https://www.mikrocontroller.net/api.php?action=feedcontributions&feedformat=atom&user=200.69.24.9 Mikrocontroller.net - Benutzerbeiträge [de] 2026-04-13T03:59:49Z Benutzerbeiträge MediaWiki 1.39.7 https://www.mikrocontroller.net/index.php?title=DA-Wandler&diff=12000 DA-Wandler 2006-03-16T03:12:10Z <p>200.69.24.9: </p> <hr /> <div>Ein Digital-Analog-Wandler wandelt einen [[digital]]en Wert in eine [[analog]]e Spannung um. Im Englischen wird er als Digital Analog Converter (abgekürzt DAC) bezeichnet. Er ist das Gegenstück zum [[AD-Wandler]].<br /> <br /> Die wichtigsten Eigenschaften eines DA-Wandlers sind die Auflösung (und deren Genauigkeit) und die Geschwindigkeit. Je höher die Auflösung, desto genauer kann ein DA-Wandler eine Spannung ausgeben. Die Auflösung wird in Bit angegeben und sagt aus, wie viele Abstufungen der DA-Wandler schafft.<br /> <br /> Beispiel: <br /> Ein DA-Wandler hat 8 Bit, damit kann er &lt;math&gt;2^8=256&lt;/math&gt; verschiedene Spannungen ausgeben. Hat er einen Ausgangsspannungsbereich von 0-5V, dann beträgt die Spannungsdifferenz zwischen zwei Werten<br /> <br /> :&lt;math&gt;\frac{5\mathrm{V}}{256}=0,02\mathrm{V}=20\mathrm{mV}&lt;/math&gt;<br /> <br /> (Wandler die nach dem [[PWM]]-Verfahren arbeiten, werden manchmal als 1-Bit-Wandler bezeichnet; dies ist jedoch ein Marketing-Begriff, welcher mit der tatsächlichen Auflösung nichts zu tun hat.)<br /> <br /> Bei integrierten Schaltkreisen sind DA-Wandler, die nach dem PWM-Verfahren arbeiten, am einfachsten zu realisieren. Daher findet man sie häufig auch bei Microcontrollern.<br /> <br /> Eine einfache Form eines DA-Wandlers findet sich nachfolgend in der Umsetzung mittels eines sogenannten R2R-Netzwerks. Der dargestellte Wandler hat eine Auflösung von 4 Bit:<br /> <br /> [[Bild:R2r.png]]<br /> <br /> Die Ausgangsspannung ist vom Lastwiderstand &lt;math&gt;R_L&lt;/math&gt; abhaengig und berechnet sich nach der folgenden Formel:<br /> <br /> :&lt;math&gt;U_a = \frac{U_{ref}}{2^4} \cdot \frac{R_L}{R + R_L} \cdot Z&lt;/math&gt;<br /> <br /> Z erhaelt man, indem man die Zustaende (1/0) der digitalen Eingaenge als die einzelnen Bits einer Binaerzahl betrachtet. 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Sie beinhaltet die ersten [[AVR|AVRs]] die produziert wurden und deren Bezeichnung mit &quot;AT90S&quot; beginnt. Alle Typen wurden mit der Zeit von den beiden Nachfolgereihen ersetzt: ATmega bzw. ATtiny.<br /> <br /> Einige neue AVR-Controller tragen eine mit AT90-''ohne S'' beginnende Bezeichnung, haben aber einen &quot;moderneren&quot; Kern. Z.B. sind die Typen AT90PWM2/3 und AT90CAN128 vom Funktionsumfang (interner RC, USART etc.) den ATmegas zuzuordnen.<br /> <br /> === ATmega ===<br /> <br /> Die ATmega-[[Mikrocontroller]] sind ein Teil der AVR-Controllerfamilie. Zusammen mit den ATTiny lösen die ATmega die AT90S-Serie schrittweise ab, wobei es in den meisten Fällen weitgehend pin- und funktionskompatiblen Ersatz für die abgekündigten Controller gibt (ATmega8 statt AT90S4433, ATmega8515 statt AT90S8515 usw.).<br /> <br /> Atmel ATmega AVRs werden mit aktiviertem internem Taktgeber ausgeliefert. Schließt man ein andere externe Taktquelle an (Quarz, Quarzoszillator o.ä.), wird diese nicht automatisch genutzt. Zum Aktivieren müssen die Fuse-Bits des Controllers entsprechend eingestellt werden (siehe Datenblatt).<br /> <br /> ATmegas mit integriertem JTAG-Interface (z.Zt. solche ab 16kB Flash-Speicher und mehr als 28 Pins&lt;!-- wg. ATmega168--&gt;) werden ab Werk mit aktiviertem JTAG-Interface ausgeliefert. Dieses Interface belegt vier Port-Pins (z.B. am PORTC bei ATmega16/32), die nicht für eigene Anwendungen genutzt werden können, solange das JTAG-Interface aktiviert ist. Das Interface lässt sich über ein Fuse-Bit (JTAGEN) dauerhaft und über ein Bit (JTD) in dem (oder einem der) MC-Kontroll-Register (Datenblatt nach JTD durchsuchen) per Software zur Laufzeit an- und abschalten. Weiteres im Datenblatt des jeweiligen Controllers in den Abschnitten Memory-Programming (Fuse) und JTAG/ICE (JTD).<br /> <br /> Beim ATmega128 ist ab Werk die Mega103-Kompatibilitätsfuse gesetzt. 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Laut Hilfedatei im AVR Studio gehören diese Befehle zum Instruction set, laut Datenblatt des ATmega8 jedoch nicht. Was ist nun richtig? --[[Benutzer:Oxygene|Oxygene]] 13:16, 3. Nov 2004 (CET)<br /> <br /> Im Zweifel hat immer das Datenblatt recht. JMP und CALL würden beim Mega8 auch keinen Sinn machen da +-2k (von rjmp und rcall) völlig reichen um den gesamten Addressraum zu erreichen --[[Benutzer:Matthias|Matthias]] 17:06, 3. Nov 2004 (CET)<br /> <br /> :Ja, habe das auch ausprobiert und es geht nicht. Die Hilfedatei kann man in der Hinsicht '''garnicht''' gebrauchen, da sind nämlich z.B. auch EIJMP u.ä. drin, obwohl das kein µC unterstützt. --[[Benutzer:Oxygene|Oxygene]] 19:13, 3. Nov 2004 (CET)<br /> <br /> Hi, wäre es möglich die Tabelle, also die Spalten, irgendwie logischer zu gruppieren :) Beispielsweise die Megas und Tinys je nacheinander?<br /> :Kann man natürlich machen, ich mach da gleich mal fix was. --[[Benutzer:Oxygene|Oxygene]] 19:14, 3. Nov 2004 (CET)<br /> <br /> ----<br /> <br /> Habe die Tabelle jetzt mal (hoffentlich) schön und leserlich gemacht. Allerdings ist es jetzt natürlich nicht trivial, neue Spalten hinzuzufügen. Die Erstellung des Tabellen-Markups mache ich daher in einem kleinen PHP-Script. Wer also eine weitere Spalte hinzufügen will, der gebe mir etwas in folgendem Format. Die Reihenfolge der Zeichen entspricht den einzelnen Instructions in der Tabelle von oben nach unten gelesen (jeweils Gruppenweise).<br /> &lt;pre class=&quot;code&quot;&gt;<br /> $mega8 = array( &quot;++++++++++++++++++++++++++++&quot;,<br /> &quot;++--++--++++++++++++++++++++++++++++++&quot;,<br /> &quot;++++++++++-+++++&quot;,<br /> &quot;++++++++++++++++++++++++++++&quot;,<br /> &quot;-+++&quot;);<br /> &lt;/pre&gt;<br /> --[[Benutzer:Oxygene|Oxygene]] 20:42, 3. Nov 2004 (CET)<br /> <br /> Super :) und gleich deutlich besser lesbar. Vielen Dank. --[[Benutzer:Yahp|Yahp]] 20:56, 3. 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Pulse Width Modulation, abgekürzt '''PWM''') wird die Ein- und Ausschaltzeit eines Rechtecksignals bei fester Grundfrequenz variiert. Das Verhältnis &lt;math&gt;t_{ein} / (t_{ein} + t_{aus})&lt;/math&gt; bezeichnet man als '''Tastverhältnis'''.<br /> <br /> Wie leicht zu erkennen ist gilt für den '''Mittelwert''' der Spannung<br /> :&lt;math&gt;U_m = U_{aus} + (U_{ein} - U_{aus}) \cdot \frac{t_{ein}}{t_{ein}+t_{aus}}&lt;/math&gt;.<br /> <br /> &lt;math&gt;U_{aus}&lt;/math&gt; ist dabei normalerweise 0V, &lt;math&gt;U_{ein}&lt;/math&gt; die Betriebsspannung, z.B. 5V.<br /> <br /> ==Beispiele==<br /> <br /> Die folgenden Beispiele zeigen PWM-Signale mit einem Tastverhältnis von 75% bzw. 25%.<br /> <br /> &lt;table border=&quot;1&quot;&gt;&lt;tr&gt;&lt;td style=&quot;padding: 10px;&quot;&gt;<br /> ===Beispiel 1===<br /> <br /> &lt;math&gt;U_{ein}=5\,\mathrm{V}&lt;/math&gt;&lt;br&gt;<br /> &lt;math&gt;U_{aus}=0\,\mathrm{V}&lt;/math&gt;&lt;br&gt;<br /> &lt;math&gt;t_{ein}=3\,\mathrm{ms}&lt;/math&gt;&lt;br&gt;<br /> &lt;math&gt;t_{aus}=1\,\mathrm{ms}&lt;/math&gt;&lt;br&gt;<br /> <br /> :&lt;math&gt;U_m = 0\,\mathrm{V} + (5\,\mathrm{V} - 0\,\mathrm{V}) \cdot \frac{3\,\mathrm{ms}}{3\,\mathrm{ms}+1\,\mathrm{ms}} = 3,75\,\mathrm{V}&lt;/math&gt;<br /> <br /> [[Bild:Pwm1.png]]<br /> <br /> &lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style=&quot;padding: 10px;&quot;&gt;<br /> <br /> ===Beispiel 2===<br /> <br /> &lt;math&gt;U_{ein}=5\,\mathrm{V}&lt;/math&gt;&lt;br&gt;<br /> &lt;math&gt;U_{aus}=0\,\mathrm{V}&lt;/math&gt;&lt;br&gt;<br /> &lt;math&gt;t_{ein}=1\,\mathrm{ms}&lt;/math&gt;&lt;br&gt;<br /> &lt;math&gt;t_{aus}=3\,\mathrm{ms}&lt;/math&gt;&lt;br&gt;<br /> <br /> :&lt;math&gt;U_m = 0\,\mathrm{V} + (5\,\mathrm{V} - 0\,\mathrm{V}) \cdot \frac{1\,\mathrm{ms}}{1\,\mathrm{ms}+3\,\mathrm{ms}} = 1,25\,\mathrm{V}&lt;/math&gt;&lt;br&gt;<br /> <br /> [[Bild:Pwm2.png]]<br /> &lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;<br /> &lt;br&gt;<br /> <br /> == Leistung ==<br /> <br /> Steuert man mit einem pulsweitenmodulierten Signal direkt einen ohmschen Verbraucher an (z.B. Heizdraht), so ist darauf zu achten dass man zur Bestimmung der Leistung '''nicht''' einfach<br /> <br /> :&lt;math&gt;P = \frac{{U_m}^2}{R}&lt;/math&gt;<br /> <br /> rechnen darf, sondern die Leistung während der Ein- und Ausschaltzeit getrennt betrachten muss:<br /> <br /> :&lt;math&gt;P = \frac{{U_{ein}}^2}{R} \cdot \frac{t_{ein}}{t_{ein} + t_{aus}} +<br /> \frac{{U_{aus}}^2}{R} \cdot \frac{t_{aus}}{t_{ein} + t_{aus}}&lt;/math&gt;.<br /> <br /> &lt;table border=&quot;1&quot;&gt;&lt;tr&gt;&lt;td style=&quot;padding: 10px;&quot;&gt;<br /> === Beispiel ===<br /> <br /> &lt;math&gt;U_{ein} = 4\,\mathrm{V}&lt;/math&gt;&lt;br&gt;<br /> &lt;math&gt;U_{aus} = 0\,\mathrm{V}&lt;/math&gt;&lt;br&gt;<br /> &lt;math&gt;t_{ein} = 1\,\mathrm{ms}&lt;/math&gt;&lt;br&gt;<br /> &lt;math&gt;t_{aus} = 3\,\mathrm{ms}&lt;/math&gt;&lt;br&gt;<br /> &lt;math&gt;R = 10\,\mathrm{\Omega}&lt;/math&gt;&lt;br&gt;<br /> <br /> Der Mittelwert dieser Spannung ist<br /> :&lt;math&gt;U_m = 1\,\mathrm{V}&lt;/math&gt;.<br /> Würde man mit diesem Wert die Leistung berechnen, so käme man auf<br /> :&lt;math&gt;P = \frac{{U_m}^2}{R} = \frac{(1\,\mathrm{V})^2}{10\,\mathrm{\Omega}} = 0,1\,\mathrm{W}&lt;/math&gt;.<br /> <br /> Der richtige Wert ist jedoch<br /> <br /> :&lt;math&gt;P = \frac{(4\,\mathrm{V})^2}{10\,\mathrm{\Omega}} \cdot \frac{1\,\mathrm{ms}}{4\,\mathrm{ms}} +<br /> \frac{(0\,\mathrm{V})^2}{10\,\mathrm{\Omega}} \cdot \frac{3\,\mathrm{ms}}{4\,\mathrm{ms}} =<br /> 0,4\,\mathrm{W}<br /> &lt;/math&gt;.&lt;br&gt;<br /> &lt;br&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;<br /> <br /> == Anwendung ==<br /> <br /> === Motorsteuerung ===<br /> <br /> Eine der Hauptanwendungen für PWM ist die Ansteuerung von Motoren. Der große Vorteil von PWM ist hier der gute Wirkungsgrad. Würde man einen Digital-Analog-Wandler mit einem nachgeschalteten Verstärker zur Ansteuerung verwenden, dann würde im Verstärker eine sehr hohe Verlustleistung in Wärme umgewandelt werden; bei einem voll durchgeschalteten [[FET]] ist der Widerstand und damit die Verlustleistung dagegen sehr gering.<br /> <br /> Die verwendete Frequenz liegt meist im Bereich von einigen 10 kHz. Zur Berechnung des Drehmoments kann im Normalfall der Mittelwert der PWM-Spannung als Betriebsspannung angenommen werden.<br /> <br /> === Digital-Analog-Wandler ===<br /> <br /> Bildet man mit einem analogen [[Filter|Tiefpassfilter]] den Mittelwert der Spannung, kann man die Pulsweitenmodulation zum Erzeugen von Analogsignalen verwenden ([[DA-Wandler|Digital-Analog-Wandler]]). Da beim PWM-Signal selbst nur zwei verschiedene Spannungen verwendet werden, wird das manchmal auch als 1-Bit-DA-Wandler bezeichnet; dieser Begriff ist aber ziemlich irreführend, da er nichts mit der Auflösung des resultierenden Analogsignals zu tun hat.<br /> <br /> Der Filter könnte zum Beispiel durch eine einfache passive RC-Kombination realisiert sein. Der Filter entfernt die hohe PWM-Grundfrequenz und läßt das geglättete Analogsignal übrig. Die [[Filter#Grenzfrequenz|Grenzfrequenz]] muss so gewählt werden, dass die PWM-Grundfrequenz ausreichend unterdrückt wird (Sperrdämpfung); gleichzeitig muß sie aber auch hoch genug sein, um das gewünschte Analogsignal nicht zu verändern.<br /> <br /> Pulsweitenmodulation wird auch zur Erzeugung verschiedener Ausgangsspannungen bei [[Schaltregler]]n benutzt. Dabei wird ein [[Transistor]] mit einem variablen Tastverhältnis angesteuert und damit die Ausgangsspannung reguliert.<br /> <br /> === AD Wandlung mit PWM ===<br /> <br /> Einen recht billigen und einfachen AD-Wandler mit &quot;1-Draht Kommunikation&quot; kann man mit dem IC 556 (NE556 o.ä.) realisieren: der eine Timer des 556 arbeitet als 50% duty-cycle Rechteckgenerator bei beispielsweise 1 KHz und steuert den zweiten Timer an. Dieser besitzt ja einen Steuereingang zu Beeinflussung des Tastverhältnisses und auf diesen Pin gibt man das analoge Signal. Ein angeschlossener µC oder PC misst bei jedem Impuls die Impulslänge und man erhält so das Messergebnis. Bei &gt; 10 KHz kann man so auch prima digital Sprache übertragen oder speichern ! (Tip stammt noch aus der Zeit als es keinen Mikroprozessor mit AD-Wandler gab...) 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Dabei wird das Programm unterbrochen und ein Unterprogramm, die sogenannte '''Interrupt Service Routine (ISR)''', aufgerufen. Wenn dieses beendet ist, läuft das Hauptprogramm ganz normal weiter.<br /> <br /> Bei [[Mikrocontroller]]n werden Interrupts z.B. ausgelöst wenn:<br /> * sich der an einem bestimmten Eingangs-Pin anliegende Pegel von High auf Low ändert (oder umgekehrt)<br /> * eine vorher festgelegte Zeitspanne abgelaufen ist<br /> * eine [[Seriell|serielle]] Übertragung abgeschlossen ist<br /> * eine Umwandlung des [[AD-Wandler|Analog-Digital-Wandlers]] abgeschlossen ist<br /> <br /> ==Interrupt-feste Programmierung==<br /> <br /> Alle Variablen, Steuerregister und I/O-Ports, die sowohl im Hauptprogramm als auch in Interrupts verwendet werden, sind mit viel Sorgfalt zu behandeln.<br /> <br /> Beispiel:<br /> &lt;pre class=&quot;code&quot;&gt;<br /> port |= 0x03;<br /> &lt;/pre&gt;<br /> übersetzt sich auf AVR Prozessoren in<br /> &lt;pre class=&quot;code&quot;&gt;<br /> IN r,port<br /> ORI r,0x03<br /> OUT port,r<br /> &lt;/pre&gt;<br /> Wenn nun zwischen IN und OUT ein Interrupt auftritt, der beispielsweise Bit 7 verändert, dann geht mit dem OUT-Befehl diese Änderung verloren, da der OUT Befehl den alten Zustand vor dem Interrupt wiederherstellt.<br /> <br /> Gefährlich ist das insbesondere deshalb, weil der Fall nur selten auftritt und dies Verhalten sehr schlecht reproduzierbar ist.<br /> <br /> Bei verschiedenen Prozessor-Architekturen tritt das Problem verschieden häufig auf. So übersetzt sich obiger Code bei MSP430 Prozessoren in einen einzelnen Befehl<br /> &lt;pre class=&quot;code&quot;&gt;<br /> OR #0x03,port<br /> &lt;/pre&gt;<br /> und stellt somit kein Problem dar. Im Zweifel hilft nur ein Blick in den erzeugten Assembler-Code. Bei der Übernahme fremden Codes ist dies zu beachten. Was bei i51 kein Problem war, kann bei AVR zu einem Problem werden, u.U. sogar abhängig von verwendeten Port sein.<br /> <br /> Ein ähnliches Problem entsteht bei Variablen, deren Grösse die Wortbreite der Maschine übersteigt. Bei 8-Bit-Prozessoren wie AVR oder i51 also bereits bei normalen &quot;int&quot; Variablen. Diese Variablen werden zwangsläufig byteweise verarbeitet. Wenn genau dazwischen ein Interrupt erfolgt, wird ein falscher Wert gelesen. Wenn beispielsweise eine Interrupt-Routine einen 16-Bit-Zähler verwendet und von 0x00FF auf 0x0100 hochzählt, dann kann das Hauptprogramm auch schon mal versehentlich die Werte 0x01FF oder 0x0000 lesen.<br /> <br /> Dies ist auch ein Grund, weshalb für Programmierung auf derart &quot;niedriger&quot; Ebene Kenntnisse in Prozessorarchitektur und Assembler-Programmierung sehr hilfreich sind.<br /> <br /> '''Abhilfe''': Wenn man sich nicht wirklich ganz sicher ist, sollten um kritische Aktivitäten herum jedesmal die Interrupts abgeschaltet werden.<br /> <br /> Je nach Prozessor kann man das Problem manchmal auch ohne Abschalten von Interrupts durch geeignete Programmierung lösen. So führt<br /> &lt;pre class=&quot;code&quot;&gt;<br /> port = (port &amp; ~0x0F) | lcd_data;<br /> &lt;/pre&gt;<br /> immer zum beschriebenen Problem,<br /> &lt;pre class=&quot;code&quot;&gt;<br /> port &amp;= ~0x0F;<br /> port |= lcd_data;<br /> &lt;/pre&gt;<br /> jedoch nicht, wenn die beiden Zeilen zu jeweils einem Assembler-Befehl übersetzt werden. Was dann aber abhängig von den Optimierungs-Einstellungen des Compilers werden kann. 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