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CIRCUIT THEORY
TELLEGEN’S THEOREM
SYED HASAN SAEED
Sunday, August 18, 2019 1Syed Hasan Saeed
REFERENCE BOOKS
• Introductory Circuit Analysis, Robert L. Boylested, Pearson Education,
Prentice Hall.
• Networks And Systems, Ashfaq Husain, Khanna Book Publishing Co (P)
Ltd. Delhi.
• Networks And Systems, A Sudhakr, Shyammohan S Palli, Tata McGraw
Hill, New Delhi.
• Network Analysis, M.E. Van Valkenburg, PHI Learning Private limited,
New Delhi.
• Circuit Analysis Principle and Applications, Allan H. Robbins &Wilhelm
C. Miller, DELMAR CENGAGE Learning, Indian Reprint.
Sunday, August 18, 2019 syed hasan saeed 2
TELLEGEN‟S THEOREM
STATEMENT: This theorem states that “any time „t‟ the algebraic sum of
instantaneous power in „n‟ branches of any network is zero, if KCL and
KVL are satisfied.” Mathematically
PROOF: Consider the network shown in fig.1
Sunday, August 18, 2019 Syed Hasan Saeed 3
Fig. 1
0iv k
n
1k
k 
Z2
Z4
Z3Z1
i1
i3
i2
i4
v1 v3
v4v2v0
v1 = 6V, v2 = 4V,
v3 = 3V, v4 = 1V
i1 = 5A. i2 = 2A,
i3 = 3A, i4 = 3A
Where
Where vk = instantaneous voltage drop in
each branch
ik = instantaneous current in each branch
TELLEGEN‟S THEOREM
PROOF:
STEP 1 :Verification of KCL:
At node „a‟ : i1 = i2 + i3 (1)
5 = 2 +3 = 5
At node „b‟ : i3 =i4 (2)
3 =3
STEP 2 :Verification of KVL:
In mesh “1” : -v1 – v2 + v0 = 0
-6 -4 + 10 = 0
In mesh “2” : v2 – v3 – v4 = 0
4 – 3 – 1 = 0
Hence KVL and KCL are satisfied.
Sunday, August 18, 2019 Syed Hasan Saeed 4
TELLEGEN‟S THEOREM
STEP 3 : Calculation of Power in each branch
-v1 * i1 = -6 x 5 = -30 W -v4 * i4 = -1 * 3 = -3 W
-v2 * i2 = -4 * 2 = -8 W v0 * i1 = 10 * 5 = 50 W
-v3 * i3 = -3 * (-3) = -9 W
Sunday, August 18, 2019 Syed Hasan Saeed 5
0503-9-8-3-iv k
n
1k
k 
PROVED
OR,
Power Supplied = 50 W
Power Dissipated = - 50 W
Sunday, August 18, 2019 syed hasan saeed 6
THANK YOU
hasansaeedcontrol@gmail.com
shasansaeed@yolasite.com
hasansaeed872726549.wordpress.com
saeed.moodlecloud.com
syedhasansaeed.gnomio.com

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Tellegen's theorem

  • 1. CIRCUIT THEORY TELLEGEN’S THEOREM SYED HASAN SAEED Sunday, August 18, 2019 1Syed Hasan Saeed
  • 2. REFERENCE BOOKS • Introductory Circuit Analysis, Robert L. Boylested, Pearson Education, Prentice Hall. • Networks And Systems, Ashfaq Husain, Khanna Book Publishing Co (P) Ltd. Delhi. • Networks And Systems, A Sudhakr, Shyammohan S Palli, Tata McGraw Hill, New Delhi. • Network Analysis, M.E. Van Valkenburg, PHI Learning Private limited, New Delhi. • Circuit Analysis Principle and Applications, Allan H. Robbins &Wilhelm C. Miller, DELMAR CENGAGE Learning, Indian Reprint. Sunday, August 18, 2019 syed hasan saeed 2
  • 3. TELLEGEN‟S THEOREM STATEMENT: This theorem states that “any time „t‟ the algebraic sum of instantaneous power in „n‟ branches of any network is zero, if KCL and KVL are satisfied.” Mathematically PROOF: Consider the network shown in fig.1 Sunday, August 18, 2019 Syed Hasan Saeed 3 Fig. 1 0iv k n 1k k  Z2 Z4 Z3Z1 i1 i3 i2 i4 v1 v3 v4v2v0 v1 = 6V, v2 = 4V, v3 = 3V, v4 = 1V i1 = 5A. i2 = 2A, i3 = 3A, i4 = 3A Where Where vk = instantaneous voltage drop in each branch ik = instantaneous current in each branch
  • 4. TELLEGEN‟S THEOREM PROOF: STEP 1 :Verification of KCL: At node „a‟ : i1 = i2 + i3 (1) 5 = 2 +3 = 5 At node „b‟ : i3 =i4 (2) 3 =3 STEP 2 :Verification of KVL: In mesh “1” : -v1 – v2 + v0 = 0 -6 -4 + 10 = 0 In mesh “2” : v2 – v3 – v4 = 0 4 – 3 – 1 = 0 Hence KVL and KCL are satisfied. Sunday, August 18, 2019 Syed Hasan Saeed 4
  • 5. TELLEGEN‟S THEOREM STEP 3 : Calculation of Power in each branch -v1 * i1 = -6 x 5 = -30 W -v4 * i4 = -1 * 3 = -3 W -v2 * i2 = -4 * 2 = -8 W v0 * i1 = 10 * 5 = 50 W -v3 * i3 = -3 * (-3) = -9 W Sunday, August 18, 2019 Syed Hasan Saeed 5 0503-9-8-3-iv k n 1k k  PROVED OR, Power Supplied = 50 W Power Dissipated = - 50 W
  • 6. Sunday, August 18, 2019 syed hasan saeed 6 THANK YOU hasansaeedcontrol@gmail.com shasansaeed@yolasite.com hasansaeed872726549.wordpress.com saeed.moodlecloud.com syedhasansaeed.gnomio.com