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in many circuits (Amplifiers, Filters etc) at the input terminal I saw a sinusoidal voltage together with a DC term, i.e. a voltage like v(t) = sin(wt) + 1 [V]. We may imagine that this signal is produced by the series between an AC voltage source and a DC voltage source, as shown in the following picture:

enter image description here

Now my questions are:

1) I saw the previous scheme in a lot of theoretical analysis of circuits. But is it physically possible to connect an AC voltage source and a DC voltage source in that way? Or is there the risk of damaging them?

2) If this connection is allowed, is it ok for any frequency? May for instance an AC radiofrequency voltage source create a disturb on a DC voltage source?

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For it to work in real life a few requirements need to be met:

If the AC amplitude is high enough and the DC bias is low enough that the current flow through the DC source actually reverses, then the DC source needs to be able to both source and sink current. Many can only source current.

Your schematic only shows the output terminals of both sources, but if they are not true sources (like a battery) but are instead actually voltage regulators (like a bench supply) then they will have input terminals as well. In that case, at least one supply must be constructed so their input and output terminals are isolated from each other otherwise a short-circuit will occur somewhere.

It will not work at all frequencies because the DC source has to be able to pass low impedance for the the AC frequency. This is dependent on the construction of the DC source. You can't expect a 100MHz wave to be able to travel through the terminals of just any DC source cleanly with little attenuation.

Conversely, depending on how the AC source is constructed, it may not like the DC bias introduced across its outputs (i.e. if it had a transformer output and the DC-bias was high enough to saturate the core).

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1) I saw the previous scheme in a lot of theoretical analysis of circuits. But is it physically possible to connect an AC voltage source and a DC voltage source in that way? Or is there the risk of damaging them?

Yes it is , if you have an isolated power supply then there should be no problem with this setup. Assuming that you don't violate some current, voltage or power condition on the supplies.

An isolated supply has independent outputs from any other ground or power, and can be floated. Usually the isolation barrier is the limit to what voltage either terminal of the supply can float to with respect to it's ground.

If this connection is allowed, is it ok for any frequency? May for instance an AC radio frequency voltage source create a disturb on a DC voltage source?

Most power supplies are built for low frequencies (under 100Hz) and running a large amount of RF power into them is probably not a good idea. I'd consult with the manufacturer of the supplies if I want to run a setup like this for RF purposes.

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