From 0fd9d8558b3f05d27c857bfbf969e7247ef1cc51 Mon Sep 17 00:00:00 2001 From: wieerwill Date: Tue, 30 Nov 2021 10:04:10 +0100 Subject: [PATCH] Revert "Kapitel 2" This reverts commit e8ba892779e1be42b65a95bd7c5c1fc2533799ec. --- Assets/Biosignalverarbeitung-AD289.png | Bin 195199 -> 0 bytes ...signalverarbeitung-Diff-und-Gleichtakt.png | Bin 84904 -> 0 bytes ...ignalverarbeitung-Diff-und-Gleichtakt2.png | Bin 16018 -> 0 bytes ...itung-Differenzverstärker-asymmetrisch.png | Bin 148934 -> 0 bytes ...arbeitung-Differenzverstärker-funktion.png | Bin 141966 -> 0 bytes .../Biosignalverarbeitung-Filtertheorie.png | Bin 63102 -> 0 bytes .../Biosignalverarbeitung-Filtertheorie2.png | Bin 209729 -> 0 bytes ...ignalverarbeitung-Galvanische-trennung.png | Bin 44695 -> 0 bytes ...signalverarbeitung-Isolationsverstäker.png | Bin 114240 -> 0 bytes ...iosignalverarbeitung-aktive-elektroden.png | Bin 339406 -> 0 bytes .../Biosignalverarbeitung-aktive-filter.png | Bin 135600 -> 0 bytes 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Biosignalverarbeitung.md b/Grundlagen der Biosignalverarbeitung.md index 64c3795..da8e975 100644 --- a/Grundlagen der Biosignalverarbeitung.md +++ b/Grundlagen der Biosignalverarbeitung.md @@ -26,32 +26,7 @@ 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) - - [Abtastung, Aliasing](#abtastung-aliasing) - - [Digitalisierung](#digitalisierung) - - [Telemetrie](#telemetrie) - [Digitale Filterung](#digitale-filterung) # Sensorik @@ -473,822 +448,8 @@ 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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