Voltage Divider

If two circuit elements are in series, there is a voltage drop across each element, but the current through both must be the same. The voltage at any point in the chain divides according to the resistances. A simple circuit with two (or more) resistors in series with a source is called a voltage divider.

Figure A: Voltage Divider circuit.

Transfer Function of Voltage Divider

Consider the circuit in Figure A. According to KVL the voltage ${\displaystyle V_{in}}$ is dropped across resistors ${\displaystyle R_{1}}$ and ${\displaystyle R_{2}}$. If a current i flows through the two series resistors then by Ohm's Law.

${\displaystyle i={\frac {V_{in}}{R_{1}+R_{2}}}}$.

So

${\displaystyle V_{out}=iR_{2}\,\!}$

Therefore

${\displaystyle V_{out}=V_{in}{\frac {R_{2}}{R_{1}+R_{2}}}}$

${\displaystyle V_{out}=V_{in}{\frac {R_{2}}{R_{1}+R_{2}}}}$