Voltage is not really generated, current is, but let me use this colloquial term. What is limitation for generating electrical voltage very low (DC power supply)? What voltage is the real low limit just above 0?
Also if one wishes to generate a sinusoid function of very low amplitude above 0, what is the limitation of that amplitude?
Also if one wishes to generate a sinusoid function of very low amplitude above 0, what is the limitation of that amplitude?
You can generate a sinusoid with as low an amplitude as you like. Simply generate a 1 V sine wave, then attenuate it to the level you like. You could easily apply 100 dB attenuation, for example, giving 10 uV output; Then apply another 100 dB attenuation giving 100 pV amplitude; and so on.
The practical limitation is that there is inherent noise in any circuit, and a small enough signal will eventually be too small to detect relative to the noise. In a 50-ohm rf system with 1 Hz detection bandwidth, for example, you'd have about 0.9 nV rms noise inherent in the receiver, so any signal much below that would be very difficult to detect.
any lower voltage and you'll have to roll your own
As commented by 'PlasmaHH' that it depend on whether you are asking about a power supply or any other voltage generation method in lab.
Consider this one:
In BJT Ciruits currnets in the Base region(Ib) is nearly in uA range. You can easily generates a voltage in few mV/uV by using a small registor connected with Base and taking output across it.
You mention DC power supply, but you don't specify the output current capability, which maybe a limiting factor. Anyway, from a theoretical point of view, there is no limit, if you don't want high power: a simple opamp powered with dual supplies and connected as a voltage follower whose input is tied to the output of a voltage divider allows you to maintain a stable voltage equal to the voltage at the output of the divider. This may count as a "power supply". This in theory, neglecting the major limitation in low voltage tracking: noise.
If the generated voltage is too low it will be swamped by electrical noise, which depends on many factors: noise of the reference voltage, noise introduced by the opamp, environmental interferences, etc.
