this paper. The analog part of the amplifier operates under a single 0.5 V power supply voltage. Compared to the corresponding already published configuration, the proposed scheme offers the benefits of reduced operating voltage and dc power dissipation. The performance of the intermediate stages, as well as of the whole system, has been evaluated through the utilization of the Analog Design Environment of the Cadence software and, also, the design kit provided by the AMS 0.35 μm CMOS process.


Introduction
A pacemaker is a closed-loop system where the intracardiac signal events are monitored and detected by a cardiac sense amplifier.The output of the amplifier is directly connected to a microcontroller which provides the appropriate signals to the stimulator in order to establish a therapy scheme for the heart.Taking into account that the biological signals are handled in the body's noisy environment, the cardiac sense amplifier should offer a relatively high signal-to-noise ratio.In addition, this device should be capable of operating in an ultralow voltage environment and, simultaneously, of drawing as small as possible power from the battery in order to achieve maximum life of operation for the pacemaker.
A promising technique for realizing circuits with high dynamic range is the Log-Domain technique.This originated from its companding nature, where the input current is converted into a compressed voltage and then is processed by the nonlinear core.The derived output compressed voltage is converted into a linear current, in order to preserve the linear operation of the whole system.In addition, the internal compressed voltages offer the capability for operation in a low-voltage environment, because of their reduced swings in comparison with those observed in the conventional linear filters.Log-Domain filters could be realized through the utilization of bipolar transistors in the forward active region or MOS transistors in the subthreshold region.The last approach offers potential for reducing the power consumption and this is very important in biomedical applications, since such devices should have a long battery life.Taking also the low-frequency range of biological signals into account, the employment of MOS transistors in the subthreshold region offers the benefit for realizing Log-Domain filters with small capacitor area, due to the large values of the realized equivalent resistors [1][2][3][4][5][6][7][8][9].
The concept of Log-Domain filtering has been followed in the realization of a cardiac sense amplifier in [10].Due to the utilization of bipolar transistors in the forward active region, the topology in [10] suffers from the following drawbacks: a power supply voltage equal to 2 V is required and, also, the required power consumption (240 nW) is relatively high for biomedical applications.
In order to overcome the aforementioned drawbacks, a novel topology of a cardiac sense amplifier is presented in this paper.It is constructed from a 4th-order bandpass filter realized using the concept of Log-Domain filtering, a current absolute value circuit, an RMS-DC converter, and a current comparator circuit.The analog part of the amplifier operates in a 0.5 V environment, while the digital part (i.e., the comparator) in a 1 V environment.The power consumption of this topology is 2.92 nW.The paper is organized as follows: the 4th-order bandpass filter is presented in Section 2, while the other stages are provided in Section 3. The performance of the proposed topology is evaluated, through simulation results, in Section 4 using the Analog Design Environment of the Cadence software and the design kit provided by the AMS 0.35 m process.

Log-Domain 4th-Order Bandpass Filter
The Functional Block Diagram (FBD) of a cardiac sense amplifier is depicted in Figure 1.According to this, the input signal is fed to a bandpass filter which is used for selecting the QRS complex or R-wave and minimizing the effect of the overlapping myocardial interference signals and lowfrequency breathing artifacts.Immunization of the measurements from the position of electrodes is achieved through the utilization of an absolute value circuit, where its output is fed to an RMS-DC converter in order to extract information about the energy of the signal.The resulted output is then compared with the output of the bandpass filter in order to detect the presence of the specific cardiac activity.
In order to describe the operation of the proposed Log-Domain filter topology, the following set of operators will be used: In ( 1)-( 2)   and  DC are a dc current and a dc voltage, respectively;   is the thermal voltage, and  is the subthreshold slope factor of an MOS transistor.Variables with a circumflex represent compressed voltages [5][6][7][8].
The above operators describe the compression of the input current into a compressed voltage and the expansion of the intermediate compressed voltage into linear currents.The realization of Log-Domain circuits is performed by employing non-linear transconductors, denoted as + and − cells, which are given in Figure 2. The expression of the output current for both of them is given by the following formula: where υin and υout are the input and output voltages, respectively.
Using (1)-(3) the realization of LOG and EXP operators could be achieved by the topologies given in Figure 3.The topology of a Log-Domain two-input lossless integrator is presented in Figure 4.The current that flows through the capacitor Ĉ is given by the expression as follows: Multiplying both terms in (4) with the factor  (υ out − DC )/  and employing the definition of the EXP operator in (3) it is derived, after some algebraic manipulation, that where τ = Ĉ  /  is the realized time constant.Using (2) the expression in ( 5) could be also written as in (6): The topology of a Log-Domain two-input lossy integrator is depicted in Figure 5. Performing a similar analysis the expressions in (7) and ( 8) are obtained: or The FBD of a 4th-order bandpass filter is given in Figure 6, where the transfer function is The realization of the FBD in Figure 6, using the integrators in Figures 4 and 5 and the compression and expansion blocks in Figure 3, is given in Figure 7.The required gain factors  1 and  2 are realized through appropriate sizing of the transistors and dc currents in the corresponding expansion blocks.Also, the realized time constants are given by the formulas: τ1 = Ĉ1   /  , τ2 = Ĉ2   /  , τ3 = Ĉ3   /  , and τ4 = Ĉ4   /  , respectively.

Absolute Value, RMS-DC Converter, and Comparator
A topology that performs the conversion of current into its absolute value is presented in Figure 8 [11].The operation of this circuit is the following: in the case that the current  in is entering to the topology, transistor  1 is in conduction and the input current is conveyed into the output terminal through the current mirror formed by the transistors  1 and  2 .In the case that the current  in leaves the topology, then transistors  2 and  3 are in conduction and the input current is again conveyed into the output terminal through the current mirror formed by transistors  1 and  2 .Thus, the output current has a constant direction and, simultaneously, its value is equal to that of the input current.This is mathematically described by the following: A topology of an RMS-DC converter is depicted in Figure 9 [12].The dynamic translinear loop is formed by the Figure 7: Log-Domain realization of the FBD in Figure 6.
transistors  4 - 6 and the capacitor  rms implementing the following equation:  CAP  out =  rms   iout , while the static translinear loop formed by the transistors  1 - 6 implements the equation: The expression in (11) could be alternatively rewritten as According to (12) the output current is equal to the rms value of the input current.
A topology of a current comparator is given in Figure 10, where the core introduced in [13] has been employed along with the addition of two inverters in order to increase the speed of operation and achieve rail-to-rail output voltages.When  in <  REF , then the output voltage will be equal to zero.In the case that  in >  REF , the output voltage will be equal to  DD DIG .

Simulation and Comparison Results
As a first step, the behavior of the building blocks of the cardiac sense amplifier will be evaluated through the utilization of the Analog Design Environment of the Cadence software.MOS transistor parameters provided by the AMS 0.35 m CMOS process will be used in simulations.
Regarding the bandpass filter, the power supply voltages were chosen to be  DD = 0.5 V and  DC = 100 mV, while the dc current   was equal to 100 pA.Considering that the MOS transistors operate in the subthreshold region, the aspect ratios of  1 and  2 - 3 of the  cells     P in (dBm) Figure 13: Linear performance of the filter in Figure 7.
Comparing ( 9) and ( 13) it is derived that  1 = 1.24,  2 = 1.65 while the capacitor values will be Ĉ1 = 58.3pF, Ĉ2 = 4.57 pF, Ĉ3 = 77.6 pF, and Ĉ4 = 6.08 pF.The obtained gain response of the filter is demonstrated in Figure 11, where the dc current   has been adjusted to 110 pA in order to realize a center frequency equal to 25 Hz.The tunability of the filter is demonstrated in Figure 12, where the frequency responses at   = 15 pA, 55 pA, and 110 pA are simultaneously given.The center frequency at   = 15 pA was 4 Hz, while at   = 55 pA the corresponding frequency was 13.2 Hz.
The linear performance of the filter has been studied through the application of two closely spaced tones, located at 25 Hz and 26 Hz, at the input of the filter.The simulated 3rd order intermodulation distortion plot is given in Figure 13, where the output referred 3rd-order intersect point (IIP3) was at −189.4 dBm (76 pA rms value).The noise has been integrated within the passband of the filter, and the rms value of the output referred noise was 0.51 pA.Consequently, the predicted value of the Dynamic Range (DR) of the filter will be 43.4 dB.The dc power consumption of the filter was 2.71 nW.
The sensitivity of the filter with regards to the effects of the process parameters variations and MOS transistor parameters mismatching has been evaluated through the employment of the Monte Carlo analysis offered by the Analog Design Environment.The derived statistical plots are given in Figure 14, where the standard deviation of the gain was 0.12, while the corresponding value for the bandwidth The behavior of the absolute value circuit has been evaluated by employing a power supply voltage scheme as  DD = 0.5 V and  DC = 100 mV.The aspect ratios of  1 ,  2 - 3 , and  1 - 2 of the topology in Figure 8 were 16 m/0.4m, 4 m/0.4m, and 20 m/1 m, respectively.The dc transfer characteristic of the topology is demonstrated in Figure 15.It is worth mentioning at this point that the input current has a range of variation between −100 pA and +100 pA, which is the possible range of variation for the output current of the bandpass filter.The behavior of the topology in the time domain is given in Figure 16, where the output waveform is plotted for an input current with an amplitude equal to 40 pA.
The performance of the RMS-DC converter circuit has been evaluated by employing the following bias scheme:  DD = 0.5 V,  DC = 100 mV, and   = 5 pA.Moreover, the capacitor value was 11 pF.The aspect ratio of  1 - 6 of the topology in Figure 9 was 500 m/0.35m.The distribution of the bias current has been performed using pMOS and nMOS current mirrors with aspect ratios 200 m/1 m and 35 m/4 m, respectively.The obtained output current waveform for an input signal equal to that obtained from the output of the absolute value circuit (Figure 16) is given in Figure 17.Although there is a variation presented at the output current this is not a problem in the detection of an intracardiac signal, as it was confirmed through exhaustive simulations.This choice has been performed in order to avoid the significantly large capacitor value required for the accurate operation of the RMS-DC converter, which is impractical from the fabrication point of view.
The comparator given in Figure 10 has been biased at  DD DIG = 1V.The aspect ratios were 1 m/1.5 m for  1 - 2 , 0.5 m/2 m for  1 - 2 , 1 m/0.35m for  3 - 4 , and 0.5 m/0.35m for  3 - 4 .The obtained dc transfer characteristic of the comparator for a reference current equal to 20 pA is given in Figure 18, where it is easily concluded that the topology behaves correctly.
The whole system of the cardiac sense amplifier has been simulated using the following conditions:  DD = 0.5 V,  DC = 100 mV, and  DD DIG = 1 V.In addition the bias currents for the bandpass filter and the rms converter were 110 pA and 5 pA, respectively.The reference dc current for the comparator was equal to 44 pA.The capacitor values were Ĉ1 = 58.3pF, Ĉ2 = 4.57 pF, Ĉ3 = 77.6 pF, and Ĉ4 = 6.08 pF for the bandpass filter and 11 pF for the RMS-DC converter.The MOS transistors aspect ratios were the same as those chosen in the simulations performed for the intermediate stages of the amplifier.Considering cardiac signals which are available from [14], the derived waveforms from the intermediate stages and the output of the amplifier are simultaneously given in Figure 19.Also, in Figure 20 the corresponding waveforms obtained from a reversed position of electrodes are given and the conclusion is that the operation of the amplifier is independent from the position of electrodes.The total power dissipation of the amplifier was 2.92 nW, instead of 240 nW of the topology in [10].Taking also into account that the analog part of the amplifier operates in a 0.5 V environment and only the comparator requires a 1 V power supply voltage, while the employed bias in the topology in [10] was 2 V, it is concluded that the proposed topology simultaneously offers the benefits of reduced power supply voltage requirement and dc power consumption.
The layout of the whole amplifier is demonstrated in Figure 21; its dimensions were 1818.2m × 267.4 m.Performing post layout simulations, the derived input and output  waveforms for both possible orientations of electrodes are given in Figures 22 and 23, where it is readily obtained that the proposed topology behaves as it was expected.

Conclusion
The proposed cardiac sense amplifier, realized by employing MOS transistors in the subthreshold region and the concept of the Log-Domain filtering, offers the benefits of the capability of operation in an ultralow voltage environment and the reduced dc power consumption.The postlayout simulation results confirmed its correct behavior, and, thus, it could be an attractive candidate for realizing high performance modern biomedical signal processing systems.

Figure 1 :
Figure 1: FBD of a cardiac sense amplifier.

Figure 8 :
Figure 8: Topology of an absolute value circuit.

Figure 11 :
Figure 11: Frequency response of the bandpass filter.

Figure 12 :
Figure 12: Demonstration of the electronic tunability of the filter in Figure 7.

Figure 14 :
Figure 14: Monte Carlo analysis results about the (a) gain and (b) bandwidth of the filter in Figure 7.

Figure 15 :Figure 16 :
Figure 15: DC transfer characteristic of the absolute value circuit.

Figure 17 :Figure 18 :
Figure 17: Time-domain behavior of the RMS-DC converter.

Figure 19 :
Figure 19: Waveforms for the cardiac sense amplifier.

Figure 20 :
Figure 20: Waveforms for the cardiac sense amplifier with opposite orientation of electrodes.

Figure 21 :
Figure 21: Layout design of the cardiac sense amplifier.

Figure 22 :
Figure 22: Postlayout simulation results of the cardiac sense amplifier.

Figure 23 :
Figure 23: Postlayout simulation results of the cardiac sense amplifier with opposite orientation of electrodes.