View source for Polarity (mutual inductance)

{{Short description|Magnetically coupled transformer winding polarities}}
{{About|magnetically coupled transformer winding polarities|motor winding polarity|Electric motor}}
{{Redir|Dot convention|similar terms|Dot notation (disambiguation)}}
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{{Use list-defined references|date=July 2022}}
[[Image:Instrument Transformer HV terminals.jpg|thumb|180px| An instrument transformer, looking at the high voltage side with dot convention and H1 marking.]]
[[Image:Instrument Transformer LV terminals.jpg|thumb|180px|The low voltage side of the instrument transformer, with dot and X1 marking. The X1 and H1 terminals are adjacent.]]
In [[electrical engineering]],  dot marking convention, or alphanumeric marking convention, or both, can be used to denote the same relative instantaneous [[Electrical polarity|polarity]] of two [[Mutual inductance#Coupled inductors and mutual inductance|mutually inductive]] components such as between [[transformer]] windings. These markings may be found on transformer cases beside terminals, winding leads, nameplates, schematic and wiring diagrams.

The convention is that current entering a transformer at the end of a winding marked with a dot, will tend to produce current exiting other windings at their dotted ends.{{citation needed|date=May 2020}}

Maintaining proper polarity is important in power system protection, measurement and control systems. A reversed [[instrument transformer]] winding may defeat [[protective relay]]s, give inaccurate power and energy measurements, or result in display of negative [[power factor]]. Reversed connections of paralleled transformer windings will cause circulating currents or an effective [[short circuit]]. In signal circuits, reversed connections of transformer windings can result in incorrect operation of amplifiers and speaker systems, or cancellation of signals that are meant to add.

==Polarity== 
Leads of primary and secondary windings are said to be of the same polarity when instantaneous current entering the primary winding lead results in instantaneous current leaving the secondary winding lead as though the two leads were a continuous circuit.<ref name="Knowlton_1949"/><ref name="Alexander_2009"/>
In the case of two windings wound around the same core in parallel, for example, the polarity will be the same on the same ends: A sudden (instantaneous) current in the first coil will induce a voltage opposing the sudden increase ([[Lenz's law]]) in the first and also in the second coil, because the magnetic field produced by the current in the first coil traverses the two coils in the same manner. 
The second coil will, therefore, show an induced current opposite in direction to the inducing current in the first coil. Both leads behave like a continuous circuit, one current entering into the first lead and another current leaving the second lead.

==Transformer windings==
Two methods are commonly used to denote which terminals present the same relative polarity. A dot may be used, or an alphanumeric designation. Alphanumeric designations are typically in the form H<sub>1</sub> for primaries, and for secondaries, X<sub>1</sub>, (and Y<sub>1</sub>, Z<sub>1</sub>, if more windings present).

Unlike single-phase transformers, three-phase transformers may have a phase shift due to different winding configurations (for example, a wye connected primary and a delta connected secondary), resulting in a multiple of 30 degree phase shift between H1 and X1 bushing designations. The [[vector group]] in the nameplate of the transformer gives information about such phase shift.

==Terminal layout conventions==
Transformers are said to have "additive" or "subtractive" polarity based on their physical arrangement of terminals and the polarity of windings connected to the terminals. The convention used for North American transformers is that, facing the high voltage side of the transformer, the H1 terminal is on the observer's right. A transformer is called "additive" if, conceptually, connecting the high-voltage terminal to the adjacent low-voltage terminal gives a total voltage between the other two terminals that is the sum of the high voltage and low voltage ratings, when the high-voltage winding is excited at rated voltage. The H1 and X2 terminals are physically adjacent. In the "subtractive" arrangement, the H1 and X1 terminals are adjacent, and the voltage measured between H2 and X2 would be the difference of the  high voltage and low voltage windings.<ref name="Croft_1987"/> Pole mounted distribution transformers are manufactured with additive polarity, while instrument transformers are made with subtractive polarity.  Where markings have been obscured or are suspect, a test can be made by interconnecting the windings and exciting the transformer, and measuring the voltages.<ref name="IDC_2002"/>

==Three phase transformers==
Three-phase transformers used in electric power systems will have a nameplate that indicate the phase relationships between their terminals. This may be in the form of a [[phasor]] diagram, or using an alpha-numeric code to show the type of internal connection (wye or delta) for each winding.

==See also==
* [[Electrical polarity]]

==References==
{{reflist|refs=
<ref name="Alexander_2009">{{cite book |title=Fundamentals of electric circuits |author-last=Alexander |author-first=Charles |publisher=[[McGraw-Hill]] |date=2009 |isbn=978-0-07352955-4 |pages=559–560}}</ref>
<ref name="Knowlton_1949">{{cite book |title=Standard Handbook for Electrical Engineers |editor-last=Knowlton |editor-first=Archer E. |edition=8 |date=1949 |publisher=[[McGraw-Hill]] |pages=552 §6-15, p. 606 §6-162}}</ref>
<ref name="Croft_1987">{{cite book |title=American Electricians' Handbook |author-first1=Terrell |author-last1=Croft |author-link1=Terrell Croft |author-first2=Wilford |author-last2=Summers |edition=11 |publisher=[[McGraw-Hill]] |date=1987 |isbn=0-07-013932-6 |pages=5-44 – 5-45}}</ref>
<ref name="IDC_2002">{{cite web |title=Transformer Polarity |publisher=Kilowatt Classroom, LLC |date=2002 |url=http://www.idc-online.com/technical_references/pdfs/electrical_engineering/Transformer_Polarity.pdf |access-date=2018-01-16 |url-status=live |archive-url=https://web.archive.org/web/20220703122751/http://www.idc-online.com/technical_references/pdfs/electrical_engineering/Transformer_Polarity.pdf |archive-date=2022-07-03}} (4 pages)</ref>
}}

==Further reading==
* {{cite conference |book-title=Analysis of Electric Circuits |title=§18.1 'Symbols and Polarity of Mutual Inductance' in Chapter 18 - Circuits with Magnetic Circuits |author-last1=Brenner |author-first1=Egon |author-last2=Javid |author-first2=Mansour |date=1959 |publisher=[[McGraw-Hill]] |series=McGraw-Hill Electrical and Electronic Engineering Series |pages=589–590 |url=https://books.google.com/books?id=V4FrAAAAMAAJ |access-date=2022-07-03}}
* {{cite book |title=Electrical and Mechanical Networks: An introduction to their analysis |chapter=10-2. Transformers |series=McGraw-Hill Electrical and Electronic Engineering Series |author-first1=Willis W. |author-last1=Harman |author-link1=Willis W. Harman |author-first2=Dean W. |author-last2=Lytle |publisher=[[McGraw-Hill Book Company, Inc.]] / [[The Maple Press Company]], York, PA. |publication-place=New York, USA |date=1962 |edition=1 |lccn=61-17340 |id=Order No. 26590 |pages=353–354 |quote-page=354 |quote=The voltage ''drop'' from the dotted to the undotted end of a coil, induced by a current ''i'' flowing in at the dotted end of the other coil, is ''M'' ''di''/''dt''. If ''M'' is assumed positive, the four markings of Fig. 10-3a. correspond exactly and may be freely interchanged. The same holds true for the four markings of Fig. 10-3b.}}
* {{cite book |title=Transformers for Electronic Circuits |author-last=Grossner |author-first=Nathan |publisher=[[McGraw-Hill]] |date=1967 |isbn=0-07024979-2 |page=26}}
* {{cite book |title=Schaum's outline of theory and problems of electric circuits |author-first1=Mahmood |author-last1=Nahvi |author-first2=Joseph |author-last2=Edminister |publisher=[[McGraw-Hill Professional]] |date=2002 |edition=4 |series=Schaum's outline of theory and problems / Schaum's outline series |isbn=0-07-139307-2 |page=338 |url=https://books.google.com/books?id=nrxT9Qjguk8C&pg=PA338 |access-date=2022-07-03}}
* {{cite book |title=Introductory Circuit Analysis |chapter=Section 21.8: Series connection of mutually coupled coils |author-last=Boylestad |author-first=Robert L. |author-link=Robert Boylestad |date=2003 |edition=10 |publisher=[[Prentice Hall]] |isbn=0-13-097417-X |page=[https://archive.org/details/introductorycirc00boyl_106/page/n954 954] |url=https://archive.org/details/introductorycirc00boyl_106 |url-access=limited |access-date=2022-07-03}}
* {{cite conference |book-title=The Electronics Handbook |title=§2.5.5 'Transformers' & §10.1.3 'The Ideal Transformer' |author-last=Parker |author-first=Martin R. |author-last2=Ula |author-first2=Sadrul |author-last3=Webb |author-first3=William E. |editor-first=Jerry C. |editor-last=Whitaker |date=2005 |publisher=[[Taylor & Francis]] |edition=2 |isbn=0-8493-1889-0 |pages=172, 1017 |url=https://books.google.com/books?id=FdSQSAC3_EwC&q=transformer+polarity+dot+convention&pg=PA1017 |access-date=2022-07-03}}
* {{cite book |title=Electric machines |chapter=Chapter 3 - Transformers |author-first1=Dwarkadas Prahladadas |author-last1=Kothari |author-link1=Dwarkadas Prahladadas Kothari |author-last2=Nagrath |author-first2=Inder Jit |date=2010 |publisher=[[Tata McGraw-Hill]] |isbn=978-0-07-069967-0 |edition=4 |at=p. 73, §3.7 'Transformer Testing' |url=https://books.google.com/books?id=fR1rNJhBbmcC&q=dot+convention+polarity+of+transformer&pg=PA72 |access-date=2022-07-03}}
* {{cite book |title=ANSI/IEEE C57.13, American National Standard Requirements for Instrument Transformers}}

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[[Category:Electric transformers]]