Oxygen Sensor Analyze

OXYGEN SENSOR OUTPUT VOLTAGE ANALYSIS

Reference Chapter 7, Section 7.4, Feedback Systems, pp 301~304, "Internal Combustion Engine

According to the above reference, an oxygen (O2) sensor puts out a voltage signal between zero

and 1.0 volt when hot enough, and there is a difference in the partial pressure of O2

between the exhaust gas and the outside atmosphere. The O2 sensor is designed to produce

an electrochemical reaction, in two separate "gas chambers" (one in the exhaust gas, and one

in the outside atmosphere). The O2 sensor is therefore an "oxygen concentration cell" which

generates its own voltage between a positive electrode (center wire) and negative electrode (sensor

body). The solid electrolyte is yttria (Y2O3) stabilized zirconia (ZrO2) ceramic, and the electrodes

are Platinum coated, non-corrosive metal. This particular electrochemical reaction produces four

free electrons during equilibrium which carry the current between the two metal electrodes.

The following formula represents the voltage output from an automotive O2 sensor:

Voutput = (R*)(T) / (n)(F) * ln[(Po, air)/(Po, exh)]

(known as the Nernst Equation)

where,

Voutput = O2 sensor's output voltage ( 0 to 1.0 volt is normal range)

R* = Universal Gas Constant = 8.3143 [Joule/gram-mole * K]

T = Temperature of the exhaust gas [Deg K]

n = number of electrons involved in the reaction = 4 in this case

F = Faraday constant = 96,480 [Coulomb/gram-mole]

Po, air = Partial pressure of O2 in the atmosphere [Pascals]

Po, exh = Partial pressure of O2 in the exhaust gas at temp [Pascals]

Note: Volt = [J/Coulomb] or Coulomb = J/V

1.0 psi = 6894.8 Pascals = 6.8948 kPa

Per Heywood, atmospheric O2 partial pressure is ~ 20 kN/m^2 (kPa) = 20,000 Pa

Assume that dry air at 1.0 Atm (sea-level), and 70 deg F is the reference point for the O2 sensor

output. Calculate the partial pressure of O2 of this reference air to see if it agrees with Heywood.

d = (1.3254 * inHg) / T

d = (1.3254 * 29.92) / (459.7 + 70) = 0.07486 lbm/ft^3

O2 mass % = 23.142%, Therefore,

density of O2 = (0.23142)(0.07486) = 0.01732 lbm/ft^3

Po, air = (d)(R)(T)

In this case, R = (R*)/(M of O2) = (0.7302)/(32) = 0.02282 [(atm-ft^3) / (lbm-mole * R)]

(Po, air) will be in [atm] units

Po, air = (0.01732)(0.02282)(529.7) = 0.20936 atm = 3.078 psi = 21219.4 Pa = 21.22 kPa

Therefore, Heywood's statement for (Po, air) and this calculation is very close.

Based on this, assume that Heywood's numbers in Figure 7-17 (p. 302) are based on dry air

at sea-level, and 70 deg F.

According to Heywood, the partial pressure of O2 in exhaust gas changes very quickly at the

point of Stoichiometric combustion, and is also a function of the A/F ratio and the temperature

of the exhaust gas when the A/F ratio is greater than Stoichiometric (14.7 to 1), per Figure 7-17.

The O2 partial pressure in the exhaust is a function of exhaust temperature in the richer than

Stoichiometric region. Therefore, the O2 sensor output will be more dependent on the exhaust gas

temperature when the A/F ratio is less than Stoichiometric (rich burn) vs the lean burn region.

Exhaust Gas Temperature Conversion

Deg C

500

750

900

Deg K = Deg C + 273.15

Deg K

773.15

1023.15

1173.15

The following numbers are taken off Figure 7-17 (a) in Heywood. Numbers are approximate readings

off the graph (not calculated), and have been "tweaked" slightly to agree with the O2 sensor output

voltages shown in Heywood's corresponding graph in Figure 7-17 (b).

O2 Partial Pressure in Exhaust Gas, (Po, exh) [Pascals]

Exhaust Gas Temp [Deg K]

A/F

773.15

1023.15

1173.15

10.3

2.00E-22

1.00E-14

2.00E-11

11.8

8.00E-22

3.00E-14

6.00E-11

13.2

6.00E-21

2.00E-13

6.00E-10

14.7

5.00E-18

5.00E-11

1.00E-07

(Po, exh) increases to ~50 Pa on the lean end of

14.7

Stoichiometric before increasing above an A/F = 14.7.

16.2

1500

In the leaner than Stoichiometric region, (Po, exh) does

17.6

4000

not change with exhaust temperature.

19.0

7000

Calculate the O2 sensor output voltage to see if it agrees with Heywood's chart in Figure 7-17 (b),

using the Nernst Equation.

Voutput = (R*)(T) / (n)(F) * ln[(Po, air)/(Po, exh)]

Use reference O2 of dry air at sea-level and 70 deg F, then (Po, air) = 21,219 Pa

R = Universal Gas Constant = 8.3143 [(Joule/gram-mole * K)]

n = number of electrons involved in the reaction = 4 in this case

F = the Faraday constant = 96,480 Coulomb/gram-mole

O2 Sensor Output [Volts]

Exhaust Gas Temp [Deg K]

773.15

1023.15

1173.15

A/F

500 C

750 C

900 C

10.3

0.998

0.930

0.874

11.8

0.975

0.906

0.847

13.2

0.942

0.864

0.788

14.7

0.830

0.742

0.659

Rich end of Stoichiometric

14.7

0.101

0.133

0.153

Lean end of Stoichiometric

16.2

0.044

0.058

0.067

17.6

0.028

0.037

0.042

19.0

0.018

0.024

0.028

Graph of Calculated O2 Sensor Output Voltage

Now, verify what effect there is on the O2 sensor voltage output if there is a large change in atmosphere

oxygen level due to altitude and/or humidity. This will change the (Po, air) value in the Nernst Equation

for the O2 sensor voltage output. The actual A/F ratio will remain constant because the FD maintains a

constant absolute manifold pressure (and therefore charge density) by increasing boost pressure with

altitude. Assume that the car is at an elevation of 7000 feet, and the air is dry (no humidity) at 70 deg F.

The humidity ratio at this temperature is small and will be neglected to simplify this analysis. Any humidity

would only slightly reduce the atmospheric oxygen level, and hence the partial pressure of O2 (Po, air).

Find the partial pressure of O2 in this air due to decreased atmospheric pressure.

Po, air = 11.34 psia = 23.09 inHg at 7000 ft

(From another spreadsheet)

d = (1.3254 * inHg) / T

d = (1.3254 * 23.09) / (459.7 + 70) = 0.05778 lbm/ft^3

O2 mass % = 23.142%, Therefore,

density of O2 = (0.23142)0(0.05778) = 0.01337 lbm/ft^3

Po, air = (d)(R)(T)

In this case, R = (R*)/(M of O2) = (0.7302)/(32) = 0.02282 [(atm-ft^3) / (lbm-mole * R)]

(Po, air) will be in [atm] units

Po, air = (0.01337)(0.02282)(529.7) = 0.16162 atm = 2.376 psi = 16,380 Pa = 16.38 kPa

Again, use the Nernst Equation, but use 16,380 Pa for the atmosphere O2 partial pressure.

Voutput = (R*)(T) / (n)(F) * ln[(Po, air)/(Po, exh)]

Use reference O2 of dry air at sea-level and 70 deg F, then (Po, air) = 16,380 Pa

R* = Universal Gas Constant = 8.3143 [(Joule/gram-mole * K)]

n = number of electrons involved in the reaction = 4 in this case

F = the Faraday constant = 96,480 Coulomb/gram-mole

O2 Sensor Output [Volts] @ 7000 ft

Exhaust Gas Temp [Deg K]

O2 Sensor Volts @ Sea-Level

773.15

1023.15

1173.15

for Comparison to 7000 ft

A/F

500 C

750 C

900 C

A/F

500 C

% Change

10.3

0.994

0.924

0.868

10.3

0.998

0.43

11.8

0.971

0.900

0.840

11.8

0.975

0.44

13.2

0.937

0.858

0.782

13.2

0.942

0.46

14.7

0.825

0.737

0.653

Rich end of Stoich

14.7

0.830

0.52

14.7

0.096

0.128

0.146

Lean end of Stoich

14.7

0.101

4.28

16.2

0.040

0.053

0.060

16.2

0.044

9.77

17.6

0.023

0.031

0.036

17.6

0.028

15.51

19.0

0.014

0.019

0.021

19.0

0.018

23.34

As can be seen between the two tables above (at Texh = 500 C), that the O2 sensor output voltage has

not changed much on the rich side of Stoichiometric when the car is at 7000 ft elevation, even though

the amount of oxygen mass in the air has decreased by approximately 23%.

Therefore, if you are at a high elevation, and in a WOT escapade watching the A/F meter, you can

feel confident that its output has not shifted due to the high elevation causing a lack of O2 in the air.

A correctly functioning O2 sensor and A/F meter should give accurate A/F readings in the rich

region of Stoichiometric regardless of elevation or humidity.

A larger concern is the O2 sensor voltage shift in the rich A/F region due to increasing exhaust gas

temperatures. It is unknown at this time if the stock FD O2 sensor exhibits this phenomena. If it does,

you could see as much as ~0.15 volt difference (3 LEDs out of 20 on A/F meter) between 500 C and

750 C exhaust gas temperature, at an A/F of ~13 to 1.

Plot showing the negligible shift in an O2 sensor due to oxygen reduction from elevation and/or

humidity.