II. BackgroundFig. 2. Small-signal MOSFET modelIII. Pre-Laboratory ExerciseIV. Laboratory ExerciseEE 462: Laboratory Assignment 5Small Signal Models: The MOSFET Common Source AmplifierbyDr. A.V. RadunDr. K.D. Donohue (5/25/04)Department of Electrical and Computer EngineeringUniversity of KentuckyLexington, KY 40506(Lab 4 report due at beginning of the period) (Pre-lab5 and Lab-5 Datasheet due at the end of the period)I. Instructional Objectives- Estimate small-signal MOSFET model parameters from measurements- Analyze circuit using the small-signal transistor model12See 6.1, 7.3.3, and 7.4.3 in HorensteinII. BackgroundLab 4 established the quiescent operating point of (biased) a common source amplifier employing an N-channel MOSFET. The common source amplifier is general-purpose amplifier with a good negative voltage gain, but poor high frequency characteristics. The N-channel MOSFET common source amplifier may be used as a voltage amplifier by connecting an input signal to the gate of the transistor, and connecting a load to the drain. Toensure the input signal and output load do not upset the amplifier’s bias, these connections are capacitively coupled. This means a capacitor is connected in series with the signal source and load, providing an open circuit during DC operation in order to prevent the source and load from changing the circuit’s quiescent operating point. These capacitor values are chosen so that they behave as an effective short-circuit for the AC signal components and thus that they do not significantly effect the AC signal losses. The circuit used for this lab is shown in Fig. 1, and the small-signal model of the MOSFET used in this circuit is shown in Fig. 2, where rd and rin are the MOSFET’s output resistance and input resistances, respectively.Recall that in saturation region: 22trVGSVpKDI (1)The parameters for the small signal model are given by (take partial derivatives of Eq. (1)): DQtrGSQVVGSGSDGSDmIKVVKVVIvigGSQGS22)(ˆ/ˆ(2) where K is the notation used in Horenstein, or  DQtrGSQVVGSGSDGSDmIKpVVKpVVIvigGSQGS2)(ˆ/ˆ(3)where Kp is the notation used in SPICE. Let gm denote the MOSFET’s transconductance. Two other circuits useful for this lab in measuring the total amplifier's input and output resistances are given in Figs. 3 and 4 below.VDD D G S Vout + - RD R2 Rs R1 Vs Cin Rsin RL Cout Cs Fig. 1. N-channel MOSFET common source amplifier Fig. 2. Small-signal MOSFET model V1 V2 Amplifier Rsense VDD Vout Vin Iin Fig. 3 Circuit for measuring Rin.Relationship for input resistance in terms of measured quantities from the circuit in Fig. 3:212212VVRVRVVVIVIVIVIVRsensesenseinrmsinrmsinpinpinppinppininin(4) Amplifier Vopen VDD Vin Amplifier VDD Vin Ishort Vshort + - Rshort Fig. 4. Circuit for measuring Rout. Relationship for input resistance in terms of measured quantities from the circuit in Fig. 4:G+vGS_rinrogmvGSSDshortshortopenshortshortopenshortrmsopenrmsshortpopenpshortppopenppshortopenthoutVRVRVVIVIVIVIVRR (5)Note that two separate tests are required to measure the input and output resistances. The sensing resistor (Rshort) is used to make a current measurement that emulates a short circuit (through the DC blocking capacitor). If Rshort is much smaller than the output resistance it should not affect the measurement significantly. If Rshort is significant, then a relationship analogous to equation should be derived that account for the parallel interaction between Rout and Rshort, which results in: shortshortshortopenoutVRVVR(6) III. Pre-Laboratory ExerciseFor the pre-lab assignments assume rd and rin to be infinite. In addition, assume that Rsin = 1 k-, RD = 1 k-, Rs = 100 -, RL = 1k-, K = Kp / 2 =0.1125 A/V2, Vtr = 1.8V, (or you can use the values you measured in the previous labs) IR1 =IR2 = 1.475mA, and VDD = 15 V. In general the capacitor values should be large to minimize the AC voltage drops for the frequencies considered. Value of Cs will be computed in pre-lab and Cin and Cout can be set to the value of Cs or greater. DC Circuit Set Up1. Draw the DC model of the circuit and derive the DC load line equation for the circuit.2. Find the values of R1 and R2 to set the operating point VDSQ = VDD / 2, which is approximately the desired intersection of the midpoint of the load line and the characteristic curves for the n-channel MOSFET. Since most of the operation will be in the saturation region, the following relationship is all that is needed to relate the gate voltage to the drain current for trGSDSVVV 3.    222trGStrGSDVVKpVVKI  (1)Plot the load line and TC curves knowing K or Kp, Vtr and VGS, as done in a previous lab using Matlab. AC Circuit Set Up4. Draw the AC or incremental model of the circuit.5. Using the AC or incremental model, determine the small signal voltage gain (inoutvvˆ/ˆ) and current gain (inoutiiˆ/ˆ) of the circuit for CS = 0. For these calculations assume Rsin is zero and RL is infinite. Repeat the voltage gain calculation with the given values of Rsin and RL (1 k-). Comment on how input and output resistances affect gain.6. Determine the value of CS in order to effectively short-out Rs. Assume the signal frequency is 10 kHz.7. Determine the small signal voltage (inoutvvˆ/ˆ) and current gain (inoutiiˆ/ˆ) of the circuit where CS is so large that it shorts out RS. For this calculation you may again assume Rsin is zero and RL is infinite. Repeat the voltagegain calculation with the given values of Rsin and RL. Compare to results in Problem 5 and comment on how the source (feedback) resistor affects the gain.Input and Output Impedances8. From the AC model, determine the input resistance and the output resistance (Thévenin equivalent resistance with respect to the output terminals) of the amplifier circuit (Rsin and RL are not considered part of the amplifier circuit). Do the input and output resistances depend on CS?9. Explain a way to determine the input resistance and the output resistance of the circuit above in terms of experimental measurements (note the output resistance is the same as the Thévenin equivalent resistance at the output terminal).IV. Laboratory Exercise1. Transfer Characteristics of MOSFET: Measure the transfer characteristics of your MOSFET on the curve tracer. Estimate the MOSFETs threshold voltage. This