The differential Howland current source with high signal to noise ratio for bioimpedance measurement system Jinzhen Liu, Xiaoyan Qiao, Mengjun Wang, Weibo Zhang, Gang Li, and Ling Lin Citation: Review of Scientific Instruments 85, 055111 (2014); doi: 10.1063/1.4878255 View online: http://dx.doi.org/10.1063/1.4878255 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A very low noise, high accuracy, programmable voltage source for low frequency noise measurements Rev. Sci. Instrum. 85, 044702 (2014); 10.1063/1.4870248 Low noise constant current source for bias dependent noise measurements Rev. Sci. Instrum. 82, 013906 (2011); 10.1063/1.3509385 Four probe architecture using high spatial resolution single multi-walled carbon nanotube electrodes for electrophysiology and bioimpedance monitoring of whole tissue Appl. Phys. Lett. 96, 093701 (2010); 10.1063/1.3292216 Some Basic Techniques in Bioimpedance Research AIP Conf. Proc. 724, 28 (2004); 10.1063/1.1811815 Noncontact scanning impedance imaging in an aqueous solution Appl. Phys. Lett. 85, 1080 (2004); 10.1063/1.1778469
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 055111 (2014)
The differential Howland current source with high signal to noise ratio for bioimpedance measurement system Jinzhen Liu,1 Xiaoyan Qiao,2 Mengjun Wang,3 Weibo Zhang,4 Gang Li,1 and Ling Lin1,a) 1 State Key Laboratory of Precision Measurement Technology and Instruments, Tianjin University, Tianjin, People’s Republic of China, and Tianjin Key Laboratory of Biomedical Detecting Techniques and Instruments, Tianjin University, Tianjin, People’s Republic of China 2 College of Physics and Electronic Engineering, Shanxi University, Shanxi, People’s Republic of China 3 School of Information Engineering, Hebei University of Technology, Tianjin, People’s Republic of China 4 Institute of Acupuncture and Moxibustion China Academy of Chinese Medical Sciences, Beijing, China
(Received 20 March 2014; accepted 5 May 2014; published online 21 May 2014) The stability and signal to noise ratio (SNR) of the current source circuit are the important factors contributing to enhance the accuracy and sensitivity in bioimpedance measurement system. In this paper we propose a new differential Howland topology current source and evaluate its output characters by simulation and actual measurement. The results include (1) the output current and impedance in high frequencies are stabilized after compensation methods. And the stability of output current in the differential current source circuit (DCSC) is 0.2%. (2) The output impedance of two current circuits below the frequency of 200 KHz is above 1 M, and below 1 MHz the output impedance can arrive to 200 K. Then in total the output impedance of the DCSC is higher than that of the Howland current source circuit (HCSC). (3) The SNR of the DCSC are 85.64 dB and 65 dB in the simulation and actual measurement with 10 KHz, which illustrates that the DCSC effectively eliminates the common mode interference. (4) The maximum load in the DCSC is twice as much as that of the HCSC. Lastly a two-dimensional phantom electrical impedance tomography is well reconstructed with the proposed HCSC. Therefore, the measured performance shows that the DCSC can significantly improve the output impedance, the stability, the maximum load, and the SNR of the measurement system. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4878255] frequency stimulus signal, especially in the application of multi-frequency impedance measurement8 and frequency-difference EIT.9 r Because of the unknown impedance variation range and the effect of the contact impedance between the object and electrode,10 the current source circuit will work over a large variation in load impedance. r In the impedance measurement, to detect the weakly useful information, the measurement system must reach to high accuracy and signal to noise ratio (SNR).11
I. INTRODUCTION
The bioelectrical impedance measurement is a noninvasive, fast operation. and low cost method reflecting the functional structure feature of the object.1 The current source and voltage source are the two signal sources in the bioimpedance measurement system. However, in the voltage source circuit the input signal is needed to be adjusted according to different load down to the safety limit of the human injection current, which is relatively complicated.2, 3 Thus the current source has a wide range of applications especially in electrical impedance tomography (EIT).4 The imaging system is also the measurement system, the accuracy and stability of the current source circuit is the key factor determining the quality of the reconstruction imaging. In EIT, the current source is required to stable over the frequency ranging 1 KHz to 1 MHz with several mA, thus the current source circuit should arrive to the following requirements.5
r The output impedance of the current source is high enough to stable the output current within different load and frequency.6 r The maximum output frequency should be above 1 MHz. According to the dispersion characteristic of biomaterial dielectric property,7 the high frequency information of impedance can be collected with high a) Author to whom correspondence should be addressed. Electronic mail:
[email protected].
0034-6748/2014/85(5)/055111/6/$30.00
The performance of Howland circuit and current mirror type circuit were compared,12 which illustrates that both circuits are stable over the frequency ranging 1 KHz to 1 MHz, and the two circuits suggest that there is little to choose between them in terms of a practical implementation. The generalized impedance converter (GIC)13 was designed in the enhanced Howland topology current source circuit to create a high precision, multiple frequency, capacitance compensated current source for EIT applications. Although the SNR performance of the current excitation sub-system had been addressed,14 which presented a prototype EIT current excitation subsystem with 80 dB SNR, but it justly discussed the factor in terms of the SNR of the current excitation signal. A new integrated current source design in CMOS technology was addressed,15 its performance with the modified Howland circuit was compared, and the impedance is greater than 160 K up to 1 MHz due to the presence of stray
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capacitance. In a new multi-frequency EIT system called the KHU Mark2,5 the output impedance of the Howland current source with multiple GICs is up to 10 M in the frequency of 1 MHz. The latest study about the improved Howland current source circuit (HCSC) with the lead-lag compensation2 has stable output impedance of 3.3 M up to 200 KHz, which provides 80 dB precision for EIT application. The main circuitries of the impedance measurement system are the current source circuit, signal amplifier, and filter circuit and data collection circuit, one circuit of which can significantly affect the stability and SNR of the whole system. The above researches present several current sources mainly based on the HCSC and some compensation to improve the high frequencies output performance. In the actual measurement, the compensation method can effectively improve the performance of current source circuit. However, in previous work the factor that contributing to the SNR of measurement system is limited to the precision of current excitation signal, the SNR of the current source circuit is ignored to be considered which is very important for improving the performance of the measurement system.14 In the single-ended output current source circuit, the noise level mainly depends on the input signal and the anti-noise performance of the operational amplifier.16–18 In this paper, we propose a novel differential current source circuit based on the Howland topology current source circuit. First, the performance of the Howland and differential current circuits were analyzed. Then the stability, the compensation method, the output impedance, the SNR, and the loading ability of the differential current source circuit (DCSC) were discussed in the simulation and measurement experiments. Lastly we applied the proposed DCSC for EIT. To our knowledge, the novel DCSC proposed in this paper based on the enhanced Howland current source is improved not only in terms of output performance but also the SNR of the whole measurement system. II. THE HOWLAND CURRENT SOURCE CIRCUIT
The single-ended Howland current pump19, 20 using a single operational amplifier with both negative and positive feedback shown in Fig. 1 is a popular current source as one part of the bioelectrical impedance measurement system. When the parameters in the circuit satisfy, R2A + R2B R4 = , R3 R1
FIG. 1. The Howland current pump.
(1)
the output current is given by I=
Vi R2B
R2A + R2B R1
.
(2)
When the feedback paths are balanced, the output current is 2B justly linear with the input voltage. When RR43 = R2AR+R = 1, 1 the output current is given by I=
Vi . R2B
(3)
Then the output impedance is given by Rout =
R3 R2B (R1 + R2A ) . R3 (R2A + R2B ) − R1 R4
(4)
When the parameters are balanced in (1), the output impedance in (4) is infinite. Actually, the stray capacitance in the environment and the existing resistors tolerance degrade the high-frequency performance of the output current and impedance.
III. THE DIFFERENTIAL CURRENT SOURCE
Fig. 2 shows the DCSC, the left part of which is the Howland topology current source circuit, the reverse amplifier circuit from one end of the resistorRL is connected to the other end ofRL . This architecture of DCSC is able to dramatically reduce the common mode interference. In Fig. 2, the operational amplifier has high input impedance, and the current inputting to operational amplifier A2 is approximately equal to zero, so the output current of the current source can be expressed by (3). In order to satisfy the requirement of the frequency of 1 MHz, A1 , A2 , and A3 are all high speed operational amplifiers. We choose the Texas Instruments OPA842 with the unity-gain bandwidth of 400 MHz. To meet this precision requirement and to realize the necessary noise level, output impedance, and voltage swing, we set R1 = R3 = R4 = R5 = R6 = 2 k, R2A = R2B = 1 k. NI Multisim is used to evaluate the input and output performance of the current source circuit. The resistor mismatch is simulated assuming 0.01% tolerance.
FIG. 2. The differential current source circuit.
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Rev. Sci. Instrum. 85, 055111 (2014) TABLE I. The comparison of output impedance of the HCSC and DCSC in simulation. F (KHz)
1
5
10
20
50
100
200
HCSC (M) 24.97 42.85 49.97 24.98 42.8 23.06 12.48 DCSC (M) 499.8 124.9 27.75 45.44 125 21.72 24.98 300 400 500 600 700 800 900 1000 5.98 3.55 2.42 1.83 1.49 1.27 1.12 1.02 11.88 7.22 5.03 3.82 3.05 2.60 2.29 2.09
FIG. 3. The compensation circuit for the DCSC.
IV. PERFORMANCE EVALUATION AND MEASUREMENT RESULTS A. The compensation method for the DCSC stability
In actually, the operational amplifier with high speed cannot remain stable in high frequencies. In the measurement circuit, the parasitic capacitance is ubiquitous such as cable capacitance, the capacitance between electrode lead, the stray capacitance between the circuit signal ground and the earth, and the stray capacitance from the placement and routing of the lead.21 The parasitic capacitance can seriously damage the balance of the feedback paths leading to the unstable current output especially in the case of high frequencies. The GIC13 is used in combination with the HCSC to compensate the parasitic capacitance corresponding to the frequency, but it is inconvenient for the application of multi-frequency measurement. We perform the two compensation methods for the circuit in Fig. 3, one is the capacitor C1 for the lead-lag compensation without sacrificing high frequency output impedance.2 Another is the capacitor C2 for hindering the free oscillation and stabling the high frequencies performance. We mainly assess the compensation method of capacitor C2 . In the measurement for the DCSC, the input voltage Vi = 0.25 mV, C2 = 5 pF, C1 = 100 pF, RL = 1.9952 K. The input voltage is produced by the 7280 DSP Lock-in Amplifier from Signal Recovery,22 and the precision (0.01%) resistors with low temperature coefficient (2 ppm ◦ C−1 ) are chosen to ensure high output impedance. Fig. 4 shows the comparison of the voltages at the resistor RL with and without C2 . Fig. 4 illustrates that the output voltage is stable below 100 KHz, the voltage drops rapidly above 100 KHz without
compensation, but after compensation the maximum variation of output voltage with the frequency of 1 MHz is 0.2%. B. The output impedance
In order to evaluate the output performance, we measure the output impedance of the differential and Howland topology current source circuits. In simulation, the load in parallel with 10 pF capacitance is analyzed as capacitive load. Then we change the load RL and measure two different load voltages to calculate the output impedance according to Eq. (5). The two load resistors are 10 K and 11 K. The output impedances in the frequency from 1 KHz to 1 MHz of the Howland and differential current circuits are shown in Table I. r=
R1 R2 (U2 − U1 ) , U 1 R 2 − U2 R 1
(5)
where U1 and U2 , respectively, are the output voltages at the load of R1 and R2 and r is the output impedance. From Table I we can see that output impedance gradually reduces with the frequency increasing. The output impedances in the two current circuits are over 1 M in below 1 MHz and are over 10 M in below 200 KHz. The important is that the output impedance of the DCSC is higher than that of the HCSC. In actual measurement, the input voltage is produced by the 7280 DSP Lock-in Amplifier from Signal Recovery, the two load resistors are 1.9952 K and 2.6833 K, C2 = 5 pF. In the DCSC, the compensation capacitances C1 , respectively, are 100 pF and 150 pF. In the HCSC, the compensation capacitances are 197 pF and 288 pF. Then the output voltages at the load in different frequency are collected by the 7280 DSP Lock-in Amplifier. The calculated output impedances are shown in Table II. The results shown in Table II are similar as in Table I. In actual measurement, the output impedance is over 1 M TABLE II. The comparison of output impedance of the HCSC and DCSC in actual measurement. F (KHz)
FIG. 4. The comparison of the voltages at the resistor RL with and without C2 .
1
5
10
20
50
100
200
HCSC (M) 2.12 2.44 2.44 2.07 1.80 1.62 1.52 DCSC (M) 14.85 13.3 13.3 6.69 4.46 2.26 2.34 300 400 500 600 700 800 900 1000 0.82 0.78 0.89 0.58 0.57 0.44 0.40 0.29 0.92 0.87 1.00 0.87 0.73 0.77 0.53 0.36
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below 200 KHz, and over 200 K below 1 MHz, and the output impedance is higher in the DCSC. From Tables I and II we can see that in some frequencies such as the frequency of 100 kHz the output impedances of the current source circuit are exceptions to the rule in the DCSC, which are mainly impacted by the present of the zero or pole in the system. Because of the present of the capacitance and inductance in the current source circuit, zero and pole will be produced in some frequencies,23, 24 which will influence the amplitude as well as the phase of the output signal, and the output performances such as the output impedance. The reasons that lead to the remarkable difference of the output impedance in the simulation and actual measurement as shown in Tables I and II contain the following three respects. First, the input signal of the current source circuit has limited resolution and precision, which can influence the SNR of the output signal and the output impedance. Second, under the limitation of the circuit parameters such as the resistor tolerance in the actual measurement, the output impedance expressed in the equation of (4) will be degraded. Lastly, because of the ubiquitous distribution parameters, the power frequency interference and the high frequency noise in the actual measurement, the actual performance of the current source circuit can’t achieve that in the theoretical model. C. The evaluation of the SNR
In Fig. 2, the voltages at two ends of the load RL are VO1 and VO2 , then VO2 = −VO1 ,
(6)
and the common mode signal in the output of the DCSC can be defined as 1 (7) Vc = (VO1 + VO2 ), 2 where Vc is the common mode signal. Therefore, in theory the common mode signal in the DCSC is zero, the commonmode rejection ratio (CMRR) of the circuit is infinite, which illustrates this DCSC can effectively improve the SNR of the whole system because there is no common mode noise flowing into the next stage circuit. We define the SNR in the measurement as vd , (8) SNR = 20 log vc where vd and vc are, respectively, the differential and common mode voltages at the two ends of the load. We design the adder circuit to measure the common mode signal using the operational amplifier AD8051 from Aanlog Devices. The common mode and differential mode voltages are collected by the 7280 DSP Lock-in Amplifier. The measurement frequency is 10 KHz and the load resistor is 1.9952 K. In the simulation, The 10 pF capacitance is paralleled with the load RL , by calculation the SNR is 85.64 dB. In actual measurement, the SNR is 65 dB. In contrast, the value of the differential mode signal is twice as much as that of the common mode signal in the HCSC, which fails to cancel out any common mode signal and improve the anti-noise performance of the current source circuit.
FIG. 5. The output spectrum of the DCSC.
The output spectrum while driving a 1.9952 K load is shown in Fig. 5 using Data Acquisition Card 6281 from National Instruments. This spectrum shows that out-of-band noise level is at least 100 dB below the operating frequency. D. The loading capacity of the DCSC
When the parameter satisfies as (1), the output voltage of vL is expressed by vL ≤ vSAT − vi
R2A + R2B , R1
(9)
where vSAT is the saturation voltage of the operational amplifier, the corresponding loading is vL . (10) RL = I Based on (9) and (10), the maximum loading for the HCSC is given by vSAT − R2B . RLmax = (11) I For the DCSC the maximum loading can be expressed as v SAT − R2B . (12) RLmax = 2 I Therefore, the maximum load of the DCSC is twice as much as that of the HCSC from (11) and (12), which can effectively enhance the loading capacity without changing the other parameter. V. THE EIT EXPERIMENT
We apply the proposed differential current source circuit for the open electrical impedance tomography system25
FIG. 6. The five measurements of the boundary voltages.
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FIG. 7. The reconstruction imaging of a two-dimensional phantom.
with the scanning electrode and a saline phantom for the twodimensional electrical impedance imaging. We fill the phantom with a background of 0.2 S m−1 . The width of the phantom is 0.225 m with 0.115 m long including 2116 cells and 1128 nodes. We place ten copper electrodes for the current injecting electrode and two copper electrodes for the voltage measuring electrode driven by the motor scanning along the boundary of the phantom. Then with nine current injections of 2 mA by the cross current injection mode 126 independence voltages are obtained by the Data Acquisition Card NI6281 using the neighboring protocol from the phantom with an anomaly of steel stick. The diameter of the steel stick is 10 mm in the depth of 10 mm. Fig. 6 shows the five measurements of the boundary voltages without anomaly. From Fig. 6 we can see that the five measurements are quite consistent, which illustrates the feasibility and stability of the electrical impedance system with the proposed differential current source circuit and the scanning electrode. And by measurement the SNR of the electrical impedance tomography system can achieve above 75 dB. Fig. 7 displays the reconstruction image using the variation regularization algorithm,25 which shows that the position and shape of the anomaly is well reconstructed. Therefore, the proposed differential current source circuit can effectively reduce the common mode interference and improve the SNR of the measurement system. VI. CONCLUSION AND DISCUSSION
A new differential topology current source circuit as well as compensation method is proposed. On the basis of the HCSC, the reverse circuit is introduced to form the differential architecture. Though the simulation and actual measurement, the DCSC has many advantages over the meaningful characteristics of output impedance, loading capacity and SNR in comparison with the HCSC. Owing to the ubiquitous parasitic capacitance, the feedback paths are unbalanced if the compensation method is not performed in the circuit. Thus the compensation method must be used to ensure the stability of output performance. In this work, two compensation capacitors are introduced as shown in Fig. 3. The capacitor C1 is used to compensate the high frequency lead-lag, which has been in detail illustrated.2 The capacitor C2 is to compensate the stay capacitance, prevent the self-induced oscillation and stable the output voltage which is in detail evaluated in this paper. In the actual measurement, the capacitance of C2 should be chosen as the real circuit,
Rev. Sci. Instrum. 85, 055111 (2014)
while the larger capacitance value will lead to effective phase error and reduce the SNR of the current source. From the results in Fig. 4, the output of the circuit is stabile without compensation below the frequency of 100 KHz, while the circuit turns back to stable output below 1 MHz after compensation. Under the limitation of the resistor tolerance and the stray capacitance in the actual measurement, the output impedances shown in Table II are lower compared with the output impedances shown in Table I. However, the output impedances in the DCSC are at least 2.34 M up to 200 KHz in the actual measurement, which is adequate for the most bioelectrical impedance applications. However, the common mode rejection ratio of the amplifier is finite, and the interference and noise requires each stage of the circuit for high SNR. The differential amplifier circuit is often used in the bioelectrical signal detection to improve the accuracy and SNR. Then the proposed DCSC is the key design which significantly reduces the common mode signal in the current source circuit and the whole bioelectrical collection system. In addition, the fourth remarkable improvement is the output loading capacity of the DCSC, which is twice bigger than that of the HCSC. Thus the impedance measurement scope is expanded effectively with DCSC. Lastly, with the proposed DCSC we design the electrical impedance imaging system, the reconstruction imaging shown in Fig. 7 shows that the proposed differential current source circuit can be used in the impedance measurement system. In order to improve the performance of the proposed DCSC, we will in further improve the resolution and precision of the input signal, simplify the circuit configuration, and reduce the influence of the distribution parameters and the parasitic parameters. Future work will target the DCSC in EIT to promote its development into clinical application. ACKNOWLEDGMENTS
This work was supported by the basic scientific research expenses of independent subject project supported by the China Academy of Chinese Medical Sciences. 1 Z.
M. A. Azevedo et al., Clin. Nutr. 32, 824 (2013).
2 S. Tucker, R. M. Fox, and R. J. Sadleir, IEEE Trans. Biomed. Circuits Syst.
7, 63 (2013). Mohamadou, T. I. Oh, H. Wi, H. Sohal, A. Farooq, E. J. Woo, and A. L. McEwan, Meas. Sci. Technol. 23, 105703 (2012). 4 L. Borcea, Inverse Probl. 18, R99 (2002). 5 T. I. Oh, H. Wi, D. Y. Kim, P. J. Yoo, and E. J. Woo, Physiol. Meas. 32, 835 (2011). 6 K. Hayatleh, N. Terzopoulos, and B. L. Hart, Int. J. Electron. 99, 1739 (2012). 7 A. Romsauerova, A. McEwan, L. Horesh, R. Yerworth, R. H. Bayford, and D. S. Holder, Physiol. Meas. 27, S147 (2006). 8 P. Withers, Physiol. Meas. 16, 71 (1995). 9 T. I. Oh, K. H. Lee, S. M. Kim, H. Koo, E. J. Woo, and D. Holder, Physiol. Meas. 28, 1175 (2007). 10 T. D. Marco, F. Ries, M. Guermandi, and R. Guerrieri, IEEE Trans. Biomed. Eng. 59, 1229 (2012). 11 W. R. B. Lionheart, Physiol. Meas. 25, 125 (2004). 12 P. Bertemes-Filho, B. H. Brown, and A. J. Wilson, Physiol. Meas. 21, 1 (2000). 13 A. S. Ross, G. J. Saulnier, J. C. Newell, and D. Isaacson, Physiol. Meas. 24, 509 (2003). 3 Y.
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Rafiei-Naeini and H. McCann, Physiol. Meas. 29, S173 (2008). W. Hong, M. Rahal, A. Demosthenous, and R. H. Bayford, Physiol. Meas. 30, 999 (2009). 16 I. Jivet and B. Dragoi, Physiol. Meas. 29, S193 (2008). 17 N. Li, H. Xu, Z. Zhou, J. L. Xin, Z. L. Sun, and X. Xu, IEEE Trans. Biomed. Circuits Syst. 7, 460 (2013). 18 F. Seoane, R. Macias, and R. Bragos, Meas. Sci. Technol. 22, 115801 (2011). 19 S. Franco, Design with Operational Analog Integrated Circuits (McGrawHill, New York, 2002). 15 H.
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X. Chen, X. Deng, and W. Q. Yang, Rev. Sci. Instrum. 81, 034704 (2010). 21 G. D. Hammond, C. C. Speake, M. Stiff, K. Hayatleh, N. Terzopoulos, and B. L. Hart, Int. J. Electron. 95, 351 (2008). 22 See http://www.signalrecovery.com/Our-Products/Lock-in-Amplifiers/ 7280.aspx for Model 7280 - Documents. 23 A. Sadkowski, J. P. Diard, and C. Montella, J. Electrochem. Soc. 156, F7 (2009). 24 M. B. Farshad, J. Process Control 23, 817 (2013). 25 J. Z. Liu, L. Lin, W. B. Zhang, and G. Li, Physiol. Meas. 34, 823 (2013).
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 055111 (2014)
The differential Howland current source with high signal to noise ratio for bioimpedance measurement system Jinzhen Liu,1 Xiaoyan Qiao,2 Mengjun Wang,3 Weibo Zhang,4 Gang Li,1 and Ling Lin1,a) 1 State Key Laboratory of Precision Measurement Technology and Instruments, Tianjin University, Tianjin, People’s Republic of China, and Tianjin Key Laboratory of Biomedical Detecting Techniques and Instruments, Tianjin University, Tianjin, People’s Republic of China 2 College of Physics and Electronic Engineering, Shanxi University, Shanxi, People’s Republic of China 3 School of Information Engineering, Hebei University of Technology, Tianjin, People’s Republic of China 4 Institute of Acupuncture and Moxibustion China Academy of Chinese Medical Sciences, Beijing, China
(Received 20 March 2014; accepted 5 May 2014; published online 21 May 2014) The stability and signal to noise ratio (SNR) of the current source circuit are the important factors contributing to enhance the accuracy and sensitivity in bioimpedance measurement system. In this paper we propose a new differential Howland topology current source and evaluate its output characters by simulation and actual measurement. The results include (1) the output current and impedance in high frequencies are stabilized after compensation methods. And the stability of output current in the differential current source circuit (DCSC) is 0.2%. (2) The output impedance of two current circuits below the frequency of 200 KHz is above 1 M, and below 1 MHz the output impedance can arrive to 200 K. Then in total the output impedance of the DCSC is higher than that of the Howland current source circuit (HCSC). (3) The SNR of the DCSC are 85.64 dB and 65 dB in the simulation and actual measurement with 10 KHz, which illustrates that the DCSC effectively eliminates the common mode interference. (4) The maximum load in the DCSC is twice as much as that of the HCSC. Lastly a two-dimensional phantom electrical impedance tomography is well reconstructed with the proposed HCSC. Therefore, the measured performance shows that the DCSC can significantly improve the output impedance, the stability, the maximum load, and the SNR of the measurement system. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4878255] frequency stimulus signal, especially in the application of multi-frequency impedance measurement8 and frequency-difference EIT.9 r Because of the unknown impedance variation range and the effect of the contact impedance between the object and electrode,10 the current source circuit will work over a large variation in load impedance. r In the impedance measurement, to detect the weakly useful information, the measurement system must reach to high accuracy and signal to noise ratio (SNR).11
I. INTRODUCTION
The bioelectrical impedance measurement is a noninvasive, fast operation. and low cost method reflecting the functional structure feature of the object.1 The current source and voltage source are the two signal sources in the bioimpedance measurement system. However, in the voltage source circuit the input signal is needed to be adjusted according to different load down to the safety limit of the human injection current, which is relatively complicated.2, 3 Thus the current source has a wide range of applications especially in electrical impedance tomography (EIT).4 The imaging system is also the measurement system, the accuracy and stability of the current source circuit is the key factor determining the quality of the reconstruction imaging. In EIT, the current source is required to stable over the frequency ranging 1 KHz to 1 MHz with several mA, thus the current source circuit should arrive to the following requirements.5
r The output impedance of the current source is high enough to stable the output current within different load and frequency.6 r The maximum output frequency should be above 1 MHz. According to the dispersion characteristic of biomaterial dielectric property,7 the high frequency information of impedance can be collected with high a) Author to whom correspondence should be addressed. Electronic mail:
[email protected].
0034-6748/2014/85(5)/055111/6/$30.00
The performance of Howland circuit and current mirror type circuit were compared,12 which illustrates that both circuits are stable over the frequency ranging 1 KHz to 1 MHz, and the two circuits suggest that there is little to choose between them in terms of a practical implementation. The generalized impedance converter (GIC)13 was designed in the enhanced Howland topology current source circuit to create a high precision, multiple frequency, capacitance compensated current source for EIT applications. Although the SNR performance of the current excitation sub-system had been addressed,14 which presented a prototype EIT current excitation subsystem with 80 dB SNR, but it justly discussed the factor in terms of the SNR of the current excitation signal. A new integrated current source design in CMOS technology was addressed,15 its performance with the modified Howland circuit was compared, and the impedance is greater than 160 K up to 1 MHz due to the presence of stray
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capacitance. In a new multi-frequency EIT system called the KHU Mark2,5 the output impedance of the Howland current source with multiple GICs is up to 10 M in the frequency of 1 MHz. The latest study about the improved Howland current source circuit (HCSC) with the lead-lag compensation2 has stable output impedance of 3.3 M up to 200 KHz, which provides 80 dB precision for EIT application. The main circuitries of the impedance measurement system are the current source circuit, signal amplifier, and filter circuit and data collection circuit, one circuit of which can significantly affect the stability and SNR of the whole system. The above researches present several current sources mainly based on the HCSC and some compensation to improve the high frequencies output performance. In the actual measurement, the compensation method can effectively improve the performance of current source circuit. However, in previous work the factor that contributing to the SNR of measurement system is limited to the precision of current excitation signal, the SNR of the current source circuit is ignored to be considered which is very important for improving the performance of the measurement system.14 In the single-ended output current source circuit, the noise level mainly depends on the input signal and the anti-noise performance of the operational amplifier.16–18 In this paper, we propose a novel differential current source circuit based on the Howland topology current source circuit. First, the performance of the Howland and differential current circuits were analyzed. Then the stability, the compensation method, the output impedance, the SNR, and the loading ability of the differential current source circuit (DCSC) were discussed in the simulation and measurement experiments. Lastly we applied the proposed DCSC for EIT. To our knowledge, the novel DCSC proposed in this paper based on the enhanced Howland current source is improved not only in terms of output performance but also the SNR of the whole measurement system. II. THE HOWLAND CURRENT SOURCE CIRCUIT
The single-ended Howland current pump19, 20 using a single operational amplifier with both negative and positive feedback shown in Fig. 1 is a popular current source as one part of the bioelectrical impedance measurement system. When the parameters in the circuit satisfy, R2A + R2B R4 = , R3 R1
FIG. 1. The Howland current pump.
(1)
the output current is given by I=
Vi R2B
R2A + R2B R1
.
(2)
When the feedback paths are balanced, the output current is 2B justly linear with the input voltage. When RR43 = R2AR+R = 1, 1 the output current is given by I=
Vi . R2B
(3)
Then the output impedance is given by Rout =
R3 R2B (R1 + R2A ) . R3 (R2A + R2B ) − R1 R4
(4)
When the parameters are balanced in (1), the output impedance in (4) is infinite. Actually, the stray capacitance in the environment and the existing resistors tolerance degrade the high-frequency performance of the output current and impedance.
III. THE DIFFERENTIAL CURRENT SOURCE
Fig. 2 shows the DCSC, the left part of which is the Howland topology current source circuit, the reverse amplifier circuit from one end of the resistorRL is connected to the other end ofRL . This architecture of DCSC is able to dramatically reduce the common mode interference. In Fig. 2, the operational amplifier has high input impedance, and the current inputting to operational amplifier A2 is approximately equal to zero, so the output current of the current source can be expressed by (3). In order to satisfy the requirement of the frequency of 1 MHz, A1 , A2 , and A3 are all high speed operational amplifiers. We choose the Texas Instruments OPA842 with the unity-gain bandwidth of 400 MHz. To meet this precision requirement and to realize the necessary noise level, output impedance, and voltage swing, we set R1 = R3 = R4 = R5 = R6 = 2 k, R2A = R2B = 1 k. NI Multisim is used to evaluate the input and output performance of the current source circuit. The resistor mismatch is simulated assuming 0.01% tolerance.
FIG. 2. The differential current source circuit.
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Rev. Sci. Instrum. 85, 055111 (2014) TABLE I. The comparison of output impedance of the HCSC and DCSC in simulation. F (KHz)
1
5
10
20
50
100
200
HCSC (M) 24.97 42.85 49.97 24.98 42.8 23.06 12.48 DCSC (M) 499.8 124.9 27.75 45.44 125 21.72 24.98 300 400 500 600 700 800 900 1000 5.98 3.55 2.42 1.83 1.49 1.27 1.12 1.02 11.88 7.22 5.03 3.82 3.05 2.60 2.29 2.09
FIG. 3. The compensation circuit for the DCSC.
IV. PERFORMANCE EVALUATION AND MEASUREMENT RESULTS A. The compensation method for the DCSC stability
In actually, the operational amplifier with high speed cannot remain stable in high frequencies. In the measurement circuit, the parasitic capacitance is ubiquitous such as cable capacitance, the capacitance between electrode lead, the stray capacitance between the circuit signal ground and the earth, and the stray capacitance from the placement and routing of the lead.21 The parasitic capacitance can seriously damage the balance of the feedback paths leading to the unstable current output especially in the case of high frequencies. The GIC13 is used in combination with the HCSC to compensate the parasitic capacitance corresponding to the frequency, but it is inconvenient for the application of multi-frequency measurement. We perform the two compensation methods for the circuit in Fig. 3, one is the capacitor C1 for the lead-lag compensation without sacrificing high frequency output impedance.2 Another is the capacitor C2 for hindering the free oscillation and stabling the high frequencies performance. We mainly assess the compensation method of capacitor C2 . In the measurement for the DCSC, the input voltage Vi = 0.25 mV, C2 = 5 pF, C1 = 100 pF, RL = 1.9952 K. The input voltage is produced by the 7280 DSP Lock-in Amplifier from Signal Recovery,22 and the precision (0.01%) resistors with low temperature coefficient (2 ppm ◦ C−1 ) are chosen to ensure high output impedance. Fig. 4 shows the comparison of the voltages at the resistor RL with and without C2 . Fig. 4 illustrates that the output voltage is stable below 100 KHz, the voltage drops rapidly above 100 KHz without
compensation, but after compensation the maximum variation of output voltage with the frequency of 1 MHz is 0.2%. B. The output impedance
In order to evaluate the output performance, we measure the output impedance of the differential and Howland topology current source circuits. In simulation, the load in parallel with 10 pF capacitance is analyzed as capacitive load. Then we change the load RL and measure two different load voltages to calculate the output impedance according to Eq. (5). The two load resistors are 10 K and 11 K. The output impedances in the frequency from 1 KHz to 1 MHz of the Howland and differential current circuits are shown in Table I. r=
R1 R2 (U2 − U1 ) , U 1 R 2 − U2 R 1
(5)
where U1 and U2 , respectively, are the output voltages at the load of R1 and R2 and r is the output impedance. From Table I we can see that output impedance gradually reduces with the frequency increasing. The output impedances in the two current circuits are over 1 M in below 1 MHz and are over 10 M in below 200 KHz. The important is that the output impedance of the DCSC is higher than that of the HCSC. In actual measurement, the input voltage is produced by the 7280 DSP Lock-in Amplifier from Signal Recovery, the two load resistors are 1.9952 K and 2.6833 K, C2 = 5 pF. In the DCSC, the compensation capacitances C1 , respectively, are 100 pF and 150 pF. In the HCSC, the compensation capacitances are 197 pF and 288 pF. Then the output voltages at the load in different frequency are collected by the 7280 DSP Lock-in Amplifier. The calculated output impedances are shown in Table II. The results shown in Table II are similar as in Table I. In actual measurement, the output impedance is over 1 M TABLE II. The comparison of output impedance of the HCSC and DCSC in actual measurement. F (KHz)
FIG. 4. The comparison of the voltages at the resistor RL with and without C2 .
1
5
10
20
50
100
200
HCSC (M) 2.12 2.44 2.44 2.07 1.80 1.62 1.52 DCSC (M) 14.85 13.3 13.3 6.69 4.46 2.26 2.34 300 400 500 600 700 800 900 1000 0.82 0.78 0.89 0.58 0.57 0.44 0.40 0.29 0.92 0.87 1.00 0.87 0.73 0.77 0.53 0.36
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below 200 KHz, and over 200 K below 1 MHz, and the output impedance is higher in the DCSC. From Tables I and II we can see that in some frequencies such as the frequency of 100 kHz the output impedances of the current source circuit are exceptions to the rule in the DCSC, which are mainly impacted by the present of the zero or pole in the system. Because of the present of the capacitance and inductance in the current source circuit, zero and pole will be produced in some frequencies,23, 24 which will influence the amplitude as well as the phase of the output signal, and the output performances such as the output impedance. The reasons that lead to the remarkable difference of the output impedance in the simulation and actual measurement as shown in Tables I and II contain the following three respects. First, the input signal of the current source circuit has limited resolution and precision, which can influence the SNR of the output signal and the output impedance. Second, under the limitation of the circuit parameters such as the resistor tolerance in the actual measurement, the output impedance expressed in the equation of (4) will be degraded. Lastly, because of the ubiquitous distribution parameters, the power frequency interference and the high frequency noise in the actual measurement, the actual performance of the current source circuit can’t achieve that in the theoretical model. C. The evaluation of the SNR
In Fig. 2, the voltages at two ends of the load RL are VO1 and VO2 , then VO2 = −VO1 ,
(6)
and the common mode signal in the output of the DCSC can be defined as 1 (7) Vc = (VO1 + VO2 ), 2 where Vc is the common mode signal. Therefore, in theory the common mode signal in the DCSC is zero, the commonmode rejection ratio (CMRR) of the circuit is infinite, which illustrates this DCSC can effectively improve the SNR of the whole system because there is no common mode noise flowing into the next stage circuit. We define the SNR in the measurement as vd , (8) SNR = 20 log vc where vd and vc are, respectively, the differential and common mode voltages at the two ends of the load. We design the adder circuit to measure the common mode signal using the operational amplifier AD8051 from Aanlog Devices. The common mode and differential mode voltages are collected by the 7280 DSP Lock-in Amplifier. The measurement frequency is 10 KHz and the load resistor is 1.9952 K. In the simulation, The 10 pF capacitance is paralleled with the load RL , by calculation the SNR is 85.64 dB. In actual measurement, the SNR is 65 dB. In contrast, the value of the differential mode signal is twice as much as that of the common mode signal in the HCSC, which fails to cancel out any common mode signal and improve the anti-noise performance of the current source circuit.
FIG. 5. The output spectrum of the DCSC.
The output spectrum while driving a 1.9952 K load is shown in Fig. 5 using Data Acquisition Card 6281 from National Instruments. This spectrum shows that out-of-band noise level is at least 100 dB below the operating frequency. D. The loading capacity of the DCSC
When the parameter satisfies as (1), the output voltage of vL is expressed by vL ≤ vSAT − vi
R2A + R2B , R1
(9)
where vSAT is the saturation voltage of the operational amplifier, the corresponding loading is vL . (10) RL = I Based on (9) and (10), the maximum loading for the HCSC is given by vSAT − R2B . RLmax = (11) I For the DCSC the maximum loading can be expressed as v SAT − R2B . (12) RLmax = 2 I Therefore, the maximum load of the DCSC is twice as much as that of the HCSC from (11) and (12), which can effectively enhance the loading capacity without changing the other parameter. V. THE EIT EXPERIMENT
We apply the proposed differential current source circuit for the open electrical impedance tomography system25
FIG. 6. The five measurements of the boundary voltages.
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FIG. 7. The reconstruction imaging of a two-dimensional phantom.
with the scanning electrode and a saline phantom for the twodimensional electrical impedance imaging. We fill the phantom with a background of 0.2 S m−1 . The width of the phantom is 0.225 m with 0.115 m long including 2116 cells and 1128 nodes. We place ten copper electrodes for the current injecting electrode and two copper electrodes for the voltage measuring electrode driven by the motor scanning along the boundary of the phantom. Then with nine current injections of 2 mA by the cross current injection mode 126 independence voltages are obtained by the Data Acquisition Card NI6281 using the neighboring protocol from the phantom with an anomaly of steel stick. The diameter of the steel stick is 10 mm in the depth of 10 mm. Fig. 6 shows the five measurements of the boundary voltages without anomaly. From Fig. 6 we can see that the five measurements are quite consistent, which illustrates the feasibility and stability of the electrical impedance system with the proposed differential current source circuit and the scanning electrode. And by measurement the SNR of the electrical impedance tomography system can achieve above 75 dB. Fig. 7 displays the reconstruction image using the variation regularization algorithm,25 which shows that the position and shape of the anomaly is well reconstructed. Therefore, the proposed differential current source circuit can effectively reduce the common mode interference and improve the SNR of the measurement system. VI. CONCLUSION AND DISCUSSION
A new differential topology current source circuit as well as compensation method is proposed. On the basis of the HCSC, the reverse circuit is introduced to form the differential architecture. Though the simulation and actual measurement, the DCSC has many advantages over the meaningful characteristics of output impedance, loading capacity and SNR in comparison with the HCSC. Owing to the ubiquitous parasitic capacitance, the feedback paths are unbalanced if the compensation method is not performed in the circuit. Thus the compensation method must be used to ensure the stability of output performance. In this work, two compensation capacitors are introduced as shown in Fig. 3. The capacitor C1 is used to compensate the high frequency lead-lag, which has been in detail illustrated.2 The capacitor C2 is to compensate the stay capacitance, prevent the self-induced oscillation and stable the output voltage which is in detail evaluated in this paper. In the actual measurement, the capacitance of C2 should be chosen as the real circuit,
Rev. Sci. Instrum. 85, 055111 (2014)
while the larger capacitance value will lead to effective phase error and reduce the SNR of the current source. From the results in Fig. 4, the output of the circuit is stabile without compensation below the frequency of 100 KHz, while the circuit turns back to stable output below 1 MHz after compensation. Under the limitation of the resistor tolerance and the stray capacitance in the actual measurement, the output impedances shown in Table II are lower compared with the output impedances shown in Table I. However, the output impedances in the DCSC are at least 2.34 M up to 200 KHz in the actual measurement, which is adequate for the most bioelectrical impedance applications. However, the common mode rejection ratio of the amplifier is finite, and the interference and noise requires each stage of the circuit for high SNR. The differential amplifier circuit is often used in the bioelectrical signal detection to improve the accuracy and SNR. Then the proposed DCSC is the key design which significantly reduces the common mode signal in the current source circuit and the whole bioelectrical collection system. In addition, the fourth remarkable improvement is the output loading capacity of the DCSC, which is twice bigger than that of the HCSC. Thus the impedance measurement scope is expanded effectively with DCSC. Lastly, with the proposed DCSC we design the electrical impedance imaging system, the reconstruction imaging shown in Fig. 7 shows that the proposed differential current source circuit can be used in the impedance measurement system. In order to improve the performance of the proposed DCSC, we will in further improve the resolution and precision of the input signal, simplify the circuit configuration, and reduce the influence of the distribution parameters and the parasitic parameters. Future work will target the DCSC in EIT to promote its development into clinical application. ACKNOWLEDGMENTS
This work was supported by the basic scientific research expenses of independent subject project supported by the China Academy of Chinese Medical Sciences. 1 Z.
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