Current divider

A general formula for the current IX in a resistor RX that is in parallel with a combination of other resistors of total resistance RT (see Figure 1) is[1] where IT is the total current entering the combined network of RX in parallel with RT.

In the general case: and the current IX is given by[2] where ZT refers to the equivalent impedance of the entire circuit.

[3] Instead of using impedances, the current divider rule can be applied just like the voltage divider rule if admittance (the inverse of impedance) is used: Take care to note that YT is a straightforward addition, not the sum of the inverses inverted (as would be done for a standard parallel resistive network).

Using the formula below, the current in the resistor is where ZC = 1/(jωC) is the impedance of the capacitor, and j is the imaginary unit.

When an amplifier is terminated by a finite, non-zero termination, and/or driven by a non-ideal source, the effective gain is reduced due to the loading effect at the output and/or the input, which can be understood in terms of current division.

The loading factors in these cases must employ the true amplifier impedances including these bilateral effects.

[4] Carrying out the analysis for this circuit, the current gain with feedback Afb is found to be That is, the ideal current gain Ai is reduced not only by the loading factors, but due to the bilateral nature of the two-port by an additional factor[5] (1 + β(RL/RS) Aloaded), which is typical for negative-feedback amplifier circuits.

Figure 1: Schematic of an electrical circuit illustrating current division. Notation R T refers to the total resistance of the circuit to the right of resistor R X .
Figure 2: A low-pass RC current divider
Figure 3: A current amplifier (gray box) driven by a Norton source ( i S , R S ) and with a resistor load R L . Current divider in blue box at input ( R S , R in ) reduces the current gain, as does the current divider in green box at the output ( R out , R L )
Figure 4: Current amplifier as a bilateral two-port network; feedback through dependent voltage source of gain β V/V