Duality What is a dual circuit? Building the Dual of a circuit (Example 1) Duality Explained Example 2

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Session 16F: Focus
 Duality
◦ What is a dual circuit?
◦ Building the Dual of a circuit (Example 1)
◦ Duality Explained
◦ Example 2

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Duality

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Which are dual circuits?
 We shall define duality in terms of the circuit
equations.
 Two circuits are “duals” if the mesh equations that
characterize one of them have the same
mathematical form as the nodal equations that
characterize the other
 They are said to be exact duals if each mesh
equation of one circuit is numerically identical
with the corresponding nodal equation of the other;
4

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Duality: Example 1
Mesh Equations:
The value of the inductor current
at t = 0; in other words, vC (0) = 10 V
The voltage shown here is the initial value of voltage across the capacitor. It does
Not mean that an electrolytic capacitor is connected here. Note that electrolytic
Capacitors are not normally used with AC circuits.

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Duality: Example 1… contd.
 Construct a dual of the above equations by replacing
current terms with voltage terms
Mesh Equations:
In the above equation, -10 indicates current.

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Example 1: Dual of the Circuit
 Dual of a circuit can be constructed using the above method
 Initial voltage across the capacitor (8F) becomes initial
current (iL(0)) through the inductor (8H) in the dual circuit
Dual of the circuit
Nodal equation
Of the Dual circuit

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Example 1: Constructing the Dual of a
Circuit
 Construct the dual of the circuit by starting from a point
inside each loop and crossing over each element to Ref
point.
 Now for each element being crossed add the dual of that
element between the center point and the reference.

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Duality Explained
 The concept of duality applies to many fundamental
engineering concepts.
 Two circuits are “duals” if the mesh equations that
characterize one of them have the same mathematical
form as the nodal equations that characterize the other.
 They are said to be exact duals if each mesh equation
of one circuit is numerically identical with the
corresponding nodal equation of the other;
◦ The current and voltage variables themselves cannot be
identical, of course.

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Example 2: Duality
 Duality is defined on the basis of mesh and nodal
equations.
 Since non-planar circuits cannot be described by a
system of mesh equations
◦ A circuit that cannot be drawn in planar form does not possess
a dual

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Session 16E: Summary
 Duality
◦ What is a dual circuit?
◦ Building the Dual of a circuit (Example 1)
◦ Duality Explained
◦ Example 2

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References
Ref 1 Ref 2