In
electronics
Electronics is a scientific and engineering discipline that studies and applies the principles of physics to design, create, and operate devices that manipulate electrons and other Electric charge, electrically charged particles. It is a subfield ...
, a voltage divider (also known as a potential divider) is a
passive
Passive may refer to:
* Passive voice, a grammatical voice common in many languages, see also Pseudopassive
* Passive language, a language from which an interpreter works
* Passivity (behavior), the condition of submitting to the influence of ...
linear circuit
A linear circuit is an electronic circuit which obeys the superposition principle. This means that the output of the circuit ''F(x)'' when a linear combination of signals ''ax1(t) + bx2(t)'' is applied to it is equal to the linear combination o ...
that produces an output
voltage
Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...
(''V''
out) that is a fraction of its input voltage (''V''
in). 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
resistor
A resistor is a passive two-terminal electronic component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active e ...
s connected in
series
Series may refer to:
People with the name
* Caroline Series (born 1951), English mathematician, daughter of George Series
* George Series (1920–1995), English physicist
Arts, entertainment, and media
Music
* Series, the ordered sets used i ...
, 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 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
An oscilloscope (formerly known as an oscillograph, informally scope or O-scope) is a type of electronic test instrument that graphically displays varying voltages of one or more signals as a function of time. Their main purpose is capturing i ...
probe), a voltage divider may have capacitive elements added to compensate load capacitance. In
electric power transmission
Electric power transmission is the bulk movement of electrical energy from a generating site, such as a power plant, to an electrical substation. The interconnected lines that facilitate this movement form a ''transmission network''. This is ...
, 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 impedance
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of Electrical_resistance, resistance and Electrical_reactance, reactance in a electrical circuit, circuit.
Quantitatively, the impedan ...
s in series, as shown in Figure 1. The input voltage is applied across the series impedances ''Z''
1 and ''Z''
2 and the output is the voltage across ''Z''
2.
''Z''
1 and ''Z''
2 may be composed of any combination of elements such as
resistor
A resistor is a passive two-terminal electronic component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active e ...
s,
inductor
An inductor, also called a coil, choke, or reactor, is a Passivity (engineering), passive two-terminal electronic component, electrical component that stores energy in a magnetic field when an electric current flows through it. An inductor typic ...
s and
capacitor
In electrical engineering, a capacitor is a device that stores electrical energy by accumulating electric charges on two closely spaced surfaces that are insulated from each other. The capacitor was originally known as the condenser, a term st ...
s.
If the current in the output wire is zero then the relationship between the input voltage, ''V''
in, and the output voltage, ''V''
out, is:
:
Proof (using
Ohm's law
Ohm's law states that the electric current through a Electrical conductor, conductor between two Node (circuits), points is directly Proportionality (mathematics), proportional to the voltage across the two points. Introducing the constant of ...
):
:
:
:
:
The
transfer function
In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a function (mathematics), mathematical function that mathematical model, models the system's output for each possible ...
(also known as the divider's voltage ratio) of this circuit is:
:
In general this transfer function is a
complex
Complex commonly refers to:
* Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe
** Complex system, a system composed of many components which may interact with each ...
,
rational function
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be ...
of
frequency
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
.
Examples
Resistive divider

A resistive divider is the case where both impedances, ''Z''
1 and ''Z''
2, are purely resistive (Figure 2).
Substituting ''Z''
1 = ''R''
1 and ''Z''
2 = R
2 into the previous expression gives:
:
If ''R''
1 = ''R''
2 then
:
If ''V''
out = 6 V and ''V''
in = 9 V (both commonly used voltages), then:
:
and by solving using
algebra
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...
, ''R''
2 must be twice the value of ''R''
1.
To solve for ''R''
1:
:
To solve for ''R''
2:
:
Any ratio ''V''
out / ''V''
in greater than 1 is not possible. That is, using resistors alone it is not possible to either invert the voltage or increase ''V''
out above ''V''
in.
Low-pass RC filter

Consider a divider consisting of a resistor and
capacitor
In electrical engineering, a capacitor is a device that stores electrical energy by accumulating electric charges on two closely spaced surfaces that are insulated from each other. The capacitor was originally known as the condenser, a term st ...
as shown in Figure 3.
Comparing with the general case, we see ''Z''
1 = ''R'' and ''Z''
2 is the impedance of the capacitor, given by
:
where ''X''
C is the
reactance of the capacitor, ''C'' is the
capacitance
Capacitance is the ability of an object to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related ...
of the capacitor, ''j'' is the
imaginary unit
The imaginary unit or unit imaginary number () is a mathematical constant that is a solution to the quadratic equation Although there is no real number with this property, can be used to extend the real numbers to what are called complex num ...
, and ''ω'' (omega) is the
radian frequency
In physics, angular frequency (symbol ''ω''), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine fu ...
of the input voltage.
This divider will then have the voltage ratio:
:
The product ''τ'' (tau) = ''RC'' is called the ''
time constant
In physics and engineering, the time constant, usually denoted by the Greek language, Greek letter (tau), is the parameter characterizing the response to a step input of a first-order, LTI system theory, linear time-invariant (LTI) system.Concre ...
'' 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)
low-pass filter
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filt ...
. The ratio contains an imaginary number, and actually contains both the amplitude and
phase shift
In physics and mathematics, the phase (symbol φ or ϕ) of a wave or other periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is expressed in such a s ...
information of the filter. To extract just the amplitude ratio, calculate the
magnitude
Magnitude may refer to:
Mathematics
*Euclidean vector, a quantity defined by both its magnitude and its direction
*Magnitude (mathematics), the relative size of an object
*Norm (mathematics), a term for the size or length of a vector
*Order of ...
of the ratio, that is:
:
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;
mutual inductance (as in an
autotransformer
In electrical engineering, an autotransformer is an electrical transformer with only one winding. The " auto" (Greek for "self") prefix refers to the single coil acting alone. In an autotransformer, portions of the same winding act as both the p ...
) will alter the results.
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
An oscilloscope (formerly known as an oscillograph, informally scope or O-scope) is a type of electronic test instrument that graphically displays varying voltages of one or more signals as a function of time. Their main purpose is capturing i ...
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
electrical load
An electrical load is an electrical component or portion of a Electric Circuit, circuit that consumes (active) electric power, such as electrical appliances and Electric light, lights inside the home. The term may also refer to the power Power con ...
. The effective source impedance coming from a divider of ''Z''
1 and ''Z''
2, as above, will be ''Z''
1 in
parallel with ''Z''
2 (sometimes written ''Z''
1 // ''Z''
2), that is: (''Z''
1 ''Z''
2) / (''Z''
1 + ''Z''
2) = ''HZ''
1.
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.
[ ]Voltage regulator
A voltage regulator is a system designed to automatically maintain a constant voltage. It may use a simple feed-forward design or may include negative feedback. It may use an electromechanical mechanism or electronic components. Depending on the ...
s 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
A Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. The primary benefit of the circuit is its ability to prov ...
and a multimeter
A multimeter (also known as a multi-tester, volt-ohm-milliammeter, volt-ohmmeter or VOM, avometer or ampere-volt-ohmmeter) is a measuring instrument that can measure multiple electrical properties. A typical multimeter can measure voltage, elec ...
both include voltage dividers. A potentiometer
A potentiometer is a three- terminal resistor with a sliding or rotating contact that forms an adjustable voltage divider. If only two terminals are used, one end and the wiper, it acts as a variable resistor or rheostat.
The measuring instrum ...
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.[ The sensor is wired in series with a known resistance to form a voltage divider and a known voltage is applied across the divider. The microcontroller's analog-to-digital converter is connected to the center tap of the divider so that it can measure the tap voltage and, by using the measured voltage and the known resistance and voltage, compute the sensor resistance. This technique is commonly used to measure the resistance of temperature sensors such as ]thermistor
A thermistor is a semiconductor type of resistor in which the resistance is strongly dependent on temperature. The word ''thermistor'' is a portmanteau of ''thermal'' and ''resistor''. The varying resistance with temperature allows these devices ...
s and RTDs.
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 high voltage
High voltage electricity refers to electrical potential large enough to cause injury or damage. In certain industries, ''high voltage'' refers to voltage above a certain threshold. Equipment and conductors that carry high voltage warrant sp ...
so that it can be measured by a volt meter. The high voltage is applied across the divider, and the divider output—which outputs a lower voltage that is within the meter's input range—is measured by the meter. High voltage resistor divider probes designed specifically for this purpose can be used to measure voltages up to 100 kV. Special high-voltage resistors are used in such probes as they must be able to tolerate high input voltages and, to produce accurate results, must have matched temperature coefficient
A temperature coefficient describes the relative change of a physical property that is associated with a given change in temperature. For a property ''R'' that changes when the temperature changes by ''dT'', the temperature coefficient α is def ...
s and very low voltage coefficients. Capacitive divider probes are typically used for voltages above 100 kV, as the heat caused by power losses in resistor divider probes at such high voltages could be excessive.
Logic level shifting
A voltage divider can be used as a crude logic level shifter to interface two circuits that use different operating voltages. For example, some logic circuits operate at 5 V whereas others operate at 3.3 V. Directly interfacing a 5 V logic output to a 3.3 V input may cause permanent damage to the 3.3 V circuit. In this case, a voltage divider with an output ratio of 3.3/5 might be used to reduce the 5 V signal to 3.3 V, to allow the circuits to interoperate without damaging the 3.3 V circuit. For this to be feasible, the 5 V source impedance and 3.3 V input impedance must be negligible, or they must be constant and the divider resistor values must account for their impedances. If the input impedance is capacitive, a purely resistive divider will limit the data rate. This can be roughly overcome by adding a capacitor in series with the top resistor, to make both legs of the divider capacitive as well as resistive.
See also
* Current divider
* DC-to-DC converter
A DC-to-DC converter is an electronic circuit or electromechanical device that converts a source of direct current (DC) from one voltage level to another. It is a type of Electric power conversion, electric power converter. Power levels range from ...
* Voltage amplifier
References
External links
Voltage Divider Calculator
{{DEFAULTSORT:Voltage Divider
Analog circuits
Divider