Massachusetts Institute of TechnologyDepartment of Electrical Engineering and Computer Science6.002 – Circuits & ElectronicsSpring 2006Problem Set #5Issued 3/8/06 – Due 3/15/05Exercise 5.1: This problem studies the MOSFET amplifier shown below. Assuming that theMOSFET operates in its saturation region, defined by iD=0.5K(vGS− VT)2and 0 ≤ vGS− VT≤vDS, determine vOUTas a function of vIN. Also, determine the range of vIN, and the correspondingrange of vOUT, over which the MOSFET operates in its saturation region.+vOUT−VSRvINProblem 5.1: Both amplifiers shown below are constructed with a (non-quadratic) MOSFEThaving the vDS-iDcharacteristics shown graphically below. The characteristics are plotted for vGS= 0.5 V, 0.55 V, 0.6 V, 0.65 V, 0.7 V, 0.8 V ... 1.5 V. For vGS< 0.5 V, the MOSFET is cut off.Note that the last page of this problem set contains a larger graph of the MOSFET characteristics.It may be turned in with your problem set solutions.5V10 kΩ+vOUT−vGSAmplifier A5V10 kΩ+vOUT−vINR2R1Amplifier B0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 500.10.20.30.40.50.60.70.80.91vDS [V]iD [mA]MOSFET CharacteristicsvGS = 0.5 VvGS = 0.55 VvGS = 0.6 VvGS = 0.65 VvGS = 0.7 VvGS = 0.8 VvGS = 0.9 VvGS = 1.0 VvGS = 1.1 V(A) Consider Amplifier A. Using graphical analysis, plot vOUTas a function of vGSfor 0 V ≤ vGS≤1.5V.(B) Using your results from Part (A) determine the range of vGS, and the corresponding range ofvOUT, over which the small-signal voltage gain of Amplifier A from vGSto vOUTis reasonablyconstant at its largest value; use “engineering judgment”. (It is over this range that theamplifier provides its largest voltage gain with little distortion.) What is the correspondingsmall-signal voltage gain? Also, what is the small-signal voltage gain near vGS=0? (Youranswer to the last question explains why small signals can not be input directly at vGSif theyare to be amplified.)(C) Consider Amplifier B. This amplifier builds on Amplifier A, and uses the resistor networkcomprising R1and R2to bias vGSand vOUT. In this way, the amplifier will be designed toamplify vINwhen it is centered around 0 V. Determine vGSin terms of R1, R2, vINand thepower supply voltage of 5 V.(D) Let R1= 10 kΩ. Using your results from Parts (A), (B) and (C), determine R2so that theperformance of Amplifier B satisfies the following two criteria.For vIN= 0 V, resistors R1and R2establish the bias value of vOUT.AsvINvaries around 0 V,vOUTvaries around its bias value. With this in mind, the first criterion is that vOUTmust beallowed to vary within ±1 V of its bias value while remaining within the range identified inPart (B). That is, Amplifier B must be designed to provide voltage gain with little distortionover a 2-V range of vOUT. Note that the range for vOUTfound in Part (B) is wider than 2 Vand so this criterion does not uniquely specify R2.The second criterion is that the small-signal voltage gain of Amplifier B from vINto vOUTshould be maximized when vOUTis within the range established by the first criterion. Withthis additional criterion, R2is uniquely specified.(E) GivenyourdesignofR1and R2found in Part (D), what is the small-signal voltage gain ofAmplifier B for values of vINnear 0 V?(F) The small-signal voltage gain found in Part (E) should be smaller than that found in Part (B).Why?Problem 5.2: This problem continues to study the two-stage amplifier studied first in Prob-lem 4.3. In this problem, let vIN= VIN+ vinand vOUT= VOUT+ vout, where VINand VOUTarethe large-signal components of vINand vOUT, respectively, and vinand voutare the small-signalcomponents of vINand vOUT, respectively.(A) Assume that both MOSFETs are biased so that they operate in their saturation regions.Develop a small-signal circuit model for the amplifier that can be used to determine voutasa function of vin. In doing so, assume that VINdefines the operating point around which thesmall-signal model is constructed, and evaluate all small-signal model parameters in terms ofVINas necessary.(B) Use the small-signal model to determine voutas a function of vin.(C) Compare the small-signal voltage gain found in Part (B), defined as vout/vin, to that found inPart (F) of Problem 4.3. Explain any differences.(D) Determine the small-signal Thevenin equivalent of the amplifier when it is viewed through itsoutput port.Problem 5.3: Consider again the amplifier described in Exercise 5.1. In this problem, letvIN= VIN+ vinand vOUT= VOUT+ vout, where VINand VOUTare the large-signal componentsof vINand vOUT, respectively, and vinand voutare the small-signal components of vINand vOUT,respectively.(A) Using your result from Exercise 5.1, determine the small-signal voltage gain of the amplifier asa function of the input bias voltage vIN. That is, determine vout/vin= dvOUT/dvINevaluatedat VIN.(B) Again assume that the MOSFET is biased so that it operates in its saturation region. Developa small-signal circuit model for the amplifier that can be used to determine voutas a functionof vin. In doing so, assume that VINdefines the operating point around which the small-signal model is constructed, and evaluate all small-signal model parameters in terms of VINasnecessary.(C) Use the small-signal model to determine the small-signal voltage gain vout/vin. Compare thissmall-signal gain to that found in Part (A) and explain any differences.(D) Determine the small-signal Thevenin equivalent of the amplifier when it is viewed through itsoutput port.Figure For Problem 5.10 0.5 1 1.5 2 2.5 3 3.5 4 4.5 500.10.20.30.40.50.60.70.80.91vDS [V]iD [mA]MOSFET CharacteristicsvGS = 0.5 VvGS = 0.55 VvGS = 0.6 VvGS = 0.65 VvGS = 0.7 VvGS = 0.8 VvGS = 0.9 VvGS = 1.0 VvGS = 1.1
View Full Document
Unlocking...