Electronic Circuits Laboratory EE462G Lab #6AC and DC AnalysisCommon Source AmplifierBlocking CapacitorsSmall Signal ModelSlide 6Small-Signal System ParametersGain About a Quiescent PointAC Circuit for Gain MeasurementAC Gain of AmplifierAmp DistortionScript for Distortion AnalysisSlide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Electronic Circuits LaboratoryEE462GLab #6Small Signal Models: The MOSFET Common Source AmplifierAC and DC AnalysisAmplifier circuits have DC and AC components that can be analyzed separately.The purpose of the DC component is to bias currents and voltages to a static operating point in a region where the input and output relationship is reasonably linear for small deviations about the operating point.The purpose of the AC component is to provide gain and/or impedance coupling for the information component of a signal, so it can be measured, processed, or used to drive an output device.The AC and DC components can be analyzed separately if the AC components are small relative to the DC components, and blocking capacitors are inserted to block DC biasing voltages and currents from the points at which the AC signal couples to the input and output.Common Source Amplifier The input and output share a common node at ground through the source of the NMOS transistor. Determine how “good” capacitor values should be chosen to isolate the DC from the AC without significantly affecting the AC operation or DC settings.For DC blocking, any capacitor value will do: VDD D G S Vout + - RD R2 Rs R1 Vs Cin Rsin RL Cout Cs 0 as 1CjTo pass AC components, capacitor impedance should behave as an effective short:LoutsssininRCjRCjRCj1, 1 , 1Blocking Capacitors If the expected frequency of operation was between 300 and 4kHz, determine good capacitor values to isolate the DC from the AC without significantly affecting the AC operation. VDD D G S Vout + - RD R2 Rs R1 Vs Cin Rsin RL Cout Cs The capacitive impedance will be largest for the smallest frequencies, choose worse case, f=300 Hz and assume smallest resistor value in circuit to be 500: 1CRsin F1130050021C.))((Between 10 to 100 times bigger than this value is good rule of thumbSmall Signal ModelFor a common source connection and small-signal AC analysis in the linear range, the MOSFET can be modeled with the following circuit: G+vgs_rinrdgmvgsSDrin – Input resistance (typically very large compared with biasing resistors)rd – Output resistance (typically very large compared with biasing resistors)gm - MOSFET transconductanceSmall Signal ModelThe small-signal equivalent of the common source amplifier results from deactivating all DC sources and treating the blocking capacitors as short circuits:If Cs is not in the original circuit (Cs=0), Rs would be present between the source and ground along with Cs. This complicates the analysis and limits the gain. To study capacitive effects, leave the capacitors in and redraw and analyze the above circuit.vs G+vgs_rinrdgmvgsSDRDRLR2RsinR1+vin_+vout_ioutiinSmall-Signal System ParametersIn general, the internal resistor of the source, Rsin, and load, RL, are not considered part of the system; however they will affect critical system parameters listed below:inoutvvvAˆˆSmall-signal voltage gain:inoutiiiAˆˆSmall-signal current gain:inininivRˆˆInput resistance:outoutoutivRˆˆOutput resistance:Explain how to compute these quantities.Explain how to measure these quantities.Gain About a Quiescent Point0 2 4 6 8 10 120123456x 10-3VDS in VoltsID in AmpsVGS=2.5+70mV VGS=2.5+110mV VGS=2.5+150mV 2.7V, 4.63mA 10.04V, 9.8mA If changes about VGSQ are consider the input, and changes in VDSQ are considered the output, then the gain of this system is:Note gain is dependent on the transconductance of the MOSFET (related to Kp and the bias point) and the slope of the load line.mV)70150(V)04.107.2(GSDSVVVG75.91VGAC Circuit for Gain Measurement Vin will perturb the voltage at the gate causing a perturbation in Vout V DD D G S V out + - R D R 2 R S R 1 V in C + - What is the purpose of the capacitor in this circuit?AC Gain of AmplifierOnce the quiescent point is set, small perturbations around VGS, driven by variations Vin will perturb IDS , which cause larger perturbations in Vout. The ratio of the change in Vout to the change in Vin is the gain of the amplifier. To measure the gain, the quiescent or DC component resulting from the bias must be subtracted out, so the ratios of the AC components are computed. The removal of the DC component happens naturally with a peak to peak measurement (under either AC or DC coupling) and for rms measurement under AC coupling. What kind of coupling on the oscilloscope channels would be best to use for the measurements to compute the gain?Does it make a difference in the gain computations if the AC voltages are measured in peak, peak-to-peak, or RMS?  inQinoutQoutinoutVtVVtVvv)(max)(maxˆˆGainAmp DistortionA Matlab script was written to compute the transfer characteristics of an NMOS amplifier and map signals from input to output. It finds the operating point and computes the intersection of the load line with the FET transfer characteristic for a series of inputs (see mfile qpoint_iter.m on web page).A function was then written to map a signal through the tabulated input-output relationship (see mfile ampdist.m on web page).The script will be used to show examples of distortion from the non-linearity introduced by the amplifier (see mfile scrpdist.m on web page)Script for Distortion Analysis% This script runs an example of a load line analysis for a MOSFET amp% to:% 1. find the operating point for Vgs through iteration% 2. then compute a table of input (Vgs) and output (Vds)amplitude values% to get the transfer characteristic (TC) curve for the amp.% 3. then apply the resulting TC curve to an input sinusoid with% increasing amplitude to illustrate distorion. The sine wave% will be plotted and played in the demonstration.% The functions nmos.m and ampdist.m are needed to run this script%% Set Parameters: Operating point will be set to half VDDK=.5; vto = 1.8; % Nmos parametersW=1; L=1; KP=2*K; % Nmos parametersVDD=15; RS=400; RD=1e3; % Load line parametersidsmax = VDD/(RD+RS); % Maximum Load line value on Drain current