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Reciprocity in electrical networks is a property of a circuit that relates voltages and currents at two points. The reciprocity theorem states that the current at one point in a circuit due to a voltage at a second point is the same as the current at the second point due to the same voltage at the first.
There is also an analogous theorem in electrostatics, known as Green's reciprocity, relating the interchange of electric potential and electric charge density. Forms of the reciprocity theorems are used in many electromagnetic applications, such as analyzing electrical networks and antenna systems. [ 1 ]
In the special case of a modal analysis this is known as Maxwell's reciprocity theorem. [1] In electromagnetism the concept is known as Lorentz reciprocity, a special case of which is the reciprocity theorem of electrical networks. The reciprocity principle is also used in the analysis of structures. [2]
Most analysis methods calculate the voltage and current values for static networks, which are circuits consisting of memoryless components only but have difficulties with complex dynamic networks. In general, the equations that describe the behaviour of a dynamic circuit are in the form of a differential-algebraic system of equations (DAEs).
Figure 1: Example two-port network with symbol definitions. Notice the port condition is satisfied: the same current flows into each port as leaves that port.. In electronics, a two-port network (a kind of four-terminal network or quadripole) is an electrical network (i.e. a circuit) or device with two pairs of terminals to connect to external circuits.
There are several equivalent ways to define or represent reciprocity. A convenient one for circuits at microwave frequencies (where distributed-element circuits are used) is in terms of their S-parameters. A reciprocal circuit will have an S-parameter matrix, [S], which is symmetric. From the definition of a circulator, it is clear that this ...
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Since electrical conductance is reciprocal to resistance, the expression for total conductance of a parallel circuit of resistors is simply: = = = + + +. The relations for total conductance and resistance stand in a complementary relationship: the expression for a series connection of resistances is the same as for parallel connection of ...