Explain to me all these offset concepts

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Adding a DC offset to an AC signal, such as a sine wave, involves incorporating a constant voltage term, resulting in a new waveform that combines both AC and DC components. This process shifts the entire waveform vertically on a graph, which can be essential for various applications, such as telecommunication systems. For instance, in a POTS line, a -48V DC offset is used to power the phone while allowing AC signals for audio transmission. To remove the DC offset and return to an AC-only signal, a DC blocking capacitor can be utilized. Understanding these concepts is crucial for effectively managing signal processing in electronic communications.
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Maybe I'm just really dense here but can someone please explain to me all these offset concepts like what does it mean to add a DC offset and what does adding a DC offset do to an AC signal? For instance, adding it to a sine wave or whatever other waveforms and decreasing it. Can someone please explain the general concept of it. Also, what is offset voltage? I just don't really understand these concepts. Thank you!
 
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If you have an AC voltage like V(t) = Asin(wt), then adding a DC offset just is adding a DC term V(t) = Vdc + Asin(wt). Or if you have the second waveform with the DC offset and you want to eliminate the DC offset, you can often just use a DC blocking capacitor in series with the signal source to get back to the AC-only waveform (where the average voltage over time is zero).

One practical example is a POTS line (plain old telephone service). The telco standard is a -48V DC voltage across the tip and ring wires when the phone is on-hook. To ring the mechanical bell for an incoming call, a large AC voltage is added to the -48Vdc. When you pick up the handset, the DC voltage falls from -48V to about -5V or so (I forget). When you speak into the microphone or push the DTMF tone buttons to dial, the AC audio waveform is combined with the DC offset as the waveform that is on the tip-ring wire pair. If you are using an oscilloscope at 1V/div to watch the waveform (careful -- the POTS voltages are already referenced to Earth ground, so you have to be sure to put your scope ground on the correct wire), you would see about a 5 division offset down from 0V when the phone is offhook, and then as you push the buttons, you'd see the AC audio dual tone riding on top of the average -5Vdc. Make sense?

The most common use of a DC offset is to combine power with data transmission. That's why the POTS has a DC offset -- to power the telephones from the central office.
 
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