In electronics, a voltage divider (also known as a potential divider) is a passive linear circuit that produces an output voltage (Vout) that is a fraction of its input voltage (Vin). Voltage division is the result of distributing the input voltage among the components of the divider. A simple example of a voltage divider is two resistors connected in series, with the input voltage applied across the resistor pair and the output voltage emerging from the connection between them. Resistor voltage dividers are commonly used to create reference voltages, or to reduce the magnitude of a voltage so it can be measured, and may also be used as signal attenuators at low alternating current frequencies. For direct current and relatively low alternating current frequencies, a voltage divider may be sufficiently accurate if made only of resistors; where frequency response over a wide range is required (such as in an oscilloscope probe), a voltage divider may have capacitive elements added to compensate load capacitance. In electric power transmission, a capacitive voltage divider is used for measurement of high voltage.
General case
A voltage divider referenced to ground is created by connecting two electrical impedances in series, as shown in Figure 1. The input voltage is applied across the series impedances Z1 and Z2 and the output is the voltage across Z2. Z1 and Z2 may be composed of any combination of elements such as resistors, inductors and capacitors. If the current in the output wire is zero then the relationship between the input voltage, Vin, and the output voltage, Vout, is:
V o u t = Z 2 Z 1 + Z 2 ⋅ V i n {\displaystyle V_{\mathrm {out} }={\frac {Z_{2}}{Z_{1}+Z_{2}}}\cdot V_{\mathrm {in} }}
Proof (using Ohm's law):
V i n = I ⋅ ( Z 1 + Z 2 ) {\displaystyle V_{\mathrm {in} }=I\cdot (Z_{1}+Z_{2})}
V o u t = I ⋅ Z 2 {\displaystyle V_{\mathrm {out} }=I\cdot Z_{2}}
I = V i n Z 1 + Z 2 {\displaystyle I={\frac {V_{\mathrm {in} }}{Z_{1}+Z_{2}}}}
V o u t = V i n ⋅ Z 2 Z 1 + Z 2 {\displaystyle V_{\mathrm {out} }=V_{\mathrm {in} }\cdot {\frac {Z_{2}}{Z_{1}+Z_{2}}}}
The transfer function (also known as the divider's voltage ratio) of this circuit is:
H = V o u t V i n = Z 2 Z 1 + Z 2 {\displaystyle H={\frac {V_{\mathrm {out} }}{V_{\mathrm {in} }}}={\frac {Z_{2}}{Z_{1}+Z_{2}}}}
In general this transfer function is a complex, rational function of frequency.
Examples
Resistive divider
A resistive divider is the case where both impedances, Z1 and Z2, are purely resistive (Figure 2). Substituting Z1 = R1 and Z2 = R2 into the previous expression gives:
V o u t = R 2 R 1 + R 2 ⋅ V i n {\displaystyle V_{\mathrm {out} }={\frac {R_{2}}{R_{1}+R_{2}}}\cdot V_{\mathrm {in} }}
If R1 = R2 then
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