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MOSFET Small Signal Model & OperationMOSFET Small Signal Model & Operation
1Lecture # 5Lecture # 5
Small Signal Operation & ModelsSmall Signal Operation & Models
The DC Bias PointThe DC Bias Point
The Signal Current in the DrainThe Signal Current in the Drain
The Voltage GainThe Voltage Gain
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2
DC Bias PointDC Bias Point
For dc bias point we set the signal vgs to be zero
DDDDD
tGSnD
VVV
RIVV
VVL
WKI
2)(
2
1
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tGSD VVV
The required signal swing depend on VD, which should besufficiently greater than (VGS – Vt).
Small Signal Drain CurrentSmall Signal Drain Current
2
1)()(
2
1
)(2
1
22
2
gsngstGSntGSnD
tgsGSnD
gsGSGS
vL
WKvVV
L
WKVV
L
WKi
VvVL
WKi
vVv
last term. neglecting
2)(2
)(2
1 2
dDD
OVtGSgs
gstGSngsn
W
iIi
VVVv
vVVL
WKv
L
WK
First component is the dc bias current, second is the current component directly proportional to the applied signal and last is proportional to square of input signal
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2
2
, 2
)(
)(
'
ov
D
tGS
DmDnm
OVntGSngs
dm
gstGSnd
V
I
VV
IgILWKg
VL
WKVV
L
WK
v
ig
vVVL
WKi
3
Voltage GainVoltage Gain
Dmgs
dV
DgsmDdd
dDDdDDdDDDDD
DdDDDD
DDDDD
Rgv
vA
RvgRiv
vVRiVRiRIVv
RiIVv
RiVv
)(
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Total Instantaneous VoltagesTotal Instantaneous Voltages
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4
Separating DC Analysis & Signal AnalysisSeparating DC Analysis & Signal Analysis
InIn thethe smallsmall signalsignal analysisanalysis signalssignals areare superimposedsuperimposed onon thethe DCDCquantities,quantities, wewe havehave seenseen thatthat draindrain currentcurrent iiDD isis equalequal toto IIDD currentcurrent plusplus thethesignalsignal currentcurrent iidd andand similarlysimilarly draindrain voltagevoltage vvDD isis equalequal toto thethe dcdc voltagevoltage VVDDplusplus thethe signalsignal voltagevoltage vvdd.. ThisThis meansmeans thethe analysisanalysis cancan bebe simplifiedsimplified ifif weweseparateseparate thethe two,two, soso onceonce dcdc conditionsconditions areare establishedestablished andand allall dcdc quantitiesquantitiesareare calculatedcalculated wewe cancan performperform thethe signalsignal analysisanalysis andand totallytotally ignoringignoring thethe dcdcquantitiesquantities..
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Small Signal Equivalent ModelsSmall Signal Equivalent ModelsFrom a signal point of view FET behaves like a voltage controlled currentsource device.
This model assume (short coming) that drain current insaturation is independent of the drain voltage, we havelearnt that in reality drain current depend on the VDS in alinear manner and which is modeled by a finite resistance ro
(10 KΩ t 1000 KΩ) b t d i d V i
2
1 2
ovnD v
L
WKI
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(a) Neglecting the dependence of iD on vDS in saturation (the channel-length modulation effect); and (b) Including the effect of channel-length modulation, modeled by output resistance ro = |VA| /ID.
(10 KΩ to 1000 KΩ) between drain and source. VA isMOSFET parameter (It is proportional to the MOSFETchannel length.
1
where
)||(
AD
Ao
DgsmDddoDmgs
dv
VI
Vr
RvgRivrRgv
vA
5
Example 4.10Example 4.10
First find ID and VD and then find gm, ro and Av from the following equations.
)5.1(*25.0*2
1
) socurrent gate (No )(2
1
2
2
DD
DGStGSnD
VI
VVVVL
WKI
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)||||(
)(
oLDmi
ov
D
Ao
tGSnm
DDDDD
rRRgv
vA
I
Vr
VVL
WKg
IRVV
From slide 4
i
iin
Goii
i
vR
Rvvi
/)(
The T Equivalent Circuit ModelThe T Equivalent Circuit Model
Let us add this and as we can see thatcircuit properties are not changed.
Even joining X point with G will noth h l f I ( i )
We can replace controlledsource with a resistance ifthe current through itremains the same.
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Development of the T equivalent-circuit model for the MOSFET. For simplicity, ro has been omitted but can be added between D and S in the T model of (d).
Resistance = V/I=vgs/gmvgs
change the value of IG (remain zero).
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Alternative T Equivalent Circuit ModelAlternative T Equivalent Circuit Model
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(a) The T model of the MOSFET augmented with the drain-to-source resistance ro. (b) An alternative representation of the T model.
Exercise 4.23Exercise 4.23
22
2
1)()(
2
1gsngstGSntGSnD v
L
WKvVV
L
WKVV
L
WKi
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22 LLL
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Exercise 4.24, 4.25, 4.26, 4.27, 4.28 & 4.29Exercise 4.24, 4.25, 4.26, 4.27, 4.28 & 4.29
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Basic Structure of a Single Stage AmplifierBasic Structure of a Single Stage Amplifier
2
12
1ovoxn v
L
WCI
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Exercise 4.30Exercise 4.30
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Common Source AmplifierCommon Source Amplifier
GsigG
sigin
sigin
sigi
Ging
RRR
vR
RR
vv
RRi
0
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(a) Common-source amplifier based on the circuit of Fig. 4.42. (b) Equivalent circuit of the amplifier for small-signal analysis. (c) Small-signal analysis performed directly on the amplifier circuit with the MOSFET model implicitly utilized.
v
o
sigi
sigG
A
v
vv
RR
9
Common Source Amplifier with ResistanceCommon Source Amplifier with Resistance
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(a) Common-source amplifier with a resistance RS in the source lead. (b) Small-signal equivalent circuit with ro neglected. It has been observed that ro
fortunately does not effect the operation significantly in discrete circuit amplifiers.
Exercise 4.32 & 4.33Exercise 4.32 & 4.33
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Common Gate Amplifier Common Gate Amplifier
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(a) A common-gate amplifier based on the circuit of Fig. 4.42. (b) A small-signal equivalent circuit of the amplifier in (a). (c) The common-gate amplifier fed with a current-signal input.
Three observations:
CS CS vsvs CG Amplifier CG Amplifier
CS is inverting where as CG is non inverting.
CS has high input resistance where as CG has low input resistance, which is useful for cascading circuit operation (unity gain current amplifier or current follower).
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The gain for both configuration is identical, the over all gain for CG is small by a factor of 1 + gmRsig.
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Exercise 4.34Exercise 4.34
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Common Drain or Source Follower Common Drain or Source Follower AmplifierAmplifier
CD has high input resistance,low output resistance, gainnear to unity
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(a) A common-drain or source-follower amplifier. (b) Small-signal equivalent-circuit model. (c) Small-signal analysis performed directly on the circuit. (d) Circuit for determining the output resistance Rout of the source follower.
near to unity.
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Exercise 4.35Exercise 4.35
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Summary of ComparisonSummary of Comparison
The common source is best suited for obtaining bulk of the gain required in the amplifier, multiple stages can be used depending upon the requirement of the magnitude.
The performance can be improved if a resistance is introduced in the source terminal, however, gain is reduced.
The common gate is useful for some specific applications due to its low input resistance.
The source follower finds application as a voltage buffer for connecting high resistance source to a low resistance load in a multistage amplifier.
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Exercise 4.36 & 4.37Exercise 4.36 & 4.37
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Frequency Response of CS AmplifierFrequency Response of CS Amplifier
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(a) Capacitively coupled common-source amplifier. (b) A sketch of the frequency response of the amplifier in (a) delineating the three frequency bands of interest.
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High Frequency ResponseHigh Frequency Response
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Determining the high-frequency response of the CS amplifier: (a) equivalent circuit; (b) the circuit of (a) simplified at the input and the output;
High Frequency ResponseHigh Frequency Response
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(Continued) (c) the equivalent circuit with Cgd replaced at the input side with the equivalent capacitance Ceq; (d) the frequency response plot, which is that of a low-pass single-time-constant circuit.
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Low Frequency ResponseLow Frequency Response
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Analysis of the CS amplifier to determine its low-frequency transfer function. For simplicity, ro is neglected.
Low Frequency ResponseLow Frequency Response
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Sketch of the low-frequency magnitude response of a CS amplifier for which the three break frequencies are sufficiently separated for their effects to appear distinct.
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Exercise 4.38, 4.39 & 4.40Exercise 4.38, 4.39 & 4.40
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CMOS InverterCMOS Inverter
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Circuit OperationCircuit Operation
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Operation of the CMOS inverter when vI is high: (a) circuit with vI = VDD (logic-1 level, or VOH); (b) graphical construction to determine the operating point; (c) equivalent circuit.
Circuit OperationCircuit Operation
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Operation of the CMOS inverter when vI is low: (a) circuit with vI = 0 V (logic-0 level, or VOL); (b) graphical construction to determine the operating point; (c) equivalent circuit.
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Voltage Transfer CharacteristicsVoltage Transfer Characteristics
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Dynamic Operation of CMOS InverterDynamic Operation of CMOS Inverter
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Dynamic operation of a capacitively loaded CMOS inverter: (a) circuit; (b) input and output waveforms; (c) trajectory of the operating point as the input goes high and C discharges through QN; (d) equivalent circuit during the capacitor discharge.
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Current in the CMOS InverterCurrent in the CMOS Inverter
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Exercise 4.41, 4.42, 4.43 & 4.44Exercise 4.41, 4.42, 4.43 & 4.44
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Exercise 4.45 & 4.46Exercise 4.45 & 4.46
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Exercise 4.47, 4.48 & 4.49Exercise 4.47, 4.48 & 4.49
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The Depletion Type MOSFETThe Depletion Type MOSFET
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(a) Circuit symbol for the n-channel depletion-type MOSFET. (b) Simplified circuit symbol applicable for the case the substrate (B) is connected to the source (S).
The Depletion Type MOSFETThe Depletion Type MOSFET
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The current-voltage characteristics of a depletion-type n-channel MOSFET for which Vt = –4 V and kn(W/L) = 2 mA/V2: (a) transistor with current and voltage polarities indicated; (b) the iD–vDS characteristics; (c) the iD–vGS characteristic in saturation.
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The Depletion Type MOSFETThe Depletion Type MOSFET
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The relative levels of terminal voltages of a depletion-type NMOS transistor for operation in the triode and the saturation regions. The case shown is for operation in the enhancement mode (vGS is positive).
The Depletion Type MOSFETThe Depletion Type MOSFET
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Sketches of the iD–vGS characteristics for MOSFETs of enhancement and depletion types, of both polarities (operating in saturation). Note that the characteristic curves intersect the vGS axis at Vt. Also note that for generality somewhat different values of |Vt| are shown for n-channel and p-channel devices.