Voltage divider

The voltage divider is a series combination of passive electrical two poles, is divided by an electrical voltage.

Magnetic circuits with respect to the term voltage divider is also used to describe the distribution of the magnetic power ( flux ) along magnetic resistances.

• 3.1 Example with multiple applications
• 3.2 Example of magnetic circuit

Simple voltage divider with two ohmic resistors

The voltage divider is described in the standard case by the series connection of two ohmic resistors.

For the calculation of the partial voltage V2 across R2 is the total resistance by the number of circuits for control is first calculated as follows:

The total voltage and the values ​​of resistors are generally known, which can be determined according to the Ohm's law, the current I:

According to the rules for series circuits the current is the same through all components and thus results in the desired U2 to:

Is the formula used for the common power here, the output voltage is a function of the dividing resistors and the input voltage in general:

Equivalence transformation further generalized by the following relationship between the input and output voltage in response to the divider resistors.

This transformed expression is readily apparent that the ratio of the voltage drop across to the total voltage is identical to the ratio of resistance to the total resistance and.

Voltage divider rule

By means of the voltage divider rule, partial voltages can be calculated directly from the partial resistors and the total voltage. The final equation for the previous circuit represents the special case of the voltage divider rule for exactly two partial resistances represents the voltage divider rule is applicable only when all the components to which the total voltage is divided, are linear and passive. Once active components such as occur sources, must be used on the node potential method or mesh current method.

Verbal is the voltage divider rule:

Generalized to n series-connected resistors ( i = 1, ..., n) are obtained for the partial voltage across the resistor k, the following equations for the respective applications (where n and k is an integer, n ≥ 1, 1 ≤ k ≤ n ). Resistance in parallel connections must first be combined to form a resistance in order to correspond to the equations in the form shown. The total resistance of only refers to the resistance, the overall voltage drop across the. Any resistors that are under consideration for section before, after or in parallel branches will not be considered. For circuits with two inner parallel branches, the formula may need to be applied several times to obtain the desired voltage part.

DC case

With DC voltage occur only real-valued resistor values ​​, to so-called ohmic resistors.

With direct voltage, the individual part voltages are always lower than the total voltage. The ratio of the divided voltage to the total voltage takes values ​​between 0 and 1. A typical example of an adjustable voltage divider is a potentiometer, wherein the division ratio can be variably set via a movable contact on a continuous resistor body. Partial voltages are proportional to the resistances through which they fall. That is, the smaller ( larger), the resistance, the smaller ( larger) the divided voltage.

AC case

When can ω harmonic AC voltage at a constant angular frequency additionally complex resistors, so-called impedances, in the form of capacity ( capacitive voltage divider ) and inductance ( inductive voltage dividers ) may occur. The calculation of a voltage divider is then a part of the complex AC circuit analysis.

For AC voltage and impedances occur the part voltages on the capacitors and inductors through resonance can be the energy storage in the impedances greater than the total voltage. It is important in the application of the voltage divider rule, with an alternating voltage, that the impedances, in particular inductances, are not mutually coupled by means of its stored energy in the electrical or magnetic field. This fact is equivalent to the requirement of passive two poles which have no voltage or current sources.

Magnetic circuits

In magnetic circuits, the magnetic tension splits only on magnetic resistance.

Examples

Example with multiple applications

We are looking for the voltage across the adjacent circuit. Due to the nested position of the resistance, a repeated application of the voltage divider rule is necessary. For this, the voltage is calculated by the parallel circuit. The voltage divider rule yields the equation:

With

The partial voltage divided from the series circuit and. By repeated application of the voltage divider rule, the voltage is determined by a function of:

If both equations are multiplied together, produce an overall equation in which is directly dependent on U:

Example of magnetic circuit

In magnetic circuits, the rule is applied the same way. For the partial voltages across and the resulting equations:

Or for the other branch

The total resistance:

Charged voltage divider

In the circuit in the section Simple voltage divider with two ohmic resistors is at the terminals of R2 of the output. There is a consumer is connected to the resistor R2 in parallel, creating a loaded voltage divider for the voltage calculations have to be performed again. The resistance of the parallel circuit, and is smaller than the smallest component resistor of the parallel circuit. It is calculated with:

As a result of reducing the resistance the voltage drops after the voltage divider rule proportionally. It results now:

To illustrate the influence of the load resistor, the original circuit without RL can be converted into a Zweipolersatzschaltung a replacement voltage source U2, LL and a internal resistance Ri. According to the rules for the calculation of equivalent circuits for active two-terminal result for this example the following equations:

The load resistance is not affected by the change and its effect on the output voltage of the voltage divider protrudes significantly. It now creates a simpler voltage divider consisting of R and RL.

With the help of Ri can express a recommendation on the appropriate selection of resistors. So that the load resistance has a small influence on the output voltage, the internal resistance should have a significantly smaller value than the load.

Application

The application examples overlap with the applications of potentiometers ( variable voltage divider ). Voltage dividers are used:

• For level matching
• In attenuators, eg also for volume control
• For voltage measurement; Multimeters have a switchable voltage divider for measuring in different areas.
• In probes for oscilloscopes: here are mostly voltage divider with divider ratios of 10 to find 1 or 100 to 1. These probes (English probes ) in addition to the resistive voltage divider having a frequency compensation, which compensates for the cable and input capacitance for AC voltage measurements. The compensation is often adjustable or calibratable. It represents a plane parallel capacitive voltage divider
• High voltage metering (high-voltage probes or probes ); Divider ratios of 1000:1 or greater. Input voltages up to 40 kV are common. The upper part of resistance is about 1 ... 100 Gohms, often, the input resistance of the measuring device is taken into account ( for example, 1 or 10 MOhm ). High-voltage probes, there are uncompensated for DC measurements, but also frequency compensated for AC voltage measurements.
• Inductive and resistive voltage dividers are used to position and angle determination and used in accelerometers. The inductive voltage divider employed for this work without contacts with a sliding soft magnetic core as a double variometer.
• Inductive voltage divider provide in metrology precision voltage ratios that are almost exclusively by the turns ratio of the transformer being used. Inductive voltage dividers are available with fixed voltage ratios as well as adjustable decades in use.
• To create a bridge circuit by combining of voltage dividers.
• A special design with fixed resistors and step switch for switching, the Kelvin - Varley voltage divider dar. It allows repeatable adjustment of the values ​​of the voltage divider ratio.