Inelectronics, avoltage divider (also known as apotential divider) is apassivelinear circuit that produces an outputvoltage (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 tworesistors connected inseries, 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 signalattenuators at lowalternating current frequencies. Fordirect current and relatively low alternating current frequencies, a voltage divider may be sufficiently accurate if made only of resistors; wherefrequency response over a wide range is required (such as in anoscilloscope probe), a voltage divider may havecapacitive elements added to compensate load capacitance. Inelectric power transmission, a capacitive voltage divider is used for measurement of high voltage.
A voltage divider referenced toground is created by connecting twoelectrical impedances in series, as shown in Figure 1. The input voltage is applied across the series impedancesZ1 andZ2 and the output is the voltage acrossZ2.Z1 andZ2 may be composed of any combination of elements such asresistors,inductors andcapacitors.
If the current in the output wire is zero then the relationship between the input voltage,Vin, and the output voltage,Vout, is:
Proof (usingOhm's law):
Thetransfer function (also known as the divider'svoltage ratio) of this circuit is:
In general this transfer function is acomplex,rational function offrequency.
A resistive divider is the case where both impedances,Z1 andZ2, are purely resistive (Figure 2).
SubstitutingZ1 =R1 andZ2 = R2 into the previous expression gives:
IfR1 =R2 then
IfVout = 6 V andVin = 9 V (both commonly used voltages), then:
and by solving usingalgebra,R2 must be twice the value ofR1.
To solve forR1:
To solve forR2:
Any ratioVout /Vin greater than 1 is not possible. That is, using resistors alone it is not possible to either invert the voltage or increaseVout aboveVin.
Consider a divider consisting of a resistor andcapacitor as shown in Figure 3.
Comparing with the general case, we seeZ1 =R andZ2 is the impedance of the capacitor, given by
whereXC is thereactance of the capacitor,C is thecapacitance of the capacitor,j is theimaginary unit, andω (omega) is theradian frequency of the input voltage.
This divider will then have the voltage ratio:
The productτ (tau) =RC is called thetime 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)low-pass filter. The ratio contains an imaginary number, and actually contains both the amplitude andphase shift information of the filter. To extract just the amplitude ratio, calculate themagnitude of the ratio, that is:
Inductive dividers split AC input according toinductance:
(with components in the same positions as Figure 2.)
The above equation is for non-interacting inductors;mutual inductance (as in anautotransformer) will alter the results.
Inductive dividers split AC input according to the reactance of the elements as for the resistive divider above.
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 parallelR andC elements in the proper proportions, the same division ratio can be maintained over a useful range of frequencies. This is the principle applied in compensatedoscilloscope probes to increase measurement bandwidth.
The output voltage of a voltage divider will vary according to the electric current it is supplying to its externalelectrical load. The effective source impedance coming from a divider ofZ1 andZ2, as above, will beZ1 inparallel withZ2 (sometimes writtenZ1||Z2), that is: (Z1Z2) / (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.[1]Voltage regulators are often used in lieu of passive voltage dividers when it is necessary to accommodate high or fluctuating load currents.
Voltage dividers are used for adjusting the level of a signal, for bias of active devices in amplifiers, and for measurement of voltages. AWheatstone bridge and amultimeter both include voltage dividers. Apotentiometer is used as a variable voltage divider in the volume control of many radios.
Voltage dividers can be used to allow a microcontroller to measure the resistance of a sensor.[2] 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 asthermistors andRTDs.
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.
A voltage divider can be used to scale down a veryhigh voltage so that it can be measured by avolt 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 matchedtemperature coefficients 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.
A voltage divider can be used as a crudelogic 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.
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)
