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1351_9 | It was first thought to be a single tornado event of over , but a meticulous damage survey by the renowned severe weather expert Ted Fujita documented the complex interactions of downbursts, microbursts, and tornadoes, and much was learned meteorologically from this event. Downbursts, a recent concept by Fujita at the time (the 1974 Super Outbreak the year before was also significant in their conceptual development), covered a very large area; these as well as a continuous series of smaller but very intense microbursts were responsible for the meandering course of the tornadoes (although the average of the path was linear) and for some changes in intensity. It is thought that a microburst may be responsible for breaking up the first tornado. A continuous damage swath connected the events regardless. Conversely, another microburst seems to have caused the tornado to intensify on the eastern side of Canton and coincided with the two deaths. The most intense pure tornadic damage width |
1351_10 | was . |
1351_11 | 1835 Canton tornado
Canton and surrounding areas were devastated by an earlier tornado on June 18, 1835. Touching down around 10 p.m., it decimated rural farms, killing four; before it traversed through Canton, killing four in town, including the town's founder and his young son. Injuries totaled forty. This tornado damaged or destroyed about fifty buildings in Canton with a total damage width of about .
See also
List of North American tornadoes and tornado outbreaks
Rear flank downdraft and forward flank downdraft
References
"Tornado Kills Three in Illinois". The Washington Post; Jul 24, 1975; A7.
F3 tornadoes
Tornadoes of 1975
Fulton County, Illinois
Tornadoes in Illinois
Canton, Illinois Tornado, 1975
1975 natural disasters in the United States
Canton, Illinois
July 1975 events in the United States |
1352_0 | Mariàngela Vilallonga Vives (Girona, 3 April 1952) is a Spanish professor of Latin philology at the University of Girona. Between 2017 and 2019 she was second vice-president of the Institute of Catalan Studies, an institution where she held several senior positions. On 25 March 2019 she became the minister of culture in the Quim Torra Government of the Generalitat de Catalunya. Her term as minister of culture ended on 3 September 2020. |
1352_1 | Her father was the tailor Josep Vilallonga. Born in Girona, she grew up in Llagostera. She studied primary school in the Carmelites of the municipality and the elementary baccalaureate at the Institut de Girona. Later she studied at the Institut Jaume Vicens Vives in Girona. She began a degree in Philosophy and Literature at the University of Girona, and graduated in Classical Philology at the Autonomous University of Barcelona. In September 1974 she defended her dissertation, La estructura omfàlica a l'epístola Ad Pisones d'Horaci, directed by Àngel Anglada Anfruns. In the same year she began to work as a teacher at the University College of Girona and married in 1975. |
1352_2 | University
With a PhD in classical philology from the Autonomous University of Barcelona, she is professor of Latin philology at the University of Girona and director of the Maria Àngels Anglada – Carles Fages de Climent Chair of Literary Heritage, since its creation in 2004, and of the Literary Heritage Research Group. She has directed research projects on the relations between the humanists of the Crown of Aragon and Europe during the 15th and 16th centuries. In this field, the book La literatura latina en Cataluña en el siglo XV and his contributions on the cardinal and bishop of Gerona Joan Margarit y Pau and Jeroni Pau, of whom she is a specialist, are particularly noteworthy.
She coordinates the Studia Humanitatis working group, in which fourteen researchers from Germany, Italy, the United Kingdom, Belgium and Spain participate. He has created a virtual library where biographies of the main Catalan humanists and some of their Latin texts can be found. |
1352_3 | Academy
Since 28 February 2005 she has been a numerary member of the Institute of Catalan Studies with the number 255, and since 2017 she has been the institution's vice-president. She had already been previously, between 11 November 2010 and 2013, replacing Joan Solà, who died on 27 October 2010.
She has been a member of the Governing Board and the Advisory Council of the Institució de les Lettres Catalanes since 2015. She has been a member of the Arts and Culture Council of Girona (2008–2011), member of the School Council of Catalonia (2011–2015), member of the Social Council of Culture of the Government of Catalonia (2014–2015), president of the Advisory Council of the CRUSCAT Network (2010–2015), member of the Organising Committee of the Commemorations of the Government of Catalonia (2011–2013) and coordinator of the "Leaves" of the Journal of Girona (1985–2008). |
1352_4 | Politics
On 22 March 2019 she was announced as the future Minister of Culture in Quim Torra's government, replacing Laura Borràs. Borràs left the post to run as an independent candidate in the Spanish general elections in April 2019. In 2020 some controversy was caused in reference to the in her opinion excessive use of Spanish on TV3, making particular reference to a new bilingual series, Drama. In September of the same year she was relieved of her post.
Publications
She is the author of more than a dozen monographs and books. She has also translated Rainer M. Rilke's French Poems (2011). She has collaborated with several media (El Punt, Presencia, Revista de Girona, Sierra d'Or, La Vanguardia, Avui, Ara.)
Vida i obra de Jeroni Pau (Resum de Tesi Doctoral) (1984)
Jeroni Pau. Obres (dos volums, 1986, )
Els arbres (1986)
Dos opuscles de Pere Miquel Carbonell (1988)
Llengua i literatura de l'Edat Mitjana al Renaixement (1991) amb Albert Rossich |
1352_5 | La literatura llatina a Catalunya al segle XV. Repertori bio-bibliogràfic (1993, )
El Renaixement i l'Humanisme (2002, )
Atles literari de les terres de Girona (segles XIX i XX) (2003) amb Narcís-Jordi Aragó
Johannes Burckard. Dietari secret (2003)
Recrear Rodoreda Romanyà (2008)
Awards and recognitions
On 26 April 2016, she received the Cross of Sant Jordi for her "research focused on the Latin humanistic literature of the Crown of Aragon".
References
1952 births
Autonomous University of Barcelona alumni
Women members of the Parliament of Catalonia
Living people
Spanish philologists |
1353_0 | This article lists the fugal works of Johann Sebastian Bach, defined here as the fugues, fughettas, and canons, as well as other works containing fugal expositions but not denoted as fugues, such as some choral sections of the Mass in B minor, the St Matthew Passion, the St John Passion, and the cantatas.
This sub-list of the complete list of compositions by Johann Sebastian Bach is intended to facilitate the study of Bach's counterpoint techniques. Each work cited in this list will be annotated with the fugal subject(s) and any countersubjects in musical notation. |
1353_1 | Organ fugues
BWV 531 – Prelude and Fugue in C major
BWV 532 – Prelude and Fugue in D major
BWV 532a – Fugue in D major (alternative version of BWV 532)
BWV 533 – Prelude and Fugue in E minor
BWV 534 – Prelude and Fugue in F minor
BWV 535 – Prelude and Fugue in G minor
BWV 535a – Prelude and Fugue in G minor (alternative, simplified version of BWV 535)
BWV 536 – Prelude and Fugue in A major
BWV 536a – Prelude and Fugue in A major (alternative version of BWV 536 based on the original manuscript)
BWV 537 – Fantasia (Prelude) and Fugue in C minor
BWV 538 – Toccata and Fugue in D minor ("Dorian")
BWV 539 – Prelude and Fugue in D minor
BWV 539a – Fugue in D minor (see BWV 1000 for the lute arrangement, movement 2 of BWV 1001 for the violin arrangement)
BWV 540 – Toccata and Fugue in F major
BWV 541 – Prelude and Fugue in G major
BWV 542 – Fantasia and Fugue "Grand" in G minor
BWV 542a – Fugue in G minor (alternative version of the fugue from BWV 542) |
1353_2 | BWV 543 – Prelude and Fugue in A minor
BWV 544 – Prelude and Fugue in B minor
BWV 545 – Prelude and Fugue in C major
BWV 545a – Prelude and Fugue in C major (alternative version of BWV 545)
BWV 545b – Prelude, Trio and Fugue in B-flat major (alternative version of BWV 545)
BWV 546 – Prelude and Fugue in C minor
BWV 547 – Prelude and Fugue in C major "9/8"
BWV 548 – Prelude and Fugue in E minor "Wedge"
BWV 549 – Prelude and Fugue in C minor
BWV 550 – Prelude and Fugue in G major
BWV 551 – Prelude and Fugue in A minor
BWV 552 – Prelude and Fugue in E-flat major "St. Anne" (published in Clavier-Übung III)
Eight Short Preludes and Fugues (553–560)
BWV 553 – Short Prelude and Fugue in C major (spurious, possibly by Johann Tobias Krebs)
BWV 554 – Short Prelude and Fugue in D minor (spurious, possibly by Johann Tobias Krebs)
BWV 555 – Short Prelude and Fugue in E minor (spurious, possibly by Johann Tobias Krebs) |
1353_3 | BWV 556 – Short Prelude and Fugue in F major (spurious, possibly by Johann Tobias Krebs)
BWV 557 – Short Prelude and Fugue in G major (spurious, possibly by Johann Tobias Krebs)
BWV 558 – Short Prelude and Fugue in G minor (spurious, possibly by Johann Tobias Krebs)
BWV 559 – Short Prelude and Fugue in A minor (spurious, possibly by Johann Tobias Krebs)
BWV 560 – Short Prelude and Fugue in B-flat major (spurious, possibly by Johann Tobias Krebs)
BWV 561 – Fantasia and Fugue in A minor (spurious)
BWV 562 – Fantasia and Fugue in C minor (fugue unfinished)
BWV 563 – Fantasia with imitation in B minor (spurious)
BWV 564 – Toccata, Adagio and Fugue in C major
BWV 565 – Toccata and Fugue in D minor
BWV 566 – Toccata and Fugue in E major
BWV 566a – Toccata in E major (earlier version of BWV 566)
BWV 567 – Prelude in C major
BWV 568 – Prelude in G major
BWV 569 – Prelude in A minor
BWV 570 – Fantasia in C major
BWV 571 – Fantasia (Concerto) in G major (spurious) |
1353_4 | BWV 572 – Fantasia in G major
BWV 573 – Fantasia in C major (incomplete, from the 1722 Notebook for Anna Magdalena Bach)
BWV 574 – Fugue in C minor
BWV 574a – Fugue in C minor (alternative version of BWV 574)
BWV 575 – Fugue in C minor
BWV 576 – Fugue in G major
BWV 577 – Fugue in G major "à la Gigue" (spurious)
BWV 578 – Fugue in G minor "Little"
BWV 579 – Fugue on a theme by Arcangelo Corelli (from Op. 3, No. 4); in B Minor
BWV 580 – Fugue in D major (spurious)
BWV 581 – Fugue in G major (not by Bach, composed by Gottfried August Homilius)
BWV 581a – Fugue in G major (spurious)
BWV 582 – Passacaglia and Fugue in C minor
BWV 1086 – Canon concordia discors
BWV 1087 – 14 canons on the First Eight Notes of Goldberg Variations Ground |
1353_5 | Keyboard fugues |
1353_6 | The Well-Tempered Clavier (BWV 846–893)
BWV 846 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 1 in C major
BWV 846a – Prelude and Fugue in C major (alternative version of BWV 846)
BWV 847 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 2 in C minor
BWV 848 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 3 in C-sharp major
BWV 849 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 4 in C-sharp minor
BWV 850 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 5 in D major
BWV 851 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 6 in D minor
BWV 852 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 7 in E-flat major
BWV 853 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 8 in E-flat minor
BWV 854 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 9 in E major
BWV 855 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 10 in E minor
BWV 855a – Prelude and Fugue in E minor (alternative version of BWV 855) |
1353_7 | BWV 856 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 11 in F major
BWV 857 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 12 in F minor
BWV 858 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 13 in F-sharp major
BWV 859 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 14 in F-sharp minor
BWV 860 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 15 in G major
BWV 861 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 16 in G minor
BWV 862 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 17 in A-flat major
BWV 863 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 18 in G-sharp minor
BWV 864 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 19 in A major
BWV 865 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 20 in A minor
BWV 866 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 21 in B-flat major
BWV 867 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 22 in B-flat minor |
1353_8 | BWV 868 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 23 in B major
BWV 869 – Well-Tempered Clavier, Book 1: Prelude and Fugue No. 24 in B minor
BWV 870 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 1 in C major
BWV 870a – Prelude and Fugue in C major (alternative version of BWV 870)
BWV 870b – Prelude in C major (alternative version of BWV 870)
BWV 871 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 2 in C minor
BWV 872 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 3 in C-sharp major
BWV 872a – Prelude and Fugue in C-sharp major (alternative version of BWV 872)
BWV 873 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 4 in C-sharp minor
BWV 874 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 5 in D major
BWV 875 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 6 in D minor
BWV 875a – Prelude in D minor (alternative version of BWV 875)
BWV 876 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 7 in E-flat major |
1353_9 | BWV 877 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 8 in D-sharp minor
BWV 878 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 9 in E major
BWV 879 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 10 in E minor
BWV 880 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 11 in F major
BWV 881 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 12 in F minor
BWV 882 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 13 in F-sharp major
BWV 883 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 14 in F-sharp minor
BWV 884 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 15 in G major
BWV 885 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 16 in G minor
BWV 886 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 17 in A-flat major
BWV 887 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 18 in G-sharp minor
BWV 888 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 19 in A major |
1353_10 | BWV 889 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 20 in A minor
BWV 890 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 21 in B-flat major
BWV 891 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 22 in B-flat minor
BWV 892 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 23 in B major
BWV 893 – Well-Tempered Clavier, Book 2: Prelude and Fugue No. 24 in B minor |
1353_11 | Preludes and fugues, toccatas and fantasias (BWV 894–923)
BWV 894 – Prelude and Fugue in A minor
BWV 895 – Prelude and Fugue in A minor
BWV 896 – Prelude and Fugue in A major
BWV 897 – Prelude and Fugue in A minor
BWV 898 – Prelude and Fugue in B-flat major on the name B-A-C-H (doubtful)
BWV 899 – Prelude and Fughetta in D minor
BWV 900 – Prelude and Fughetta in E minor
BWV 901 – Prelude and Fughetta in F major
BWV 902 – Prelude and Fughetta in G major
BWV 902a – Prelude in G major (alternative version of BWV 902)
BWV 903 – Chromatic Fantasia and Fugue in D minor
BWV 903a – Chromatic Fantasia in D minor (alternative version of BWV 903)
BWV 904 – Fantasia and Fugue in A minor
BWV 905 – Fantasia and Fugue in D minor
BWV 906 – Fantasia and Fugue in C minor (Fugue unfinished)
BWV 907 – Fantasia and Fughetta in B-flat major
BWV 908 – Fantasia and Fughetta in D major
BWV 909 – Concerto and fugue in C minor
BWV 910 – Toccata in F-sharp minor
BWV 911 – Toccata in C minor |
1353_12 | BWV 912 – Toccata in D major
BWV 913 – Toccata in D minor
BWV 914 – Toccata in E minor
BWV 915 – Toccata in G minor
BWV 916 – Toccata in G major |
1353_13 | Fugues and fughettas (BWV 944–962)
BWV 944 – Fugue in A minor
BWV 945 – Fugue in E minor
BWV 946 – Fugue in C major
BWV 947 – Fugue in A minor
BWV 948 – Fugue in D minor
BWV 949 – Fugue in A major
BWV 950 – Fugue in A major on a theme by Tomaso Albinoni
BWV 951 – Fugue in B minor on a theme by Tomaso Albinoni
BWV 951a – Fugue in B minor (alternative version of BWV 951)
BWV 952 – Fugue in C major
BWV 953 – Fugue in C major
BWV 954 – Fugue in B-flat major on a theme by Johann Adam Reincken
BWV 955 – Fugue in B-flat major
BWV 956 – Fugue in E minor
BWV 957 – Fugue in G major
BWV 958 – Fugue in A minor
BWV 959 – Fugue in A minor
BWV 960 – Fugue in E minor
BWV 961 – Fughetta in C minor
BWV 962 – Fughetta in E minor
Lute fugues
BWV 997 – Lute Suite No. 2 in C minor (Fuge)
BWV 998 – Prelude, Fugue and Allegro in E-flat major
BWV 1000 – Fugue in G minor |
1353_14 | Choral fugues
BWV 232 – Mass in B minor: Credo in unum deum, Confiteor unum baptisma, etc.
BWV 105 – Herr, gehe nicht ins Gericht mit deinem Knecht: 1. Chorus (begins at m.47)
Concerto movements
BWV 1047 – Brandenburg Concerto No. 2 in F major: 3. Allegro assai
BWV 1050 – Brandenburg Concerto No.5 in D Major: 3. Allegro
BWV 1061 – Concerto for 2 harpsichords and strings in C major: 3. Fuga
Sonata movements
Sonatas and partitas for solo violin (BWV 1001–1006)
BWV 1001 – Sonata No. 1 in G minor: 2. Fuga (Allegro) – Transcribed for organ as BWV 539 and for lute as BWV 1000
BWV 1003 – Sonata No. 2 in A minor: 2. Fuga – Transcribed for harpsichord as BWV 964
BWV 1005 – Sonata No. 3 in C major: 2. Fuga (Alla breve) |
1353_15 | Sonatas for violin and harpsichord (BWV 1014–1019)
BWV 1014 – Sonata No. 1 in B minor: 2. Allegro and 4. Allegro
BWV 1015 – Sonata No. 2 in A major: 2. Allegro assai and 4. Presto
BWV 1016 – Sonata No. 3 in E major: 2. Allegro and 4. Allegro
BWV 1017 – Sonata No. 4 in C minor: 2. Allegro and 4. Allegro
BWV 1018 – Sonata No. 5 in F minor: 2. Allegro and 4. Vivace
BWV 1019 – Sonata No. 6 in G major: 5. Allegro
Other sonatas
BWV 965 – Sonata in A minor: 2. Fugue
BWV 1021 – Sonata in G major: 4. Presto
Canons and fugal works in the last two chapters of the Bach-Werke-Verzeichnis (1998) |
1353_16 | |- id="BWV Chapter 12" style="background: #D8D8D8;"
| data-sort-value="1071.z99" | 12.
| data-sort-value="437.000" colspan="8" | Canons (see also: List of canons by Johann Sebastian Bach)
| data-sort-value="1257a" | Up ↑
|- id="BWV 1072"
| data-sort-value="1072.000" | 1072
| data-sort-value="437.001" | 12.
|
| Canon trias harmonica a 8
| D maj.
| data-sort-value="Vx8" | 8V
| data-sort-value="000.45 1: 131" | 451: 131
| data-sort-value="VIII/01: 003, 006" | VIII/l: 3, 6
| Friedrich Wilhelm Marpurg. Abhandlung von der Fuge Vol. 2. Berlin (1754), TAB XXXVII
|
|- id="BWV 1073" style="background: #E3F6CE;"
| data-sort-value="1073.000" | 1073
| data-sort-value="437.002" | 12.
| 1713-08-02
| Canon â 4. Voc: perpetuus
| A min.
| data-sort-value="Vx4" | 4V
| data-sort-value="000.45 1: 132" | 451: 132
| data-sort-value="VIII/01: 003" | VIII/l: 3
| in US-CAh bMS Eng 870 (35b)Neumann/Schulze, Dok I, Nr. 147Spitta I: 386
|
|- id="BWV 1074" style="background: #E3F6CE;" |
1353_17 | | data-sort-value="1074.000" | 1074
| data-sort-value="437.003" | 12.
| data-sort-value="1727-07-01" | 1727
| Canon a 4 (for )
| A min.
| data-sort-value="Vx4" | 4V
| data-sort-value="000.45 1: 134" | 451: 134
| data-sort-value="VIII/01: 003" | VIII/l: 3
| Johann Mattheson. Der vollkommene Capellmeister. Hamburg (1739), p. 412Friedrich Wilhelm Marpurg. Abhandlung von der Fuge nach den Grundsätzen und Exemplen der besten deutschen und ausländischen Meister entworfen ... Vol. 2. Berlin (1754), TAB XXXIII, Fig. 2–3Spitta II: p. 478 / 798
|
|- id="BWV 1075" style="background: #E3F6CE;"
| data-sort-value="1075.000" | 1075
| data-sort-value="438.001" | 12.
| 1734-01-10
| Canon a 2. perpetuus
| D maj.
| data-sort-value="Vx2" | 2V
|
| data-sort-value="VIII/01: 003" | VIII/l: 3
|
|
|- id="BWV 1076" style="background: #E3F6CE;"
| data-sort-value="1076.000" | 1076
| data-sort-value="438.002" | 12.
| data-sort-value="1746-07-01" | 1746
| Canon triplex a 6
| G maj.
| data-sort-value="Vx6" | 6V |
1353_18 | | data-sort-value="000.45 1: 138" | 451: 138
| data-sort-value="VIII/01: 003" | VIII/l: 3
| data-sort-value="after BWV 1087/13" | after BWV 1087/13Johann Sebastian Bach. Canon triplex à 6 Voc:. Leipzig (1747)ClementNeumann/Schulze, Dok II, Nr. 559Nowak. "Ein Bach-Fund" in Fontes artis musicae (1966), pp. 95ffWolff Stile antico
|
|- id="BWV 1077" style="background: #E3F6CE;"
| data-sort-value="1077.000" | 1077
| data-sort-value="438.003" | 12.
| 1747-10-15
| data-sort-value="Canon doppio sopr' il soggetto" | Canone doppio sopr' il soggetto (dedicated to )
| G maj.
| data-sort-value="Vx5" | 4V Bc
|
| data-sort-value="VIII/01: 004" | VIII/1: 4IX/2: 81
| data-sort-value="after BWV 1087/11" | after BWV 1087/11Neumann/Schulze, Dok I, Nr. 174
|
|- id="BWV 1078" style="background: #F6E3CE;"
| data-sort-value="1078.000" | 1078
| data-sort-value="439.002" | 12.
| 1749-03-01
| Canon Fa Mi, et Mi Fa est Tota Musica, a.k.a. Canon super Fa Mi, a 7. post Tempus Musicum
| F maj. |
1353_19 | | data-sort-value="Vx7" | 7V Bc
| data-sort-value="000.45 1: 136" | 451: 136
| data-sort-value="VIII/01: 004" | VIII/l: 4
| data-sort-value="in SBB P 0611" | in SBB P 611Neumann/Schulze, Dok I, Nr. 177
|
|- id="BWV 1086" style="background: #F6E3CE;"
| data-sort-value="1086.000" | 1086
| data-sort-value="439.003" | 12.
| data-sort-value="1750-04-15" | 1750?
| Canon Concordia discors
| D maj.
| data-sort-value="Vx2" | 2V
|
| data-sort-value="VIII/01: 004" | VIII/l: 4III/1: VIII
| in SLB Dresden R 291sNBA VIII/1 Krit. Bericht: 36fReich. "Johann Sebastian Bach und Johann Gottfried Müthel – zwei unbekannte Kanons" in Mf 1960, pp. 449f
|
|- style="background: #E3F6CE;"
| data-sort-value="1087.000" | 1087
| data-sort-value="439.004" | 12.
| data-sort-value="1748-01-01" | 1747/1748 or earlier
| data-sort-value="Canonx14 on the first eight notes of the Goldberg ground" | 14 Canons on the first eight notes of the Goldberg ground
| G maj.
| data-sort-value="Vx6" | 6V
| |
1353_20 | | data-sort-value="V/02: 119" | V/2: 119
| data-sort-value="after BWV 0988/1" | after BWV 988/1; /11 → BWV 1077; /13 → 1076; in BN Paris Ms. 17669, Bl. 18vBN Paris Ms. 17669, Bl. 18v at Gárdonyi. "Zu einigen Kanons von J. S. Bach" in Studia Musicologica: Academiae Seientiarum Hungaricae Vol. 28 (1986), pp. 321–324Wolff. "Bach's Handexemplar of the Goldberg Variations" in JAMS (1976), pp. 224ff
|
|- id="BWV Chapter 13" style="background: #D8D8D8;"
| data-sort-value="1078.z99" | 13.
| data-sort-value="442.000" colspan="8" | Musical Offering, Art of the Fugue (see also: List of late contrapuntal works by Johann Sebastian Bach)
| data-sort-value="1264a" | Up ↑
|- style="background: #E3F6CE;"
| data-sort-value="1079.000" | 1079
| data-sort-value="442.001" | 13.
| 1747-07-07
| Musical Offering
|
| Kb Fl 2Vl Bc
| data-sort-value="000.31 2" | 312
| data-sort-value="VIII/01: 046" | VIII/1: 46
|
|
|- style="background: #E3F6CE;"
| data-sort-value="1080.100" | 1080.1 |
1353_21 | | data-sort-value="442.002" rowspan="2" | 13.
| data-sort-value="1745-12-31" |
| The Art of Fugue (autograph)
| rowspan="2" |
| data-sort-value="Hs?" rowspan="2" | Hc (?)
| data-sort-value="000.50" | 251
| data-sort-value="VIII/02: 003" | VIII/2.1
| data-sort-value="in SBB P 0200" | → BWV 1080.2
|
|- style="background: #E3F6CE;"
| data-sort-value="1080.200" | 1080.2
| data-sort-value="1747-12-31" |
| The Art of Fugue (print version)
| data-sort-value="000.50" | 47
| data-sort-value="VIII/02: 003" | VIII/2.2
| data-sort-value="in SBB P 0200" | after BWV 1080.1
|
|} |
1353_22 | Canons (BWV 1072–1078)
BWV 1072 – Canon trias harmonica a 8
BWV 1073 – Canon a 4 perpetuus
BWV 1074 – Canon a 4
BWV 1075 – Canon a 2 perpetuus
BWV 1076 – Canon triplex a 6
BWV 1077 – Canone doppio sopr'il soggetto
BWV 1078 – Canon super fa mi a 7 post tempus musicum
Later additions to the BWV catalogue:
BWV 1086 – Canon concordia discors
BWV 1087 – 14 canons on the First Eight Notes of Goldberg Variations Ground (discovered 1974)
Late contrapuntal works (BWV 1079–1080)
BWV 1079 – The Musical Offering (Musikalisches Opfer)
BWV 1080 – The Art of Fugue (Die Kunst der Fuge)
Doubtful fugues
BWV 131a – Fugue in G minor, BWV 131a for organ. Doubtful arrangement of a choral fugue from BWV 131
BWV 1026 – Fugue in G minor for violin and harpsichord. Once considered spurious, current thinking is that this is an early work by Bach.
Notes
Fugal works by Johann Sebastian Bach, List of |
1354_0 | Mars Needs Moms is a 2011 American 3D computer-animated science fiction film produced by ImageMovers Digital and released by Walt Disney Pictures. Based on the Berkeley Breathed book of the same title, the film is centered on Milo, a nine-year-old boy who, after being grounded, finally comes to understand the needs of family, and has to rescue his mother after she is abducted by Martians. It was co-written and directed by Simon Wells. The film stars both Seth Green (motion capture) and newcomer Seth Dusky (voice) as Milo. The voice cast also includes Dan Fogler, Elisabeth Harnois, Mindy Sterling and Joan Cusack. This was the last film by ImageMovers Digital before it was re-absorbed into ImageMovers. |
1354_1 | Mars Needs Moms was released in theaters on March 11, 2011, in the Disney Digital 3D, RealD 3D and IMAX 3D formats. The film received mixed-to-negative reviews from critics, who praised the visuals, voice acting, score, and set design but criticized its story, drama, and characters. Opinions of the motion capture animation were mixed. Some praised it for looking realistic and others criticized it for falling into the uncanny valley and looking creepy. It grossed $39 million worldwide on a $150 million budget, making it a box-office disaster, with a loss of $100–144 million.
Plot |
1354_2 | Unannounced to humans, there is a thriving, technologically sophisticated society of Martians living below the surface of Mars. The Martians' Supervisor, while observing Earth, sees a mother persuading her son, Milo, to do his chores. The Martians decide to bring her to Mars, where her "momness" will be extracted and implanted into the next generation of nannybots. Meanwhile, Milo, who doesn't like to follow house rules and do chores and has been sent to his room for feeding broccoli to his cat, Cujo, sarcastically tells his mother that his life would be better without her, which hurts her deeply. |
1354_3 | Later that night, Milo goes to apologize, but discovers his mom is being abducted. He runs after her, but they end up in separate parts of the Martian spaceship. On Mars, Milo is taken to an underground cell. He escapes and is chased by Martian guards, but he follows a voice that tells him to jump down a chute, and lands in a lower subterranean level. There, he sees a trash-covered landscape that is inhabited by furry creatures. |
1354_4 | Milo is whisked away by the creatures to meet Gribble, a.k.a. George Ribble, the childlike adult human who had told him to jump down the chute. Gribble explains to Milo that the Martians plan to extract Milo's mom's memories at sunrise, using a process that will kill her. Gribble, who is lonely and does not want Milo to leave, pretends to help Milo rescue his mother. His plan goes awry, leading to Gribble being captured and Milo being pursued by Martian guards. Milo is rescued by Ki, one of the supervisors who raise Martian babies. Milo tells her about his search for his Mom and what a human relationship with a mom is like, as Ki and her kin were mentored by only nannybots and supervisors and do not know of love. |
1354_5 | Milo returns to Gribble's home but finds him missing. Gribble's robotic spider, Two-Cat, takes Milo to the Martian compound where Gribble is being prepared for execution. Milo is captured by the guards, but Ki tosses him a laser gun, allowing him to escape. Milo and Gribble retreat to an even lower uninhabited level, where Gribble describes his own mom's abduction and murder by the Martians 20 years ago. Gribble blames himself for her being chosen and regrets that he had not been able to save her. Milo convinces Gribble to actually help him just as Ki finds them. They discover an ancient mural of a Martian family and realize that Martian children were not always raised by machines. Gribble explains that Martian female babies are currently raised by nannybots in the technologically advanced society, while the male babies are sent down below to be raised by adult male Martians, which are the furry creatures he encountered earlier. |
1354_6 | Milo, Gribble, and Ki save Milo's mom just before sunrise, causing the energy of the extraction device to short out the electronic locks to the control room. This lets the adult males and babies enter, where they run amok, attacking the guards and robots. Milo and his mom steal oxygen helmets and try to escape across the Martian surface, but the Supervisor, while attempting to kill them, causes Milo to trip and his helmet shatters. His mom gives him her own helmet, saving Milo but causing herself to suffocate in the planet's air. The Martians are awed, as this is the first time they have seen love. Gribble finds his own mother's helmet and gives it to Milo's mom, saving her. Milo apologizes to his mom for his earlier words and the two reconcile. Ki brings a ship for them to escape in, but the Supervisor intervenes. Ki argues that Martians were meant to be raised in families, with love, but the Supervisor insists that the current situation is better because, to her, it is more |
1354_7 | efficient. The guards realize the Supervisor's cruel nature and arrest her, deciding that they now prefer the loving vision of family life, and the other Martians celebrate. |
1354_8 | Milo, his mom, Gribble, Ki, and Two-Cat travel back to Earth. Gribble decides not to stay because he wants to pursue a relationship with Ki on Mars. Milo and his mom return to their house just before Milo's dad arrives. |
1354_9 | Cast
Seth Green as Milo (motion-capture), a 9-year-old boy who has a strained relationship with his mother
Seth Dusky as Milo (voice)
Dan Fogler as George "Gribble" Ribble, a childish human living in Mars that Milo befriends
Elisabeth Harnois as Ki, an English language knowing martian who defects from the Supervisor and teams up with Milo and Gribble
Mindy Sterling as The Supervisor, the tyrannical leader of the Martians who seek to abduct children's moms and extract their momness to nannybots
Joan Cusack as Milo's mother
Kevin Cahoon as Wingnut, a male martian and one of Gribble's friends
Dee Bradley Baker as Two Cat (voice), Gribble's bug-like robot assistant
Tom Everett Scott as Milo's father
Raymond, Robert, and Ryan Ochoa as Martian Hatchlings
Matthew Henerson, Adam Jennings, Stephen Kearin, Amber Gainey Meade, Aaron Rapke, Julene Renee, Kirsten Severson, and Matthew Wolf as Martians |
1354_10 | Production
Simon Wells had known Zemeckis since the mid-1980s when he was supervising animator and storyboard artist for Who Framed Roger Rabbit. He also worked on Back to the Future Part II and III and later worked on The Polar Express, which was why he was attracted to making Mars Needs Moms. The production designer was Doug Chiang, and the supervising art director was Norm Newberry. The title of the film (and to an extent, the source material) is a twist on the title of American International Pictures' 1966 film Mars Needs Women.
The makers came up with their own alien language. In developing the language, all of the actors
spent a day where they recorded different interpretations of a list of words; the producers picked their favorite interpretations from that recording and put them in a book documenting the fictional language for the actors to speak. |
1354_11 | Elisabeth Harnois stated in an interview that she and the cast were given scenarios by Wells to which they acted out responses in improvised Martian language.
Seth Green described doing the motion-capture as physically demanding work: "A lot of running, jumping, falling, hitting, spinning. I wore a harness for, like, 85 percent of the movie. It was uncomfortable." After spending six weeks outfitted in a special sensor-equipped performance-capture suit while simultaneously performing Milo's lines, Seth Green's voice sounded too mature for the character and was dubbed over by that of 12-year-old newcomer Seth R. Dusky. |
1354_12 | For the auditions, Kevin Cahoon performed two scenes, including the ending; he recalled the instructions saying, "create your Martian language and play the scene." He previously played Ed, another non-speaking role, in the Broadway musical version of The Lion King (1994): "it's almost like silent film. You have speak with your heart and soul and face, and you have to act as if you have dialogue with everyone else. I think that's where you find the humanity, or the martiananity, of the character." Cahoon's mannerisms were also used for the other martians. Mars Needs Moms is Cahoon's first time collaborating with Dan Fogler since the two worked with each other in New York stage theater. As he described his opinion on the film, "I was blown away. It's beautiful. The technology is incredible and the IMAX is awesome. I was so impressed with the score, but also the heart. I got misty-eyes towards the end with the mom/Milo relationship. I thought it really connected in a wonderful way and am |
1354_13 | so honored to be a part of it." |
1354_14 | In 2020, Brie Larson revealed via YouTube that she had auditioned for the character Ki, who was eventually portrayed by Elisabeth Harnois.
Release
Mars Needs Moms was released in theaters on March 11, 2011. The film's premiere was held at the El Capitan Theatre in Los Angeles on March 6, 2011. |
1354_15 | Home media
The film was released on Blu-ray, Blu-ray 3D, DVD, and movie download on August 9, 2011. The release is produced in three different physical packages: a four-disc combo pack (Blu-ray, Blu-ray 3D, DVD, and "Digital Copy"); a two-disc Blu-ray combo pack (Blu-ray and DVD); and a single-disc DVD. The "Digital Copy" included with the four-disc combo pack is a separate disc that allows users to download a copy of the film onto a computer through iTunes or Windows Media Player software. The film is also a movie download or On-Demand option. All versions of the release (except for the On-Demand option) include the "Fun With Seth" and "Martian 101" bonus features, while the Blu-ray 2D version additionally includes deleted scenes, the "Life On Mars: The Full Motion-Capture Experience" feature, and an extended opening film clip. The Blu-ray 3D version also has an alternate scene called "Mom-Napping", a finished 3D alternate scene of the Martian abduction of Milo's mom.
Reception |
1354_16 | Box office |
1354_17 | Mars Needs Moms was a box-office disaster, and the worst financial loss for a Disney-branded film. It earned $1,725,000 on its first day, for a weekend total of $6,825,000. This is the 22nd-worst opening ever for a film playing in 3,000+ theaters. Adjusted for inflation, considering the total net loss of money (not the profit-to-loss ratio), it was still the fourth-largest box office failure in history. In 2014, the Los Angeles Times listed the film as one of the most expensive box-office disasters of all time. On March 14, 2011, Brooks Barnes of The New York Times commented that it was rare for a Disney-branded film to do so badly, with the reason for its poor performance being the unoriginal premise, the style of animation, which fails to cross the uncanny valley threshold, and negative word of mouth on social networks, along with releasing it on the same week as Battle: Los Angeles which had more hype with the general movie goers. Barnes concluded, "Critics and audiences alike, |
1354_18 | with audiences voicing their opinions on Twitter, blogs and other social media, complained that the Zemeckis technique can result in character facial expressions that look unnatural. Another common criticism was that Mr. Zemeckis focuses so much on technological wizardry that he neglects storytelling." |
1354_19 | Critical response
The review aggregator website Rotten Tomatoes reported a 37% approval rating with an average rating of 5.00/10 based on 116 reviews. The website's consensus reads, "The cast is solid and it's visually well-crafted, but Mars Needs Moms suffers from a lack of imagination and heart." On Metacritic, the film had a score of 49 out of 100 based on 22 critics, indicating "mixed or average reviews". Audiences polled by CinemaScore gave the film an average grade of "B" on an A+ to F scale.
The Sydney Morning Herald labeled the motion-capture animation superior to Avatar (2009), and while noting the story had "pure Disney cheese," Wells "thankfully know[s] precisely when to inject action and humour when the mush-o-meter approaches the red." |
1354_20 | Some critics favorably compared the set design to Tron: Legacy (2010), including Tim Grierson of Screen Daily, who opined that the motion-capture "improved significantly since the days of The Polar Express." He also spotlighted the film's attempt at a "tonal divide," as it has both comic sequences typical for a kids film and themes about sacrifice. However, he criticized the "chaotic" story and two "irksome" protagonists: Milo, whose voice actor "overdoes the character's whiny anxiousness to the point that it's hard to root for him;" and Gribble, a "predictably wisecracking sidekick." Us Weekly also panned the characters: "[Milo] makes a whiny hero, and Dan Fogler (as his buddy on Mars) fails to amuse. Plus, why is Milo's stay-at-home mom a saint and the working alien moms evil?" |
1354_21 | The Hollywood Reporter praised Mars Needs Moms's motion-capture visuals, but analogized its story as too much like a Disneyland ride and also called it "odd [...] how a movie meant to glorify moms is so riddled with anti-feminist concepts." Time Out New York called it not that much different from other children's science fiction movies: "After the novelty of these backgrounds and comin’-at-ya bits wears off, Mars Needs Moms has to rely on Fogler's obnoxious Jack Black Jr. shtick, a weak subplot involving a ’60s-obsessed Martian graffiti artist (Harnois) and rote video-game-y action sequences to carry it along—and that simply won't cut it." |
1354_22 | Entertainment Weekly positively described the film as a children's movie version of Avatar: "Enhanced by nimble ad-libbing from the comedy-trained cast, the screenplay is delightful, by turns funny and emotional, as befits a Disney family fable in which, through wacky adversity, Mom and kid reaffirm their love for each other while Dad is nowhere in sight. (He's not dead, just away on business.) And with its splendid use of computer-generated motion-capture animation and 3-D effects, the movie is also visually magnificent — modestly so." Mike Hale of the New York Times also gave the film a negative review, saying, "Mars, once again, looks to Earth to supplement its female population because, it seems, the women who run Mars think Earth mothers are skilled at child rearing." |
1354_23 | Lael Loewenstein of Variety magazine gave the film a mixed review and called it "A modestly enjoyable performance-capture creation bearing the unmistakable imprint of producer Robert Zemeckis." In addition to acclaiming the visuals,
SFX also opined gave some praises towards the writing "there are some good laughs, it's pacy enough to whizz us on by the sometimes repetitive narrative [...] and although it's hard to see little boys admitting that they really do love their mummies – as much as the film wants them to – Mars Needs Moms does provoke a few lumps in older throats, for all you may decry its mawkish Stateside sensibilities." |
1354_24 | Nick Schager of The Village Voice was very harsh; panning the "rubbery," "unreal," and "unsettling" character animation, which he called a "jarring dissonance" with the science fiction setting; and the stealing of common tropes in other well-known science fiction films. He also noted a major plot hole, specifically Supervisor's stealing of mothers' disciplinary skills for use on technological devices: "The plot thus hinges on a fundamental illogicality, since the chief differentiating characteristic between mothers and machines isn't discipline but compassion." William Thomas of Empire Magazine gave the film a two out of five stars, saying, "An uninvolving mo-cap adventure that's well below par. Marvin the Martian would be unhappy to share his planet with this bunch."
Some reviewers questioned the film's moral about well-behaved kids having their very good mothers taken by aliens. |
1354_25 | Accolades
Mars Needs Moms received a nomination for a Movieguide Award for Best Film for Family Audiences; while John Powell's work on it, Rio (2011), and Kung Fu Panda 2 (2011) garnered him a nomination for the 2011 World Soundtrack Award for Film Composer of the Year.
Seth Green's original dialogue
Actor Seth Green, on top of being the motion capture actor for Milo, was also initially cast as his voice actor before his performance was deemed as sounding too mature for the character. It was subsequently cut and re-recorded by child actor Seth R. Dusky prior to the film's release despite the first trailer for the film featuring Green's dialogue.
On December 5, 2018, YouTuber RebelTaxi uploaded a video covering the production history of and reviewing every film released by ImageMovers Digital, where he jokingly advocated for the release of Seth Green's original performance complete with the hashtag “#ReleaseTheSethGreenCut”. |
1354_26 | Earlier that year, YouTuber Justin Wilton ripped the film from its Blu-Ray release to use for his review of the film. After converting the video file, he found that a lower quality recording of Green's dialogue tracks were used in his ripped copy instead of Dusky's, despite his performance being the only English language setting on the disc menu and Green's not even being displayed as an accessible option. Assuming that the availability of the Seth Green cut was already known, its existence remained unknown to the wider public until he was prompted by #ReleaseTheSethGreenCut comments he saw online to announce his discovery on May 29, 2020.
The following day, he uploaded the Seth Green cut of the movie to the Internet Archive.
See also
List of biggest box-office bombs
List of films set on Mars
List of films featuring extraterrestrials
Mars in fiction
References |
1354_27 | External links
Mars Needs Moms at the Big Cartoon Database
Pictures of the scoring sessions of Mars Needs Moms at Scoringsessions.com
2011 films
American films
2010s English-language films
2011 science fiction films
2010s American animated films
2011 3D films
2011 animated films
2011 computer-animated films
Alien abduction films
Alien invasions in films
American 3D films
American adventure comedy films
American animated science fiction films
Animated films based on children's books
Animated films based on novels
Animated films about extraterrestrial life
2010s children's animated films
Disney animated films
Mars in film
Matriarchy
Films using motion capture
Walt Disney Pictures films
ImageMovers films
IMAX films
Films directed by Simon Wells
Films scored by John Powell
Adaptations of works by Berkeley Breathed
3D animated films
2010s children's fantasy films |
1355_0 | Scattering parameters or S-parameters (the elements of a scattering matrix or S-matrix) describe the electrical behavior of linear electrical networks when undergoing various steady state stimuli by electrical signals.
The parameters are useful for several branches of electrical engineering, including electronics, communication systems design, and especially for microwave engineering. |
1355_1 | The S-parameters are members of a family of similar parameters, other examples being: Y-parameters, Z-parameters, H-parameters, T-parameters or ABCD-parameters. They differ from these, in the sense that S-parameters do not use open or short circuit conditions to characterize a linear electrical network; instead, matched loads are used. These terminations are much easier to use at high signal frequencies than open-circuit and short-circuit terminations. Contrary to popular belief, the quantities are not measured in terms of power (except in now-obsolete six-port network analyzers). Modern vector network analyzers measure amplitude and phase of voltage traveling wave phasors using essentially the same circuit as that used for the demodulation of digitally modulated wireless signals. |
1355_2 | Many electrical properties of networks of components (inductors, capacitors, resistors) may be expressed using S-parameters, such as gain, return loss, voltage standing wave ratio (VSWR), reflection coefficient and amplifier stability. The term 'scattering' is more common to optical engineering than RF engineering, referring to the effect observed when a plane electromagnetic wave is incident on an obstruction or passes across dissimilar dielectric media. In the context of S-parameters, scattering refers to the way in which the traveling currents and voltages in a transmission line are affected when they meet a discontinuity caused by the insertion of a network into the transmission line. This is equivalent to the wave meeting an impedance differing from the line's characteristic impedance. |
1355_3 | Although applicable at any frequency, S-parameters are mostly used for networks operating at radio frequency (RF) and microwave frequencies where signal power and energy considerations are more easily quantified than currents and voltages. S-parameters change with the measurement frequency, so frequency must be specified for any S-parameter measurements stated, in addition to the characteristic impedance or system impedance.
S-parameters are readily represented in matrix form and obey the rules of matrix algebra. |
1355_4 | Background
The first published description of S-parameters was in the thesis of Vitold Belevitch in 1945. The name used by Belevitch was repartition matrix and limited consideration to lumped-element networks. The term scattering matrix was used by physicist and engineer Robert Henry Dicke in 1947 who independently developed the idea during wartime work on radar. In these S-parameters and scattering matrices, the scattered waves are the so-called traveling waves. A different kind of S-parameters was introduced in the 1960s. The latter was popularized by Kaneyuki Kurokawa, who referred to the new scattered waves as 'power waves.' The two types of S-parameters have very different properties and must not be mixed up. In his seminal paper, Kurokawa clearly distinguishes the power-wave S-parameters and the conventional, traveling-wave S-parameters. A variant of the latter is the pseudo-traveling-wave S-parameters. |
1355_5 | In the S-parameter approach, an electrical network is regarded as a 'black box' containing various interconnected basic electrical circuit components or lumped elements such as resistors, capacitors, inductors and transistors, which interacts with other circuits through ports. The network is characterized by a square matrix of complex numbers called its S-parameter matrix, which can be used to calculate its response to signals applied to the ports. |
1355_6 | For the S-parameter definition, it is understood that a network may contain any components provided that the entire network behaves linearly with incident small signals. It may also include many typical communication system components or 'blocks' such as amplifiers, attenuators, filters, couplers and equalizers provided they are also operating under linear and defined conditions.
An electrical network to be described by S-parameters may have any number of ports. Ports are the points at which electrical signals either enter or exit the network. Ports are usually pairs of terminals with the requirement that the current into one terminal is equal to the current leaving the other. S-parameters are used at frequencies where the ports are often coaxial or waveguide connections. |
1355_7 | The S-parameter matrix describing an N-port network will be square of dimension N and will therefore contain elements. At the test frequency each element or S-parameter is represented by a unitless complex number that represents magnitude and angle, i.e. amplitude and phase. The complex number may either be expressed in rectangular form or, more commonly, in polar form. The S-parameter magnitude may be expressed in linear form or logarithmic form. When expressed in logarithmic form, magnitude has the "dimensionless unit" of decibels. The S-parameter angle is most frequently expressed in degrees but occasionally in radians. Any S-parameter may be displayed graphically on a polar diagram by a dot for one frequency or a locus for a range of frequencies. If it applies to one port only (being of the form ), it may be displayed on an impedance or admittance Smith Chart normalised to the system impedance. The Smith Chart allows simple conversion between the parameter, equivalent to the |
1355_8 | voltage reflection coefficient and the associated (normalised) impedance (or admittance) 'seen' at that port. |
1355_9 | The following information must be defined when specifying a set of S-parameters:
The frequency
The nominal characteristic impedance (often 50 Ω)
The allocation of port numbers
Conditions which may affect the network, such as temperature, control voltage, and bias current, where applicable.
The power-wave S-parameter matrix
A definition
For a generic multi-port network, the ports are numbered from 1 to N, where N is the total number of ports. For port i, the associated S-parameter definition is in terms of incident and reflected 'power waves', and respectively.
Kurokawa defines the incident power wave for each port as
and the reflected wave for each port is defined as
where is the impedance for port i, is the complex conjugate of , and are respectively the complex amplitudes of the voltage and current at port i, and |
1355_10 | Sometimes it is useful to assume that the reference impedance is the same for all ports in which case the definitions of the incident and reflected waves may be simplified to
and
Note that as was pointed out by Kurokawa himself, the above definitions of and are not unique. The relation between the vectors a and b, whose i-th components are the power waves and respectively, can be expressed using the S-parameter matrix S:
Or using explicit components:
Reciprocity
A network will be reciprocal if it is passive and it contains only reciprocal materials that influence the transmitted signal. For example, attenuators, cables, splitters and combiners are all reciprocal networks and in each case, or the S-parameter matrix will be equal to its transpose. Networks which include non-reciprocal materials in the transmission medium such as those containing magnetically biased ferrite components will be non-reciprocal. An amplifier is another example of a non-reciprocal network. |
1355_11 | A property of 3-port networks, however, is that they cannot be simultaneously reciprocal, loss-free, and perfectly matched.
Lossless networks
A lossless network is one which does not dissipate any power, or: . The sum of the incident powers at all ports is equal to the sum of the reflected powers at all ports. This implies that the S-parameter matrix is unitary, that is , where is the conjugate transpose of and is the identity matrix.
Lossy networks
A lossy passive network is one in which the sum of the incident powers at all ports is greater than the sum of the reflected powers at all ports. It therefore dissipates power: . Thus , and is positive definite.
Two-port S-parameters
The S-parameter matrix for the 2-port network is probably the most commonly used and serves as the basic building block for generating the higher order matrices for larger networks. In this case the relationship between the reflected, incident power waves and the S-parameter matrix is given by:
. |
1355_12 | Expanding the matrices into equations gives:
and
.
Each equation gives the relationship between the reflected and incident power waves at each of the network ports, 1 and 2, in terms of the network's individual S-parameters, , , and . If one considers an incident power wave at port 1 () there may result from it waves exiting from either port 1 itself () or port 2 (). However, if, according to the definition of S-parameters, port 2 is terminated in a load identical to the system impedance () then, by the maximum power transfer theorem, will be totally absorbed making equal to zero. Therefore, defining the incident voltage waves as and with the reflected waves being and ,
and .
Similarly, if port 1 is terminated in the system impedance then becomes zero, giving
and
The 2-port S-parameters have the following generic descriptions: |
1355_13 | is the input port voltage reflection coefficient
is the reverse voltage gain
is the forward voltage gain
is the output port voltage reflection coefficient.
If, instead of defining the voltage wave direction relative to each port, they are defined by their absolute direction as forward and reverse waves then and . The S-parameters then take on a more intuitive meaning such as the forward voltage gain being defined by the ratio of the forward voltages .
Using this, the above matrix may be expanded in a more practical way |
1355_14 | S-parameter properties of 2-port networks
An amplifier operating under linear (small signal) conditions is a good example of a non-reciprocal network and a matched attenuator is an example of a reciprocal network. In the following cases we will assume that the input and output connections are to ports 1 and 2 respectively which is the most common convention. The nominal system impedance, frequency and any other factors which may influence the device, such as temperature, must also be specified.
Complex linear gain
The complex linear gain G is given by
.
That is the linear ratio of the output reflected power wave divided by the input incident power wave, all values expressed as complex quantities. For lossy networks it is sub-unitary, for active networks .
It will be equal with the voltage gain only when the device has equal input and output impedances.
Scalar linear gain
The scalar linear gain (or linear gain magnitude) is given by
. |
1355_15 | This represents the gain magnitude (absolute value), the ratio of the output power-wave to the input power-wave, and it equals the square-root of the power gain.
This is a real-value (or scalar) quantity, the phase information being dropped.
Scalar logarithmic gain
The scalar logarithmic (decibel or dB) expression for gain (g) is:
dB.
This is more commonly used than scalar linear gain and a positive quantity is normally understood as simply a "gain", while a negative quantity is a "negative gain" (a "loss"), equivalent to its magnitude in dB. For example, at 100 MHz, a 10 m length of cable may have a gain of −1 dB, equal to a loss of 1 dB.
Insertion loss
In case the two measurement ports use the same reference impedance, the insertion loss () is the reciprocal of the magnitude of the transmission coefficient expressed in decibels. It is thus given by:
dB. |
1355_16 | It is the extra loss produced by the introduction of the device under test (DUT) between the 2 reference planes of the measurement. The extra loss may be due to intrinsic loss in the DUT and/or mismatch. In case of extra loss the insertion loss is defined to be positive. The negative of insertion loss expressed in decibels is defined as insertion gain and is equal to the scalar logarithmic gain (see: definition above).
Input return loss
Input return loss () can be thought of as a measure of how close the actual input impedance of the network is to the nominal system impedance value. Input return loss expressed in decibels is given by
dB.
Note that for passive two-port networks in which , it follows that return loss is a non-negative quantity: . Also note that somewhat confusingly, return loss is sometimes used as the negative of the quantity defined above, but this usage is, strictly speaking, incorrect based on the definition of loss. |
1355_17 | Output return loss
The output return loss () has a similar definition to the input return loss but applies to the output port (port 2) instead of the input port. It is given by
dB.
Reverse gain and reverse isolation
The scalar logarithmic (decibel or dB) expression for reverse gain () is:
dB.
Often this will be expressed as reverse isolation () in which case it becomes a positive quantity equal to the magnitude of and the expression becomes:
dB.
Reflection coefficient
The reflection coefficient at the input port () or at the output port () are equivalent to and respectively, so
and .
As and are complex quantities, so are and .
The reflection coefficients are complex quantities and may be graphically represented on polar diagrams or Smith Charts
See also the Reflection Coefficient article. |
1355_18 | Voltage standing wave ratio
The voltage standing wave ratio (VSWR) at a port, represented by the lower case 's', is a similar measure of port match to return loss but is a scalar linear quantity, the ratio of the standing wave maximum voltage to the standing wave minimum voltage. It therefore relates to the magnitude of the voltage reflection coefficient and hence to the magnitude of either for the input port or for the output port.
At the input port, the VSWR () is given by
At the output port, the VSWR () is given by
This is correct for reflection coefficients with a magnitude no greater than unity, which is usually the case. A reflection coefficient with a magnitude greater than unity, such as in a tunnel diode amplifier, will result in a negative value for this expression. VSWR, however, from its definition, is always positive. A more correct expression for port k of a multiport is; |
1355_19 | 4-port S-parameters
4 Port S Parameters are used to characterize 4 port networks. They include information regarding the reflected and incident power waves between the 4 ports of the network.
They are commonly used to analyze a pair of coupled transmission lines to determine the amount of cross-talk between them, if they are driven by two separate single ended signals, or the reflected and incident power of a differential signal driven across them. Many specifications of high speed differential signals define a communication channel in terms of the 4-Port S-Parameters, for example the 10-Gigabit Attachment Unit Interface (XAUI), SATA, PCI-X, and InfiniBand systems.
4-port mixed-mode S-parameters
4-port mixed-mode S-parameters characterize a 4-port network in terms of the response of the network to common mode and differential stimulus signals. The following table displays the 4-port mixed-mode S-parameters. |
1355_20 | Note the format of the parameter notation SXYab, where "S" stands for scattering parameter or S-parameter, "X" is the response mode (differential or common), "Y" is the stimulus mode (differential or common), "a" is the response (output) port and b is the stimulus (input) port. This is the typical nomenclature for scattering parameters. |
1355_21 | The first quadrant is defined as the upper left 4 parameters describing the differential stimulus and differential response characteristics of the device under test. This is the actual mode of operation for most high-speed differential interconnects and is the quadrant that receives the most attention. It includes input differential return loss (SDD11), input differential insertion loss (SDD21), output differential return loss (SDD22) and output differential insertion loss (SDD12). Some benefits of differential signal processing are;
reduced electromagnetic interference susceptibility
reduction in electromagnetic radiation from balanced differential circuit
even order differential distortion products transformed to common mode signals
factor of two increase in voltage level relative to single-ended
rejection to common mode supply and ground noise encoding onto differential signal |
1355_22 | The second and third quadrants are the upper right and lower left 4 parameters respectively. These are also referred to as the cross-mode quadrants. This is because they fully characterize any mode conversion occurring in the device under test, whether it is common-to-differential SDCab conversion (EMI susceptibility for an intended differential signal SDD transmission application) or differential-to-common SCDab conversion (EMI radiation for a differential application). Understanding mode conversion is very helpful when trying to optimize the design of interconnects for gigabit data throughput. |
1355_23 | The fourth quadrant is the lower right 4 parameters and describes the performance characteristics of the common-mode signal SCCab propagating through the device under test. For a properly designed SDDab differential device there should be minimal common-mode output SCCab. However, the fourth quadrant common-mode response data is a measure of common-mode transmission response and used in a ratio with the differential transmission response to determine the network common-mode rejection. This common mode rejection is an important benefit of differential signal processing and can be reduced to one in some differential circuit implementations. |
1355_24 | S-parameters in amplifier design
The reverse isolation parameter determines the level of feedback from the output of an amplifier to the input and therefore influences its stability (its tendency to refrain from oscillation) together with the forward gain . An amplifier with input and output ports perfectly isolated from each other would have infinite scalar log magnitude isolation or the linear magnitude of would be zero. Such an amplifier is said to be unilateral. Most practical amplifiers though will have some finite isolation allowing the reflection coefficient 'seen' at the input to be influenced to some extent by the load connected on the output. An amplifier which is deliberately designed to have the smallest possible value of is often called a buffer amplifier. |
1355_25 | Suppose the output port of a real (non-unilateral or bilateral) amplifier is connected to an arbitrary load with a reflection coefficient of . The actual reflection coefficient 'seen' at the input port will be given by
.
If the amplifier is unilateral then and or, to put it another way, the output loading has no effect on the input.
A similar property exists in the opposite direction, in this case if is the reflection coefficient seen at the output port and is the reflection coefficient of the source connected to the input port. |
1355_26 | Port loading conditions for an amplifier to be unconditionally stable
An amplifier is unconditionally stable if a load or source of any reflection coefficient can be connected without causing instability. This condition occurs if the magnitudes of the reflection coefficients at the source, load and the amplifier's input and output ports are simultaneously less than unity. An important requirement that is often overlooked is that the amplifier be a linear network with no poles in the right half plane. Instability can cause severe distortion of the amplifier's gain frequency response or, in the extreme, oscillation. To be unconditionally stable at the frequency of interest, an amplifier must satisfy the following 4 equations simultaneously: |
1355_27 | The boundary condition for when each of these values is equal to unity may be represented by a circle drawn on the polar diagram representing the (complex) reflection coefficient, one for the input port and the other for the output port. Often these will be scaled as Smith Charts. In each case coordinates of the circle centre and the associated radius are given by the following equations:
values for (output stability circle)
Radius
Center
values for (input stability circle)
Radius
Center
In both cases
and the superscript star (*) indicates a complex conjugate.
The circles are in complex units of reflection coefficient so may be drawn on impedance or admittance based Smith charts normalised to the system impedance. This serves to readily show the regions of normalised impedance (or admittance) for predicted unconditional stability. Another way of demonstrating unconditional stability is by means of the Rollett stability factor (), defined as |
1355_28 | The condition of unconditional stability is achieved when and
Scattering transfer parameters
The Scattering transfer parameters or T-parameters of a 2-port network are expressed by the T-parameter matrix and are closely related to the corresponding S-parameter matrix. However, unlike S parameters, there is no simple physical means to measure the T parameters in a system, sometimes referred to as Youla waves. The T-parameter matrix is related to the incident and reflected normalised waves at each of the ports as follows:
However, they could be defined differently, as follows : |
1355_29 | The RF Toolbox add-on to MATLAB and several books (for example "Network scattering parameters") use this last definition, so caution is necessary. The "From S to T" and "From T to S" paragraphs in this article are based on the first definition. Adaptation to the second definition is trivial (interchanging T11 for T22, and T12 for T21).
The advantage of T-parameters compared to S-parameters is that providing reference impedances are purely, real or complex conjugate, they may be used to readily determine the effect of cascading 2 or more 2-port networks by simply multiplying the associated individual T-parameter matrices. If the T-parameters of say three different 2-port networks 1, 2 and 3 are , and respectively then the T-parameter matrix for the cascade of all three networks () in serial order is given by: |
1355_30 | Note that matrix multiplication is not commutative, so the order is important. As with S-parameters, T-parameters are complex values and there is a direct conversion between the two types. Although the cascaded T-parameters is a simple matrix multiplication of the individual T-parameters, the conversion for each network's S-parameters to the corresponding T-parameters and the conversion of the cascaded T-parameters back to the equivalent cascaded S-parameters, which are usually required, is not trivial. However once the operation is completed, the complex full wave interactions between all ports in both directions will be taken into account. The following equations will provide conversion between S and T parameters for 2-port networks.
From S to T:
Where indicates the determinant of the matrix ,
.
From T to S
Where indicates the determinant of the matrix . |
1355_31 | 1-port S-parameters
The S-parameter for a 1-port network is given by a simple 1 × 1 matrix of the form where n is the allocated port number. To comply with the S-parameter definition of linearity, this would normally be a passive load of some type. An antenna is a common one-port network for which small values of indicate that the antenna will either radiate or dissipate/store power. |
1355_32 | Higher-order S-parameter matrices
Higher order S-parameters for pairs of dissimilar ports (), where may be deduced similarly to those for 2-port networks by considering pairs of ports in turn, in each case ensuring that all of the remaining (unused) ports are loaded with an impedance identical to the system impedance. In this way the incident power wave for each of the unused ports becomes zero yielding similar expressions to those obtained for the 2-port case. S-parameters relating to single ports only () require all of the remaining ports to be loaded with an impedance identical to the system impedance therefore making all of the incident power waves zero except that for the port under consideration. In general therefore we have:
and
For example, a 3-port network such as a 2-way splitter would have the following S-parameter definitions
Measurement of S-parameters
S-parameters are most commonly measured with a vector network analyzer (VNA). |
1355_33 | Output format of measured and corrected S-parameter data
The S-parameter test data may be provided in many alternative formats, for example: list, graphical (Smith chart or polar diagram).
List format
In list format the measured and corrected S-parameters are tabulated against frequency. The most common list format is known as Touchstone or SNP, where N is the number of ports. Commonly text files containing this information would have the filename extension '.s2p'. An example of a Touchstone file listing for the full 2-port S-parameter data obtained for a device is shown below:
! Created Fri 21 July, 14:28:50 2005
# MHZ S DB R 50
! SP1.SP
50 -15.4 100.2 10.2 173.5 -30.1 9.6 -13.4 57.2
51 -15.8 103.2 10.7 177.4 -33.1 9.6 -12.4 63.4
52 -15.9 105.5 11.2 179.1 -35.7 9.6 -14.4 66.9
53 -16.4 107.0 10.5 183.1 -36.6 9.6 -14.7 70.3
54 -16.6 109.3 10.6 187.8 -38.1 9.6 -15.3 71.4 |
1355_34 | Rows beginning with an exclamation mark contains only comments. The row beginning with the hash symbol indicates that in this case frequencies are in megahertz (MHZ), S-parameters are listed (S), magnitudes are in dB log magnitude (DB) and the system impedance is 50 Ohm (R 50). There are 9 columns of data. Column 1 is the test frequency in megahertz in this case. Columns 2, 4, 6 and 8 are the magnitudes of , , and respectively in dB. Columns 3, 5, 7 and 9 are the angles of , , and respectively in degrees.
Graphical (Smith chart)
Any 2-port S-parameter may be displayed on a Smith chart using polar co-ordinates, but the most meaningful would be and since either of these may be converted directly into an equivalent normalized impedance (or admittance) using the characteristic Smith Chart impedance (or admittance) scaling appropriate to the system impedance.
Graphical (polar diagram)
Any 2-port S-parameter may be displayed on a polar diagram using polar co-ordinates. |
1355_35 | In either graphical format each S-parameter at a particular test frequency is displayed as a dot. If the measurement is a sweep across several frequencies a dot will appear for each.
Measuring S-parameters of a one-port network
The S-parameter matrix for a network with just one port will have just one element represented in the form , where n is the number allocated to the port. Most VNAs provide a simple one-port calibration capability for one port measurement to save time if that is all that is required. |
1355_36 | Measuring S-parameters of networks with more than 2 ports |
1355_37 | VNAs designed for the simultaneous measurement of the S-parameters of networks with more than two ports are feasible but quickly become prohibitively complex and expensive. Usually their purchase is not justified since the required measurements can be obtained using a standard 2-port calibrated VNA with extra measurements followed by the correct interpretation of the results obtained. The required S-parameter matrix can be assembled from successive two port measurements in stages, two ports at a time, on each occasion with the unused ports being terminated in high quality loads equal to the system impedance. One risk of this approach is that the return loss or VSWR of the loads themselves must be suitably specified to be as close as possible to a perfect 50 Ohms, or whatever the nominal system impedance is. For a network with many ports there may be a temptation, on grounds of cost, to inadequately specify the VSWRs of the loads. Some analysis will be necessary to determine what the |
1355_38 | worst acceptable VSWR of the loads will be. |
1355_39 | Assuming that the extra loads are specified adequately, if necessary, two or more of the S-parameter subscripts are modified from those relating to the VNA (1 and 2 in the case considered above) to those relating to the network under test (1 to N, if N is the total number of DUT ports). For example, if the DUT has 5 ports and a two port VNA is connected with VNA port 1 to DUT port 3 and VNA port 2 to DUT port 5, the measured VNA results (, , and ) would be equivalent to , , and respectively, assuming that DUT ports 1, 2 and 4 were terminated in adequate 50 Ohm loads . This would provide 4 of the necessary 25 S-parameters.
See also
Admittance parameters
Impedance parameters
Two-port network
X-parameters, a non-linear superset of S-parameters
Belevitch's theorem
References |
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