Voltage divider
In
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 frequencies. For direct current and relatively low 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:
Proof (using Ohm's law):
The transfer function (also known as the divider's voltage ratio) of this circuit is:
In general this transfer function is a
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:
If R1 = R2 then
If Vout = 6 V and Vin = 9 V (both commonly used voltages), then:
and by solving using algebra, R2 must be twice the value of R1.
To solve for R1:
To solve for R2:
Any ratio Vout / Vin greater than 1 is not possible. That is, using resistors alone it is not possible to either invert the voltage or increase Vout above Vin.
Low-pass RC filter
Consider a divider consisting of a resistor and capacitor as shown in Figure 3.
Comparing with the general case, we see Z1 = R and Z2 is the impedance of the capacitor, given by
where XC is the
This divider will then have the voltage ratio:
The product τ (tau) = RC is called the time constant of the circuit.
The ratio then depends on frequency, in this case decreasing as frequency increases. This circuit is, in fact, a basic (first-order)
Inductive divider
Inductive dividers split AC input according to inductance:
(with components in the same positions as Figure 2.)
The above equation is for non-interacting inductors;
Inductive dividers split AC input according to the reactance of the elements as for the resistive divider above.
Capacitive divider
Capacitive dividers do not pass DC input.
For an AC input a simple capacitive equation is:
(with components in the same positions as Figure 2.)
Any leakage current in the capactive elements requires use of the generalized expression with two impedances. By selection of parallel R and C elements in the proper proportions, the same division ratio can be maintained over a useful range of frequencies. This is the principle applied in compensated oscilloscope probes to increase measurement bandwidth.
Loading effect
The output voltage of a voltage divider will vary according to the electric current it is supplying to its external
To obtain a sufficiently stable output voltage, the output current must either be stable (and so be made part of the calculation of the potential divider values) or limited to an appropriately small percentage of the divider's input current. Load sensitivity can be decreased by reducing the impedance of both halves of the divider, though this increases the divider's quiescent input current and results in higher power consumption (and wasted heat) in the divider.[1] Voltage regulators are often used in lieu of passive voltage dividers when it is necessary to accommodate high or fluctuating load currents.
Applications
Voltage dividers are used for adjusting the level of a signal, for bias of active devices in amplifiers, and for measurement of voltages. A Wheatstone bridge and a multimeter both include voltage dividers. A potentiometer is used as a variable voltage divider in the volume control of many radios.
Sensor measurement
Voltage dividers can be used to allow a microcontroller to measure the resistance of a sensor.
Another example that is commonly used involves a potentiometer (variable resistor) as one of the resistive elements. When the shaft of the potentiometer is rotated the resistance it produces either increases or decreases, the change in resistance corresponds to the angular change of the shaft. If coupled with a stable voltage reference, the output voltage can be fed into an analog-to-digital converter and a display can show the angle. Such circuits are commonly used in reading control knobs.
High voltage measurement
A voltage divider can be used to scale down a very
Logic level shifting
A voltage divider can be used as a crude
See also
- Current divider
- DC-to-DC converter
- Voltage amplifier
References
- Texas Instruments Incorporated. June 2020 [February 2020]. p. 11. SCLS801A. Archived(PDF) from the original on 2023-07-20. Retrieved 2023-07-20. p. 11:
It is required for the R1 resistor to be at least ten times larger than R2 to avoid a divider circuit (R2 ≤ 10 R1).
(23 pages) - ^ "A very quick and dirty introduction to Sensors, Microcontrollers, and Electronics; Part Three: how sensors and actuators work and how to hook them up to a microcontroller" (PDF). 2014-07-02. Archived (PDF) from the original on 2023-07-20. Retrieved 2015-11-02.