# Does exhaust gas pressure impact the output of narrowband lambdas?

In the course of writing this answer I learnt that the current output of wideband lambda sensors is sensitive to exhaust gas pressure.

This technical document for Bosch LSU 4.2 widebands explains how changes in absolute gas pressure with alter current signal:

10.6 Pressure dependency of the sensor signal

A pressure change of the measured gas gives a deviation of the sensor output signal of:

Ip(P) = Ip(P0) * P/(k+P) * (k+P0)/P0


There is also a nice graphical representation of the deviation which I can post up later.

I wonder if the same is true for narrowband sensors. They operate quite differently from widebands, but it is known that certain cars dislike certain brands/models of narrowband sensor, even though the waveform should not change.

There are currently two kinds of narrowband sensors used these days: titania sensors (NTK) and zirconia (Bosch). This answer only addresses the zirconia sensors which are the most common type.

Referring to the diagram (which was created by Michael Handrich and shared under a Creative Commons license), the sensor is a galvanic cell that generates what's called the Nernst voltage which is proportional to the natural logarithm of the ratio of the two different oxygen concentrations. Specifically, this is the Nernst voltage equation:

dU = -T*k_B/e_0 * ln(c1/c2)

Where k_B is the Boltzmann constant in J/K, T is temperature in K, e_0 is the charge of an electron in C. c1 and c1 are both ion concentrations.

Another important physical law is Dalton's law which says that the total pressure of a mixture of ideal gasses is equal to the sum of partial pressures.

p_total = p_1 + p_2 + p_3 + ... + p_n

So the ratio of partial pressure of oxygen on one side of the cell to the partial pressure of oxygen on the other is identical to the ratio of ion concentration. It should be apparent that the partial pressure of any particular gas is directly proportional the total pressure (all other things being equal).

This means that a higher total pressure on the exhaust gas side should mean a higher concentration of oxygen and therefore a higher voltage compared to the voltage that would be present if there were no pressure differential. That is exactly what your equation says (although it is somewhat curiously related to the current rather than the voltage in that equation).

I can't find an authoritative source which gives the exact coefficients for a narrowband zirconia sensor, but I'd expect it to be identical to the equation you gave with the only difference being the values for the constants.

Also, since we are talking about a narrow band sensor in this case, the effect would be only on the narrow linear range of the sensor -- "too lean" or "too rich" voltages would be unchanged. Only the points at which the curve changes from flatline to linear would shift slightly.

• This answer would have been a lot prettier if we had MathJax available here. – Edward Jan 12 '16 at 15:50
• Makes sense, good analysis. It would be interesting to know how sensitive the sensor voltages are to changes in pressure – Zaid Jan 12 '16 at 18:23
• If I get ambitious, I'll make a little mathematical model and post the result to this answer. I don't currently have the kind of lab facilities to actually test real sensors. – Edward Jan 12 '16 at 18:28
• @Edward Very nice answer. Glad you are here taking these on. Very informative for me. TY. – DucatiKiller Jan 12 '16 at 18:31
• @Edward just to motivate you, I've seen some forum posts where an E39 M5 has its cats removed and the owner complained of flat performance thereafter. It would be interesting to see the extent to which this effect would explain such an observation – Zaid Jan 12 '16 at 18:58