This paper introduces a novel compact low-power amperometric instrumentation design with current-to-digital output for electrochemical sensors. By incorporating the double layer capacitance of an electrochemical sensor’s impedance model, our new design can maintain performance while dramatically reducing circuit complexity and size. Electrochemical experiments with potassium ferricyanide, show that the circuit output is in good agreement with results obtained using commercial amperometric instrumentation. A high level of linearity (R^{2} = 0.991) between the circuit output and the concentration of potassium ferricyanide was also demonstrated. Furthermore, we show that a CMOS implementation of the presented architecture could save 25.3% of area, and 47.6% of power compared to a traditional amperometric instrumentation structure. Thus, this new circuit structure is ideally suited for portable/wireless electrochemical sensing applications.

Electrochemical sensors are widely used for environmental monitoring such as gaseous pollutants [

Amperometric instrumentation consists of two parts: a potentiostat and a current readout circuit. The potentiostat provides current required for the reaction while maintaining the electrode/electrolyte interface at the correct potential. The current readout circuit conditions the electrochemical measurement and digitizes the reaction current. It is common to use bulky instrumentation to collect the amperometric readout. Many of the electrochemical instruments reported utilize commercial instrumentation and do not focus on the challenges of miniaturization for portable applications [

This paper introduces a novel compact and low power amperometric instrumentation circuit topology that utilizes the inherent nature of electrochemical sensor interfaces to enable system-level optimization. The new amperometric circuit provides complete current-to-digital readout with reduced component count compared to traditional amperometric instrumentation. Specifically, our new topology saves two operational amplifiers (opamp) and one integrator capacitor, thus significantly lowering circuit power and area compared to a traditional design. Therefore, the new electrochemical instrumentation circuit is well suited for portable, wireless, and implantable sensory microsystem applications. This paper makes major reuse of the content published in Xiaoyi’s thesis [

Electrochemical sensors in amperometric mode work under the following sensing principle: the reaction current is proportional to the analyte concentration when reacted electrode/electrolyte interface is biased at a constant voltage. To accurately control the reaction taking place at the interface, three-electrode cell configuration has been applied to amperometric electrochemical sensors. In such three-electrode cell, the reaction takes place at the interface between the working electrodes (WE) and electrolyte. A constant potential is maintained between the reference electrode (RE) and the WE. The third electrode, counter electrode (CE), provides a current path to the WE.

To analyze the electrochemical sensor’s electrical response, equivalent circuit models have been proposed in electrochemical impedance spectroscopy (EIS) theory. Randles circuit model [_{s} (relatively small), in series with the parallel combination of the double layer capacitor C_{dl} at the WE interface (charging current i_{C} follows through this path), and an impedance of a faradaic reaction caused by AC stimulus (AC faradaic current i_{f} follows through this path). The faradaic reaction consists of a charge transfer resistor R_{ct} and Warburg element Z_{w} which can be calculated as:
_{w} is the Warburg coefficient and ω is the angular frequency. Since our only interest is in the WE interface, the impedance between the CE and the RE is denominated as simple impedance Z. Notice that this model only represents sensor’s response to small AC stimulus. To represent both AC and DC response, a complete equivalent circuit model is shown in _{f}. Here, I_{f} is the constant reaction current proportional to the analyte concentration in amperometric electrochemical sensors, which is the main interest in sensor current measurements. In general, i_{f} ≪ I_{f}, and R_{s} is relative small. They can be considered as second-order effects in sensors response. For analysis simplicity, R_{s} and i_{f,ac} are omitted during following instrumentations derivation and will be re-discussed in

As introduced in _{RE}), the negative input node is connected to the RE, and the output is connected with the CE to provide the current path. The current readout circuit collects I_{f} either at the WE or the CE, then conditions and digitizes it. Two topologies have been used to implement the current readout circuit: a current-to-voltage convertor followed by a voltage-mode analog-to-digital convertor (ADC) [_{ref} of opposite direction are alternately connected with the integrator through switches, which are controlled by the digital output of the hysteresis comparator Dn. Thus, the input current of the integrator I_{int} is given by

As the waveforms in _{int}. Consequently, the output of the integrator V_{int} rises/falls corresponding to I_{int} direction. While V_{int} reaches the hysteresis comparator upper/lower bound (V_{ref}+/−ΔV/2) (where ΔV is the hysteresis window width and V_{ref} is the reference voltage), Dn flips, changing I_{int} according to _{1} of the digital “high” for Dn is given by
_{0} of the digital “low” for Dn is

From _{f} can be expressed as a function of I_{ref}, T_{1}, and T_{0} by

If the duty cycle α of Dn is defined as
_{f} can be expressed as a function of α and I_{ref} given by

Therefore, given a known I_{ref}, I_{f} is obtained by measuring duty cycle of Dn. Notice that I_{f} is independent of both the integrator capacitor C_{int} and the hysteresis comparator parameters (ΔV and V_{ref}).

In the model amperometric instrumentation circuit in _{dl} and only I_{f} is collected in the readout circuit. From a system point of view, the sensor system contains two capacitors: Cdl and Cint. Cint is part of the readout circuit and used for charging/discharging; Cdl is the inherent interface capacitor. Since capacitors occupy large area in integrated circuits, if C_{dl} could be utilized to play the role of C_{int}, then C_{int} could be eliminated from the circuit to save area. Modifying the traditional structure to incorporate C_{dl} into the circuit and eliminate C_{int}, we develop a compact amperometric instrumentation topology.

As shown in _{f} can be used to represent the electrochemical sensor equivalent model. Given that node B is a low-impedance node, folding the current source to the output of the integrator is equivalent to the typical topology of the current readout circuit. Notice that the parallel connection of I_{f} and C_{int} is the same as the equivalent circuit between RE and WE in _{int} is arbitrary. I_{f} still can be calculated from _{int} is replaced with C_{dl}.

To satisfy sensor’s bias condition, a potentiostat function is incorporated into the current-mode ADC by the following modification steps. First, by flipping the direction of I_{f}, and substituting V_{ref} and V_{WE} with V_{WE} and V_{RE}, the voltage between the RE and the WE can be held by feedback loops of the integrator (loop1) and of the ADC (loop2). Although WE potential is not strictly held constant due to a nonzero value of ΔV in the loop2, the perturbation on WE does not affect the sensor’s steady state as long as ΔV is set small enough (less than 10 mV) [

Following the modification described above, a modified amperometric instrumentation circuit with the sensor model can be illustrated as _{f}_{f}_{f}

This topology successfully realizes the functions of both current-mode ADC and potentiostat. Compared to a traditional topology in _{dl} for integrator, and eliminates one opamp required by the potentiostat and C_{int} required by the integrator. Notice that voltages at RE and WE in _{RE} and V_{WE} from circuit perspective. Therefore, nodes RE and WE are interchangeable. By swapping WE with RE, the simplified structure shown in _{RE} with V_{RE-WE}, the resulting schematic in _{RE}>V_{WE} and thus V_{RE-WE}>0. If the sensor bias requires V_{RE}<V_{WE}, the WE could alternatively be connected to the power supply.

Following the derivation from the schematic in _{ref} is set to V_{RE-WE}, and ΔV is set to 10mV.

Although the function of the CCDAI is equivalent to the traditional amperometric instrumentation, structure differences and additional constrains will cause performance differences. In addition, as mentioned in

Compared to the traditional potentiostat that drives the electrochemical cell from an opamp output, the CCDAI drives the electrochemical cell by a constant current source with much a lower current value. Therefore, it would take longer time to stabilize the electrochemical cell potential. Nevertheless, differences in the potential stabilization time would not affect steady state operation of the electrochemical cell.

Compared to a traditional current mode ADC, the main differences of the CCDAI include: 1). the integrator capacitor C_{int} is replaced by sensor’s double layer capacitor C_{dl}; 2). the hysteresis comparator voltage window is limited to 10mV. These two differences could affect the resolution of the calculated I_{f}. From _{f} is obtained by calculating measured α with a known I_{ref} value. From _{0} and T_{1} are given a fixed counter reference clock frequency. From _{0} and T_{1} are proportional to C_{dl} and ΔV. Therefore, C_{dl} and ΔV do affect the resolution of I_{f}. Assuming ∣I_{f}∣<I_{max}, the given max time interval width is expressed by

For a fixed counter reference clock frequency f_{0}, the maximum relative quantization error [

The ADC’s effective resolution (in bits) N is determined by

Therefore, larger ΔV and C_{dl} would improve the effective resolution N. In the traditional current-mode ADC, ΔV can be up to the power supply voltage, Vdd, which can be 5V in a portable device. In the CCDAI, ΔV is restricted to maximum 10 mV. ΔV in the CCDAI is 500 times smaller than in the traditional current-mode ADC, resulting in 9 bits of effective resolution loss for the CCDAI. However, in the meantime, electrochemical double layer capacitor C_{dl} has much larger capacitance density than a capacitor that can be fabricated by CMOS process in a single IC chip. For instance, double layer formed on 1 mm^{2} electrode can generate μF level capacitance; while a capacitor in a single IC chip is up to tens of pF. The 10000 times larger capacitance in the CCDAI would result in 13 bits of effective resolution improvement for the CCDAI. Therefore, the total effect of C_{dl} and ΔV provides an improvement of around 4 bits of the effective resolution. As a tradeoff, the sampling rate drops as the effective resolution increases. Fortunately, electrochemical systems typically have a slow response and do not need a fast sampling rate.

The derivation in _{s} and AC Faradaic components in the complete equivalent circuit model would introduce significant errors.

If we first consider adding R_{s} to the circuit, the corresponding waveform of V_{int} is illustrated in _{int} caused by R_{s} can be observed, this does not change T_{1} and T_{0}. Thus _{ref}·R_{s}. In a standard electrochemical cell configuration, the RE is placed close to the WE and a typical experimental value of R_{s} is on the order of 10 ~ 10^{2} Ω. With μA level of I_{ref}, this only gives 10 ~ 100μV error, which is less than 1% of 10 mV. Therefore, R_{s} has negligible impact on the resolution.

Next, AC Faradaic components were evaluated. The AC Faradaic components are in parallel with the double layer capacitor C_{dl} and the DC Faradaic current source I_{f}. Because both the Warburg element and C_{dl} block DC current, only AC current i_{f} can pass through those AC Faradaic components. The sensor current I_{sens} is the sum of the DC current I_{f} and the AC current i_{c} + i_{f}. Observe that the sensor current I_{sens} should be equal to the current provided by the current source at any time,
_{1} is the time interval when Dn = 1 in the CCDAI, T_{0} is the time interval when Dn=0 in the CCDAI. Here T_{1} and T_{0} do not follow _{sens} is illustrated in _{sens} can also be expressed by Fourier series as
_{c} = 1/(T_{1}+T_{0}). The first term in _{sens}, and the second term represents the AC part. Because the AC components (C_{dl} and Warburg elements) block DC currents, and DC current source blocks AC currents, I_{f} is equal to the DC part of I_{sens}. Thus I_{f} is

Because

To verify the functionality and performance of the CCDAI, the test setup shown in _{ref} was set to 1 μA, which are suitable values for a portable sensor application. To implement a hysteresis comparator with upper and lower bounds that can be adjusted independently during testing, the circuit shown in _{RE-WE}, and the comparator’s upper/lower bound voltages, V_{h} and V_{1}. It was also used to measure the time intervals T_{1} and T_{0} of comparator output Dn using an internal 10MHz clock. A Labview user interface was built for communication between a PC and the data acquisition card. The current I_{f} was calculated using _{1} and T_{0} values.

To evaluate the ADC performance of the CCDAI, an electrical test model was connected with the CCDAI board. To implement the simplified model in _{f} from −800 nA to 800 nA with 2 nA step. Differential non-linearity (DNL) and integral non-linearity (INL) of the readout current are plotted in _{dl}, and f_{0}. In theory, resolution will be enhanced by increasing ΔV. However, as described in _{dl} is an inherent parameter of the electrochemical cell and is already much higher than the capacitors implemented on chip in conventional CMOS designs. The resolution could be enhanced by increasing f_{0} at the expense of higher power consumption. Considering this tradeoff, in our design, we set the f_{0} as 100 kHz. It is a remarkable fact that, increasing f_{0} for better resolution, not only increase the power consumption of the counter, but also increase the size of the counter to support greater number of bits. Therefore, by considering a fixed counter clock frequency of f_{0}=100 kHz, 8 bit resolution has been implemented which enables us to reach 6 nA resolution. This resolution meets the requirements for many electrochemical sensor applications [

To verify the electrochemical functionality of the CCDAI board, an electrochemical test was performed using an electrochemical cell with potassium ferricyanide as the analyte. The electrolyte consists of 0.1M potassium chloride as buffer solution and potassium ferricyanide with varied concentrations (from 0 to 6 mM). Ag/AgCl (CH Instrumentations Inc.) was used as standard RE. Pt wire (CH Instrumentations Inc.) was used as the CE. Au plate with 1 mm^{2} area (CH Instrumentations Inc.) was used as the WE. V_{WE-RE} was set to 190 mV.

The faradaic current generated by potassium ferricyanide redox reaction was recorded by the CCDAI as a function of time. The commercial electrochemical instrumentation CHI760C was used as a reference to record current data at the same condition setup. As an example, data for a 6mM concentration is plotted in _{WE-RE} to the desired voltage in the very short time; while CCDAI applies a constant current to raise V_{WE-RE} to the desired voltage in a gentle way. In addition, initial current recorded by CHI760C includes charging current caused by step stimulus, while current recorded by the CCDAI does not contain the charging current. Due to unavoidable convection in the solution [^{2}) of the fitting curve are 0.991 and 0.996 for the data acquired by CCDAI and CHI760C respectively. The electrochemical experiment results demonstrate the functionality and the accuracy of the CCDAI.

The CCDAI realizes a compact topology while maintaining the functionality of a traditional amperometric instrumentation circuit. Compared to the model instrumentation circuit presented in

A novel compact amperometric instrumentation design with current-to-digital readout for electrochemical sensor was presented. Compared to a model amperometric instrumentation structure, the new design dramatically saves area, cost and power by utilizing the sensor’s double layer capacitor as a circuit element and adopting EIS mode, without sacrificing its resolution and detection of limitation performance. A board-level CCDAI was implemented and tested, demonstrating an 8-bit effective resolution in the range of −800 nA to 800 nA. Functionality of the instrumentation was verified by an electrochemical experiment in potassium ferricyanide. High linearity of current-to-concentration transfer was acquired with an R^{2} of 0.991. A CMOS implementation of the CCDAI is estimated to save 25.3% of area and 47.6% of power compared to the model amperometric instrumentation structure. Thus this new compact circuit topology is well suited for portable/wireless electrochemical sensor applications.

This work was supported by the National Institutes of Health under Grant NIH_R01ES022302 and the National Institute for Occupational Safety and Health (NIOSH) under Grant R01OH009644.

Equivalent circuit model of electrochemical sensor cell. (a) Randles model (b) Complete model considering both AC and DC stimulus. (c) Simplified model for circuit analysis.

Schematic of a model amperometric instrumentation circuit including potentiostat and current-mode ΣΔ ADC.

Waveforms of the current on the integrator input I_{int}, the voltage on the integrator output V_{int}, and the digital output of the comparator Dn.

Schematic of the electrochemical sensor system consisting of a model amperometric instrumentation circuit and the simplified electrochemical sensor equivalent circuit model.

Derivation of the instrumentation topology. The input current source is folded into parallel connection with the integrator capacitor.

Schematic of the modified amperometric instrumentation circuit with sensor equivalent circuit model.

Schematic of the simplified compact amperometric instrumentation circuit with electrochemical sensor equivalent circuit model.

Schematic of CCDAI with electrochemical sensor equivalent circuit model.

V_{int} waveform illustration when considering R_{s} in the equivalent circuit model.

Illustration of I_{sens} in time domain.

Test setup for electrical and chemical experiment.

A hysteresis comparator realization with adjustable upper/lower bound.

DNL and INL of the CCDAI. Both DNL and INL in the current range are better than −49dB, implying an 8 bit of effective resolution.

The faradaic current generated by 6 mM of potassium ferricyanide as function of time when V_{WE-RE}=190mV. Red line represents data recorded by CHI760C and blue line represents data recorded by CCDAI.

The faradaic current recorded by the CCDAI at V_{WE-RE}=190mV as function of time for 0- 6 mM of potassium ferricyanide. The dot and dash curves present the data recorded by CHI760C for reference.

Calibration curve of faradaic current vs potassium ferricyanide concentration. The current values were the average values from 200s to 300s. Fitting curve was presented as a straight line. R^{2} values of the fitting line are 0.991 and 0.996 for the data acquired by CCDAI and CHI760C, respectively.

Area occupation of IC blocks in a 0.5μM CMOS fabrication process for comparison between the model amperometric instrumentation circuit and the CCDAI.

Area(μm^{2}) | Model | CCDAI | Savings | |
---|---|---|---|---|

Opamp | 1200 | 2 | 0 | |

Comparator | 1000 | 1 | 1 | |

Current source pair (with switch) | 600 | 1 | 1 | |

8-bit counter @100kHz | 12000 | 1 | 1 | |

Capacitor(μF) | 2200 | 1 | 0 | |

Total area(μm^{2}) |

Power consumption of IC blocks in a 0.5μM CMOS fabrication process for the comparison between the model amperometric instrumentation circuit and the CCDAI.

Power@5V | Model | CCDAI | Savings | |
---|---|---|---|---|

Opamp | 7.5 | 2 | 0 | |

Comparator | 5 | 1 | 1 | |

Current source pair (with switch) | 0.5 | 1 | 1 | |

8-bit counter @100kHz | 11 | 1 | 1 | |

Capacitor(1pF) | N/A | 1 | 0 | |

Total power(μW) |

COMPARISON OF THE POTENTIOSTAT WITH PREVIOUS WORK.

Work | Tech | Supply | Resolution | Power | Area^{2}) |
---|---|---|---|---|---|

[ | 2.5μm CMOS | 5V | ~μA | 25 | 6.44 |

[ | 0.18μm CMOS | 1.8V | 50-200nA | 71.7 | 0.0179 |

[ | 0.13μm CMOS | 1.2V | 150nA | 3 | 0.36 |

[ | PCB | 5v | ~μA | 12.6/CCM | |

CCDAI | 0.5 μm CMOS | 5V | 16.5^{Δ} | 0.0136^{Δ} | |

PCB | 5V | 6 nA | 25 |

CCM: Continuous current mode; DCM: Discrete current mode

Analytical calculation