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electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
, 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 o ...
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 electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to ...
(''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 electrical 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, 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 (informally a scope) is a type of electronic test instrument that graphically displays varying electrical voltages as a two-dimensional plot of one or more signals as a function of time. The main purposes are to display repetiti ...
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 Ground may refer to: Geology * Land, the surface of the Earth not covered by water * Soil, a mixture of clay, sand and organic matter present on the surface of the Earth Electricity * Ground (electricity), the reference point in an electrical c ...
is created by connecting two
electrical impedance In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit. Quantitatively, the impedance of a two-terminal circuit element is the ratio of the c ...
s 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
resistor A resistor is a passive two-terminal electrical 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 passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
s and
capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of ...
s. If the current in the output wire is zero then the relationship between the input voltage, Vin, and the output voltage, Vout, is: : V_\mathrm = \frac \cdot V_\mathrm Proof (using
Ohm's Law Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equa ...
):
:V_\mathrm = I\cdot(Z_1+Z_2) :V_\mathrm = I\cdot Z_2 :I = \frac :V_\mathrm = V_\mathrm \cdot\frac 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 mathematical function that theoretically models the system's output for each possible input. They are widely used ...
(also known as the divider's voltage ratio) of this circuit is: : H = \frac = \frac In general this transfer function is a complex,
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. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
.


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_\mathrm = \frac \cdot V_\mathrm If ''R''1 = ''R''2 then : V_\mathrm = \frac \cdot V_\mathrm If ''V''out = 6V and ''V''in = 9V (both commonly used voltages), then: : \frac = \frac = \frac = \frac and by solving using
algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...
, ''R''2 must be twice the value of ''R''1. To solve for R1: : R_1 = \frac - R_2 = R_2 \cdot \left(\right) To solve for R2: : R_2 = R_1 \cdot \frac 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 A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of ...
as shown in Figure 3. Comparing with the general case, we see Z1 = R and Z2 is the impedance of the capacitor, given by : Z_2 = -\mathrmX_ =\frac \ , where XC is the reactance of the capacitor, C is the
capacitance Capacitance is the capability of a material object or device 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 ...
of the capacitor, ''j'' is the
imaginary unit The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition an ...
, and ''ω'' (omega) is the radian frequency of the input voltage. This divider will then have the voltage ratio: : \frac = \frac = \frac = \frac \ . The product ''τ (tau) = RC'' is called the ''
time constant In physics and engineering, the time constant, usually denoted by the Greek letter (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system.Concretely, a first-order LTI system is a s ...
'' 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)
lowpass 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 filter ...
. The ratio contains an imaginary number, and actually contains both the amplitude and
phase shift In physics and mathematics, the phase of a 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 denoted \phi(t) and expressed in such a scale that it ...
information of the filter. To extract just the amplitude ratio, calculate the magnitude of the ratio, that is: : \left, \frac \ = \frac \ .


Inductive divider

Inductive dividers split AC input according to inductance: V_\mathrm = \frac \cdot V_\mathrm (with components in the same positions as Figure 2.) The above equation is for non-interacting inductors; mutual inductance (as in an autotransformer) will alter the results. Inductive dividers split AC input according to the resistance 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: V_\mathrm = \frac \cdot V_\mathrm = \frac \cdot V_\mathrm = \frac \cdot V_\mathrm (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 (informally a scope) is a type of electronic test instrument that graphically displays varying electrical voltages as a two-dimensional plot of one or more signals as a function of time. The main purposes are to display repetiti ...
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. The effective source impedance coming from a divider of Z1 and Z2, as above, will be Z1 in
parallel Parallel is a geometric term of location which may refer to: Computing * Parallel algorithm * Parallel computing * Parallel metaheuristic * Parallel (software), a UNIX utility for running programs in parallel * Parallel Sysplex, a cluster o ...
with Z2 (sometimes written Z1 // Z2), that is: (Z1 Z2) / (Z1 + Z2)=HZ1. 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. A voltage regulator may use a simple feed-forward design or may include negative feedback. It may use an electromechanical mechanism, or electronic components ...
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 provid ...
and a
multimeter A multimeter is a measuring instrument that can measure multiple electrical properties. A typical multimeter can measure voltage, resistance, and current, in which case it is also known as a volt-ohm-milliammeter (VOM), as the unit is equipped w ...
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 type of resistor whose resistance is strongly dependent on temperature, more so than in standard resistors. The word thermistor is a portmanteau of ''thermal'' and ''resistor''. Thermistors are divided based on their conduction ...
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 A voltmeter is an instrument used for measuring electric potential difference between two points in an electric circuit. It is connected in parallel. It usually has a high resistance so that it takes negligible current from the circuit. Ana ...
. 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 5V whereas others operate at 3.3V. Directly interfacing a 5V logic output to a 3.3V input may cause permanent damage to the 3.3V circuit. In this case, a voltage divider with an output ratio of 3.3/5 might be used to reduce the 5V signal to 3.3V, to allow the circuits to interoperate without damaging the 3.3V circuit. For this to be feasible, the 5V source impedance and 3.3V 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 converter. Power levels range from very low (small batteries) ...
* Voltage amplifier


References

{{DEFAULTSORT:Voltage Divider Analog circuits Divider