Current divider
The power splitter is a parallel circuit comprising the passive electrical or magnetic bipoles, through which an electric current or a magnetic flux into a plurality of partial streams / flows is divided.
Power divider for AC can also be realized with transformers, they are then called current transformers.
General current divider rule
For ease of calculation of the partial currents to offer the current divider rule. This rule applies only if all branches to which divides the total current are passive. In direct current, these are ohmic resistors. In alternating current, capacitors ( capacitive current divider ) and coils ( inductive current divider ) would be possible. In magnetic circuits, there is only magnetic resistances. Once active components such as sources occur, must be made to the mesh current method. Common applications for the current divider rule even with calculation of a network using the superposition method.
The current divider rule:
Expressed or with guide:
With
Generalized to n parallel branches (i = 1 .. n) are obtained for the current in branch k:
- For resistive circuits
The total resistance and the total conductance
- For complex circuits
With the total impedance and the total admittance
- For magnetic circuits
The total resistance and the total conductance
The resistances of each branch to be first of all combined to form a resistance for each branch to correspond to the equations in the form shown above. The total resistance of only refers to the considered parallel circuit in which splits of the total current. Any resistance that be before or after the parallel circuit in series will not be considered. In more complex circuits with multiple branches, the formula may need to be applied several times in order to obtain this partial flow.
For a rough check of the calculated with this rule flows, two simple maxims are. For each part of a current is less than the total flow, as it corresponds to the sum of all sub-streams. Secondly, the partial currents in the branches are inversely proportional to their branch resistances. That is, the smaller (greater ) the branch resistance is, the greater ( smaller) the partial stream.
In some sources, the rule is expressed somewhat modified. Initially, this variant seems a bit more difficult, but it falls experienced users with time as easily as the first variant. It reads as follows:
Derivation rule for a simple example
According to Kirchhoff's laws, the total current is divided between the two branches on:
As to the two resistors connected in parallel drops the same voltage, according to Ohm's law is valid:
Solving this equation with respect to at
And puts the result in yields:
Dividing by and forms on both sides of the reciprocal value, the result is the same result as for the current divider rule:
The total current and the values of resistors are generally known.
Example with multiple application
The current is searched. For this purpose, first the current is calculated in the lowest branch. The current divider rule yields the equation:
With and
The part of current flows through the parallel circuit and. By repeated application of the current divider rule, the current is determined by a function of:
If both equations are multiplied together, resulting in a total equation in which is directly related to I:
Example of magnetic circuit
In magnetic circuits, the rule is applied the same way. For the partial fluxes and by the equations yield:
Application
Power divider are used especially for measuring high currents, they are then called shunt, where the meter is one of the current paths. In essence, however, it measures the voltage drop across the main path, as it is traversed by only a very small portion of stream. In multimeters are switchable power divider for current measurement in various fields.