In a photoelectric smoke sensor, an LED periodically emits light into a chamber. The light scatters off smoke particles and enters a photodiode. The photodiode outputs a current proportional to the incident light, which is proportional to the smoke concentration. The LED current must be pulsed and regulated, and the photodiode current must be amplified with low noise and high linearity. Therefore, smoke detectors require a LED driver and photodiode amplifier to obtain an accurate signal from the sensor. With the signal amplified, an analog-to-digital converter (ADC) on the MCU captures samples of the signals and the MCU calculates the smoke concentration.

The TPS880x AFE integrates the regulators, drivers and amplifiers to interface the smoke detector’s power supply, sensors, and microcontroller unit (MCU). The TPS880x has adjustable LED driver current, LED pulse width, amplifier bandwidth, amplifier gain, and output filter bandwidth. Each of these parameters, along with the ADC timing, affects the SNR. When all of these parameters are adjusted, reliable smoke sensing with only nanoamps of photodiode current is achieved.

This report analyzes how each of the system parameters affects the SNR. Modeling the system provides valuable insight on how to optimize the SNR. Measurements verify the trends in the model and provide configurations for users to start their designs.

SNR is commonly defined as the ratio of signal power to noise power. In a smoke detector, the signal of interest is the smoke concentration, calculated from measurements of the photodiode current. Amplifying the photodiode current adds noise which makes the smoke concentration measurement fluctuate even if the actual smoke concentration is constant. Therefore, having high SNR is essential to quickly and accurately decide if the smoke concentration is at a dangerous level.

In this report, SNR is presented as the smoke measurement amplitude divided by the smoke measurement standard deviation. This metric provides the designer with the statistics of the smoke measurement. Because the smoke measurement amplitude is proportional to the smoke concentration, SNR increases with the smoke concentration. Therefore, the SNR in this report is specified at 1 nA photodiode current. The conversion from smoke concentration to photodiode current depends on the LED, photodiode, and chamber geometry. In general, the photodiode current is proportional to the LED current. To calculate the SNR at a different current, multiply the SNR by the new current and divide by 1 nA.

A smoke concentration measurement follows this general procedure:

1. Enable the photo amplifier and analog multiplexer (AMUX) buffer.
2. Take one or more ADC measurements after the photo amplifier and AMUX settles. This measures the ambient light entering the photo chamber. ADC samples taken before the LED is enabled are referred to as base samples in this report.
3. Enable the LED.
4. Take one or more ADC measurements after the photo amplifier and AMUX settles. This measures the ambient light and scattered light in the photo chamber. ADC samples taken after the LED is enabled are referred to as top samples in this report.
5. Disable the LED, photo amplifier, and AMUX buffer.
6. Process the ADC measurements to determine the smoke concentration. The photo chamber responsivity must be known to obtain an accurate measurement.

The SNR of the smoke concentration measurement depends on many parameters in the system, including amplifier speeds, LED current, LED pulse width, ADC sample rate and digital filtering. These parameters can be adjusted to improve the SNR. The LED and photodiode parameters, such as quantum efficiency and half-angle, and the photo chamber geometry also have an effect on the SNR but are beyond the scope of this report. Table 2-1 lists various measurement configurations and the SNR at 1 nA of photodiode current. The SNR at 1 nA is reported here as a unitless ratio and can be converted to decibels by taking the base-10 logarithm and multiplying by 20. Table 2-1 provides a reference for users to design a smoke detector using the TPS880x AFE. The parameters in the table are discussed in Section 2.3 and Section 2.4. The configurations in Table 2-1 are selected from measurements in Section 4. Section 4 also outlines the measurement process.

Optimally amplifying the photodiode current requires careful selection of the amplifier gains, amplifier speeds, LED current and LED pulse width. The photodiode current can be as low as 1 nA, making the amplified signal highly susceptible to noise.

The first component to select is the photo input amplifier gain resistor R_PH. This resistor sets the transimpedance of the first stage amplifier. Resistance of less than 200 kΩ introduce thermal noise into the output, reducing SNR. Resistance of less than 5 MΩ limit the maximum speed of the amplifier and may require impractically low compensation capacitance. A resistance of 1.5 MΩ works in most applications and is a good resistance to start the design with. Select the photo input amplifier gain resistor and second stage gain such that the maximum photodiode current generates an output voltage of 2 V. This utilizes the full dynamic range of the TPS880x amplifiers and reduces ADC quantization noise. With thermal noise and quantization noise mitigated, the amplifier current noise is the primary contributor to the output noise. The photo input amplifier gain resistor equally amplifies the photodiode current and the amplifier current noise. In this condition, the R_PH resistance has a minimal effect on SNR.

The optimal photo amplifier and AMUX speeds depend on the LED pulse width and ADC sample rate. The photo amplifier time constant τ₁ is equal to the gain resistor R_PH times C_PH. τ₁ is adjusted by varying C_PH once R_PH is selected. The AMUX time constant τ₂ is equal to the AMUX buffer resistance R_AMUX times C_AMUX. τ₂ is adjusted by varying R_AMUX after setting C_AMUX between 330 pF and 1nF. Adjusting the amplifier speeds is an effective way to improve the SNR. This is demonstrated with configurations 3 and 4 in Table 2-1.

The highest SNR for a fixed pulse width is achieved with a fast amplifier speed and fast ADC sample rate, then taking multiple ADC samples over the width of the photo pulse and averaging them together. For example, configuration 5 in Table 2-1 has a higher SNR than configuration 4 because a faster amplifier speed and multiple ADC samples are taken. If the ADC sample rate is slow, or if only one top ADC sample is taken, then a slow amplifier speed achieves the highest SNR. Using higher and lower speeds than shown in Table 2-1 may improve the SNR further.

Increasing the LED current and pulse width improves the SNR at the cost of increased power consumption. LED current directly increases the LED output intensity and the smoke sensitivity of the detector. Increasing the LED current is a simple and effective way to increase the SNR.

Increasing the LED pulse width improves the SNR by allowing the photodiode current to be amplified for more time. Table 2-1 demonstrates the improvement in configurations 1 and 3 and configurations 4 and 8, where t_LED is the LED pulse width. Increasing the LED pulse width and proportionally decreasing the amplifier speed also improves the SNR, shown in configurations 1 and 8.

For battery operated smoke detectors, increasing the LED current or pulse width may not be possible due to limited system power capacity. In this case, the LED current can be increased and the pulse width decreased to improve SNR while consuming the same amount of power. The benefit is small but evident when comparing configurations 1 and 4. The SNR and power consumption in configuration 1 is about half of configuration 4. If the LED current is doubled in configuration 1, the power consumption is the same as configuration 4 and the SNR is slightly higher than configuration 4. Since the 50 µs pulse width was tested with only one τ₁ and τ₂ combination, it is likely that the SNR of configuration 1 can be improved by varying τ₁ and τ₂.

If multiple ADC samples are taken, fewer top ADC samples can be taken with shorter pulse widths. This may reduce the benefit of using a shorter pulse width. Always take measurements to confirm the SNR improvement when modifying system parameters.

Increasing the LED current increases the LED forward voltage and the LED power consumption. The LED power consumption is equal to the LED current times the LED forward voltage. Because the TPS880x uses a linear regulating LED driver, the power consumed by the driver and LED is equal to the LED current times the LED supply voltage. In applications where the SNR is too low and power consumption must be minimized, it is optimal to first increase the LED current until a higher LED supply voltage is required, then increase the LED pulse width. At high LED currents, the LED output power per input current and lifespan drops.

The TPS880x LED driver has a propagation delay and rise time that limits the minimum pulse width. It is recommended to use a pulse width longer than 20 microseconds to mitigate propagation delay and rise time variation effects on the signal.

Taking multiple ADC samples is an effective way to improve the SNR. Comparing configurations 3 and 5 in Table 2-1, the SNR is significantly improved by averaging multiple top ADC samples. The number of top ADC samples is displayed as N_TOP and the time of the first top ADC sample is t_TOP. Faster ADC sample rates allow more samples to be taken at the top of the photo pulse and improve the SNR further. This is demonstrated in configurations 5 and 7. Table 2-1 displays the time between ADC samples as t_SAMP.

Higher ADC resolutions improve the SNR to a limit. Figure 4-21 displays the effect of varying the ADC LSB size for a 260 mV amplitude pulse. The SNR drops when the ADC least significant bit (LSB) is greater than 5 mV. In this case, a 10-bit ADC with a 2 V to 3 V full-scale voltage is sufficient for maximizing SNR.

Taking multiple ADC samples of the signal before the LED is enabled is effective in systems that measure the ambient light level before the LED is enabled. This is displayed as N_BASE in Table 2-1. The benefit is shown in Figure 4-20. Because the LED is not enabled for these ADC samples, low power is consumed when taking the multiple ADC samples before the LED is enabled.

If the ADC sample rate is different from the examples in Table 2-1, take samples for the same amount of time as done in Table 2-1. For example, if a 5 µs t_SAMP is used with τ₁ and τ₂ set to 15 µs, take 40 base samples and 16 top samples.

Averaging the multiple ADC samples together is an effective way to process the ADC samples. Using a digital matched filter improves the SNR further. The matched filter weighs each sample by the noiseless DC-removed waveform voltage before averaging the samples together. An example DC-removed waveform and corresponding filter weights are shown in Figure 4-7 and Figure 4-8. The filter weights can be obtained dynamically by averaging measured each DC-removed ADC sample across multiple pulses. While the matched filter is more complex than the averaging filter, it can be used to increase the SNR without affecting power consumption.

It is shown in Figure 4-13 that other digital filters can improve the SNR further. The unconstrained filter has weights optimized for SNR. An example of the unconstrained filter weights is shown in Figure 4-8. The unconstrained filter is included to demonstrate how SNR can be improved beyond matched filtering.

Modeling the photo amplifier system explains why the methods discussed in Section 2 improve the SNR. The model is included here to further the user’s understanding of the system and provide a framework for further optimization.

Calculating the impulse response of the system can be done by modeling the photo input amplifier, photo gain amplifier, and AMUX buffer.

Using a photodiode model consisting of a capacitor and current source, the photo input amplifier system can be modeled as a combination of linear circuit elements shown in Figure 3-1. To simplify the analysis, the PREF photo reference is approximated as a small-signal ground, and the two photo resistors and capacitors are combined in series. The simplified circuit is shown in Figure 3-2. The op-amp is modeled with frequency-dependent open-loop gain A(s). The op-amp open-loop gain is 1 at the gain-bandwidth frequency f_GBW.

Equation 1 shows the open loop transfer function from PDO to PDN. This equation provides insight on how to stabilize the feedback loop. The compensation capacitor C_PH must be sized to place the zero frequency below the closed loop unity gain frequency for sufficient phase margin. A phase margin of over 70° prevents overshoot and reduces noise on the output. This is achieved when the zero frequency is less than the unity gain frequency by at least a factor of 3. The zero frequency and unity gain frequency are calculated in Equation 2 and Equation 3. These two equations set a lower limit on the compensation capacitance, shown in Equation 4, using the assumption that C_PH is less than C_PD. The photo input amplifier has a minimum unity gain bandwidth f_GBW of 1 MHz. Set f_GBW to 1 MHz when calculating the minimum compensation capacitance.

The compensation capacitance sets the closed loop bandwidth of the amplifier. Solving the closed loop amplifier output PDO in terms of the input current I_PD results in Equation 5. The Equation 5 denominator approximately equals 1 at frequencies below the unity gain frequency calculated in Equation 3. In this condition, Equation 5 can be simplified to Equation 6. Equation 6 demonstrates that the photo amplifier output is approximately equal to the photocurrent scaled by the gain resistors and low-pass filtered by the compensation capacitors. Above the unity gain frequency, additional low-pass filtering occurs on the signal.

The photo gain amplifier can be modeled as an ideal voltage amplifier at the bandwidths and gains explored in this report. In applications where lower first stage gains or higher bandwidths are used, additional measurements may be required to accurately model the photo gain amplifier.

The AMUX buffer has sufficient bandwidth and capacitance driving capability to be modeled as an ideal buffer. The RC filter can also be modeled as ideal.

The signal at the buffered AMUX output can be calculated using the models for each stage, as shown in Equation 7. τ₁ and τ₂ represent the photo input amplifier and AMUX filter time constants, respectively. Taking an integral and inverse Laplace transform of Equation 7 results in the time-dependent step response in Equation 8. Here, H(t) is the Heaviside step function, taking the value 0 for negative inputs and 1 for non-negative inputs. The step response assumes that the photocurrent is stepped from 0 to I_PD when t is equal to 0. The step response calculation in Equation 8 is undefined when τ₁ and τ₂ are equal. In this case, the limit can be taken to solve for the step response.

With the step response calculated, the response to a rectangular pulse input is calculated in Equation 9, where t_LED is the LED pulse width. Equation 10 and Equation 11 calculate the baseline DC voltage of the buffered photo signal with and without a 470 kΩ resistor installed on PREF. V_PDO(OFS) is the DC offset caused by the photo input amplifier and V_PGAIN(OFS) is the DC offset caused by the photo gain amplifier. Because there is a propagation delay on the TPS880x LED driver, the output may be shifted from when the LED is enabled.