1 / 40

Lecture-04 Non-linear Elements, Active Elements MOSFETS Operational Amplifiers

Fundamentals of Analog and Digital Design ET-IDA-134. Lecture-04 Non-linear Elements, Active Elements MOSFETS Operational Amplifiers. 11.12.2018, v13 Prof. W. Adi. Source: Analog Devices, Digilent course material.

tammys
Télécharger la présentation

Lecture-04 Non-linear Elements, Active Elements MOSFETS Operational Amplifiers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Fundamentals of Analog and Digital Design ET-IDA-134 Lecture-04 Non-linear Elements, Active Elements MOSFETS Operational Amplifiers 11.12.2018, v13 Prof. W. Adi Source: Analog Devices, Digilent course material

  2. Agarwal, Anant, and Jeffrey H. Lang. Foundationsof 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 Course Contents Lecture Material: Recommended Textbook: - Provided in theclass. Source: Digilent/Analog Devices Course material - Suplimentaryadvanced analog and digital design topicswithlaboratory Laboratory: - Digilent Analog Discovery withlab‘skit. Web Digilent material Link: http://www.digilentinc.com/Classroom/RealAnalog/

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

  4. The pn-Junction Diode Circuit Symbol Schematic description ID Anode Cathode 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

  5. 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 [ISis 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 UD (V) 0.7 V für Si IS ≈ 1 nA (Si) Threshold voltage

  6. The Ideal Diode: Modell for the pn-Diode I-U Curve As switch Circuit Symbol ID ID (A) + UD – ID UD Backward Direction Forward Direction UD (V) • An ideal diode allows current flow only in one direction. • An Ideal Diodehas 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

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

  8. 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 UBD Breakdown Voltage UD (V)

  9. 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 Solve two equations with two unknowns! UTh The result is a non-linear equation with one unknown: - (1/ RTh ) UD +UTh/RTh = Hard to solve! Therefore a graphical solution!

  10. 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 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

  11. MOSFET Amplification Principle Drain Basic principle of a MOSFET amplifier: The drain current flow IDis 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

  12. MOSFET Transistor Types NMOS G G G S D n+ poly-Si n+ n+ S S p-doped Si Substrate G PMOS G G S D p+ poly-Si S S p+ p+ n-doped Si Substrate

  13. 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 UGS = 1 V > UT UGS< UT UDS IDS = 0 if UGS< UT

  14. 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 ProzessTranskonductance Parameter UGS= 2.0 V UGS= 1.5 V UGS= 1.0 V UDS (V) IDSAT= f(UGS) = constant “CUTOFF” Region: UG < UT

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

  16. 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 UGS >UT VDS UGS< UT(off-condition) S

  17. 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 The value of Reqis selected to attain the required delay time td. (td is often considered as the time required to reach ½ UDD ): UDSdischarging from UDD UDD/2 UDD UDD Clast ID Cload Req 

  18. Typical MOSFET Parameters • A sample MOSFET parameters: • UT (~0.5 V) • Coxand k (<0.001 A/V2) • UDSAT ( 1 V) • l ( 0.1 V-1) ExampleReqvalue for 0.25 mm Technology (W = L): UDD (V)

  19. iD uDS 0 How does a MOSFET Transistor amplify? Amplifying the input signal us UDD RD uDS= uGS–UT  UDSAT iD us “LINEAR” orr “TRIODE” UDD RD + UOut= uDS   + “Saturation” + uGS  + – UBIAS uGS=UBIAS + US Input signal at gate uGS = UBIAS + us uGS=UBIAS uGS uGS=UBIAS -US UDD UOut= uDS Operating point Output Voltage Swing Range

  20. Input Signal and bias for a linear amplifier UDD us UDD = ID RD +uOut + uGS  + – UBIAS RD ID R1 UBIAS = UDD R2/(R1+R2) UBIAS uOut R2 us uGS UBIAS: DC voltage component uGS uS : Changing voltage component uGS

  21. MOSFET When discharging UDS goes from UDD to 0 V slope UDD / IDSAT MOSFET switches on (UGS = UDD) and UDS = UDD slope UDD / 2 IDSAT NMOSFET Summary: Digital Circuit Model • For digital circuits a MMOSFET is modeled as a switched resistor Change from 1 to 0: UDSDischarged from UDD UDD/2 UGS > UT Req UGS = UDD S D Clast Clast ID Req UGS = 0  iD UGS = UDD= “1” IDSAT UGS = 0 UDS 0 UDD/2 UDD • UDS =“0” • UDS =“1”

  22. B C-MOSFET (Complementary Symmetric ) Digital Switch On for 1 P-MOS B B Req-P B N-MOS Req-N On for 0

  23. UDD S G D UA UE D G S CMOS Inverter: model and operating points Circuit Switch modelsforbothestates UDD UDD Rp Low UAL = 0 V High UAH = UDD UA UA Rn Low energy consumption as no current flow in both low and high states UE = UDD UE = 0 V

  24. CMOS Inverter: Models and operationpoints Switch modelforlowoutput UA=0 and high output UA=UDD UDD UDD Rp UA-high = UDD UA UA CL UA-low = 0 V CL Rn UDD UDD UA UA UE = 0 V UE = UDD tpHL tpLH

  25. Example : C-MOS Circuit and switching speed computation • Set up the truth table of the function F(A,B,C) • Implement the function in C-MOS transistors • Compute the maximum and minimum (best-case and worst case) possible operating speed of the function F. Assume that the switching resistance for P-MOS transistor is RP=7 kΩand for N-MOS transistor RN=5kΩ and the load capacitor is 3 pF. Solution: 1. From the truth table: 2. By Boolean reduction/manipulation and reorganization/minimization of the function: (notice other solutions are possible):

  26. B B B UDD A B C A F C B A B C USSD

  27. B B B Worst case Best case UDD UDD 5. Any switching to high=1 state involves two P transistors in series UDD 7kΩ 7kΩ A 7kΩ 7kΩ T1 Any switching to low=0 state involves on of the two cases B C 5kΩ 5kΩ UA UA T2 c=3pF c=3pF F 5kΩ 5kΩ 5kΩ tpLH=0.69 RpC = 0,69 (7+7)kΩ x 3pF tpLH= 29 ns B A CL Best case: tpHL=0.69 RnC = 0,69 (5+2,5)kΩ x 3pF tpHL= 15,5 ns T3 B Worst case: tpHL=0.69 RnC = 0,69 (5+10)kΩ x 3pF tpHL= 31,05 ns C T5 T4 USSD Maximum operating frequency FMax= 1/2(tpHL+ tpLH) =1/2(29+15,n)ns = 11,24 MHz Minimum operating frequency FMax= 1/2(tpHL+ tpLH) =1/2(29+31,05)ns = 8,33 MHz

  28. 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!

  29. 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

  30. Amplifire Abstraction Abstract description Amplifire principle UDD UDD A RD ID uin uout uout= A . uin uout Or simply: uin A uout= A . uin uin A = uout/uinas Amplification factor

  31. 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 • IdealOperational 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 A . u u-

  32. 8 V 8 μV uA= A . u = 106 x 8 μV = 8 V Characteristic Response of an operational amplifier Op-Amp equivalent circuit Abstract Symbol +12V + - u+ u+ + - u=u+–u- uA uA = A u A . u u- u- -12V uA • Example • Input resistance Ri= 10 MΩ • output resistance Ro = 10 Ω • Amplification factor A = 106=> ∞ Saturation +12V u Linear active region A is very high Temperature dependent! -12V Saturation

  33. uA741 op-amp schematic

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

  35. Operational Amplifire with Feedback1- (Non-Inverting Mode) Op-Amp equiv. circuit analysis R1 R2 R1 R2 uA U- 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-) Rein=∞ Amplification factor in feedback mode uA/uEis independent on A!

  36. Op-amp circuit – Non-Inverting Mode • Find Vout 0 A 0 V i 0 A Rin i

  37. Operational Amplifire with Feedback1-(Non-Inverting Buffer) R1 R2 uA U- - + uE=u+ (Special case: Buffer Amplifire) Called Buffer amplifire: Amplification factor uA/uE= 1 Input resistance Rein=∞ Output resistance RAusg= 0 Current amplification = ∞ - + uA = uE uE

  38. Operational Amplifire with Feedback2- (Inverting Mode) Op-Amp equivalent circuit R1 uE R2 R1 R2 uE u- uA u- - + u+=0 u- u=u+–u- uA=A(u+–u-) A . u u+=0 How is the relationship between uA and uE? uA = A (u+ - u-) Rin= R1 Amplification factor in feedback mode uA/uEis independent on A!

  39. Op-amp circuit – Inverting-Mode • Find Vout i -i 0 A 0 V

  40. Examples: Operational Amplifire with Feedback 1- Inverting Mode: uE R1= 1 kΩ R2= 15 kΩ uA - + Rin= R1= 1 kΩ 2- Non-Inverting Mode: R2= 9 kΩ R1= 1 kΩ uA - + uE Rin=∞

More Related