Connunications update following Polls:

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Paul's right, all receivers have a local oscillator. And many other electrical gadgets too

These include:
Transistor radios for AM/FM/LW broadcasts
Mobile telephones
Electronic calculators
Televisions
Digital cameras
Computers
Sat Navs
Kindles
Digital clocks
Quartz wrist watches

The list goes on and on and on. Radio is at the heart of much of todays high technology.

But the radio output from these oscillators is tiny.

Who's going to be listening for these tiny signals post SHTF? I'd say no one at all.

And today, with so many devices giving off similar levels of local oscillator radio noise, it'd be quite difficult to find an individual CB receiver. And again, who's looking.... no one at all.

When constructing radios I sometimes have to listen for Local oscillator tone. The reality is that even out of its shielded metal box, and using a sensitive receiver 10 to 15 feet is the realistic range from which I can detect it. Once the radio is in its metal box this shields the Local oscilator and it can only be detected from a few feet away.

I'd say not to wory about being DF'd if you are just using a CB to receive. If someone's really looking so hard to find you that they are going to the trouble of Direction Finding Local oscillator signals, there will be plenty of easier ways for them to find you (noise, smell, heat, smoke, refuse etc)