Copyright 20 13 Dorling Kindersley (India) Pvt. Ltd

14. Magnetically Coupled Circuits 
14.1
14.1 The mutual Inductance Element 
14.2
14.1.1 Why Should M
12
 Be Equal to M
21
? 
14.4
14.1.2 Dot Polarity Convention 
14.5
14.1.3 maximum Value of mutual Inductance and Coupling Coefficient 
14.7
14.2 The Two-Winding Transformer 
14.7
14.3 The Perfectly Coupled Transformer and the Ideal Transformer 
14.10
14.4 Ideal Transformer and Impedance matching 
14.13
14.5 Transformers in Single-Tuned and Double-Tuned Filters 
14.14
14.5.1 Single-Tuned Amplifier 
14.15
14.5.2 Double-Tuned Amplifier 
14.16
14.6 Analysis of Coupled Coils Using Laplace Transforms 
14.19
14.6.1 Input Impedance Function of a Two-Winding Transformer 
14.20
14.6.2 Transfer Function of a Two-Winding Transformer 
14.21
14.7 Flux Expulsion by a Shorted Coil 
14.24
14.8 Breaking the Primary Current in a Transformer 
14.26
14.9 Summary 
14.27
14.10 Problems 
14.28
Index 
I.1
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P r e f a c e
The field of electrical and electronic engineering is vast and diverse. However, two topics hold the key 
to the entire field. They are ‘Circuit Theory’ and ‘Signals and Systems’. Both these topics provide a 
solid foundation for later learning, as well as for future professional activities.
This undergraduate textbook, the first of a two-book series, deals with one of these two pivotal 
subjects in detail. In addition, it connects ‘Circuit Theory’ and ‘Signals and Systems’, thereby preparing 
the student-reader for a detailed study of this important subject either concurrently or subsequently.
The theory of electric circuits and networks, a subject derived from the more basic subject of 
electromagnetic fields, is the cornerstone of electrical and electronics engineering. Students need to 
master this subject and assimilate its basic concepts in order to become competent engineers.
my book Electric Circuits and Networks (ISBN 978-81-317-1390-7), published by Pearson 
Education in 2009, was an attempt to provide a solid foundation on electric circuits and networks 
to the undergraduate students. However, this book was perceived as being too voluminous and too 
comprehensive for a first-level course on Circuits. Hence, for better acceptability and better utilization 
of the content, I decided to rewrite the material and present it in two books. Of these, the first one 
on Electric Circuit Analysis has been designed to serve as a textbook for first/second level course 
on circuits and the second one on Electric Network Analysis and Synthesis has been envisaged for 
an advanced level course on network analysis and synthesis. The latter text is being augmented with 
additional content that caters to the needs of the advanced user. This text, Electric Circuit Analysis, is 
the first of the series, while work on the second text with new material included on network functions, 
electric filters and passive network design, is currently in progress.