# 0.5 V Cardiac Sense Amplifier Realization Using Log-Domain Filtering

Authors: Christos Giagkoulovits; Costas Psychalinos
Journal: ISRN Biomedical Engineering
 (2013)

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## Abstract

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 0.35μm CMOS process.


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## Body

## 1. 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 [1–9].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 Section2, 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 μm process.


## 2. Log-Domain 4th-Order Bandpass Filter

The Functional Block Diagram (FBD) of a cardiac sense amplifier is depicted in Figure1. 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 low-frequency 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.Figure 1
FBD of a cardiac sense amplifier.In order to describe the operation of the proposed Log-Domain filter topology, the following set of operators will be used:(1)υ^=LOG(i)≡VDC+nVT·ln(i+IoIo),(2)i=EXP(υ^)≡Io·e(υ^-VDC)/nVT-Io.
In (1)-(2) Io and VDC are a dc current and a dc voltage, respectively; VT is the thermal voltage, and n is the subthreshold slope factor of an MOS transistor. Variables with a circumflex represent compressed voltages [5–8].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 asE+ and E- cells, which are given in Figure 2. The expression of the output current for both of them is given by the following formula:
(3)iout=Io·e(υ^in-υ^out)/nVT,
where υ^in and υ^out are the input and output voltages, respectively.Realization of nonlinear transconductors (a)E+ cell and (b) E- cell.
(a)
(b)Using (1)–(3) the realization of LOG and EXP operators could be achieved by the topologies given in Figure 3.Realization of (a) LOG and (b) EXP operators.
(a)
(b)The topology of a Log-Domain two-input lossless integrator is presented in Figure4. The current that flows through the capacitorC^ is given by the expression as follows:
(4)iC=C^dυ^outdt=Io·e(υ^in1-υ^out)/nVT-Io·e(υ^in2-υ^out)/nVT.
Multiplying both terms in (4) with the factor e(υ^out-VDC)/nVTand employing the definition of the EXP operator in (3) it is derived, after some algebraic manipulation, that
(5)EXP(υ^out)=1τ^s[EXP(υ^in1)-EXP(υ^in2)],
where τ^=C^nVT/Io is the realized time constant.Figure 4
Two-input Log-Domain lossless integrator.Using (2) the expression in (5) could be also written as in (6):
(6)iout=1τ^s(iin1-iin2).
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:
(7)EXP(υ^out)=1τ^s+1[EXP(υ^in1)-EXP(υ^in2)]
or
(8)iout=1τ^s+1(iin1-iin2).Figure 5
Two-input Log-Domain lossy integrator.The FBD of a 4th-order bandpass filter is given in Figure6, where the transfer function is
(9)H(s)=G1(1/τ^1)ss2+(1/τ^1)s+(1/τ^1τ^2)·G2(1/τ^3)ss2+(1/τ^3)s+(1/τ^3τ^4).
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 G1 and G2 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: τ^1=C^1nVT/Io,  τ^2=C^2nVT/Io,  τ^3=C^3nVT/Io,  and  τ^4=C^4nVT/Io, respectively.Figure 6
FBD of a 4th-order bandpass filter.Figure 7
Log-Domain realization of the FBD in Figure6.


## 3. Absolute Value, RMS-DC Converter, and Comparator

A topology that performs the conversion of current into its absolute value is presented in Figure8 [11]. The operation of this circuit is the following: in the case that the current iin is entering to the topology, transistor Mp1 is in conduction and the input current is conveyed into the output terminal through the current mirror formed by the transistors Mn1 and Mn2. In the case that the current iinleaves the topology, then transistors Mp2 and Mp3 are in conduction and the input current is again conveyed into the output terminal through the current mirror formed by transistors Mn1 and Mn2. 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:
(10)iout={iinifiin>0-iinifiin<0.Figure 8
Topology of an absolute value circuit.A topology of an RMS-DC converter is depicted in Figure9 [12]. The dynamic translinear loop is formed by the transistors Mp4–Mp6 and the capacitor Crms implementing the following equation: iCAPiout=CrmsnVTi˙out, while the static translinear loop formed by the transistors Mp1–Mp6 implements the equation: (iCAP+Io)iout2=Ioiin2. Combining both equations results in
(11)CrmsnVTi˙outiout+Ioiout2=Ioiin2.Figure 9
Topology of an RMS-DC converter.The expression in (11) could be alternatively rewritten as
(12)iout=iin2¯iout.
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 Figure10, 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 iin<IREF, then the output voltage will be equal to zero. In the case that iin>IREF, the output voltage will be equal to VDD_DIG.Figure 10
Typical current comparator.


## 4. 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 0.35μm CMOS process will be used in simulations.Regarding the bandpass filter, the power supply voltages were chosen to beVDD=0.5V and VDC = 100 mV, while the dc current Io was equal to 100 pA. Considering that the MOS transistors operate in the subthreshold region, the aspect ratios of Mp1  and Mp2-Mp3 of the E cells in Figure 2 were 70 μm/1 μm and 60 μm/1 μm, respectively, while the aspect ratio of Mn1-Mn2 of the E- cell in Figure 2(b) was 8 μm/1 μm. The distribution of the bias current has been performed through the employment of pMOS and nMOS current mirrors with aspect ratios 20 μm/1 μm and 8 μm/1 μm, respectively.Considering a bandpass filter with center frequencyfo equal to 25 Hz and a Q factor equal to 2.5, the derived transfer function is given by
(13)1.2450.71·ss2+50.71·s+3.28·104·1.6538.15·ss2+38.15·s+1.856·104.
Comparing (9) and (13) it is derived that G1=1.24, G2=1.65 while the capacitor values will be C^1=58.3pF,  C^2=4.57pF,  C^3=77.6pF, and C^4=6.08pF.The obtained gain response of the filter is demonstrated in Figure11, where the dc current Io 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 Io=15pA, 55 pA, and 110 pA are simultaneously given. The center frequency at Io=15pA was 4 Hz, while at Io=55pA the corresponding frequency was 13.2 Hz.Figure 11
Frequency response of the bandpass filter.Figure 12
Demonstration of the electronic tunability of the filter in Figure7.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 Figure13, 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.Figure 13
Linear performance of the filter in Figure7.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 Figure14, where the standard deviation of the gain was 0.12, while the corresponding value for the bandwidth was 1.1 Hz. Therefore, the filter has reasonable sensitivity characteristics.Monte Carlo analysis results about the (a) gain and (b) bandwidth of the filter in Figure7.
(a)
(b)The behavior of the absolute value circuit has been evaluated by employing a power supply voltage scheme asVDD=0.5V and VDC=100mV. The aspect ratios of Mp1, Mp2-Mp3, and Mn1-Mn2 of the topology in Figure 8 were 16 μm/0.4 μm, 4 μm/0.4 μm, and 20 μm/1 μm, 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.Figure 15
DC transfer characteristic of the absolute value circuit.Figure 16
Time-domain behavior of the absolute value circuit.The performance of the RMS-DC converter circuit has been evaluated by employing the following bias scheme:VDD=0.5V, VDC=100mV, and Io=5pA. Moreover, the capacitor value was 11 pF. The aspect ratio of Mp1–Mp6 of the topology in Figure 9 was 500 μm/0.35 μm. The distribution of the bias current has been performed using pMOS and nMOS current mirrors with aspect ratios 200 μm/1 μm and 35 μm/4 μm, 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.Figure 17
Time-domain behavior of the RMS-DC converter.The comparator given in Figure10 has been biased at VDD_DIG=1V. The aspect ratios were 1 μm/1.5 μm for Mp1-Mp2, 0.5 μm/2 μm for Mn1-Mn2, 1 μm/0.35 μm for Mp3-Mp4, and 0.5 μm/0.35 μm for Mn3-Mn4. 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.Figure 18
DC transfer characteristic of the current comparator.The whole system of the cardiac sense amplifier has been simulated using the following conditions:VDD=0.5V, VDC=100mV, and VDD_DIG=1V. 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 C^1=58.3pF,  C^2=4.57pF,  C^3=77.6pF, and C^4=6.08pF 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.Figure 19
Waveforms for the cardiac sense amplifier.Figure 20
Waveforms for the cardiac sense amplifier with opposite orientation of electrodes.The layout of the whole amplifier is demonstrated in Figure21; its dimensions were 1818.2 μm×267.4 μm. 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.Figure 21
Layout design of the cardiac sense amplifier.Figure 22
Postlayout simulation results of the cardiac sense amplifier.Figure 23
Postlayout simulation results of the cardiac sense amplifier with opposite orientation of electrodes.


## 5. 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.



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