From 3d562dcfb571658a5101bf3779c64ea8a7046ed6 Mon Sep 17 00:00:00 2001 From: wieerwill Date: Tue, 30 Nov 2021 10:27:46 +0100 Subject: [PATCH] Kapitel 2 (new) --- Assets/Biosignalverarbeitung-AD289.png | Bin 0 -> 196124 bytes ...signalverarbeitung-Diff-und-Gleichtakt.png | Bin 0 -> 84961 bytes ...ignalverarbeitung-Diff-und-Gleichtakt2.png | Bin 0 -> 16001 bytes ...itung-Differenzverstärker-asymmetrisch.png | Bin 0 -> 149273 bytes ...arbeitung-Differenzverstärker-funktion.png | Bin 0 -> 142167 bytes .../Biosignalverarbeitung-Filtertheorie.png | Bin 0 -> 63122 bytes .../Biosignalverarbeitung-Filtertheorie2.png | Bin 0 -> 210481 bytes ...ignalverarbeitung-Galvanische-trennung.png | Bin 0 -> 44699 bytes ...signalverarbeitung-Isolationsverstäker.png | Bin 0 -> 120771 bytes ...iosignalverarbeitung-aktive-elektroden.png | Bin 0 -> 339221 bytes .../Biosignalverarbeitung-aktive-filter.png | Bin 0 -> 135686 bytes .../Biosignalverarbeitung-aktive-filter2.png | Bin 0 -> 73485 bytes 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Biosignalverarbeitung - [Differenzverstärker](#differenzverstärker) - [Funktionsprinzip](#funktionsprinzip) - [Differenz- und Gleichtaktverhalten](#differenz--und-gleichtaktverhalten) + - [Instrumentationsverstärker](#instrumentationsverstärker) + - [Mehrstufiger Verstärker](#mehrstufiger-verstärker) + - [Hoher Eingangswiderstand](#hoher-eingangswiderstand) + - [Hohe Gleichtaktunterdrückung](#hohe-gleichtaktunterdrückung) + - [Isolationsverstärker](#isolationsverstärker) + - [Funktionsprinzip](#funktionsprinzip-1) + - [Galvanische Trennung und ihre Auswirkung](#galvanische-trennung-und-ihre-auswirkung) + - [Datenübertragung, Modulation und Demodulation](#datenübertragung-modulation-und-demodulation) + - [Guardingtechnik](#guardingtechnik) + - [Funktionsprinzip](#funktionsprinzip-2) + - [Realisierung](#realisierung) + - [Aktive Elektroden](#aktive-elektroden) + - [Funktionsprinzip](#funktionsprinzip-3) + - [Störungsresistenz](#störungsresistenz) + - [Gleichtaktunterdrückung](#gleichtaktunterdrückung) + - [Analoge Filter](#analoge-filter) + - [Passive Filter](#passive-filter) + - [Grundlagen der Filtertheorie](#grundlagen-der-filtertheorie) + - [Filterentwurf](#filterentwurf) + - [Aktive Filter](#aktive-filter) + - [Linearer Phasenfrequenzgang](#linearer-phasenfrequenzgang) - [Signalkonditionierung, Abtastung und Digitalisierung](#signalkonditionierung-abtastung-und-digitalisierung) + - [Pegelanpassung](#pegelanpassung) + - [Abstastung, Aliasing](#abstastung-aliasing) + - [Digitalisierung](#digitalisierung) + - [Telemetrie](#telemetrie) - [Digitale Filterung](#digitale-filterung) # Sensorik @@ -266,11 +291,11 @@ Signalanalytisch wichtige Eigenschaften: - aus signalanalytischer Sicht Eingangsdaten - aus messtechnischer Sicht Systemeingang -Ziele | Realisierbarkeit ---- | --- -geringe Elektrodenspannung | durch Materialwahl (AgAgCl) -geringer Drift der Elektrodenspannung | physiologisch bedingt, daher kaum beeinflussbar -geringes Eigenrauschen | Materialwahl und Technologie +| Ziele | Realisierbarkeit | +| ------------------------------------- | ----------------------------------------------- | +| geringe Elektrodenspannung | durch Materialwahl (AgAgCl) | +| geringer Drift der Elektrodenspannung | physiologisch bedingt, daher kaum beeinflussbar | +| geringes Eigenrauschen | Materialwahl und Technologie | Aus signalanalytischer Sicht sind die Ziele ganz klar vorgegeben. In der Praxis muss jedoch immer ein Kompromiss zwischen diesen Zielen und den Anforderungen der Anwendung und Praktikabilität gefunden werden: Wie diese Beispiele zeigen, hängt die Konstruktion der Elektrode von ihrer Bestimmung ab und daraus ergeben sich auch die Signaleigenschaften. So z.B. muss eine subkutane EMG-Elektrode die Form eine Nadel haben und aus einem Edelmetall sein. Dies hat zur Folge, dass die EMG-Elektroden relativ schlechte Signaleigenschaften aufweist: Riesige Elektrodenimpedanz (bis einige MOhm), stark kapazitives Verhalten, sehr hohe Elektrodenspannung (bis in den Voltbereich). Im Vergleich dazu haben die EKG-Elektroden -vor allem auf Grund ihrer großen Fläche und des Materials (AgAgCl, NaCl) -sehr günstige Eigenschaften: Niedrige Elektrodenimpedanz (kOhm-Bereich), sehr tieffrequent (bis DC), niedrige Elektrodenspannung (um 100 mV). @@ -280,11 +305,11 @@ Aus signalanalytischer Sicht sind die Ziele ganz klar vorgegeben. In der Praxis - aus signalanalytischer Sicht Ausgangsdaten - aus messtechnischer Sicht Systemausgang -Ziele | Realisierbarkeit ---- | --- -geringe Impedanz | durch Materialwahl (beschichtet Cu) -geringer Drift der Impedanz | physiologisch bedingt -Langzeitstabilität | Materialwahl und Technologie +| Ziele | Realisierbarkeit | +| --------------------------- | ----------------------------------- | +| geringe Impedanz | durch Materialwahl (beschichtet Cu) | +| geringer Drift der Impedanz | physiologisch bedingt | +| Langzeitstabilität | Materialwahl und Technologie | Ebensowichtig wie die Eigenschaften der diagnostischen Elektroden, sind es auch die der therapeutischen Elektroden. Dies liegt darin begründet, dass die Therapie von den zuvor analysierten diagnostischen Daten abhängt -natürlich im signalanalytischen Sinne, denn medizinisch ist es immer so. Man muss sich also bei der gewählten Therapie darauf verlassen können, dass das, was man auf die Elektrode schickt, so auch am biologischen Objekt ankommt. Diese Forderung technologisch umzusetzen ist ungleich leichter als bei diagnostischen Elektroden, denn hier können relative große Flächen mit gutem Kontaktmaterial verwendet werden. @@ -361,14 +386,14 @@ Das EEG wird in in fünf typische Bereiche unterteilt: delta (0..4Hz), theta (4- ### Biologische und technische Störquellen -periodische | transiente ---- | --- -öffentliches Stromversorgungsnetz | Spannungsspitzen im Netz -Straßenbahn | Bewegungen im Messbereich -Monitore | Schaltvorgänge -Kommunikationsnetze | Lastschwankungen -Rotierende Maschinen | -Sender inkl. Funktelefon | +| periodische | transiente | +| --------------------------------- | ------------------------- | +| öffentliches Stromversorgungsnetz | Spannungsspitzen im Netz | +| Straßenbahn | Bewegungen im Messbereich | +| Monitore | Schaltvorgänge | +| Kommunikationsnetze | Lastschwankungen | +| Rotierende Maschinen | +| Sender inkl. Funktelefon | 1.Das biomedizinische Messsystem ist von vielen Störquellen umgeben, die meisten sind dem Bereich der Medienversorgung, Industrie, Verkehr und Nachrichtentechnik zuzuschreiben. Für die BSA sind periodische (Versorgungsnetz, Monitore) und quasiperiodische (rotierende Maschinen, Straßenbahn) Störungen noch ein vergleichsweise geringes Problem, denn diese lassen sich gezielt mit spektralen Filtern in der analogen Messkette oder digital nach ADC unterdrücken. 2.Wesentlich schwieriger ist die Situation, wenn transiente Störungen vorliegen, denn diese haben im Allgemeinen einen unbekannten, einmaligen und daher nicht reproduzierbaren Verlauf. Solange die transiente Störung die Signalerfassung nicht beeinträchtigt (durch Übersteuerung des Messverstärkers) und deutlich von der Signalform abweicht (z.B. Ausgleichsvorgang mi EKG), kann sie mit relativ einfachen Mitteln beseitigt werden, dennoch im Allgemeinen ist dies kaum möglich. @@ -393,11 +418,11 @@ Aus Sicht der BSA gestaltet sich das Problem der Störungen wesentlich schwierig Ein weiteres -messmethodisches -Problem besteh darin, dass man Biosignale nicht pauschal in Nutz-und Störsignale trennen kann. Es ist vielmehr die Messaufgabe, an Hand der man diese Klassifikation vornehmen muss. #### Eigenschaften technischer Störungen -periodische Störungen | transiente Störungen ---- | --- -NF-magnetische Felder nicht eliminierbar durch Schirmung, erzeugen Differenzspannung | kaum eliminierbar, da Signalform unbekannt und nicht reproduzierbar -NF-elektrische Felder gut beherrschbar, erzeugen Gleichtaktstörungen | bestenfalls Detektion möglich, Messdaten nicht korrigierbar -HF-Felder immer mehr vorhanden (Kommunikationsnetze), Abschirmung unwirtschaftlich | +| periodische Störungen | transiente Störungen | +| ------------------------------------------------------------------------------------ | ------------------------------------------------------------------- | +| NF-magnetische Felder nicht eliminierbar durch Schirmung, erzeugen Differenzspannung | kaum eliminierbar, da Signalform unbekannt und nicht reproduzierbar | +| NF-elektrische Felder gut beherrschbar, erzeugen Gleichtaktstörungen | bestenfalls Detektion möglich, Messdaten nicht korrigierbar | +| HF-Felder immer mehr vorhanden (Kommunikationsnetze), Abschirmung unwirtschaftlich | 1. Naturgemäß erzeugen niederfrequente magnetische Felder am Verstärkereingang Differenzspannungen, die direkt mit dem Biosignal überlagert werden, so dass sie mit der üblichen Verstäkertechnik nicht reduziert werden können. Hinzu kommt, dass auch eine Abschirmung nicht viel bringt, da in diesem Frequenzbereich mehrere 10- Zentimeter dicke Eisenplatten verwendet werden müssten, was in der Praxis nicht realisierbar ist. Da die niederfrequenten elektrischen (kapazitiv eingekoppelten) Störfelder Gleichtaktsignale sind, können sie zum Teil gut durch die Differenzverstärkertechnik reduziert werden. In immer höheren Maße stören hochfrequente Felder, vor allem aus dem Mobilfunk, Datennetzen, WLAN, Bluetooth, etc. Eine Abschirmung ist im normalen Praxisbetrieb unwirtschaftlich, so dass eine Reduktion der Störung allein durch Maßnahmen der EMV zu erreichen ist. 2. Wie schon erwähnt, transiente Störungen sind im Grunde nicht beherrschbar, da sie eigentlich nicht bekannt und nicht vorhersehbar sind. Mit Methoden der BSA ist zum Teil ihre Detektion möglich, wenn z.B. der Messbereich oder das Spektrum des Biosignals nachweislich verlassen wird. Diese Detektion kann allerdings nur dazu genutzt werden, die beeinträchtigten Daten zu verwerfen, eine Korrektur ist nicht möglich. @@ -448,8 +473,192 @@ Die wichtigste Eigenschaft der Biosignale, die von Medizinern diagnostisch genut ## Differenzverstärker ### Funktionsprinzip +Vollkommene Symmetrie (DV und Signalanbindung) +- ![](Assets/Biosignalverarbeitung-Differenzverstärker-funktion.png) +- Vg ist Quelle der massebezogenen Störung. Die Störspannung gelangt auf beide Eingänge über Streukapazitäten, deren Impedanzen mit R4 und R5 simuliert werden, in gleicher Phase und im Idealfall auch mit gleichem Pegel. Die Störsignale an den Eingängen U10 und U20 sind also gleich, werden daher als Gleichtaktsignale bezeichnet. +- Vd ist die gewünschte massefreie Spannung (aus Sicht der Signalquelle zählen R4 und R5 nicht als Masseverbindung, die ,,hängt in der Luft'', floating source). Die Signalquelle Vd liegt direkt zwischen den Eingängen an, erzeugt daher eine Differenzspannung (siehe Funktionsprinzip eines Differenzverstärkers: Durch die Verkopplung der beiden Zweige T1 und T2 hat eine Zunahme der Eingangsspannung U10 Abnahme von Ud1 und Zunahme von Ud2, analog gilt das für U20. Daher liegt zwischen Ud1 und Ud2 die verstärkte Differenz von U10 und U20 an). +- Betrachtet man Ud1 und Ud2 massebezogen, so liegen überlagerte Gleichtakt- und Differenzspannungen an (unterer Grafik). Betrachtet man die verstärkte Spannung massefrei (also als Differenz zwischen Ud1 und Ud2), so verschwindet durch die Differenzbildung die Gleichtaktstörung und die gewünschte Differenzspannung bleibt übrig. +- Alle bisherigen Erläuterungen gelten nur im Idealfall: Sowohl der Verstärker ist ideal symmetrisch (identische Transistoren und Widerstände), als auch die Einkopplung der Gleichtaktstörung erfolgt ideal symmetrisch (über R4 und R5). + +Symmetrie im DV, asymmetrische (realistische) Signalanbindung +- ![](Assets/Biosignalverarbeitung-Differenzverstärker-asymmetrisch.png) +- In der Realität lassen sich zwar Verstärker bauen, die an das Ideal gut herankommen. +- Die Einkopplung der Gleichtaktstörung ist jedoch immer unsymmetrisch, es ist unmöglich, im Messkreis Symmetrie herzustellen (R4 und R5 unterschiedlich). Daher wird aus der ihrem Wesen nach Gleichtaktstörung zum Teil eine Differenzstörung. Und die Differenzstörung erscheint in der Ausgangsspannung Ud1-Ud2 zwangsläufig auch. +- Das heißt, in der Realität wird der Gleichtaktanteil der Störung zwar unterdrückt, aber der zur Differenz gewordene Anteil bleibt am Ausgang bestehen. + ### Differenz- und Gleichtaktverhalten +![](Assets/Biosignalverarbeitung-Diff-und-Gleichtakt.png) +- $SNR_{in} = \frac{U_{d\_in}}{U_{g\_in}}=\frac{1mV}{10V}=10^{-4}\approx -80dB$ +- $V_g$: Gleichtaktstörung (Netz) +- $V_d$: Nutzsignal (EKG) +- Heute werden Differenzverstärker meistens als integrierte analoge Schaltungen mit OPVs eingesetzt. Da der Ausgang massefrei ist, folgt eine zweite Stufe zur Differenzbildung (IC3), die am Ausgang eine -wie üblich -massebezogene Spannung liefert. Diese Anordnung wird als Instrumentationsverstärker bezeichnet (instrumenation amplifier) und ist auch integriert verfügbar. +- Am Eingang liegt eine realistische Situation vor: Das gewünschte Signal hat den Pegel von 1mV (EKG), die Netzstörung erreicht (auch mehr als) 10V. Daher ist der SNR am Eingang sehr niedrig, -80dB. +- ![](Assets/Biosignalverarbeitung-Diff-und-Gleichtakt2.png) +- $CMRR=\frac{U_{d\_out}}{U_{g\_out}}*\frac{U_{g\_in}}{U_{d\_in}}=\frac{200mV}{20mV} *\frac{10V}{1mV}=10^5\approx 100dB$ +- Führt man mit dem Ausgangssignal des Verstärkers Spektralanalyse durch, so stellt man fest, dass die Netzstörung am Ausgang 20mV beträgt, während das gewünschte Signal 200mV erreicht, also der SNR am Ausgang ist 10 bzw. 20dB. Da der SNR am Eingang - 80dB betrug, wurde eine SNR-Verbesserung von 100dB erreicht. Diese Verbesserung ist auf die Gleichtaktunterdrückung selbst bei Asymmetrie am Eingang zurückzuführen, so dass in diesem Fall das CMRR identisch der SNR-Verbesserung ist. (Common-Mode Rejection Ratio, Gleichtaktunterdrückung, muss in der Medizintechnik laut Katalog mindestens 100dB, besser 120dB erreichen). + +## Instrumentationsverstärker +Der Instrumentationsverstärker (IV) ist ein mehrstufiger Verstärker, von dem in der medizinischen Messtechnik ein hoher Eingangswiderstand (besser als 100MOhm) und eine hohe CMRR (besser 100dB) gefordert wird. + +### Mehrstufiger Verstärker +- ![](Assets/Biosignalverarbeitung-mehrstufiger-verstärker.png) +- Die erste Stufe ist der Eingangs-Differenzverstärker mit massefreiem Ausgang; die Ausgangsspannung ergibt sich aus der Differenz der Ausgangsspannungen von IC1 und IC2. Die zweite Stufe verstärkt zusätzlich und bezieht die verstärkte Spannung auf Masse, so dass am Ausgang massebezogene, verstärkte Eingangsdifferenz vorliegt. +- V1: $u_{ad}=A*u_{ed}+B*u_{eg}$, $u_{ag}=C*u_{eg}+D+u_{ed}$, + - $A/B=F$: Diskriminationsfaktor + - $A/C=H$: Rejektionsfaktor +- V2: + - $u_a=V_d u_{ed}+\frac{V_d}{CMR}u_{eg}=V_d(A u_{ed}+\frac{A}{F} u_{eg})+\frac{V_d}{CMR}\frac{A}{H} u_{eg}$ + - $u_a|_{u_{ed}=0} = V_d A(\frac{1}{F}+\frac{1}{CMR*H}) u_{eg}$ + - die gesamt-Gleichtaktunterdrückung eines mehrstufigen Verstärkers ist abhängig im Wesentlichen von der ersten (Eingangs-) Stufe +- Berechnet man die Ausgangsspannung in Abhängigkeit von der Eingangs-Gleichtaktspannung und von den Verstärkerparametern, so zeigt sich, dass für den CMRR die erste Stufe (wie auch bei anderen Parametern, z.B. Eigenrauschen) entscheidend ist, die folgenden Stufen sind unwesentlich beteiligt. Daher wird in der ersten Stufe der höchste Entwicklungsaufwand getrieben. + +### Hoher Eingangswiderstand +- ![](Assets/Biosignalverarbeitung-hoher-eingangswiderstand.png) +- $R^{(1)}_{ed}=2R_D+R_C\approx 2R_D$ +- $R^{(2)}_{ed}=R_1+R_3<

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