basic resistive load circuits
DESCRIPTION
Basic Resistive Load Circuits. Dr. Paul Hasler. V dd. V dd = 5.0V. GND. What is the bias current?. I ref = (2V) / R 1. Basic Resistive Load Circuits. Output Voltage Bias = 3.0V. R 1. R 1. V out. V out. V in. V in. GND. V dd. V dd = 5.0V. GND. Basic Resistive Load Circuits. - PowerPoint PPT PresentationTRANSCRIPT
Basic Resistive Load Circuits
Dr. Paul Hasler
Basic Resistive Load CircuitsVdd
GND
R1
Vout
Vin
GND
Vdd= 5.0V
Vout
Vin
R1
Output VoltageBias = 3.0V
What is the bias current? Iref = (2V) / R1
Basic Resistive Load CircuitsVdd
GND
R1
Vout
Vin
GND
Vdd= 5.0V
Vout
Vin
R1
Output VoltageBias = 3.0V
Iref = (2V) / R1
BJT / Subthreshold VT Above Threshold (Vd > Vg - VT )
(2V) / R1 = (K/2) (Vin - VT )2 (2V) / R1 = Ico eVin/UT
Vin = UT ln ( (2V) / R1 Ico ) Vin = VT + sqrt( (4V) / (K R1) )
Small-Signal Model: Common DrainVdd
GND
R1
Vout
Vin
GND
Vdd= 5.0V
Vout
Vin
R1
Output VoltageBias = 3.0V
Iref = (2V) / R1
Have bias Vin
Small-Signal Modeling
gmV ro
V3
V2V2
r
V1 +
V
-
V3
V2
V1
V3
V2
V1
gm ror
BJT
Above VTMOSFET
Sub VTMOSFET
Av
(UT ) / I
I I
I / UT
I / UT
2I /(V1-V2 -VT)
VA / I
VA / I
VA / I
VA / UT
VA / UT
2VA/(V1-V2 -VT)
Small-Signal Model: Common DrainVdd
GND
R1
Vout
Vin
GND
Vdd= 5.0V
Vout
Vin
R1
Output VoltageBias = 3.0V
Iref = (2V) / R1
Have bias Vin
gm = I / UT = (2V) / (R1 UT)
Compute Transconductance (gm)
BJT / Subthreshold VT Above Threshold (Vd > Vg - VT )gm = 2I /(Vin -VT) = (4V) / (R1 (Vin -VT) )
Small-Signal Model: Common DrainVdd
GND
R1
Vout
Vin
GND
Vdd= 5.0V
Vout
Vin
R1
Output VoltageBias = 3.0V
Iref = (2V) / R1
Have bias Vin
gm = (2V) / (R1 UT)
gm = (4V) / (R1 (Vin -VT) )or
gmVr
GND
Vout
R1
+V-
Vin
Gain = - gmR1 = - [ (2V) /(R1UT) ] R1
= - (2V) /UT
or
Gain = -(4V) / (Vin -VT)
Small-Signal Model: Common DrainVdd
GND
R1
Vout
Vin
GND
Vdd= 5.0V
Vout
Vin
R1
Output VoltageBias = 3.0V
Iref = (2V) / R1
Have bias Vin
gm = (2V) / (R1 UT)
gm = (4V) / (R1 (Vin -VT) )or
gmVr
GND
Vout
R1
+V-
Vin Gain = - [(2V) / UT ][1 + (2V)/ VA ]
orGain = -[(4V)/(Vin -VT)][1 + (2V)/ VA ]
ro
Small-Signal Model: Common DrainVdd
GND
R1
Vout
Vin
GND
Vdd= 5.0V
Vout
Vin
R1
Output VoltageBias = 3.0V
Iref = (2V) / R1
Have bias Vin
gm = (2V) / (R1 UT)
gm = (4V) / (R1 (Vin -VT) )or
gmVr
GND
Vout
R1
+V-
Vin
Gain = - (2V) /UT
orGain = -(4V) / (Vin -VT)
Output Resistance = R1
Common E / S: Resistive Load
Follower CircuitsVdd
Vout
Vin
Vdd
Vout
Vin
R1
R1
GNDGND
Output VoltageBias = 3.0V
What is the bias current? Iref = (3V) / R1
Basic Resistive Load Circuits
Output VoltageBias = 3.0V
Iref = (3V) / R1
BJT / Subthreshold VT Above Threshold (Vd > Vg - VT )
(3V) / R1 = (K/2) (Vin - Vout - VT )2 (3V) / R1 = Ico e(Vin - Vout)/UT
Vin = Vout + UT ln ( (3V) / R1 Ico ) Vin = Vout + VT + sqrt((6V)/(KR1))
Vdd
Vout
Vin
Vdd
Vout
Vin
R1
R1
GNDGND
Small-Signal Model: Common DrainOutput VoltageBias = 3.0V
Iref = (3V) / R1
Have bias Vin
Vdd
Vout
Vin
Vdd
Vout
Vin
R1
R1
GNDGND
gm = I / UT = (3V) / (R1 UT)
Compute Transconductance (gm)
BJT / Subthreshold VT Above Threshold (Vdd > Vin - VT )gm = 2I /(Vin –3V - VT) = (6V) / (R1 (Vin - 3V- VT) )
Small-Signal Model: Common DrainOutput VoltageBias = 3.0V
Iref = (3V) / R1
Have bias Vin
gm = (3V) / (R1 UT)
gm = (6V) / (R1 (Vin-3V-VT) )or
gmV
r
GND GND
Vout
R1
+ V -Vin
Vdd
Vout
Vin
Vdd
Vout
Vin
R1
R1
GNDGND
(Vin - Vout ) / r+ (Vin - Vout ) gm = Vout / R1
(Vin-Vout )(1 + r gm) = Vout (r / R1)
Vout/Vin = 1/(1 + [(r / R1)/(1 + r gm)])
Small-Signal Model: Common DrainOutput VoltageBias = 3.0V
Iref = (3V) / R1
Have bias Vin
gm = (3V) / (R1 UT)
gm = (6V) / (R1 (Vin-3V-VT) )or
gmV
r
GND GND
Vout
R1
+ V -Vin
Vdd
Vout
Vin
Vdd
Vout
Vin
R1
R1
GNDGND
Vout / Vin = 1 / (1 + [ (r / R1) / (1 + r gm)])
r gm = (large)
Vout / Vin = 1 / ( 1 + [ 1 / (R1 gm)] )
Small-Signal Model: Common DrainOutput VoltageBias = 3.0V
Iref = (3V) / R1
Have bias Vin
gm = (3V) / (R1 UT)
gm = (6V) / (R1 (Vin-3V-VT) )or
gmV
r
GND GND
Vout
R1
+ V -Vin
Vdd
Vout
Vin
Vdd
Vout
Vin
R1
R1
GNDGND
Vout / Vin = 1 / (1 + [ 1 / (R1 gm)])
Vout / Vin = 1 / (1 + [UT/(3V)])or
Vout / Vin = 1 / (1 + [Vin-3V-VT /(3V)])
Small-Signal Model: Common DrainOutput VoltageBias = 3.0V
Iref = (3V) / R1
Have bias Vin
gm = (3V) / (R1 UT)
gm = (6V) / (R1 (Vin-3V-VT) )or
gmV
r
GND GND
Vout
R1
+ V -Vin
Vdd
Vout
Vin
Vdd
Vout
Vin
R1
R1
GNDGND
Vout/Vin = 1/(1 + [UT/(3V)])or
Vout/Vin = 1/(1+[Vin-3V-VT /(3V)])
Output Resistance: Short the input to GND
Small-Signal Model: Common DrainOutput VoltageBias = 3.0V
Iref = (3V) / R1
Have bias Vin
gm = (3V) / (R1 UT)
gm = (6V) / (R1 (Vin-3V-VT) )or
1/gm
GND
Vout
R1
Vdd
Vout
Vin
Vdd
Vout
Vin
R1
R1
GNDGND
Vout/Vin = 1/(1 + [UT/(3V)])or
Vout/Vin = 1/(1+[Vin-3V-VT /(3V)])
GNDRout = (1/gm) / (1 + gm R1) ~ 1/gm
r
GND
Common Gate: Resistive Load
Vdd
Vout
Vin
Vb
R1
Vdd
Vout
Vin
Vb
R1
Output VoltageBias = 4.0V
What is the bias current? Iref = (1V) / R1
Common G: Resistive Load
Common Gate: Resistive LoadVdd
Vout
Vin
Vb
R1
Vdd
Vout
Vin
Vb
R1
Output VoltageBias = 4.0V
Iref = (1V) / R1
BJT / Subthreshold VT Above Threshold (Vd > Vg - VT )
(1V) / R1 = (K/2) (Vb - Vin - VT )2 (1V) / R1 = Ico eVb-Vin/UT
Vin = Vb - UT ln ( (1V) / R1 Ico ) Vin = Vb - VT - sqrt((2V)/(K R1))
Common Gate: Small-SignalVdd
Vout
Vin
Vb
R1
Vdd
Vout
Vin
Vb
R1
Output VoltageBias = 4.0V
Iref = (1V) / R1
BJT / Subthreshold VT Above Threshold (Vd > Vg - VT )
Have Input Bias
gm = I / UT = (1V) / (R1 UT)
gm = 2I /(Vb - Vin -VT) = (2V) / (R1 (Vb - Vin -VT) )
Common Gate: Small-SignalVdd
Vout
Vin
Vb
R1
Vdd
Vout
Vin
Vb
R1
Output VoltageBias = 4.0V
Iref = (1V) / R1
Have Input Bias
gm = (1V) / (R1 UT)
gm = (2V) / (R1(Vb- Vin-VT) )or
gmVr
GND
GND
Vout
R1
+V-
Vin
Gain = gm R1
Gain = (1V) / UT
Gain = (2V) / (Vb- Vin-VT)
or
Common Gate: Small-SignalVdd
Vout
Vin
Vb
R1
Vdd
Vout
Vin
Vb
R1
Output VoltageBias = 4.0V
Iref = (1V) / R1
Have Input Bias
gm = (1V) / (R1 UT)
gm = (2V) / (R1(Vb- Vin-VT) )or
gmVr
GND
GND
Vout
R1
+V-
Vin
Gain = (1V) / UT
orGain = (2V) / (Vb- Vin-VT)
Output Resistance = R1
Source DegenerationVdrain
Va
Vin
Vdrain
Va
Vin
R1 R1
GNDGND
Modifygm
Small-Signal Model: Common Drain
gmV
r
GND GND
Vout
R1
+ V -Vin
Vdd
Vout
Vin
Vdd
Vout
Vin
R1
R1
GNDGND
Vout / Vin = 1 / ( 1 + [ 1 / (R1 gm)] ) = R1 gm / (1 + R1 gm)
R1 << 1/gm R1 >> 1/gm
Vout / Vin = (R1 gm) Vout / Vin ~ 1
(Resistor has a small effect) (Resistor sets gm)
Source DegenerationVdrain
Va
Vin
Vdrain
Va
Vin
R1 R1
GNDGND
Modifygm
gmV
r
GND
Va
R1
+ V -Vin
Vdrain
ro
Gm: gmV = gm(Vin - Va ) = gm(1 - ) Vin
(ignore ro here)1 + R1gm
R1 gm
= 1 + R1gm
gm Vin
R1gm >> 1
R1gm << 1 gmVin
Vin /R
Vdrain
Source DegenerationVdrain
Va
Vin
Vdrain
Va
Vin
R1 R1
GNDGND
Modifygm
Rout:
Gm = 1 /R
gmV
r
Vdrain GND
Va
R1
+ V -
Vdrain
ro
GND
Source DegenerationVdrain
Va
Vin
Vdrain
Va
Vin
R1 R1
GNDGND
Modifygm
Gm = 1 /R
Rout:
gmVa
GND
Va
r // R1
Vdrain
ro
Vdrain
Solve for Va: Va / (r // R1) + gmVa = (Vdrain - Va)/ ro small
Va [ro (gm+ (1/(r // R1)) )] = Vdrain
small
Va = Vdrain /[rogm]
Source DegenerationVdrain
Va
Vin
Vdrain
Va
Vin
R1 R1
GNDGND
Modifygm
Gm = 1 /R
Rout:
gmVa
GND
Va
r // R1
Vdrain
ro
Vdrain
Solve for Current: I = Va / (r // R1)
Va = Vdrain /[rogm]
I = Vdrain /[rogm(r // R1)] Rout = rogm(r // R1)
Source DegenerationVdrain
Va
Vin
Vdrain
Va
Vin
R1 R1
GNDGND
Modifygm
Gm = 1 /R
Rout = rogm(r // R1)
Rin: (conductance is zero for a MOSFET)
“Reflect R1 through the base”
Vdrain
Vin
R1
GND
Rin
Rin = R1 + r = R1(1 + (1/(gmR1) ) ) small
Rin = R1
Source DegenerationVdrain
Va
Vin
Vdrain
Va
Vin
R1 R1
GNDGND
Modifygm
Gm = 1 /R
Rout = rogm(r // R1)
Rin = R1
GmVRin
GND
Vdrain+V-
Vin
Rout
Voltage Gain: Gm Rout = rogm(1 // (R1/r ) )