Analysis of Photoelectric Sensor Input Noise of Pulse Oximeter

Wearable pulse oximeters are non-invasive medical devices that can be used to measure blood oxygen saturation and pulse rate. These technologies rely on the process of passing LED light through a transparent body part (usually a finger) and then detecting it.

While this is a well-understood technology, it is difficult to get an accurate reading because it relies on so many variables. On the detection side, these variables include the signal conditioning elements required to achieve optimal sensitivity, dynamic range, bandwidth, and dealing with dark current from the PIN diode. There are also issues of cost and power consumption.

Therefore, accurately detecting high and low signals using light-sensitive elements can be challenging.

For many designers, the best way forward is not to reinvent the wheel but to use an existing circuit. Using an existing design can reduce overall costs while ensuring the highest probability of a successful design.

This article discusses the requirements of the detection signal conditioning chain for a wearable pulse oximeter. It then introduces the key elements of the conditioning chain, including how to use dark current compensation diodes, and finally shows how to successfully implement the design using a reference design that combines perfectly matched elements in a practical configuration.

Pulse Oximeter Operation

Pulse oximeters continuously measure a patient's hemoglobin (Hgb), oxygen-saturated hemoglobin (HbO2) percentage, and pulse rate. During the measurement, a photodiode detects alternating infrared LED light and red LED light passing through a patient's finger, toe, or earlobe. In the patient's blood, oxygenated hemoglobin (HbO2) absorbs infrared LED light (940 nm), while deoxygenated hemoglobin (Hgb) absorbs red LED light (650 nm). In a pulse oximeter, two LEDs are excited quickly and sequentially by two current sources, and a photodiode detects the light intensity of each LED. This measurement calculates the ratio between HbO2 and Hgb, thereby estimating the blood oxygen content as a percentage. Pulse rate measurement requires several samples of the pulsating blood waveform. To accurately measure these parameters, the signal path of the high-speed photodiode must use devices with both low noise and low distortion.

Traditional photoelectric sensing circuit

The standard approach to designing a precision photo-sensing circuit is to place a photodiode (D1) across the CMOS or FET transistor input of an op amp and place a resistor in parallel with a capacitor in the feedback loop. The circuit was modeled using the Photonics Circuit Design Wizard from Analog Devices (Figure 1). To capture red and infrared light, an OSRAM Opto Semiconductors SFH 2701 photodiode was used, which has an optical range of 400 nanometers (nm) to 1050 nm.

Figure 1: A traditional photosensing circuit places a photodiode (D1) across the CMOS or FET transistor input of an op amp and a resistor in parallel with a capacitor in the feedback loop. (Image source: Bonnie Baker)

In Figure 1, incident light on the photodiode causes a current (IPHOTO) to flow from the cathode to the anode of the diode, with a maximum value of 200 microamps (mA). Since the input impedance of the inverting CMOS amplifier is very high, the photodiode can capture the incident light from the infrared LED and the red LED, causing a current to flow through the feedback resistor Rf. The voltage at the inverting input of the amplifier is maintained at ground potential by tracking the virtual voltage at the non-inverting input of the amplifier. Therefore, the output voltage changes as a result of IPHOTO x Rf.

When light strikes the photodiode, the circuit converts IPHOTO to an output voltage with the transfer function shown in Equation 1.

Equation 1

in:

OUT = Output voltage of the operational amplifier

IPHOTO = Photodiode current (amperes)

Rf = Feedback resistor value (ohms)

s = composite frequency variable (jω), where ω (radians) = 2πf

Cf = Feedback Capacitance (Farads)

Note that from Equation 1, the signal frequency pole (the frequency where the gain decreases with increasing frequency) is equal to 2 x px Rf x Cf.

This simple solution is often doomed to fail if subtle details such as amplifier and photodiode parasitic capacitance are not considered. For example, the system step response may cause the output to have an unacceptable amount of ringing. Or, the circuit may oscillate. After the instability problem is addressed and resolved, the output response may still be too noisy to obtain reliable results.

Obviously, more consideration is needed in terms of reliability and stability.

Stability and Component Selection

Implementing a stable photo-sensing circuit first requires understanding the design variables in the circuit, analyzing the overall transfer function, and then using these findings to design a reliable circuit solution.

The first design focus is to select the appropriate resistor for the photodiode response. The second design focus is to establish stability. Once the stability analysis is complete, the next step is to evaluate and adjust the output noise of the system to produce the appropriate signal-to-noise ratio (SNR) for the application requirements.

Amplifier and photodiode models help determine the frequency and noise response of the photodiode sensing circuit. However, achieving good stability in the design process begins with evaluating the transfer function of the system and determining the key variables that affect stability. The first and foremost is determining the value of the feedback resistor (RF) (Figure 2).

Figure 2: Photodiode preamplifier equivalent circuit for AC and noise analysis (Image source: Analog Devices)

The design criteria for this circuit are 5 volt full-scale output and a maximum photodiode current of 200 μA. The full-scale output voltage and maximum photodiode current determine the value of the feedback resistor according to Equation 2:

Equation 2

There are three circuit design variables to consider in stability analysis: the photodiode, the amplifier, and the parallel RF and CF (RF||CF) amplifier feedback network. The choice of the photodiode depends on its photoresponse characteristics, however, its parasitic capacitance (CS) has a significant impact on the noise gain and stability of the circuit.

The network in Figure 2 directly affects the stability and noise performance of the circuit. As with CMOS or FET input differential pairs, the op amp should have low input bias currents in the picoamp (pA) range. These differential transistor pairs maintain low input bias currents in the pA range, as well as offset errors in the tens to hundreds of microvolts. If either or both of these errors are large, nonlinear behavior will affect the amplifier’s response to the LED/photodiode result.

Additionally, the amplifier's input common-mode (CM) and differential-mode (CD) parasitic capacitances can also adversely affect the stability and overall accuracy of the system.

The bandwidth to achieve sufficient stability depends on RF, the gain-bandwidth product of the amplifier, and the total capacitance of the amplifier’s summing junction, CIN. The total capacitance of the amplifier’s summing junction includes the parasitic capacitance of the photodiode SFH 2701 and the input capacitance (differential and common mode) of the actual amplifier, the Analog Devices AD8065ARTZ-R2, and can be calculated using Equation 3:

Equation 3

in:

CIN = Total capacitance at the summing junction

CS = parasitic capacitance of the photodiode = 1.7 pF

CD = differential input capacitance of the amplifier = 4.5 pF

CM = common-mode input capacitance of the amplifier = 2.1 pF

In this article, the value of CS is the parasitic capacitance of the photodiode resulting from a 5 volt reverse bias.

The gain-bandwidth product of the amplifier is 65 megahertz (MHz) (fCR). Because the maximum achievable bandwidth of the AD8065 is greater than the design target bandwidth of 2 MHz, it is well suited for pulse oximeter circuits.

To verify acceptable AD8065 bandwidth, Equation 4 defines the signal bandwidth with 45° phase margin (f(45)):

Equation 4

in:

f(45) = System signal bandwidth with 45° phase margin

fCR = gain-bandwidth product of the amplifier

The value of f(45) exceeds the designed bandwidth of 2 MHz.

The RF and CIN poles in the amplifier loop transfer function can cause peaking and circuit instability. Increasing CF creates a zero in the loop transfer function, compensating for the pole and reducing the signal bandwidth (Figure 3).

Figure 3: Frequency response of a photodiode amplifier circuit using parasitic input capacitance, CIN. (Image source: Analog Devices)

Equation 5 uses the corner frequency of f2 (2 MHz) to determine the value of Cf:

Equation 6

The Cf value for the target signal bandwidth of 2 MHz (3.3 pF) is greater than the amplifier’s Cf value (0.903 pF). The lower capacitance value indicates a more stable system because increasing the feedback capacitance increases the phase margin.

Photodiode response time

Three factors affect the response time of a photodiode:

Carrier charge collection time in the depletion region of a photodiode

Carrier charge collection time in the undepleted region of the photodiode

Photodiode/Circuit Combination Resistor-Capacitor (RC) Time Constant

Since the junction capacitance depends on the diffusion area of ​​the photodiode and the applied reverse bias, the rise time increases with decreasing diffusion area and increasing reverse bias. The junction capacitance of the SFH 2701 PIN photodiode is 5 pF maximum at 0 volt bias, 2 pF typical at 1 volt reverse bias, and 1.7 pF at 5 volt reverse bias. For the purposes of this discussion, all measurements were made at 5 volt reverse bias.