- Tellegen’s Theorem Definition: Tellegen’s theorem is defined as the principle that the sum of instantaneous powers in all branches of an electrical network is zero.
- Importance in Network Analysis: Tellegen’s theorem is crucial for analyzing electrical networks by ensuring power balance.
- Conditions for Application: The theorem applies to networks satisfying Kirchhoff’s Current Law and Kirchhoff’s Voltage Law.
- Example Demonstration: An example network with specific voltages and currents shows how Tellegen’s theorem works in practice.
- Applicability: It applies to various types of network elements, including linear, non-linear, active, and passive components.
Bernard D.H. Tellegen, a Dutch electrical engineer, published this result in 1952. It is a power-balance tool for network analysis. Tellegen theorem says the sum of the instantaneous powers in the n branches of a network is zero. Let those n branches carry instantaneous currents i1, i2, i3, …………. in. Those currents satisfy Kirchhoff’s Current Law.
Let the same branches have instantaneous voltages v1, v2, v3, ……….. vn. If those voltages satisfy Kirchhoff Voltage Law, then
vk is the instantaneous voltage across the kth branch and ik is the instantaneous current in that branch. Tellegen theorem holds for lumped networks with linear, nonlinear, time-varying or time-invariant parts, including active and passive elements.
The next network is a worked example.
Branch-current arrows are chosen freely, and each branch voltage is marked positive at the tail of its current arrow.
The voltages are taken to satisfy Kirchhoff’s Voltage Law and the currents are taken to satisfy Kirchhoff’s Current Law at every node.
Those assumed voltages and currents then satisfy
which is the Tellegen theorem condition.
In the figure take v1, v2 and v3 as 7 V, 2 V and 3 V. Kirchhoff Voltage Law around ABCDEA then requires v4 = 2 V. Around CDFC, v5 must be 3 V and around DFED, v6 must be 2 V. Next apply Kirchhoff’s Current Law at nodes B, C and D.
At node B let ii = 5 A, so i2 = – 5 A. At node C let i3 = 3 A, so i5 = – 8 A. At node D take i4 as 4 A, so i6 = – 9 A. Form the power sum
and the result is 
so Tellegen theorem holds for this set.
