Voltage Divider - General Case

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.

Applying Ohm's Law, the relationship between the input voltage, Vin, and the output voltage, Vout, can be found:

V_\mathrm{out} = \frac{Z_2}{Z_1+Z_2} \cdot V_\mathrm{in}

Proof:

The transfer function (also known as the divider's voltage ratio) of this circuit is simply:

H = \frac {V_{out}}{V_{in}} = \frac{Z_2}{Z_1+Z_2}

In general this transfer function is a complex, rational function of frequency.


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