Fundamentals of Analog and Digital Design ET-IDA-134 Lecture-3 Non-linear Elements, Active Elements MOSFETS Operational Amplifiers and Active Filters 05.08.2015, v2 Prof. W. Adi Source: Analog Devices, Digilent course material

Recommended Textbook: Course Contents Recommended Textbook: Agarwal, Anant, and Jeffrey H. Lang. Foundations of Analog and Digital Electronic Circuits. San Mateo, CA: Morgan Kaufmann Publishers, Elsevier, July 2005. ISBN: 9781558607354. View e-book versionElsevier companion site: supplementary sections and examples Lecture Material: - Provided in the class. Source: Digilent/Analog Devices Course material - Suplimentary advanced analog and digital design topics with laboratory Laboratory: - Digilent Analog Discovery with lab‘s kit.

Water Model for a Diode rectifier PN-Diode Water Model for a Diode rectifier   pn-Diode (Symbol) Water model for a pn-Diode

The pn-Junction Diode Schematic description Circuit Symbol ID + UD – Anode Cathode ID p-doped n-doped + UD – Acceptors- Concentration NA Donators- Concentration ND ID + UD – metal SiO2 SiO2 Physical Structure: (Example) p-type Si n-type Si metal

Summary of a : pn-Junction Diode I-U Characteristics In conducting direction: The diode current ID grows exponentially with the forward voltage UD. Where UT = K T /q ≈ 26 mV, m= 1.. 2 (correction factor) (K: Boltzmann Constante = 1,38 · 10-23 VAs/K , q: Electron Charge= 1,602 · 10-19 As, T: Temperature in Kelvin = 273 + Temperature in C) In reverse mode (isolation mode) a very low current IS ≈ 1 nA (Si) flows through the diode [IS is temperature dependent( Exp.). ID (A) The result is the following I, U curve having very low current for UD <0 and high current (conducting) for UD >0 Schwellspannung? UD (V) 0.7 V für Si IS ≈ 1 nA (Si) Threshold voltage

The Ideal Diode: Modell for the pn-Diode Circuit Symbol I-U Curve As switch ID ID (A) + UD – ID UD Backward Direction Forward Direction UD (V) An ideal diode allows current flow only in one direction. An Ideal Diode has the following properties:: If ID > 0, UD = 0 If UD < 0, ID = 0 Diode operates as a switch: Closed in forward direction Open in backward direction

Large Signal Diode Model Circuit Symbol I-U Curve As switch ID ID (A) ID + UD – + UD – Uon Backward Direction Forward Direction UD (V) Uon Großsignal….? For Si pn Diode, Uon  0.7 V Rule 1: If ID > 0, UD = Uon. Rule 2: If UD < Uon., ID = 0

pn-Junction Backwards Breakdown I the reverse voltage exceeds a critical value, (Ecrit  2x105 V/cm), Then the backward current increases dramatically and destroys the junction. ID (A) Backwards diffusion current Forward current Zerstört diode -> zerstört pn übergang? Breakdown Voltage UBD UD (V)

Circuit Analysis for non-linear Elements As the pn-junction is a non-linear element, the circuit analysis becomes more complicated!! (Node and Mesh equations do not work as before) Mesh-Equation: UTh = RTh ID + UD => ID = - (1/ RTh ) UD + UTh/ RTh (1) (2) ID RTh +  UD UTh Solve two equations with two unknowns! The result is a non-linear equation with one unknown: - (1/ RTh ) UD + UTh/ RTh = Hard to solve! Therefore a graphical solution!

Graphical “Load Line“ Solution Draw I-U relationship for the non-linear element and for the rest of the circuit The operation point (or the solution of both equations) is the intersection point between the two curves. I ID + UD – RTh UTh/RTh Operation point (intersection point) UTh ID Loadline mit Kennlinien- übersetzen? U UD UTh The I-U relationship of the whole circuit without the non-linear element is called the „Load Line“. ID = - (1/ RTh ) UD + UTh/ RTh

Ausgangsspannung ist „High“ falls beide A und B „High“ sind Dioden Logik Dioden können benutzt werden um logischen Funktionen durchzuführen: UND Gatter Ausgangsspannung ist „High“ falls beide A und B „High“ sind ODER Gatter Ausgangsspannung ist „High“ falls einer oder beide A und B „High“ sind Ucc A R B C A C R Schwankt C noch zu ändern! B Eingänge A und B wechseln zwischen 0 Volt (“low”) und Ucc (“high”) Frage: In Welchem Spannungsbereich schwankt C ?

MOSFET Amplification Principle Drain Basic principle of a MOSFET amplifier: The drain current flow ID is controlled by the electrical field of the gate . ID is also proportional to the gate voltage UG. Amplification: a low voltage change on the gate produces large current changes between drain and source. ID E Gate E UG Source Mechanical Model See . Gate Drain Source

MOSFET Typen und Schaltungssymbole NMOS G G S D n+ poly-Si n+ n+ S S p-doped Si Substrate PMOS G G G S D p+ poly-Si p+ MH: Hierbei handelt es sich um amerikanische Schaltungssymbole – nach deutscher Norm sehen sie etwas anders aus. DB: müsste in den Linken Bildern nicht n- und p+ stehen, und nicht n+ und p+? MH: Zumindest in der Vorlesung sollte geklärt werden, dass n+ hoch n-dotiert bedeutet und analog dazu n-, p+ und p- p+ n-doped Si Substrate S S

For small UDS : MOSFET is seen as a controlled resistor A MOSFET acts as a resistor for small UDS : That is drain current ID grows linearly with UDS The resistance RDS between SOURCE & DRAIN depends on UGS - RDS becomes smaller when UGS is more than UT This operation mode is very important for digital circuits ! NMOSFET example: UDS UGS ID UGS = 2 V U(x) UGS = 1 V > UT UGS < UT UDS IDS = 0 if UGS < UT

Summary of ID ,UDS characteristic line The MOSFET ID-UDS curve has two regions:: 1) the Ohmic or “Trioden- region : 0 < UDS < UGS  UT 2) The Saturation region: UDS > UGS  UT D ID G UDS UGS S UGS= 2.5 V UDS = UGS  UT ID (A) Ohmic „Trioden“ region saturation UGS= 2.0 V Prozess Transkonductanz Parameter UGS= 1.5 V UGS= 1.0 V IDSAT= f(UGS) = constant UDS (V) “CUTOFF” Region: UG < UT

Measuring UT for a MOSFET UT can be quantified by measuring ID as a function of UGS for samall values of UDS ( UDS << UGS-UT ) : ID (A) UGS (V) for UGS = UT , : ID ≈ 0 UT

MOSFET as an Ohmic Switch For digital circuits, a MOSFET is either in cut-off „OFF“ (UGS < UT) or in conducting „ON“ (UGS = UDD) condition. We need to consider only two regions in the ID , UDS curve: Region where UGS < UT Region for UGS = UDD (UDD :supply voltage) D ID UGS = UDD (on-condition) Req ID UGS VDS UGS >UT UGS < UT (off-condition) S

The Equivalent Resistor Req In digital circuits an n-channel MOSFET is used to discharge a load capacity Cload under the following condition: Gate- voltage UG = UDD Source voltage US = 0 V Drain voltage UD with initial value UDD, discharged by drain current to 0 UDS discharging from UDD  UDD/2 The value of Req is selected to attain the required delay time td. (td is often considered as the time required to reach ½ UDD ): UDD UDD ID Clast Cload Req 

Typical MOSFET Parameters A sample MOSFET parameters: UT (~0.5 V) Cox and k (<0.001 A/V2) UDSAT ( 1 V) l ( 0.1 V-1) Example Req value for 0.25 mm Technology (W = L): UDD (V)

Wie verstärkt ein MOSFET Transistor? uDS iD 2. Verstärkung eine Signals us UDD uDS = uGS–UT  UDSAT RD iD us “LINEAR” oder “TRIODE” UDD RD “Sättigung”  + + UAusg = uDS  + uGS  + – UBIAS uGS =UBIAS + US uGS =UBIAS Eingangspannung am Gate ugs = UBIAS + us uGS uGS =UBIAS -US UAusg = uDS UDD Für us als Sinus-Signal: us = US cos(ωt) Arbeitspunkt Ausgangspannung

Eingangsschaltung für Linear-Verstärker UDD us + uGS  UDD = ID RD +uAUS UBIAS + – RD ID R1 UBIAS = UDD R2/(R1+R2) UBIAS uAUS us R2 uGS UBIAS: Gleichstromanteil des uGS uS : Wechselstromanteil des uGS

NMOSFET Zusammenfassung: Schaltungsmodel Für analoge Kleinsignal-Schaltungsapplikationen, wird das folgende vereinfachte Kleinsignalmodell verwendet: G D + ugs  id gmugs 1/go S S Transkonduktanz: Ausgangs-Leitwert: UGS und ID sind die Gleichstrom-Arbeitspunkt-Werte

NMOSFET Zusammenfassung: Digitales Schaltungsmodel Für Digitale Anwendungen wird der MOSFET als geschalteter Widerstand modelliert UDS Entladen von UDD  UDD/2 UGS > UT Req UGS = UDD Clast Clast S D ID Req UGS = 0  Bei Entladung der Lastkapazität, sinkt UDS auf 0 V iD UGS = UDD IDSAT slope  UDD / IDSAT slope  UDD / 2 IDSAT MOSFET schaltet ein (UGS = UDD) bei UDS = UDD UGS = 0 UDS UDD/2 UDD

Operational Amplifiers So far, with the exception of our ideal power sources, all the circuit elements we have examined have been passive Total energy delivered by the circuit to the element is non-negative We now introduce another class of active devices Operational Amplifiers (op-amps) Note: These require an external power supply!

Operational Amplifiers – overview We will analyze op-amps as a “device” or “black box”, without worrying about their internal circuitry This may make it appear as if KVL, KCL do not apply to the operational amplifier Our analysis is based on “rules” for the overall op-amp operation, and not performing a detailed analysis of the internal circuitry We want to use op-amps to perform operations, not design and build the op-amps themselves

Amplifire Abstraction Abstract description Amplifire circuit UDD UDD A RD ID uin uOut uOout= A . uin uOUT Or simply: uIN A uout = A . uiN uin A = Amplification factor

Full-Operational Amplifire Abstraction Amplifies the difference between u1 and u2 ! +UB Abstraction Symbol u+ + - + - uA u- u+ u- uA = A . ( u+ – u- ) -UB Op-Amp equivalent circuit Ideal Operational Amplifire: Has 2 inputs (negative - and positive +) and one output Where: Input resistance Ri => ∞ Output resistance Ro => 0 Amplification factor A => ∞ + - u+ Ro u =u+–u- Ri uA u- A . u

Characteristic Response of an operational amplifier Op-Amp equivalent circuit Abstract Symbol +12V + - u+ u+ + - u =u+–u- uA A . u uA = A u u- u- -12V uA Example Input resistance Ri = 10 MΩ output resistance Ro = 10 Ω Amplification factor A = 106 => ∞ Saturation +12V 8 V 8 μV uA = A . u = 106 x 8 μV = 8 V MH: Die Differenzspannung zwischen u+ und u- wird in den meisten Vorlesungen als uD bezeichnet u Linear active region A is very high Temperature dependent! -12V Saturation

uA741 op-amp schematic

Ideal Operational Amplifier “Rules” More complete circuit symbol (Power supplies shown) Assumptions: ip = 0, in = 0 vin = 0 V - < vout < V +

Operational Amplifire with Feedback (Non-Inverting Mode) Op-Amp equiv. circuit R1 R2 R1 R2 U- uA - + u- uE=u+ u- u =u+–u- uA=A(u+–u-) A . u uE=u+ How is the relationship between uA and uE? uA = A (u+ - u-) MH: Unterscheidet sich der Font auf dieser Folie absichtlich von den anderen? Rein=∞ Amplification factor in feedback mode uA/uE is independent on A!

Op-amp circuit – example 2 Find Vout 0 A 0 V i 0 A i

Operational Amplifire with Feedback (Buffer Amplifire) uA - + uE=u+ Called Buffer amplifire: Amplification factor uA/uE = 1 Input resistance Rein=∞ Output resistance RAusg= 0 Current amplification = ∞ MH: Die Bezeichnung Puffer-Verstärker ist mir unbekannt. Normalerweise nennt man die Verstärkerschaltung oben links einen Nichtinvertierer und unten rechts einen Impedanzwandler. Auch hier unterscheidet sich der Font für die Formeln von den bisherigen Folien. - + uA = uE uE

Operational Amplifire with Feedback (Inverting Mode) Op-Amp equivalent circuit uE R1 R2 R1 R2 uE u- uA - + u- u+=0 u- u =u+–u- A . u uA=A(u+–u-) u+=0 How is the relationship between uA and uE? uA = A (u+ - u-) Rin= R1 Amplification factor in feedback mode uA/uE is independent on A!

Op-amp circuit – example 1 Find Vout i -i 0 A 0 V

Examples: Operational Amplifire with Feedback uE R1= 1 kΩ R2= 15 kΩ uA - + Rin= R1= 1 kΩ R1= 1 kΩ R2= 9 kΩ MH: Der Unterschied zwischen den beiden Schaltungen ist meiner Meinung nach für jemanden, der die Thematik zum ersten Mal hört, nur schwer zu erkennen. Ich halte die Darstellungsart, bei der der R1 senkrecht nach unten auf Masse gezeichnet wird für günstiger. Zumindest solte man in der Vorlesung darauf hinweisen, dass einmal der positive und einmal der negative Eingang mit der Eingangsspannung beschaltet werden. uA - + uE Rin=∞