Extending Output of a fixed Linear Voltage Regulator

I am working on extending output voltage of a fixed linear voltage regulator.Yes, I accept I could go for the variable voltage regulator.But I am in need to use a fixed voltage regulator. My query is regarding the derivation of Output Voltage (V0) given in Datasheet Can you help me to figure out how this equation rolls out?

• What don't you understand in that equation? Commented Feb 26, 2018 at 15:04
• @Leon Heller I don't know the derivation of V0.
– VKJ
Commented Feb 26, 2018 at 15:05
• Just use the equation. You don't have to know how it is derived. Commented Feb 26, 2018 at 15:07
• @ Leon Heller It would be helpful if u explain as u know how it is derived.
– VKJ
Commented Feb 26, 2018 at 15:08
• Do not use that circuit if the input voltage exceeds the delta V limit of the device.... Commented Feb 26, 2018 at 16:14

The output voltage $V_O$ will be whatever the regulator voltage is plus whatever the voltage is at the top of $R2$.

$V_O = V_{XX} + (I_{R2}) * R2$

So, to determine the voltage at the top of $R2$ you need to know the current going through it, $I_{R2}$.

That will be $I_Q$, the quiescent current of the device plus whatever current goes through $R1$.

$V_O = V_{XX} + (I_Q + I_{R1}) * R2$

Since $R1$ has the regulator voltage across it, we know:

$I_{R1} = V_{XX}/R1$

So, substituting for $I_{R1}$, we get:

=> $V_O = V_{XX} + (I_Q + V_{XX}/R1) * R2$

=> $V_O = V_{XX} + V_{XX}.R2/R1 + I_Q.R2$

=> $V_O= V_{XX}.(1 + R2/R1) + I_Q.R2$

Note: This circuit should never be used if the input voltage exceeds the maximum input voltage, $V_I$, of the regulator chosen. I have seen folks try to use this method in an attempt to "shoe-horn" the device to work at higher voltages, and, although once in a steady state it will work ok, sooner or later the initial start-up, or shut-down voltages will kill the device if you do not surround it with protection devices.

Iq is a sort-of constant current, typically in the 5mA range, that comes out of the regulator.

You can derive the equation for the output voltage by superposition, for example.