(attempting to continue the conversation here based on exactly 0 knowledge of Russian, plus Google Translate
)
CHAPTER 1: Redox (reduction-oxidation) reactions, and your engine.
Oxygen sensors in general measure whether the atmosphere of the exhaust is reducing or oxidising. (warning: vast oversimplification incoming) If the environment is oxidising, there's an excess of oxygen. In a reducing environment, the opposite is true: it's oxygen deficient.
As you may have guessed, when an engine is running lean, there's an excess of oxygen in the exhaust. When it's rich, there are lots of chemicals in the exhaust that
really want to strip oxygen from somewhere.
More on this here:
https://en.wikipedia.org/wiki/Redox
Now let's apply this chemistry knowledge to engines. See the following diagram:
When lambda is <1 (engine is rich), the carbon monoxide content is very high. When it's >1 (engine is lean), it's very low, because carbon dioxide is produced instead. (The emissions of oxides of nitrogen, on the other hand, are caused by high combustion temperatures - that's why it increases until around lambda = 1.1, then decreases again as lean misfire causes temperature to reduce).
CHAPTER 2: what does this have to do with your O2 sensor?
Oxygen sensors have a piece of ceramic in them through which ions can diffuse, which creates a current (it's just flowing charge - electrons or not). A narrowband sensor just exploits this effect: High voltage (around 1v) means that there's a lot of oxygen trying to diffuse through, and low voltage (around 0v) means there isn't. Since it provides very little granularity about
how much oxygen is trying to flow across the cell, the characteristic curve of the sensor is very very steep at the lambda=1 point. A wideband O2 sensor simply adds the hardware to be able to sense how hard oxygen is trying to push across the cell, and in which direction.
The reason that vehicles with narrowband O2 sensors exhibit oscillation is that the sensor only provides information about whether lambda > 1 or not. So the computer slowly richens the mixture until lambda < 1, then slowly leans it out until lambda > 1 (and repeats).
CHAPTER 3: Hey, wasn't the original question about my catalytic converter?
Just like burning gasoline is a big redox reaction, so is your catalytic converter. Modern three-way cats do three reactions simultaneously:
1) Reduction of NOx to elemental nitrogen and oxygen:
NOx -> Nx + Ox
2) Oxidation of carbon monoxide to carbon dioxide:
CO + O2 -> CO2
3) Oxidation of hydrocarbons in to CO2 and water:
CxH4x + 2xO2 -> xCO2 -> 2xH2O
(note that steps 2 and 3 need oxygen to function - that's important)
It turns out that since these reactions are sort of at odds with each other (#1 prefers a reducing environment, while #2 and #3 prefer an oxidising environment), they all only work when you're right near the stoichiometric point. However: you get better catalyst performance if you oscillate the air-fuel ratio at 1-3hz. The large surface area of the catalyst can store significant amounts of oxygen, so it builds up during lean periods, then is consumed during rich periods.
(note: these reactions happen during combustion in the engine as well - it just doesn't do a very complete job of it. That's why you need a cat in the first place.)
CHAPTER 3b: So what's the downstream O2 sensor for/what's it supposed to see?
The ECU knows that the cat can store some oxygen, and it exploits this fact to check if it's working. Without a cat, one would expect a similar signal out of both O2 sensors: they should both oscillate more or less together, with a tiny phase shift. With a cat, the upstream sensor should oscillate as expected, but the downstream should either have a significant phase shift, or not oscillate at all. As the catalyst wears out, its capacity for storing oxygen is reduced, so the downstream gas composition will slowly become more like the upstream composition.