# Relationship between Vin and Vout of a linear voltage regulator in saturation region

Suppose we have a linear voltage regulator:

simulate this circuit – Schematic created using CircuitLab

If Vin is above Vth Vout is costant for all values Vin may take.However if Vin is below Vth what is the relationship between Vin and Vout?

• Some data sheets from manufacturers recommends diode for protection IC, like 7805, in this situation. It may cause the damage Dec 26, 2021 at 20:14

It depends on the internal circuitry of the regulator. If the manufacturer doesn't provide this information then you should not make any assumptions, except that the regulator no longer regulates. One thing you can be sure of is that $$\V_{out} \le V_{in}\$$

• Just observationally the difference is usually close to the rated dropout voltage. I.e., if $V_d$ is the dropout voltage, then $V_{out} \simeq V_{in} - V_d$. I'd trust this a lot more for input voltages just below what you need, and would expect it to not be true at all as the input voltage drops to well below the rated input. Dec 26, 2021 at 20:52

You have to rely on the data sheet. Some manufacturers provide schematics, but none of them claim that they are good for analyzing performance outside of recommended operating conditions: they're just to aid understanding how the part works. If you find a part that does have detailed performance data you can't depend on another part, from someone else, with the same generic number (like 7805) performing the same. If you test a part and find it meets your needs beyond the published specifications, you can't even assume that other parts from the same manufacturer also will. A later production run can be lots different. The only thing that counts is the data sheet.

Short answer: it depends

For a case where $$\V_{in} < V_{out} + V_{th}\$$ you'll have to refer to the datasheet again. Keep in mind, that you can get parts with the same number from different manufacturers. The internals of an 7805 from one manufacturer do not have to be the same as the 7805 of another one. So different things can happen.
• $$\V_{out} = V_{in} - V_{th}\$$ with no regulation
• $$\V_{out} = V_{in} - V_{min}\$$ (and $$\V_{min}\$$ can be $$\< V_{th}\$$)