A Nonuniform Sampling Lifetime Estimation Technique for Luminescent Oxygen Measurements for Biomedical Applications

Abstract

This article presents a novel technique that is immune to offset, enabling precise determination of the lifetime of luminescent materials. The technique is specifically applied to measure transcutaneous oxygen, an indicator of oxygen that diffuses through the skin and reflects arterial oxygen levels. Unlike intensity-based measurements, lifetime-based luminescence measurements are superior because they decouple oxygen information from confounding factors. The technique presented in this work involves measuring the time difference between fixed-voltage steps to extract the time constant of a decaying exponential, which represents the lifetime of luminescence. We propose a novel switched-capacitor circuit that enables long integration times and prevents the front-end amplifier from saturating. The analog subsystem was realized in 180-nm CMOS technology via a transimpedance amplifier (TIA) with a gain bandwidth product of 10 MHz, a comparator, and a switched capacitor circuit. The measured mean error is as accurate as 1.9% without postprocessing. During a 130 μs measurement period, the readout circuit consumes a maximum of 16 μJ per calculation with a ${\text{FoM}}_W=177\text{nJ}/\text{conv}$. Preliminary human subject tests have demonstrated that the sensor can effectively detect changes in transcutaneous oxygen levels resulting from arterial occlusion.

I. Introduction

Oxygenation assessment is multifaceted, requiring consideration of several key parameters. Clinically, it is typically evaluated using three main metrics: 1) arterial partial pressure of oxygen $\left({\text{PaO}}_2\right)$, representing unbound ${\mathrm{O}}_2$ molecules in plasma; 2) arterial oxygen saturation $\left({\text{SaO}}_2\right)$, which indicates the ratio of ${\mathrm{O}}_2$-bound hemoglobin to total hemoglobin; and 3) arterial oxygen content $\left({\text{CaO}}_2\right)$, reflecting the total amount of oxygen in the blood. Together, these parameters enable a comprehensive evaluation of respiratory efficiency, as well as oxygenation of the blood and tissues.

The gold standard for blood gas measurement remains invasive arterial blood gas (ABG) analysis [1]. An estimate of ${\text{SaO}}_2$ can be obtained noninvasively through peripheral oxygen saturation $\left({\text{SpO}}_2\right)$ measurements using pulse oximetry. The widespread use of pulse oximetry allows for an indirect assessment of ${\text{PaO}}_2$ based on ${\text{SpO}}_2$, with their relationship governed by the oxyhemoglobin dissociation curve, despite concerns about the limitations of this indirect method [2]. A direct estimation of ${\text{PaO}}_2$ can be achieved noninvasively through transcutaneous partial pressure of oxygen $\left({\text{PtcO}}_2\right)$, which reflects the diffusion of oxygen through the skin and is directly correlated with changes in ${\text{PaO}}_2$ [3].

Transcutaneous blood gas monitors are in high demand at neonatal intensive care units (NICUs) as they provide noninvasive and continuous measurements of critical blood gases to assess infants’ respiration effectiveness [4], [5], [6]. Researchers have been working on developing transcutaneous monitors since the 1950s, including Clark and Severinghaus electrodes [7], [8], [9], [10], [11], [12], [13]. However, limitations in blood-gas sensing, such as cost, form factor, use of wet electrodes, and the need for a heating element, have hindered their miniaturization and widespread use [14]. Recent advances in luminescent gas sensing techniques have enabled researchers to leverage solid-state circuit technology to develop miniaturized next-generation blood gas monitors [15], [16]. Luminescent oxygen $\left({\mathrm{O}}_2\right)$ sensors offer superior performance to traditional electrochemical sensors by having a small form factor, significantly less drift, and eliminating the heating requirement [17].

Designing wireless wearable biomedical devices faces numerous challenges, particularly for miniaturized luminescent ${\mathrm{O}}_2$ sensors. First, the luminescent response is a relatively weak signal and is susceptible to degradation by confounding factors such as ambient light and diode leakage currents. In addition, optical path variations due to manufacturing variation, packaging, excitation signal changes, surface reflection, patient skin color, and motion artifacts can degrade the signal intensity at the photodiode (PD) and, accordingly, the amplitude at the analog front end (AFE). Lifetime-based measurement techniques solve the challenge by separating the ${\mathrm{O}}_2$ partial-pressure information from the luminescence intensity [15], [18], [19], allowing for a more accurate blood gas measurement.

Second, noise and large offsets originating from hardware imperfections, DC leakage currents, and electrode-tissue interfaces lead to complications in extracting small signal information from the body, resulting in a low signal-to-noise ratio (SNR). Therefore, many optical readout circuits require complex DC offset cancellation circuits to minimize offsets in the measurement circuity [21], [22]. An alternative yet efficient technique would be a precisely designed algorithm that can extract sensitive information without the use of complex DC offset cancellation circuits. Additionally, an integrating frontend reduces the output noise [23] by $(1/2\pi C)$ for a given measurement period [24].

Third, designing for a small form factor and minimal power presents system-level challenges due to limited available resources, such as insufficient memory for data storage, inadequate computational power, and limited transmission bandwidth. To reduce memory requirements and data transmission power, measurement techniques that can be data sparse offer a significant advantage. Algorithms that enable the extraction of key health information from a small dataset, robust from confounding factors, such as noise and offsets, offer a notable advantage over more traditional signal paths and digital signal processing in terms of area and power.

This article presents a novel offset-immune lifetime estimation algorithm for measuring the lifetime of luminescent materials for ${\mathrm{O}}_2$ sensing by considering the above-mentioned challenges. This novel nonuniform sampling (NUS) technique uses the time differences $\left(\Delta t\right)$ between fixed-voltage steps $\left(\Delta V\right)$ to extract the time constant $\left(\tau \right)$ of the decaying exponential, which represents the lifetime of the luminescence. This algorithm, easily realizable in hardware, is a modification of rapid lifetime determination [25].

1. As previously mentioned, the lifetime-based technique at the core of the NUS algorithm is minimally affected by confounding factors.

2. The NUS algorithm removes any offsets, including offsets due to DC circuit leakage current and reactions at the sensor-tissue interface.

3. In addition, the NUS algorithm requires only three samples from the decaying luminescence signal to estimate the lifetime information for one ${\mathrm{O}}_2$ value point, a unique feature specific to this algorithm, relaxing the data rate requirements.

Another novelty of the proposed work lies in the circuit implementation technique to realize the NUS algorithm.

1. The system features a specialized AFE that employs a novel switched-capacitor circuit to implement fixed-voltage steps for quantization, enabling high transimpedance gain without saturating the front-end amplifier.

2. This technique limits the noise in the AFE by integrating the exponential current response from the luminescent material for a fixed period of time.

3. Time gating of the front-end integrator removes the need for optical filtering, simplifying signal processing and packaging requirements.

4. A control circuit automatically tunes the light-emitting diode (LED) excitation pulses to avoid overpowering or starving the AFE, as PD current varies with changes in the partial pressure of ${\mathrm{O}}_2$.

The rest of the article is organized as follows. Section II elaborates on the luminescence lifetime and its relation with ${\mathrm{O}}_2$ measurement and derives mathematical expression of the nonuniform luminescent lifetime estimation algorithm. Section III depicts the prototype system architecture and articulates the circuit details of the test chip. This section also covers the evaluation board and the auxiliary circuits used to characterize the test chip. Section IV addresses the sources of error in the system and how to minimize them. Section V covers the tests performed on the circuit to assess its performance. Section VI demonstrates early human subject test data. Section VIII concludes this article.

II. Estimation of a Single-Time-Constant Exponential Decay With NUS

A. Theoretical Background

An ${\mathrm{O}}_2$-sensitive dye (e.g., platinum-porphyrin) contains functional groups called luminophores. When luminophores are excited with high energy photons $(\lambda \approx 450\text{nm})$, their electrons jump from the ground state $\left(S_0\right)$ to a higher energy state $\left(S_1\right)$, as illustrated in Fig. 1(a). When the electron tries to return to $S_0$, it can enter a triplet state $\left(T_1\right)$. The transition of the electron from $T_1$ to $S_0$ results in the emission of a photon with a relatively longer wavelength ($\lambda \approx 650\text{nm}$). This emission is suppressed or “quenched” in the presence of ${\mathrm{O}}_2$ [26], as depicted in Fig. 1(b). The Stern–Volmer equation

$$\frac{I_0}{I}=\frac{{\tau }_0}{\tau }=1+K_{\text{SV}}{\text{PO}}_2$$ (1)

describe the dynamics of this interaction. The partial pressure of ${\mathrm{O}}_2\left({\text{PO}}_2\right)$ is related to the intensity $\left(I\right)$ and lifetime $\left(\tau \right)$ through the rate constant, $K_{\text{SV}}$, and intensity and lifetime with no ${\mathrm{O}}_2,I_0$ and ${\tau }_0$, respectively. The emitted red light’s intensity and lifetime are inversely proportional to the ${\text{PO}}_2$ surrounding the dye, as shown in Fig. 1(c).

Fig. 1.

(a) Simplified energy state diagram, (b) excitation and emission spectrum, and (c) lifetime and intensity of the emission quenched by ${\mathrm{O}}_2$ [20].

B. Lifetime Estimation With NUS Algorithm

A common way to observe ${\mathrm{O}}_2$ quenching is by measuring luminescence intensity as a function of time following the excitation of luminophores. The exponential decay of the luminescent response after excitation is an intrinsic physical property of the material, as explained in the literature [26]. As a result, the sensor exhibits consistent behavior each time it is excited. The time it takes for the intensity to reach $1/e$ of the initial intensity value is the $\tau$ (decaying rate or lifetime). Lifetime measurement has an advantage over intensity measurement due to its robustness to factors that affect intensity but not lifetime, such as variation in optical paths. Two prominent optical sensing challenges in biomedical applications, motion artifacts, and differences in skin color induce optical path changes [21], [27], [28].

To ensure an accurate assessment of transcutaneous ${\mathrm{O}}_2$, we have developed an acquisition algorithm based on lifetime estimation. In addition to selecting the appropriate optical acquisition technique, the data acquisition algorithm must minimize errors caused by offsets and nonideal circuit characteristics. To address this, we propose a novel offset immune lifetime estimation algorithm that accurately extracts the time constant of the decaying exponential of luminescent material, providing precise ${\text{PO}}_2$ information.

A decaying exponential with an offset is defined as $y\left(t\right)=a{e}^{(-t/\tau )}+b$, where $a$ is a scalar, $\tau$ is the time constant of the decaying exponential, and $b$ is the offset component (i.e., the DC current or the dark current in a PD). The integration technique is commonly employed to mitigate high-frequency noise in signals. This technique preserves the time constant while scaling the amplitude and offset of the exponential signal. Additionally, a factor $m$ may also be included as part of the signal processing mechanism, e.g., introducing gain and inverting the signal. These operations result in the following expression; $Y\left(t\right)=m\int \left(a{e}^{(-t/\tau )}+\right.b)dt$. As the signal progresses over time, three samples are obtained at specified intervals. The first sample, $Y_0$, is obtained at an arbitrary point in time at $t_0$, closer to the beginning. The other two samples, identified as $Y_1$ and $Y_2$, are obtained at subsequent signal steps at times $t_1$ and $t_2$. These three samples are separated by a fixed step size, $\Delta Y$, as illustrated in Fig. 2(a).

Fig. 2.

(a) Waveform of the proposed NUS lifetime estimation algorithm, (b) demonstration of time constant preservation during an integration process, level crossing detection using (c) resistor ladder and (d) proposed switched capacitor.

Defining the $t_i$ from the difference between adjacent signal steps eliminates the effects of constant components in the signal. The difference between $Y_2-Y_1$ yields

(2)

and the difference $Y_1-Y_0$ results in

(3)

If the constant component is relatively small or the time $\Delta \mathrm{t}$ between measurements is close enough, the constant component effectively drops out. Then, dividing the two differences in (2) and (3) cancels out the amplitude component of the exponential and leaves the time information as

$$\frac{Y_2-Y_1}{Y_1-Y_0}=\frac{\left(e^{\left(\frac{-t_2}{\tau }\right)}-e^{\left(\frac{-t_1}{\tau }\right)}\right)}{\left(e^{\left(\frac{-t_1}{\tau }\right)}-e^{\left(\frac{-t_0}{\tau }\right)}\right)}=1.$$ (4)

This can be simplified further by multiplying both the numerator and the denominator by $e^{\left(t_1/\tau \right)}/e^{\left(t_1/\tau \right)}$, resulting in

$$1=\frac{\left(e^{\left(\frac{t_1-t_2}{\tau }\right)}-1\right)}{\left(1-e^{\left(\frac{t_1-t_0}{\tau }\right)}\right)}.$$ (5)

A root-solving technique such as Brent’s method or Newton’s method can be used to solve for $\tau$ in (5). We use the time difference between fixed-sized steps $\left(\Delta Y\right)$ to extract the time constant $\left(\tau \right)$, as shown in Fig. 2(a).

C. Circuit Implementation

A transimpedance amplifier (TIA) utilizing resistive feedback is a widely used technique for converting the photocurrent into voltage. However, to achieve high gain, the feedback resistor becomes substantially large, occupying a large area and introducing additional thermal noise to the front end. An alternative approach is to convert the photocurrent into voltage by integrating it with a feedback capacitor, $V\left(t\right)=(1/C)\int \left(i_{\text{pk}}{e}^{(-t/\tau )}+i_{\text{DC}}\right)\mathit{\text{dt}}$. This substitution of the feedback resistor with a capacitor allows for a more compact chip area and reduces noise. Moreover, a TIA with an integrating capacitor ensures the preservation of the time-constant, $\tau$, information pertaining to the decaying behavior of photocurrent, as depicted in Fig. 2(b).

The hardware implementation of NUS can be achieved by the use of a resistor ladder to create the threshold levels and three different comparators to detect when the integrator output crosses each threshold, as demonstrated in Fig. 2(c). The time between each comparator output gives the time between each voltage step. The timing accuracy of the NUS algorithm can be strongly influenced by the discrepancies in resistors originating from the mismatch and delay variation of comparators. We should also note that the use of three comparators in this technique ultimately results in a higher power demand.

These disadvantages can be overcome by using a switched capacitor circuit, as demonstrated in Fig. 2(d), which can subtract $\Delta V$ amount of voltage when the threshold level $\left(V_{\text{TH}}\right)$ is reached. This technique offers several advantages over a resistor string network such as: 1) the use of a single comparator eliminates the inconsistency in the threshold level while reducing the power consumption significantly; 2) a further reduction in power consumption is achieved by eliminating passive leakage current in the resistor string; 3) the offset of the comparator and the integrator are consistent on each sample and is canceled out by the algorithm; and 4) the ratio of the feedback capacitor and the switched capacitor sets the voltage step, eliminating any mismatch concerns.

III. System Architecture

The overall system architecture of the NUS-based transcutaneous oxygen monitor consists of an AFE, an LED driver, a biasing unit, an FPGA-based controller, and a power management unit, shown in Fig. 3(a). The system’s operation is divided into an excitation phase and a readout phase. During the excitation phase, the LED driver pulses the LED $D_2$ (LXZ1-PR01, Lumileds [29]) once at a set intensity and duration, exciting the ${\mathrm{O}}_2$-sensitive platinum porphyrin film with blue light $(\lambda =450\text{nm})$. During this excitation phase, the integrator, $A_1$ and $C_F$, is set to unity-gain with a switch (${\varphi }_{\text{RST}}$). This signal gating prevents the AFE from saturating due to the high-intensity LED burst. $C_F$ is reset only during the excitation phase, reducing the impact of reset noise compared to resetting after every level crossing of $V_{\text{TH}}$. In addition, the time-domain signal gating removes the need for optical filtering to extract the relatively weak luminescent signal from the powerful excitation signal.

Fig. 3.

(a) System diagram of the NUS-based transcutaneous oxygen monitor, schematic of (b) TIA (A1), (c) comparator (A2), and (d) SCU.

In the readout phase, a PD $D_1$ (S13773, Hamamatsu [30]) captures the emitted red photons $(\lambda =650\text{nm})$, generating a current ($I_{\text{PD}}$) matching the decay of the photons. $A_1$ and $C_F$ integrate $I_{\text{PD}}$ to generate a voltage ($V_{\text{INT}}$). The integrator is assisted with a nonuniform switched-capacitor technique to improve the dynamic range of $V_{\text{INT}}$. Although a minimum of three-level crossings are required, as shown in Fig. 2(a), $V_{\text{INT}}$ can swing close to the rail multiple times. The comparator, $A_2$, detects the level crossings with respect to the threshold voltage ($V_{\text{LVL}}$) and sends a signal ($V_{\text{COMP}}$) to the switch control unit (SCU). The SCU in turn sends four nonoverlapping signals (${\varphi }_1-{\varphi }_4$) to drive the switched capacitor, $C_{\text{SW}}$. This action injects a fixed amount of charge into the summing node of the integrator, $V_{\text{SUM}}$. The charge injection causes a fixed voltage subtraction, $\Delta V$, at $V_{\text{INT}}$, allowing $A_1$ to continue integrating $I_{\text{PD}}$, as illustrated in Fig. 2(a).

A. Analog Front End

The building blocks of the AFE include a TIA, a comparator, and a switched-capacitor circuit.

1). Transimpedance Amplifier:

The TIA performs the integration step of the algorithm. The front-end amplifier, $A_1$, is a telescopic cascode with PMOS inputs along with a common source output stage [31]. A simplified schematic of the amplifier is shown in Fig. 3(b). The time constant of the front end was designed to be at least one order of magnitude less than the luminescent decay time, which is on the order of 1–30 μs. This is necessary to reduce the induced error from the front end to below 1% [32]. The bias current $I_{\text{BIAS}}$ is set by a bandgap reference circuit. The DC feedback through $M_7$ ensures that if the common source node moves, the gate voltages of $M_9$ and $M_{10}$ will track it by $\mathit{\text{VG}}{S}_7$ [31]. The feedback function enables a wider common-mode range with a relatively constant transconductance $\left(g_m\right)$. This is desirable as it allows the integrator to be biased close to the threshold voltage of the PMOS differential pair without sacrificing $g_m$. High common-mode voltage improves the bandwidth of the integrator by reducing the PD junction capacitance. Biasing close to the PMOS threshold also increases the signal dynamic range, enabling wider voltage swing during the subtraction step.

2). Comparator:

The comparator, $A_2$, performs the level-crossing detection function of the sampler. The comparator needs to have a high gain with minimal delay to reduce the error in the NUS algorithm. A simplified schematic of the comparator is shown in Fig. 3(c). The differential amplifier detects when the output crosses a fixed threshold. Since no hysteresis is used, the comparator resets quickly to detect the next level-crossing event.

3). Switched Capacitor and the Switching Unit:

A switched-capacitor unit, as seen in Fig. 3(a), is employed to perform a subtraction operation at the output of the integrator, $V_{\text{INT}}$, by constant charge injection on the summing node, $V_{\text{SUM}}$, without resetting the integrating capacitor. The charge injection causes $V_{\text{INT}}$ to drop as the amplifier balances the charge on the feedback capacitor $\left(C_F\right)$. A correct switching sequence of the capacitor, $C_{\text{SW}}$, through the switching unit is critical to ensure error-free switching. When the comparator trips, it triggers a one-shot signal. The one-shot triggers the nonoverlapping switches to switch $C_{\text{SW}}$ from the charging position (${\varphi }_4-{\varphi }_3$ connection) to the injecting position (${\varphi }_2-{\varphi }_1$ connection). The timing diagram of the switching sequence is depicted in Fig. 3(d). This charge injection forces the output of the integrator to drop by $V_C\left(C_{\text{SW}}/C_F\right)$, driven by negative feedback ensuring the inputs stay approximately equal. This prevents the integrator from saturating. After the charge payload is delivered, the switched-capacitor circuit rewinds the switching to charge the capacitor for the next voltage step.

B. LED Driver

An LED driver was designed on the evaluation board to characterize the ${\mathrm{O}}_2$ measurement system. The driver was designed to achieve narrow (<10 μs), high-intensity pulses to excite the luminescent film. Narrow, high-intensity excitation pulses reduce measurement error due to the convolution of the excitation pulse and the luminescent response [19], [33]. A simplified schematic of the LED driver is shown in Fig. 3(a). A differential LED driver architecture was adopted to switch relatively large LED currents (up to 1 A) into narrow pulses [34]. The idea is to establish the target LED current in the current source $Q_1$ using the replica branch $\left(M_2\right)$. Once the current is stable, the gate drivers are switched quickly for the current to flow in the active path $\left(M_1\right)$, illuminating the target luminescent material. This current steering technique moves the transients of establishing the current onto the replica path, away from the measurement LED and, in turn, the PD. The initial transient of establishing the current can take several $\mu \mathrm{s}$, lengthening the LED pulse time significantly. If the current is established in the replica path first, the active pulse can be arbitrarily narrowed down to tens of ns.

$M_1$ and $M_2$ are a matched pair of power MOSFETs (CSD85301Q2, Texas Instruments, Inc.) [35]. $D_2$ and $D_3$ are 500 mW and 450 nm LEDs (LXZ1-PR01, Lumileds) [29]. The gate driver IC is an LTC1693 [36]. The current source is constructed using a Nexperia PBSS4240XF low saturation voltage bipolar transistor $\left(Q_1\right)$, regulated by AD8541 operational amplifier (op amp) $\left(A_4\right)$ [37], [38]. The gate drive control signals (DRV) and the LED bias voltage (LED BIAS) are generated by the FPGA. The bias voltage is used to set the LED current from 0 to 1 A.

C. FPGA and Analog Buffers

External control and data measurement are implemented on the Micro-Nova Mercury 2 FPGA development board [39]. The board supports a Xilinx XC7A35T FPGA along with additional support circuitry. An FTDI FT2232H UART/USB bridge IC interfaces the FPGA with an external PC for programming and data transfer. Three DS4303 programmable voltage references [40] are used on the evaluation board to set the common-mode voltage of $A_1$, the level-crossing threshold of the $A_2,V_{\text{LVL}}$, and the LED driver current. An MCP 4812, a 10-bit, 0–3 V output, digital-to-analog converter (DAC) on the FPGA, sets the voltage references for the DS4303. An MCP 3008, an eight-channel 10-bit analog-to-digital converter (ADC), is used to monitor the current draw of the chip.

A wide-band, low-noise, high-speed analog buffer [41], $A_3$, is included on the evaluation board to interface the chip with external instrumentation. The analog buffer provides a 2 pF load capacitance. The gain is set to 2 to drive the 50 Ω coaxial cable, allowing for a low-noise connection with the oscilloscope and compensating for the voltage division of the 1:1 oscilloscope connection.

D. Power Supplies

A bench-top DC power supply provides power for the evaluation board. The input power is regulated by an LT3083 LDO [42], providing a stable 5 V supply. The main supply (5 V) rail for the evaluation board provides power for the onboard external analog IO buffers, the FPGA (control and measurement), the LED driver, and the various power domains of the chip. An LT3042 low dropout (LDO) regulator [43] regulates power supply rails that go into the chip. To prevent power supply noise coupling and to measure power consumption, individual supplies were designed on the evaluation board for each power domain of the chip. Four external LDOs provide the five power domains of the chip, 3.3 V analog and digital for the IO ring and buffers on the chip, and 1.8 V analog and digital for the core circuits.

IV. Sources of Error

This section examines the error sources that impact system performance. First, we investigate how the limitations in the front-end amplifier due to gain, bandwidth, noise, and systematic offsets as well as DC leakage could degrade the accuracy of the lifetime estimation. Then, we explore the impact on the accuracy of the NUS algorithm due to parameters such as the locations of the sampling points on the decay curve, time quantizer jitter, delays in the signal path, and jitter at the comparator output.

1). Finite Op Amp Gain:

Op amps are limited in gain and bandwidth [44]. For a decaying exponential input current, the output voltage of a capacitive feedback TIA is

$$v\left(t\right)=\frac{A_{\text{ol}}}{1+A_{\text{ol}}}\frac{-i_{\text{pk}}\tau }{C}{e}^{\left(-\frac{t}{\tau }\right)}+\text{constant}.$$ (6)

According to this equation, the finite open loop gain of an op amp $\left(A_{\text{ol}}\right)$ results in amplitude error in the exponential but does not distort $\tau$ significantly. This behavior, shown in Fig. 4(a), is verified in SPICE simulation with a first-order op amp model with a variable gain and bandwidth.

Fig. 4.

Simulation results of TIA’s (a) gain error and (b) bandwidth error.

2). Finite Op Amp Bandwidth:

The finite unity gain bandwidth of the op amp, ${\omega }_t$, limits how fast the integrator can respond to changes at the input. For a step input, the response of the op amp-based integrator in the time domain is

$$v_o\left(t\right)\approx \frac{1}{C}\left(t-\frac{1}{{\omega }_t}\right).$$ (7)

The response is the same as an ideal integrator, except for the time lag, i.e., $1/{\omega }_t$. Thus, the finite bandwidth of the op amp can distort the $\tau$ of an input signal by $1/{\omega }_t$, as simulated in Fig. 4(b). This error can be reduced by making the unity gain frequency of the op amp at least an order of magnitude greater than the target time constants, i.e., ${\omega }_t\gg 1/\tau$. For the luminescent sensor used in this design, the time constants range from 5 to 30 μs. To ensure the error introduced by the front-end op amp is less than 1%, the unity gain frequency was chosen such that ${\omega }_t\ge 100/\tau$.

3). Op Amp Gain Error on Voltage Step $\Delta V$:

The finite gain of the op amp can impact the size of the voltage step, $\Delta V$, created by the switch capacitor circuit and the comparator. Ideally, when the switched capacitor connects to the summing node at the switching event, the voltages at the two input terminals of the capacitor are equal. However, a tiny amount of charge remains on the switched capacitor due to the offset of the op amp. An amplitude error on $V_{\text{INT}}$ only introduces a constant error in the step size, ${\epsilon }_{\text{step}}$, which does not impact the algorithm’s accuracy. The size of the error is set by the ratio of the switched capacitor and the feedback capacitor, the output voltage of the op amp at the switching point, and the op amp gain,

$${\epsilon }_{\text{step}}\approx \frac{C_{\text{SW}}}{C_F}\frac{V_{\text{LVL}}}{A_{\text{ol}}\left(f\right)}.$$ (8)

4). Input-Referred Noise:

System noise can be referred to the op amp’s input. The noise gain, $\approx \left(C_i/C_F\right)$, is determined by the feedback capacitor, $C_F$, and the parasitic capacitance of the input, $C_i$, including the parasitic of the PD, the parasitic capacitance on the board, and the op amp’s parasitic input capacitance. Noise sources include shot noise from the PD and the gate of the input MOSFETs, $\mathit{\text{kT}}/C$ noise of the switched capacitor, and thermal and flicker noise of the op amp. Due to the relatively wide band of the system, noise is dominated by the thermal noise of the op amp, $v_n^2\approx \left(16\mathit{\text{kT}}/3g_m\right)\Delta f$ [24]. This wide band op amp noise affects comparator decisions as jitter at the output, as discussed in Section IV-9. Additionally, the sampled $\mathit{\text{kT}}/C$ noise on the switched capacitor acts as an offset. When the switches are opened from the charging voltage source, the noise from the voltage source and switch resistance is sampled onto the capacitor. This voltage contributes to the charge injected into the summing node. However, the error will consistently be $\sqrt{\mathit{\text{kT}}/C}$. Thus, the error is minimized by the subtraction and division operations of the algorithm.

5). DC Leakage Current:

Earlier in Section II-B, we assumed that the DC leakage current was small. DC leakage, $i_{\text{DC}}$, is the combination of the PD dark current, the integrator reset switch leakage, and surface currents across the chip and the PCB. In most applications, with careful part choice and layout, the surface current will be small. However, in cases where $i_{\text{DC}}$ is significant, the voltage due to this current effectively changes our voltage step, $\Delta V$, between time samples by ($i_{\text{DC}}\Delta t_{i,j}/C$), where $\Delta t_{i,j}$ is the time difference between $t_i$ and $t_j$ sample times. When we include this error in (4), we obtain the following equation:

$$\frac{\Delta V-\frac{i_{\text{DC}}\Delta t_{\mathrm{2,1}}}{C}}{\Delta V-\frac{i_{\text{DC}}\Delta t_{\mathrm{1,0}}}{C}}=\frac{\left(e^{\left(\frac{t_1-t_2}{\tau }\right)}-1\right)}{\left(1-e^{\left(\frac{t_1-t_0}{\tau }\right)}\right)}.$$ (9)

Error in this equation is proportional to the ratio of the charge, ${\epsilon }_{\text{DC}}\approx \left(Q_{\text{DC}}/Q_{\text{exp}}\right)$, where, $Q_{\text{DC}}$ is the charge due to $i_{\text{DC}}$ and $Q_{\text{exp}}$ is the charge due to the exponential signal created by $I_{\text{PD}}$.

For example, assume an exponential with a time constant of 5 μs, a 3 μA peak current, and a 100 nA offset, is integrated for 50 μs. The charge of the exponential is about 15 pC, and the charge of the DC component is about 5 pC. Thus, the error (${\epsilon }_{\text{DC}}$) is about ~30%. We visualized/simulated this example in Fig. 5(a) and (b), showing the current and charge components of the desired exponential and the DC leakage. This simulation highlights the error that can accumulate in the integrator if there is significant DC leakage.

Fig. 5.

Simulated leakage current effect on charge accumulation (a) exponential current and DC leakage current and (b) accumulated charge.

The error caused by this nonideality can be minimized in a few ways. First, we can try to make the voltage step, $\Delta V$, as big as possible to minimize the error term. The feedback capacitance can also be increased, but that reduces the response time and increases the amount of charge required to generate three sample points. A more effective way to minimize the DC error component is to add a step to the algorithm to account for the DC component directly.

We can approximate the left-hand-side of (9) as

$$\frac{\Delta V-\frac{i_{\text{DC}}\Delta t_{\mathrm{2,1}}}{C}}{\Delta V-\frac{i_{\text{DC}}\Delta t_{\mathrm{1,0}}}{C}}\approx 1+\frac{\frac{i_{\text{DC}}}{C}\left(\Delta t_{\mathrm{1,0}}-\Delta t_{\mathrm{2,1}}\right)}{\Delta V}.$$ (10)

To determine $i_{\text{DC}}/C$, we integrate the leakage current without exciting the sensor. The time required to generate the $\Delta V$ due to the leakage current is represented with $\Delta t_c$, which corresponds to the time elapsed between consecutive sample points. It exhibits an inverse relationship with the magnitude of the leakage current.

If we substitute $\Delta V/\Delta t_c$ into (10) by replacing $i_{\text{DC}}/C$, we get a correction factor, $\left(\Delta t_{\mathrm{1,0}}-\Delta t_{\mathrm{2,1}}\right)/\Delta t_c$, only dependent on the measured time samples. The updated algorithm with DC leakage error correction is

$$1=\frac{\left(e^{\left(\frac{t_1-t_2}{\tau }\right)}-1\right)}{\left(1-e^{\left(\frac{t_1-t_0}{\tau }\right)}\right)}-\frac{\Delta t_{\mathrm{1,0}}-\Delta t_{\mathrm{2,1}}}{\Delta t_c}.$$ (11)

Fig. 6 shows the results of a behavioral simulation compared with the ideal signal, showing the offset correction for different leakage currents. We can see that the correction factor improves the accuracy of the estimation significantly. However, the improvement at larger DC offsets is reduced. For higher DC offsets, higher order terms could be added to the algorithm, or additional leakage reduction circuits could be employed.

Fig. 6.

Behavioral model showing the DC leakage error correction technique, where $\tau =5$ μs and $i_{\text{pk}}=3$ μA.

6). Sampling Point Position:

The position of the sampling points on the exponential signal plays a significant role in an accurate measurement. As seen in the behavioral simulation in Fig. 7, samples too high on the curve near the start (region A) push the error envelope up due to a lack of information about the curve, making the samples susceptible to timing errors. Conversely, samples along the middle “90%–10%” region of the exponential (region B) show better performance due to the increased information. Samples can be taken well out into the tail (region C) if widely spaced. However, if the samples are more closely spaced while sampling far out on the tail, the error increases as information about the exponential decreases.

Fig. 7.

Error with the position of the sampling points.

Errors related to sampling points occur when the LED driver is operating at high intensity, resulting in an excessive number of level crossings. In such cases, it is crucial to select crossing indices that are well-distributed along the exponential to minimize errors. We addressed this issue by limiting the number of detected level crossings through careful tuning of the LED drive, ensuring the system produces the desired number of crossings naturally distributed across the exponential curve.

7). Integrator Reset:

It is important to note that the timing of opening the TIA reset switch is crucial for capturing the exponential decay. However, this decay occurs over several microseconds, typically in the range of ~30–5 μs. Since the switch response is much faster, the 90%–10% decay region is reliably captured, even in the presence of unexpected oxygen levels.

8). Comparator Delay:

Delays in time can impact the accuracy of the algorithm by shifting the sample point away from region B. Comparator delay is related to the overdrive voltage ($V_{\text{ov}}$), i.e., how much the input signal exceeds the comparator threshold, $V_{\text{LVL}}$, depicted in Fig. 8(a). The more the input exceeds $V_{\text{LVL}}$, the easier it is for the comparator to decide. Steeper rise times $(\mathit{\text{dV}}/\mathit{\text{dt}})$ cross $V_{\text{LVL}}$ faster, resulting in a larger $V_{\text{ov}}$ during the decision time of the comparator. Shallower rise times take longer to cross $V_{\text{LVL}}$ and, thus, the comparator takes longer to decide.

Fig. 8.

(a) Comparator delay variation due to varying input rise times and (b) uncertainty in time due to voltage noise at the comparator input and the slope of the input signal.

The delay error is consistent for a given $V_{\text{ov}}$. If we take the difference between the two adjacent sample points ($t_a$ and $t_b$), as we would in the lifetime estimation algorithm, the errors due to the comparator delays try to cancel

$$\left(t_b+\Delta t\left(V_{\text{ov}2}\right)\right)-\left(t_a+\Delta t\left(V_{\text{ov}1}\right)\right)=t_b-t_a+{ϵ}_{\text{delay}}.$$ (12)

The delay cancellation is not perfect because the slopes of the comparator input voltage at each sample are slightly different. Fig. 8(a) shows the comparator delay for different input $\mathit{\text{dV}}/\mathit{\text{dt}}$ for a postlayout SPICE model of the comparator. Even for relatively slow rise times, comparator delay is in the 10–15 ns range. The error between adjacent sample points, even with a relatively long comparator delay, is ~1 ns or less.

We can correct for comparator delay error by estimating the $\mathit{\text{dV}}/\mathit{\text{dt}}$ of the exponential based on the measured time point. Since the time delta, $\Delta t_i$, and the voltage step, $\Delta V$, are known, the slope of the exponential can be approximated with a linear fit

$$\frac{d{V}_{\text{exp}(-t/\tau )}}{\mathit{\text{dt}}}\approx \frac{\Delta V}{\Delta t_i},\text{for}\text{small}\Delta t_i.$$ (13)

This technique will require a foreground calibration technique to measure the comparator delay before the system is used to measure oxygen.

9). Jitter at the Comparator Output:

Jitter at the comparator output results from variations in the decision point due to noise on the comparator input signal ($V_{\text{INT}}$), the threshold voltage ($V_{\text{LVL}}$), and the slope $(\mathit{\text{dV}}/\mathit{\text{dt}})$ of $V_{\text{INT}}$. Fig. 8(b) shows the behavioral simulation of the jitter, ${\sigma }_t$, in MATLAB due to input voltage noise, $V_{\text{LVL}}$, and the slope of the input signal, $(\mathit{\text{dV}}/\mathit{\text{dt}})$. For a system with 100 μV of rms noise at the comparator input, we can expect timing errors in the 1–10 ns range depending on the slope of the input signal. As a result, jitter at the comparator output is the dominant source of error in the system.

V. Measurement Results

This section explores the measurement results from three sets of experiments: circuit characterization, error analysis, and performance characterization in a gas bench-top. The NUS circuit, shown in Fig. 3, was implemented with the TSMC 180 nm MS/RF/G process. The active area of the circuit is 0.175 mm². The micrograph of the fabricated chip, along with the evaluation board, can be seen in Fig. 9(a) and (b), respectively.

Fig. 9.

(a) Micrograph and top side of the evaluation board, (b) bottom side of the evaluation board with FPGA and gas test vessel, and (c) LED gate driver and current source waveforms.

A. LED Driver and AFE Characterization

1). LED Driver Characterization:

Fig. 9(c) shows the LED driver waveforms, with the wide replica pulse ($\overline{\text{DRV}}$) followed by a short active pulse (DRV). For this plot, the LED driver is enabled for 110 μs (100 μs replica and 10 μs active). The minor glitch in the measured bias current during the short dead time between the gate drives does not influence the LED drive current significantly as the current source recovers quickly. The replica pulse can be as short as 10 μs and the active pulse as short as several hundred ns.

The LED driver current varies between 1 and 300 mA from a 5 V supply, depending on the partial pressure of oxygen around the film. After triggering the LED pulse, the controller counts the number of comparator pulses. The controller then increments or decrements the LED biasing DAC by comparing the comparator pulses to a target number of level crossings. To complete a conversion, at least three level crossings are required. This action allows the measurement system to automatically tune the LED driver to minimize the energy consumption for exciting the sensor film.

2). AFE Characterization:

The proposed NUS algorithm given in Fig. 2, is implemented with the proposed AFE, depicted in Fig. 3(a), in hardware. The schematic of the AFE measurement test bench is given in Fig. 10(a). A −20 dB attenuator at the input was used to prevent clipping of the output signal. The functionality of the AFE is demonstrated with the example transient waveforms in Fig. 11(a), where $V_{\text{INT}}$ represents the integrated voltage at the output of the integrator. When $V_{\text{INT}}$ exceeds $V_{\text{LVL}}$, the comparator sends a signal, $V_{\text{COMP}}$, to the SCU to initiate the charge injection into the input node, $V_{\text{SUM}}$.

Fig. 10.

Schematic of the test bench for (a) AFE measurement and (b) TIA noise and DC leakage measurement.

Fig. 11.

Measured (a) transient waveforms, (b) frequency response, (c) DC leakage, and (d) input-referred noise.

To measure the bandwidth of the TIA and to determine the actual value of the feedback capacitor, $C_F$, the integrator is biased at 900 mV using the external voltage reference, DS4303 [40]. The comparator is disabled by setting the $V_{\text{LVL}}$ to $V_{\text{DD}}$. This operation allows the TIA to swing close to the rails without activating the switched-capacitor circuit, avoiding the trimming operation of the switched-capacitor circuit.

Wide-band, low-noise, high-speed analog buffers [41], ($A_3$ in Fig. 3(a), are included on the evaluation board to interface the chip with external instrumentation. The TIA drives a 2-pF load capacitance (input capacitance of $A_3$) instead of ~15 pF probe capacitance. The 50 Ω coaxial cable, allowing for a low-noise connection with the oscilloscope, is utilized, and the gain of $A_3$ is set to 2 to drive it, compensating for the voltage division of the 1:1 oscilloscope connection. The measured gain-bandwidth product of the AFE is ~10 MHz, shown in Fig. 11(b).

The DC leakage of the summing node of the TIA, $V_{\text{SUM}}$, was measured by first closing the unity-gain switch, ${\varphi }_{\text{RST}}$, and charging the capacitor $C_T$ to bias voltage $V_{\text{BIAS}}$, depicted in Fig. 10(b). Note that $V_{\text{BIAS}}$ in Fig. 10(a) and (b) serves the same purpose as $V_{\text{BIASPD}}$ in Fig. 3(a). Once the capacitor is charged, the switch is opened, and the output of the TIA is observed to see how far the output drifts over time. The feedback capacitor, $C_F$, integrates any leakage current on the summing node. We can relate the leakage current at the summing node to the observed output voltage by $i_{\text{leak}}=C_F(\Delta V/\Delta t)$. The observed leakage current was 5.7 pA, as shown in Fig. 11(c).

For the noise analysis of the circuit, the noninverting input of the TIA is biased to $V_{\text{BIAS}}(~900\text{mV})$ with a low noise precision voltage reference, Stanford Research DC205. The inverting input of the TIA, $V_{\text{SUM}}$, is also charged up to $V_{\text{BIAS}}(~900\text{mV})$ by closing ${\varphi }_{\text{RST}}$ switch. The switch is then opened, and $V_{\text{INT}}$ is sampled via measuring $V_{\text{OUT}}$ with a Stanford Research SR785 digital signal analyzer (DSA), which has a noise floor of $10\text{nV}/\sqrt{\text{Hz}}$. While the bandwidth of the DSA (100 kHz) sets the upper limit of the measurement bandwidth, the lower limit is defined by the DC bias reset period. This action is represented by the timing diagram at the top of Fig. 10. The DC leakage current at the inverting input node, $V_{\text{SUM}}$, causes the bias point of the amplifier to drift over time, measured and displayed as shown in Fig. 11(c). The influence of leakage on the bias voltage drift (i.e., the deviation in $V_{\text{SUM}}$) is observed by measuring $V_{\text{INT}}$, where $V_{\text{INT}}$ is equal to $V_{\text{SUM}}\cdot \left(C_T/C_F\right)+1$. Since there is no DC bias path for the negative input of $A_1$, the control logic resets the front end when the output voltage, $V_{\text{INT}}$, exceeds 1% of the common mode ($V_{\text{BIAS}}$) to keep the amplifier biased in the desired operating region. This reset sets the lower limit of the measurement bandwidth to 200 Hz. The noise gain of the test setup is set by the test capacitor $C_T$ and the feedback capacitor $C_F$. The input-referred noise of $A_1$ is given in Fig. 11(d). The measured integrated input referred noise at the $A_1$ is $124\mu {\mathrm{V}}_{\text{rms}}$, over a bandwidth from 200 Hz to 100 kHz, and the $1/f$ corner is ~10 kHz. If we assume the noise floor is at $80\text{nV}/\sqrt{\text{Hz}}$ and the 3 dB frequency of the amplifier, as shown in Fig. 10 is 100 kHz, and the total measurement time to calculate $\tau$ is 60 μs, then we can estimate the integrated input referred noise for measurement is $32\mu {\mathrm{V}}_{\text{rms}}$.

The AFE has an average power consumption of 890 μW, drawing ~492 μA from a 1.8 V supply. The AFE samples the luminescent response for 100 μs. For these tests, the LED driver is enabled for 30 μs(20 μs replica and 10 μs active) with a 100 mA amplitude from a 5 V supply. These energy values are used to estimate the Walden figure of merit $\left({\text{FoM}}_W\right)$,

$${\text{FoM}}_W=\frac{P}{2^{\text{ENOB}*f_s}}=\frac{\text{Energy}}{2^{\text{ENOB}}}.$$ (14)

The energy consumption for one measurement is 16 μJ. The effective number of bits (ENOB) based on the error measurement is 6.5 bits, given in Section V-B. Thus, the ${\text{FoM}}_W$ is 177 nJ/conv. The ${\text{FoM}}_W$ reduces to 11 nJ/conv, when excluding the LED energy.

B. Error and Accuracy Analysis

The Food and Drug Administration (FDA) recommends that the accuracy of ${\text{PtcO}}_2$ measurements be within 5 mmHg for ${\mathrm{O}}_2$ levels between 0 and 20.9% (ambient air ${\mathrm{O}}_2$) and comparator input, $V_{\text{INT}}$, (b) measured comparator jitter for various noise levels overlaid on the behavioral model depicted in Fig. 12(b), and (c) relating the ENOB to estimated $\tau$ error. within 10 mmHg for higher ${\mathrm{O}}_2$ concentrations [45]. In the clinically relevant range of 50–150 mmHg, the corresponding $\tau$ range is approximately 5 μs. Since 5 mmHg, the error range prescribed by the FDA, represents 5% of the 50–150 mmHg range, a thorough error analysis is critical for establishing the system’s performance parameters.

Fig. 12.

(a) Measured error between least-squares model, ${\tau }_{\text{TEST}}$, and measured NUS lifetime estimation, ${\tau }_{\text{meas}}$,for 1 $m{V}_{\text{rms}}$ and 500 $\mu {\mathrm{V}}_{\text{rms}}$ noise at the comparator input, $V_{\text{INT}}$, (b) measured comparator jitter for various noise levels overlaid on the behavioral model depicted in Fig. 12(b), and (c) relating the ENOB to estimated $\tau$ error.

To measure and analyze the accuracy and precision of the proposed AFE, we compared the lifetime calculated from measured time differences at the output of the comparator, ${\tau }_{\text{meas}}$, versus the lifetime obtained by fitting an exponential model to the current stimulus waveform, ${\tau }_{\text{TEST}}$. The exponential test voltage, $V_{\text{TEST}}$, is generated by the Tektronix AFG3021C arbitrary function generator and was coupled to the AFE by employing a resistor, $R_{\text{TEST}}$, as depicted in Fig. 10(a). This setup was used to generate a single-time constant, decaying exponential current labeled as $i_{\text{TEST}}$. The amplitude and time constant of $i_{\text{TEST}}$ could be varied to change the signal slope at the output of the integrator, $V_{\text{INT}}$. The output of the comparator, $V_{\text{COMP}}$, and $V_{\text{INT}}$ are measured using a Keysight MSOX6004A oscilloscope. The $V_{\text{INT}}$ was measured through the buffers on the evaluation board. The $V_{\text{COMP}}$ was measured through a low capacitance 20:1 probe.

Fig. 12(a) shows the measured time constant error, where $\%\text{error}=\left({\tau }_{\text{meas}}-{\tau }_{\text{TEST}}\right)/{\tau }_{\text{TEST}}$. The mean error—assuming $\tau <50$ μs—for a system with a $1m{V}_{\text{rms}}$ noise is ~−1.9%, with the error bounds from −5% to +1%, while the mean error with a $500\mu V_{\text{rms}}$ noise level is ~−0.3% with error bounds from −1.5% to +1.5%, as demonstrated in Fig. 12(a). The noise levels could be adjusted by changing the source resistance, $R_{\text{TEST}}$. We can observe that the variance of the samples for the $1m{V}_{\text{rms}}$ noise test is significantly wider. The NUS hardware is specifically designed to operate optimally in the relevant measurement range of oxygen, confirmed from the gas chamber test in Section V-C, and is deemed to be from 5 to 30 μs. The increased error outside the relevant range conditions, such as $\tau <1$ μs, is attributed to the delay in the comparator response. Conversely, the increased error observed for $\tau >50$ μs is explained by the jitter in the comparator output due to longer rise times.

The jitter at the comparator output was measured using the histogram function on the oscilloscope and taking the standard deviation, ${\sigma }_t$. The circuit test setup is shown in Fig. 10(a). Fig. 12(b) displays the measured jitter versus the slope of $V_{\text{INT}},\mathit{\text{dV}}/\mathit{\text{dt}}$, for various noise levels of $V_{\text{INT}}$, overlaying the model displayed in Fig. 8(b). The slope of the $V_{\text{INT}}$ is also measured using the oscilloscope. The resistor, $R_{\text{TEST}}$, was employed to generate various noise levels at the TIA’s input, which are subsequently reflected at the comparator’s input, $V_{\text{INT}}$. The noise at $V_{\text{INT}}$ is the root sum square (RSS) of input-referred noise of the TIA (limited by the measurement period), the thermal noise of $R_{\text{TEST}}$, and the $\mathit{\text{kT}}/C$ noise of the capacitor $\left(C_F\right)$, multiplied by the noise gain of the front end. For a measurement period of 60 μs, the noise contribution of the TIA is limited to wideband thermal noise, approximately 32 μV. In this test, $V_{\text{LVL}}$ was connected to a relatively low noise voltage reference provided by a DS4303. The $\mathit{\text{kT}}/C$ noise is approximately 45 μV. Thus, the noise generated by $R_{\text{TEST}}$ is the dominant noise source in this scenario. The test was repeated for two noise levels, $1m{V}_{\text{rms}}$ and $500\mu {\mathrm{V}}_{\text{rms}}$, measured at the comparator input. This test proves that the timing uncertainty due to the comparator can be precisely modeled using the method outlined in Section IV-9.

To make it convenient to compare the proposed measurement technique with traditional ADCs, we developed a behavioral model in MATLAB [46] to relate the measured error in the lifetime to the ENOB. In the model, the data are sampled and quantized at different rates and resolutions. These steps introduce errors in both time and voltage, respectively. To extract the time constant from the sampled data, the Levenberg–Marquardt nonlinear least-squares algorithm was used to fit an exponential model to the sampled data. The $\tau$ was determined from the coefficients of the model [47]. Using these modeled ADCs, it can be seen in Fig. 12(c) that error in lifetime estimation decreases exponentially with the increase of the number of bits. Lowering the sample rate deviates from the ideal curve as errors in time resolution contribute to the error in $\tau$ calculation. We can approximate the ENOB of our measurements from the best fit of the $\tau$ estimation error, which gives the relationship $\text{ENOB}\approx \text{ln}\left(2/\left|{\tau }_{\text{error}}\right|\right)$.

C. Bench-Top Gas Measurement

The experimental setup, seen in Fig. 13(a), for the in vitro gas measurement resembles the ratio-metric mass flow rate experiment, as explained in [21] and [27]. This setup was used to test the ${\mathrm{O}}_2$ sensor over a wide range of partial pressure of oxygen $\left({\text{PO}}_2\right)$. To control the ${\text{PO}}_2$, ${\mathrm{O}}_2$ and nitrogen $\left({\mathrm{N}}_2\right)$ were mixed in controlled ratios at 760 mmHg (1 atm). MKS 1179A mass flow controllers (MFCs) set the gas mixture ratios. For fixed volume, temperature, and pressure, the partial pressure of a gas is directly related to the mass of the gas in the mixture. The ${\text{PO}}_2$ was swept from 0 to 228 mmHg (equivalent to ~30 to ~5 μs in $\tau$ values) in incremental steps of 14.25 mmHg. PC software is used to control the mass flow set points and to readout the data.

Fig. 13.

(a) Test bench and block diagram of the gas experiment setup, (b) measured $\tau$ for ${\text{PO}}_2$ sweep, (c) corresponding Stern–Volmer plot, (d) human volunteer test setup, (e) cross section of sensor interface, and (f) preliminary measurement results.

Fig. 13(b) shows the calculated time constants plotted against ${\text{PO}}_2$ and Fig. 13(c) displays the Stern–Volmer plot of the same data. The deviation from the linear relationship at relatively high ${\text{PO}}_2$ is due to some luminophores being inaccessible to be quenched by ${\mathrm{O}}_2$ [48]. The NUS IC can measure ${\text{PO}}_2$ from 0 to 228 mmHg, covering the human-relevant range of 50–150 mmHg, with a 2.2 mmHg mean error. This is lower than the FDA standard of 5 mmHg [49].

VI. Human Subject Tests

The system was validated on a healthy human volunteer. The protocol presented in [27] was slightly modified to include a Radiometer TCM CombiM probe as a reference [55]. An overview of the test setup is shown in Fig. 13(e). A Python script controls the oscilloscope to sample the output of the DUT every 10 s. The Radiometer and DUT sensors are placed on the volunteer’s forearm, as depicted in Fig. 13(e). A pressure cuff is placed around the subject’s upper arm. It is important to ensure that the sensor’s sensitive side is completely covered by the skin to prevent ambient air from leaking in. Since the oxygen concentration in ambient air is higher than transcutaneous oxygen, any air leakage would compromise the accuracy of ${\text{PtcO}}_2$ measurements.

The Radiometer probe and the DUT are powered on and allowed to stabilize for 2600 s. Once both systems stabilize, the pressure cuff is inflated to 180 mmHg for an arterial occlusion of the arm. This causes the partial pressure of transcutaneous oxygen $\left({\text{PtcO}}_2\right)$ to decrease as the oxygenated blood flowing through the arteries starts to reduce. The occlusion is held for 120 s. At the end of the occlusion event, the pressure in the cuff is released, and the volunteer is monitored for another 2600 s to see the recovery of the system. Fig. 13(f) shows the preliminary results of the human volunteer testing with the commercial (Radiometer) and the new transcutaneous monitoring system (NUS). Commercial ${\text{PtcO}}_2$ sensors, which are widely available, typically require heat to improve gas diffusion and increase blood flow in capillaries. Unlike the Radiometer monitor, which heats the skin to 44 ∘C, the proposed sensor does not require skin heating to measure ${\text{PtcO}}_2$. Accurate ${\text{PtcO}}_2$ value conversion, future work in this project, requires developing accurate conversion algorithms that account for factors such as sensor variability and drift. In this article, we reported trends over $\tau$ rather than precise oxygen pressure values.

VII. Benchmark

Table I provides a comparison between the proposed oxygen sensor against other similar sensors reported in recent literature, including sensors that measure peripheral oxygen saturation $\left({\text{SpO}}_2\right)$ and partial pressure of oxygen $\left({\text{PO}}_2\right)$ i.e., tissue oxygenation and transcutaneous oxygen sensors. The proposed prototype in this article employs a novel technique that can accurately measure the lifetime of luminescent materials used in oxygen sensing without being affected by any offsets. The proposed technique is also highly robust against variations in the optical paths in wearable biomedical systems, which may be induced by motion artifacts and differences in skin color. The robustness of this technique has been demonstrated in [56] with the wearable prototype [53], which implemented the lifetime-based measurement technique with commercial discrete components. Unlike [53], our proposed system consists of custom-designed integrated circuits employed to implement the proposed NUS algorithm, producing one ${\mathrm{O}}_2$ value with significantly reduced data points.

TABLE I.

Benchmark Table

PARAMETERS	[22] 2019	[16] 2020	[50] 2021	[27] 2021	[51] 2022	[52] 2023	[53] 2023	[54] 2023	This Work
Publisher	IEEE TBioCAS	IEEE CICC	Nat. Biotechnol	IEEE TBioCAS	ACS Sensors	IEEE ISSCC	IEEE TBioCAS	IEEE JSSC	IEEE JSSC
Sensor
Sensor Type	${\text{SpO}}_2$	${\text{PO}}_2$	${\text{PO}}_2$	${\text{PO}}_2$	${\text{PO}}_2$	PPG	${\text{PO}}_2$	${\text{SpO}}_2$	${\text{PO}}_2$
Peak Wavelength of LED (nm)	IR/Red	450	465	453	382	NA	450	523/850	450
Peak Wavelength of PD (nm)	NA	650	621	650	643	NA	600	NA	650
LED Type	NA	NA	$\mu \text{LED}$	InGaN	NA	NA	InGaN	AlGaAs	InGaN
Hardware
Technology	CMOS 55 nm	CMOS 180 nm	CMOS 65 nm	PCB	PCB	CMOS 180 nm	PCB	CMOS 180 nm	CMOS 180 nm
Chip Area $\left({\mathit{\text{mm}}}^2\right)$	18.66†	1.04	3.84	NR	NR	NA	NR	2.08	1.7
Readout Technique	Intensity	Time	Phase	Intensity & Time	Time	Intensity	Time	Intensity	Time
TransZ Gain	10 kΩ – 1 MΩ	59 – 943 kΩ	NA	1 MΩ	NA	NA	12.5 kΩ – 200 kΩ	NA	2 pF
Bandwidth	1 MHz	80 kHz	NA	200 kHz	NA	NA	NA	10 Hz	10 MHz
${\text{V}}_{\mathit{\text{DD}}}/{\text{V}}_{\mathit{\text{LED}}}(\text{V})$	1.2/2.8	1.8/5	1.2 /3.82	1.8 – 3/5	NA	1.8/3	1.8 – 3.3/5	1/NA	1.8/5
Max. Input Range $(\mu \text{A})$	75	30	NA	3	NA	110	4 – 72	9	1.5
Voltage Noise $\left(\mu V_{\mathit{\text{RMS}}}\right)$	NA	NA	NA	3700	NA	0.22***	NA	NA	124
Current Noise $\left(\mathrm{p}{\mathrm{A}}_{\mathit{\text{RMS}}}\right)$	151	NA	NA	NA	NA	NA	1200	17.89	NA
AFE Power $(\mu \text{W})$	179	631	150*	9000*	NA	59††	690	23.3	835
Energy/conversion (nJ/conv.)	NA	NA	NA	NA	NA	NA	NA	NA	177
On-Chip Optical Filtering	No	No	No	No	NA	No	No	No	Yes
DC Offset Cancellation	Yes	No	No	No	NA	Yes	No	No	Yes
Automatic LED Gain Control	No	No	No	No	NA	No	No	No	Yes
ADC/TDC/Spike Sampling Rate	32 KSPS	NA	15.62 KSPS‡	NA	NA	NA	0.5 – 32 MSPS	1 – 3.5 KSPS**	5 MSPS
Application
Tested ${\text{O}}_2$ Range (mmHg)	NR	0–150	3.8–150.5	0–418	0–160	NR	0–418	NA	0–240
Human/Animal Testing	Yes	Yes	Yes	Yes	Yes	No	Yes	No	Yes
Invasiveness	No	No	Yes	No	Minimal	No	No	No	No

PCB: Printed Circuit Board, NA: Not Addressed, NR: Not Relevant,

^†Total chip area beyond PPG,

^††One Channel,

^*Total System Power,

^‡Time to Digital Converter (TDC) rate from [15],

^**Spike Count/Sec,

^***Per Amplifier.

A deep tissue oxygenation measurement prototype presented in [50] demonstrates lower power consumption, primarily due to a slower sampling rate in the kHz range, along with a smaller node-size integrated circuit. Similarly, the oxygen saturation measurement prototypes reported in [22] and [54] demonstrate reduced power consumption due to their relatively slower sampling rates, also in the kHz range. Additionally, the design in [22] incorporates a smaller node-sized integrated circuit. In contrast, the transcutaneous oxygen sensor prototype implemented on a printed circuit board, as presented in [27], provides a comprehensive overview of the total system power. A photoplethysmography (PPG) sensor presented in [52] as a continuous mental healthcare platform reports lower power consumption; however, it does not present any data on the applicable or testable range of ${\mathrm{O}}_2$, nor any human or animal testing. The voltage noise reported in this work is relatively higher, primarily due to the design focus on demonstrating the proof of the NUS concept. In future iterations of similar designs, particular attention can be devoted to reducing input-referred noise, which will also enhance the resolution of the overall circuitry. The higher noise levels observed in [27] are attributed to its discrete design architecture. In contrast, [52] reports very low voltage noise, though this measurement pertains to a single amplifier rather than the entire AFE. Studies in [22], [53], and [54] report only the current noise of their respective systems. Among them, [54] exhibits the best noise performance. Notably, both [22] and [54] employ integrated circuit designs, whereas [53] utilizes discrete components.

A monolithic PPG sensor that integrates a PD with an AFE into a single die to measure ${\text{SpO}}_2$ information is presented in [54]. This pixelated monolithic PPG, which claims to acquire spatial features, has a lower bandwidth and does not report any measured ${\mathrm{O}}_2$. A minimally invasive tissue oxygenation sensor introduced in [51] measures ${\mathrm{O}}_2$ levels in human and porcine skin using microneedles that penetrate the top layer of the skin. Most of the system-level design parameters have not been reported in [51].

VIII. Conclusion

This article presented a detailed derivation of the nonuniform luminescent lifetime estimation algorithm and circuit implementation. We conducted a thorough error analysis and identified critical areas a designer should consider when developing a nonuniform sampler for the luminescent lifetime estimation. Jitter at the comparator output, due to wide band thermal noise in the front-end op amp, is the system’s most significant source of error. We designed, manufactured, and then characterized the prototype circuit in TSMC 180 nm CMOS process. The AFE had a measured gain bandwidth product of 10 MHz and an input-referred noise of $124\mu {\mathrm{V}}_{\text{rms}}$ measured from 200 Hz to 100 kHz. The mean measured time constant estimation error was 0.3%, equivalent to the error of an ideal ADC with a 6.5 ENOB. The complete system consumes 16 μJ during a 130 μs measurement period for a ${\text{FoM}}_w=177\text{nJ}/\text{conv}$. The nonuniform sampler was used for preliminary human subject tests and showed promising results. This work demonstrates, for the first time, a hardware implementation of a NUS technique and algorithm to extract the $\tau$ of luminescent events for the emerging application of noninvasively measuring transcutaneous ${\mathrm{O}}_2$.

Biographies

Ian Costanzo (Member, IEEE) received the B.Sc. degree in mechanical engineering, with a minor in electrical engineering, and the M.S. and Ph.D. degrees in electrical engineering from Worcester Polytechnic Institute (WPI), Worcester, MA, USA, in 2015, 2017, and 2022, respectively.

During the master’s study, he worked on solidstate, high-power RF matching networks, and RF amplifiers for semiconductor processing applications. His Ph.D. research focused on analog and mixed-signal design for a wearable wireless sensor patch to monitor respiratory functions in premature infants. In 2022, he joined Intel Corporation, Hudson, MA, USA, as an Analog Circuit Designer, working on next-generation data center products. At the end of 2024, he joined Commonwealth Fusion Systems (CFS), Devens, MA, USA, a fusion power start-up, as an Electronics Engineer designing circuits and systems to monitor and control the balance of the plant. His research interests cover a broad range of circuits and systems, from milliwatt data converters to megawatt RF power plants.

Devdip Sen (Member, IEEE) received the B.E. degree in electronics engineering from the University of Mumbai, Mumbai, India, in 2015, and the M.S. and Ph.D. degrees in electrical and computer engineering from Worcester Polytechnic Institute (WPI), Worcester, MA, USA, in 2017 and 2021, respectively.

Since 2021, he has been a Staff Design Evaluation Engineer with Analog Devices, Inc., Santa Clara, CA, USA, in the Precision Amplifiers Group. His research interests include linear and precision operational amplifiers, biomedical sensors and instrumentation, and low-power analog/mixed-signal circuits and systems. His Ph.D. research included the development of wearable wireless sensors for monitoring respiratory functions in premature infants and wearable, wireless alert systems that would prevent painful pressure ulcers (bedsores).

Dr. Sen serves as a reviewer for IEEE Transactions on Biomedical Engineering, IEEE Reviews in Biomedical Engineering, IEEE Transactions on Biomedical Circuits and Systems, IEEE Transactions on Circuits and System II: Express Briefs, IEEE Solid-State Circuits Letters, IEEE Sensors Journal, and MDPI Sensors. He received the 2023 Award for Outstanding Research in the Ph.D. Dissertation category by the WPI Chapter of Sigma Xi.

John McNeill (Senior Member, IEEE) received the bachelor’s degree from the Dartmouth College, Hanover, NH, USA, in 1983, the master’s degree from the University of Rochester, Rochester, NY, USA, in 1991, and the Ph.D. degree from Boston University, Boston, MA, USA, in 1994.

From 1983 to 1990, he worked in industry in the design of high-resolution analog-to-digital converters and low noise electronics used in high speed, wide dynamic range imaging systems. In 1994, he joined the Electrical and Computer Engineering Department, Worcester Polytechnic Institute (WPI), Worcester, MA, USA. From 2012 to 2018, he held the positions of the Associate Head and then the Head of the ECE Department. He moved into the Dean’s office on an interim basis in 2018, and since 2021 he has been the Bernard M. Gordon Dean of WPI’s School of Engineering. His research interests are primarily in mixed signal integrated circuit design telecommunication, instrumentation, and biomedical sensing.

Dr. McNeill received the WPI Trustees’ Award for Outstanding Teaching in 1999. He was one of the inaugural winners of WPI’s Exemplary Faculty Award in 2007. In collaboration with co-authors from Analog Devices, he received the ISSCC Best Paper Award in 2005 for work on digitally assisted calibration of analog-to-digital converters.

Ulkuhan Guler (Senior Member, IEEE) received the B.Sc. degree in electronics and telecommunication engineering from Istanbul Technical University, Istanbul, Turkey, the M.E. degree in electronics engineering from the University of Tokyo, Tokyo, Japan, and the Ph.D. degree from Bogazici University, Istanbul.

She is an Associate Professor of electrical and computer engineering and the Director of the Integrated Circuits and Systems (ICAS) Laboratory, Worcester Polytechnic Institute (WPI), Worcester, MA, USA. Before joining WPI in 2018, She was a Post-Doctoral Researcher at Georgia Tech, Atlanta, GA, USA. She co-authored three book chapters. Her research interests lie in the broad area of circuits and systems, and her primary area of interest is analog/mixed-signal integrated circuits. More specifically, she is interested in the circuit design of sensing interfaces, bioelectronics, energy harvesting and wireless power transmission systems, and security for applications in healthcare. Recently, her research interest has focused on determining how electronic interfaces can be engineered along with biosensors to facilitate the creation of wireless wearable sensors that measure physiological parameters in the human body.

Dr. Guler serves as a Steering Committee Member for the IEEE CICC and a TPC Member for the IEEE BioCAS Conferences. She was a recipient of the 2022 NSF CAREER Award and the 2020 Interstellar Initiative Young Investigator Award. She serves as an Associate Editor for several IEEE journals, including IEEE Solid-State Circuits Letters, IEEE Transactions on Biomedical Circuits and Systems, and IEEE Transactions on Circuits and Systems II: Express Briefs.