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Actual passive two-terminal components can be represented by some network of lumped and distributed ideal inductors, capacitors, and resistors, in the sense that the real component behaves as the network does. Some of the components of the equivalent circuit can vary with conditions, e.g., frequency and temperature.
The two preceding statements are equivalent, except for exchanging the role of voltage and current. A circuit composed solely of components connected in series is known as a series circuit; likewise, one connected completely in parallel is known as a parallel circuit.
The Thévenin-equivalent circuit of a linear electrical circuit is a voltage source with voltage V th in series with a resistance R th. The Thévenin-equivalent voltage V th is the open-circuit voltage at the output terminals of the original circuit.
Series RL, parallel C circuit with resistance in series with the inductor is the standard model for a self-resonant inductor. A series resistor with the inductor in a parallel LC circuit as shown in Figure 4 is a topology commonly encountered where there is a need to take into account the resistance of the coil winding and its self-capacitance.
For two resistors, the "star" is simply the two resistors in series, and the transform yields a single equivalent resistor. The special case of three resistors is better known as the Y-Δ transform. Since the result also has three resistors, this transform has an inverse Δ-Y transform.
At each stage, resistors for the "rung" and "leg" are chosen so that the rung value matches the leg value plus the equivalent resistance of the previous rungs. The rung and leg resistors can be formed by pairing other resistors in series or parallel in order to increase the number of available combinations. This process can be automated.
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