®

parSYNC PLUS
Gas and Particulate Matter Sensors –Technical Overview
August 3, 2022

DRAFT

Sensor Tech Overview

Table of Contents
Introduction ..................................................................................................................................... 3
Equations to Calculate Concentration............................................................................................. 4
Equations for Gas Sensors ........................................................................................................... 4
Equations for PM Sensors ........................................................................................................... 4
Notes ............................................................................................................................................ 5
Overview of the Gas Sensors .......................................................................................................... 6
Overview of the PM Sensors .......................................................................................................... 7
PM Cartridge Layout ................................................................................................................... 7
Ionization Sensor ......................................................................................................................... 8
Scattering Sensor ......................................................................................................................... 8
Opacity Sensor............................................................................................................................. 8
Key Take-Aways of the PM Cartridge ........................................................................................ 8
Physics of the PM Sensors .............................................................................................................. 9
Ionization ..................................................................................................................................... 9
Opacity......................................................................................................................................... 9
Scattering ................................................................................................................................... 10
PM Sensor Response Curves ..................................................................................................... 11

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Introduction
This document covers the equations and working principles for the gas and particulate matter(PM) sensors in the parSYNC PLUS (pS+). For gases, the pS+ measures carbon dioxide (CO2),
carbon monoxide (CO), nitrogen oxide (NO), and nitrogen dioxide (NO2) concentrations. For
PM, the pS+ uses three sensor types – ionization, scattering, and opacity – to report particle mass(PM) and particle number (PN) concentrations. The pS+ is also called parSYNC 3.8 (pS3.8) insome documents.
The latest model, parSYNC FLEX (pS-FLEX or FLEX), has additional sensors for gases, namelyhydrocarbon (HC and oxygen (O2). The information in this document is applicable to the FLEX
with some minor exceptions. A separate document specific to the FLEX will soon be released.

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Equations to Calculate Concentration
This section describes the system of equations that are used in the parSYNC® to interpret thevoltage or current electrical response from the sensor to a concentration value for a gas moleculeor particulate matter in the exhaust sample. The electrical signals are acquired at 100 hz,
averaged over a 1 second duration to produce a 1 hz electrical signal, which is converted to a 1
hz concentration value using the equations described here.
100 hz electrical signal data acquisition  1 hz electrical signal  1 hz concentration value

Equations for Gas Sensors

V=Vr − Vz
i

Ci

Vi *

Cs − C z
Vs − Vz+ Cz

Where,
Ci instantaneous, zero corrected, concentration of measured gas, ppm or %Cs specified concentration of span gas, ppm or % (GUI name: Span Conc.)
Cz specified concentration of zero gas, ppm or % (typically zero). If using clean ambient air,
CO2 in atmosphere is not zero. Global average CO2 in 2022 is ~410 ppm (0.041%). (GUI
name: Zero Conc.).
Vi instantaneous, zero corrected, sensor voltage, V
Vr instantaneous, raw, sensor voltage, V. When sampling zero gas, ideally, Vr=Vz and thus Vi= 0V and Ci=0. But, in reality, Vr ~ Vz, and so Vi and Ci are ~ 0.
Vs average of instantaneous raw voltage when sampling span gas, V (GUI name: Span Vraw)
Vz average of instantaneous raw voltage when sampling zero gas, V (GUI name: Zero Vraw)

Equations for PM Sensors
Step-1
Calculate PM (µg/m3) and particle number, PN (#/cm3) for each sensor as per:SensorVi
PM (µg/m3)
PN (#/cm3)
2
Scattering
Vr - Vza*Vi + b*Vi
x* Vi2 + y*Vi
Ionization-(Vr - Vz)
a*Vi2 + b*Vi
x* Vi2 + y*Vi
Opacity-(Vr - Vz)
a*Vi2 + b*Vi
x* Vi2 + y*Vi
For ionization and opacity sensors, the Vi equation has a negative sign because the raw voltages
are inversely proportional to particulate matter concentration.

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Where,
a,b coefficients for each sensor for PM. User can change these in the GUI.
Vi instantaneous, zero corrected, sensor voltage, V. Written as NA during zeroing.
Vr instantaneous, raw, sensor voltage, V. When sampling zero gas, ideally, Vr=Vz and thus
Vi=0V, and subsequently PM=0 and PN=0. But, in reality, Vr ~ Vz, and so Vi, PM, andPN are ~ 0.
Vz average of instantaneous raw voltage when sampling zero gas, V (GUI name: Zero Vraw)
x,y coefficients for each sensor for PN. User can change these in the GUI.
Step-2
The final PM (µg/m3) and PN (#/cm3) reported in the data file are a weighted sum of the PM(µg/m3) and PN (#/cm3), respectively, calculated for each sensor. Individual sensor PM and PN
are neither displayed in the GUI nor recorded in the data file, however, the user can calculatethese during post-processing using the equations described here and the config file used during
measurement.
The “weight” is the fractional contribution of the individual sensor result to final reported
concentration. User can change these values in the GUI. For each sensor, the weight can be
minimum = 0.000 and maximum = 1.000. The sum of individual sensor weights must be 1.000.
Set the weight for a sensor to zero to remove its contribution.
Coefficients and Weighs for PM (µg/m3)
SensorScattering
Ionization
Opacity‘a’6534200-948.97269670‘b’
3756406319.928252

Weight
0.550
0.390
0.060

‘y’
8.8042E+8
1.4262E+7
7.6699E+7

Weight
0.010
0.860
0.130

Coefficients and Weighs for PN (#/cm3)
SensorScattering
Ionization
Opacity‘x’
3.8983E+9-2.744E+6
2.9964E+8

Notes
1. Recorded in the data file and displayed on GUI: Vi and Vr for individual gas andparticulate. sensors, and Ci for each gas sensor but only the final PM and PN value.
During zeroing, Vi, Ci, PM, and PN are reported as NA.
2. Only displayed on GUI: Cs, Cz, Vs, Vz, and PM and PN coefficients and weights.

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Overview of the Gas Sensors
The pS+ measures CO2, CO, NO, and NO2 gases. The latest model, parSYNC FLEX, alsomeasures HC and O2 and these are greyed out here to convey that they are unavailable in the pS+model.
Measurement principle
CO2, CO, HC: 3-channel non-dispersive infra-red (NDIR)
NO, NO2, O2: electro-chemical (EC), also known as micro-fuel cell
Specifications of the gas sensors
Parameter

CO2

CO

Range

0–20 %

0–15 %

T0-90 Time (s)

< 3.5

< 3.5

< 3.5

Abs

± 0.3 %

± 0.02 %± 8 ppm± 0.1 %

Rel

±3%

±3%

±3%

±2%

Accuracy

HC

NO2

O2

0–4000 ppm 0–5000 ppm 0–300 ppm

Resolution
RepeatabilityNO<5

1–2 ppm
Abs± 0.1 %

± 0.02 %± 6 ppm

Rel

±2%

±2%

±2%

< 35

0–100 %
<6

0.1 ppm± 0.1 %

±2%

±2%

±2%

This document will be updated to add basic working principles for NDIR and ECC. In themeantime, working principles of NDIR and ECC are easily found using a simple internet search.
The pS+ NDIR has three measurement channels plus one reference channel. Thus, it has a fourwindow chopper. The NO and NO2 sensors are 3-electrode ECs.

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Overview of the PM Sensors
The parSYNC device uses three different types of sensors to determine particle mass and particle
number. Each sensor is sensitive to different ranges of particle sizes and can measure the particle
throughput in real-time. A multi-plex approach is used to combine data from the three sensors
and provide the user with particle mass and particle number.
The parSYNC measures undiluted emissions using the response of three dissimilar particulate
sensors. The sensors are sensitive to different distributions of particle size:
SensorIonization
Opacity
Scattering

Greatest Sensitivity
Ultra-fine/Fine particulates, typically 0.01 to 0.3+ microns
Overall particulates, typically 0.1 to 10+ microns, peak@0.8microns
Coarse particulates, typically 0.3 to 10+ microns, peak@3.5microns

Note that although their particulate size sensitivities overlap, their optimal particle size andconcentration responsiveness is different between sensors. Thus, particle mass concentration andnumber are extrapolated based on the evaluation of sensor modality and empirical laboratory
measurements.

PM Cartridge Layout
The PM Cartridge and its sensors are illustrated below:

The exhaust sample gas is drawn through the PM cartridge at ~1 liter per minute and first enters
the Ionization Sensor.

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Ionization Sensor
The sensor consists of a flow chamber, collector plate and a low-level alpha particle source (1microcurie of Americium 241 foil) mounted on a grounded (negative) pedestal. The alpha particles
are absorbed by the few centimeters of sample air/gas and the chamber enclosure to pose no safety
risk. As the alpha particles collide with the sample gas air molecules they are split into positive
and negative ions. The ion flow creates a measured continuous current flow between the positiveplate and negative source.
As particulates enter the sensor chamber, the current flow is reduced by the disturbance of ion flow
and provides a means to measure the magnitude of particulate matter.

Scattering Sensor
The scattering sensor measures the light from a 920 nm LED that is scattered toward a lightreceiver at 45° away from the incident forward direction. An electronic amplifier circuit is used toincrease the sensitivity of the device to collaborate with the other sensors in the system. As theexhaust air sample flows through the chamber, the particulate scatter voltage signal is measured
and recorded.

Opacity Sensor
The opacity sensor measures the amount of light attenuated by the particulates along a definedcollimated light path length. Key components in the chamber tube include: (1) LED white lightsource; (2) a green light filter (to match standardized historical smoke meter preferences for green
light); (3) light baffles along the light path to block stray uncollimated light and reflections fromthe interior walls of the tube; (4) sight glass at each end of the tube chamber to seal in the flowing
sample gas and direct the light beam to the receiving light sensor; (5) photodiode (light receiver).
When we combine the relative luminous intensity of white light, spectral percent transmission of
the green filter, and the spectral responsivity of the photodiode, the final peak sensitivity is around
540 nm.
After passing through all sensors, the exhaust sample gases continue to flow out to a particulate
filter, flow pump, and an exhaust outlet.
The voltage data measured from all sensors is continuously transmitted via Bluetooth to a laptopthat records and calculates Particle Number and Mass based on standardized comparison referencedata.

Key Take-Aways of the PM Cartridge
•
•
•
•
•
•

Multi-plex approach using three dissimilar sensors to measure particulate matter.
Calibration to Particle Number and Particle Mass via inversion of empirical laboratory
data.
Small sensors are contained within easily replaceable sensor cartridges.
No dilution of the sample (No need to extrapolate the sensor values to full concentration).
Physics of measurement are fundamentally identical to classic PEMS equipment.
Comparable accuracy to larger, more expensive instrumentation.
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Physics of the PM Sensors
Ionization
Ionization sensors are far more sensitive to ultra-fine particulates than opacity and scattering
sensors. Ionization sensors have been an important part of emission analyses (see diffusion
charging sensors).
If we assume that the particles in the air are of uniform size, then the diffusion motion of ions areshown to have a linear response to the particle surface area concentration detected in the sample.
If not, then an approximation typically is be made over the range of particle sizes; typically, themodels and experimental data show that particles’ sizes would be in a log-normal distribution. Forease of use, virtually all ionization sensors have compensators to make their response linearly
proportional to the particle size.
Specifically, the following system of equations govern the detector response:
ΔI
x
Nt
Y
Y

= I1 – I0= ΔI / I0= fv / (18.62 * rm2)
= x * (2 – x) / (1 – x)
= k * Nt * rm
Where,
I0 = original current in the detector
I1 = measured current in the detectork = constant (determined empirically)
Nt = total number of particles passing through the chamber
rm = mean particle radiusy = detector response

Opacity
Opacity, also known as extinction, is governed by the Beer-Lambert law as given below.
Measuring obstruction and diffusion, the greater the number of particles per unit volume and/or
the greater the average size of the particles, the higher the opacity.
Opacity, O = 1 – exp(–n*a*q*l)
Where,
a = mean projected area (or attenuation cross-section or effective cross-sectional area)l = path length of beam through the sample (technically, the length of effluent path)n = number of particles per unit volume
q = particle extinction coefficient

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The particle extinction coefficient varies versus wavelength and particle size. These numbers havebeen determined empirically at different wavelengths for different particles. The highest spectral
responsivity of typical opacity sensors is in the green color wavelength range and the parSYNC
achieves the same result by using a white LED and green filter. Opacity is measured by the change
in the current within the circuit that the opacity meter resides. There are known limitations withusing green light, such as the cross-sensitivity to NO2. It is possible to use other color sources,
however, each option has disadvantages. For example, red light is less sensitive to smaller particles
and ultra-violet light is sensitive to methane.
The Beer-Lambert law applies over a wide range of concentrations and particles and, therefore,
opacity sensors are useful to get an overall picture of the particle mass flow. However, opacity
sensors are known to be less accurate when there is a lot of light scattering within the sample andwhen the particles are very small. To counter these issues, the parSYNC includes a scattering
sensor (sensitive to larger particles and when large amounts of scattering occur) and an ionization
sensor (sensitive to ultra-fine particles).

Scattering
A greater number of particles will result in a greater amount of scattering; different sized particles
along with greater number of particles will affect the scattering profile, which in turn varies byangle.
For non-absorbing particles, the following formula defines the scattering sensor’s response to theincoming light for Rayleigh scattering:I / I0 = (π4/ 8) * ((n2 – 1) / (n2 + 2))2 * (D6 / (r2 * λ4)) * (1 + cos2θ)Where,
n = index of refraction
D = particle diameterr = distance of particle from light source
λ = wavelength of incident lightθ = scattering angle
Experimental data show that for comparatively uniform particle geometry and particle mass, themass concentration versus scattering is log-linear in the Rayleigh region. Hence, the electronics
within a scattering sensor can convert its readings to a usable output. It is well-known that the
scattering sensors are most sensitive to larger particles, as can be inferred from the 6th power on
the particle diameter, D, factor in the above formula.

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For large particles, we are in the geometric scattering region. The equation is modelled with an
inhomogeneous wave equation with dissipation, as in:utt – Δu – r2u = f(x, t)with the appropriate initial and boundary conditions. This has known closed-form
fundamental solutions of the formekx (A(x, t) cos(ωt) + C(x, t) sin (ωt))
where k is the spatial decay constant and ω is the frequency of the light source. Thisequation applies for large particles in the geometric scattering region.
(Note: Because of the dependencies on both angle and wavelength, varied incident angles
and wavelengths can provide a more complete picture of the distribution.)

PM Sensor Response Curves
The relative sensitivity of each sensor, based on its theoretical response to particle diameter, isshown in the subsequent figure. The responses have been re-scaled to illustrate all sensors on thesame graph. Wavelengths (and angles) of incident light used in the theoretical response
calculations match the 3DATX sensors.

Note that each sensor type has a different peak sensitivity to particle size in identical situations.
The Opacity sensor has a peak in the 0.8 micron diameter range (800 nm) and Scattering sensor
peaks in the 3.5 micron diameter range. The parSYNC can perceive changes in the distribution of
the size of the particles by using this physical property. These results have been quantified inlaboratory tests.

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Evaluating the response of the parSYNC sensors in a laboratory FTP-75 dynamometer test cycle
yields measured response characteristics that closely follow the theoretical responsivity. For
example, the test of a light-duty diesel vehicle with DPF yielded the data presented in the figure
below. In this test, a TSI EEPS-3090 was used as a laboratory spectrometer reference. Whencharacterizing the measured voltage response of the sensors to the ultra-fine particles, an illustrated
log-linear graph below was determined from laboratory data measuring up to 520 nm diameter.

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