Re: Miss firing
Make sure of the first two characters of the DTC (diagnostic trouble code), ie, P(zero)XXX, meaning Powertrain(P), generic(0) followed by the definition.
P0114 would be IAT sensor 1 circuit intermittent = Intake air temperature sensor ckt could be a corroded connection or dirty sensor in the mass air flow sensor, if equipped with MAF or if Speed Density type EFI, a separate temp sensor in the air cleaner, or commonly placed in the intake manifold. Or a faulty sensor internally. Might even be a lack of reference voltage from the PCM, generally, +5 volts from the PCM and a reduced return voltage back to the PCM for monitoring.
P0144 would be O2 Sensor circuit high voltage. A broken internal sensor or since engine is misfiring, a high voltage output due to a rich mixture detected. I would consider this a secondary DTC.
P0300 would be as you suggest, random/multiple cyl misfire. Could be anything for any reason, bad coil, plug wire, spark plug, faulty injector, etc.
If you believe O2 sensor heater circuit, find the O2 sensor in the engine diagram and follow backwards its heater power from the power distribution, generally from a relay generally controlled by the PCM and/or fusible link or fuse and check to see if sensor is getting heater voltage and make sure sensor body has a good ground for completing the circuit. If there is power and a return, but no heat still, you can check the resistance of the heater coil by unplugging the connector and checking resistance of the heater through the sensor harness, should be a few ohms, not an open.
The input sensors get a reference voltage from the PCM, as said, +5 volts, and the PCM reads the return voltage. Depending upon the return voltage amount, it tells the PCM the condition of the operating engine. Example: coolant sensor - ambient temp or colder, resistance within sensor is high, above 5000 ohms. PCM reads a small amount of voltage through the circuit, cross references to a cold engine, the PCM increases the injector pulse to richen the mixture - makes injector open longer, as in closing the choke plate on a carburetor. As coolant heats up, sensor resistance goes down, generally to below 200 ohms, more voltage returns, injector pulse shortens in time decreasing the volume of fuel. By Federal mandate, engine has to be at the federal emissions spec after 90 seconds - read 'choke open' or out of enrichment mode - thus, PCM reads the O2 sensor - has to be heated by now, above 600°F, and PCM goes into 'closed loop mode' reading sensor output. MAF circuit reads the current drawn, ie, heated sensor wire by the PCM. More air drawn across the single strand of wire, more current given to keep wire heated. Current amount increase meaning more air is used, more fuel needed, so on and so on.
The PCM workings, EFI, can take volumes to explain, but hopefully, the above explanation will give some insight to your problem. This in ONLY the very top of the iceberg, about the first foot at the peak. The Haynes manual does explain the sensors function, but due to print space, is vague. Haynes does print a EFI manual explaining all EFI configurations and the differences between them.
Good luck. Think before executing.
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