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741 Op-Amp. Where we are going:. Typical CMOS Amplifier. -6. 10. -7. 10. -8. 10. Drain current (A). -9. 10. k = 0.58680 I o = 1.2104fA. -10. 10. nFET. pFET. S. D. -11. 10. 0.4. 0.45. 0.5. 0.55. 0.6. 0.65. 0.7. 0.75. 0.8. 0.85. 0.9. Gate voltage (V). G. G. B.

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741 op amp
741 Op-Amp

Where we are going:



Subthreshold mosfets

-6

10

-7

10

-8

10

Drain current (A)

-9

10

k = 0.58680

Io = 1.2104fA

-10

10

nFET

pFET

S

D

-11

10

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

Gate voltage (V)

G

G

B

D

S

Subthreshold MOSFETs

In linear scale, we

have a quadratic

dependence

In log-scale, we

have an exponential

dependence


Mosfet current voltage curves

(

)

(

)

(

)

k

-

k

-

V

V

/

u

V

V

/

u

=

-

I

I

e

e

g

S

T

g

d

T

0

MOSFET Current-Voltage Curves

(

)

-

-

=

-

/

/

kV

u

V

u

/

V

u

I

I

e

e

e

G

T

S

T

D

T

0

DS

(

)

(

)

(

)

k

-

V

V

/

u

-

-

=

-

V

V

/

u

I

e

1

e

g

S

T

d

S

T

0

(

)

-

-

=

-

(

)

/

/

kV

V

u

V

u

I

e

1

e

G

S

T

ds

T

0

>

V

4

U

-

=

(

)

/

kV

V

u

I

e

ds

T

G

S

T

0

Saturation



Current sources

Iout

Current

Sink

Vout

Vb

M5

GND

Vdd

Current

Source

V1

M6

Iout

Current Sources

Ever wonder how

we make one of these?

How “good” a current source?


Current versus drain voltage

GND

Current versus Drain Voltage

Not flat due to Early effect

(channel length modulation)

Id = Id(sat) (1 + (Vd/VA) )

Ic = Ic(sat) (1 + (Vc/VA) )

Iout

or

Id = Id(sat) eVd/VA

Rout

10mA

Ic = Ic(sat) eVc/VA


Current mirrors

Iout

Iin

Vdd

Vdd

Vout

Vb

Vb

M4

M7

Mb

M5

Iout

GND

GND

Iin

Current Mirrors

nFET Current Mirror

pFET Current Mirror

Iout = ( (W/L)5 / (W/L)b) Iin

Iout = ( (W/L)7 / (W/L)4) Iin

A good way to generate a bias current


Current mirror
Current Mirror

Iout1

Iout2

Iout3

Iin

Vout1

Vout2

Vout3

Vb

Mb

M5

M6

M7

GND

GND

GND

GND

Iout / Iin =

( (W/L)7 / (W/L)b)

Iout / Iin =

( (W/L)6 / (W/L)b)

Iout = ( (W/L)5 / (W/L)b) Iin


Diode capacitor dynamics

GND

GND

GND

Diode-Capacitor Dynamics

Iin

Iout

C (dVi/dt) = Iin - Ico exp(Vi/UT)

Iout = Ico exp(Vi/UT)

Vi

C

(C / Iout) (d Iout /dt) = Iin - Iout

C (d Iout /dt) = Iout( Iin - Iout )


Basic one transistor circuits
Basic One-Transistor Circuits

Common Source

Common Gate

Source Follower

Common Emitter

Common Base

Emitter Follower

The fundamental two-transisor circuit: Differential Pair


Multiple transistor configurations

Vdd

Vdd

GND

Multiple Transistor Configurations

Vdd

100pA

500mA

10mA

Vout

Vout

Vout

Vin

Vin

Vin

GND

GND

Subthreshold

MOS

Above threshold

MOS

BJT

JFETs as well….


Above threshold mosfet equations
Above Threshold MOSFET Equations

I = (K/2k) ( (k(Vg - VT) - Vs)2

- (k(Vg - VT ) - Vd) 2 )

If k = 1 (ignoring back-gate effects):

I = (K/2) ( 2(Vgs - VT) Vds - Vds2 )

Saturation: Qd = 0

I = (K/2k) ( (k(Vg - VT) - Vs)2


Gummel plots

-2

10

-3

10

-4

10

Gummel Plots

-5

Ic: n=1, Is = 5.52fA

10

-6

10

Currents

-7

10

-8

10

-9

10

Ib: n=1.019, Is = 0.048fA

-10

10

-11

10

-12

10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Base-Emitter Voltage (V)


Small signal modeling

V3

+

V

-

V1

rp

gmV

ro

V2

V2

Small-Signal Modeling

V3

V3

I

I

V1

V1

V2

V2

rp

gm

ro

Av

BJT

(UTb) / I

I / UT

VA / I

VA / UT

Above VT

MOSFET

2I /(V1-V2 -VT)

VA / I

2VA/(V1-V2 -VT)

Sub VT

MOSFET

kI / UT

VA / I

kVA / UT


Signal flow in transistors
Signal Flow in Transistors

  • Rules of Thumb

  • The collector or drain can never be an input terminal.

  • The base or gate can never be an output terminal.

  • In addition it is important to note polarity reversals on these signal paths.

  • The base-collector or gate-drain path inverts.

  • All other paths are noninverting.

  • (This of course assumes that there are no reactive elements causing phase shifts)

(Never is too

strong a word)


Spectrum of amplifier loads

Vdd

Vdd

Vdd

GND

GND

GND

Spectrum of Amplifier “Loads”

10mA

R1

Vb

Vout

Vout

Vout

Vin

Vin

Vin

Ideal Current

Source Load

Transistor Current

Source Load

Resistive

Load

Remember: On-chip resistors are expensive


Basic one transistor circuits1

Vdd

GND

Basic One-Transistor Circuits

Source Follower or Emitter Follower

Buffers (Isolates) the input to (from) the output

Assuming an ideal current source:

Vin

Ibias = Ieo e(Vin -Vout )/UT

Vout

Vout = -UT ln(Ibias/Ieo) + Vin

100mA

Ibias = Ibias e(DVin -DVout )/UT

D Vout = D Vin


Basic one transistor circuits2

If we use a transistor as a current source:

Id = Ibias eVout/VA = Io ekVin/UT e-Vout/UT

Vout = UT ln(Ibias/Io) + (k // (VA/UT))Vin

Basic One-Transistor Circuits

Assuming an ideal current source:

Vdd

Ibias = Io ekVin/UT e-Vout/UT

Vin

Vout

Vout = UT ln(Ibias/Io) + k Vin

10nA

Ibias = Ibias ekDVin/UT e-DVout/UT

GND

D Vout = kD Vin



Source degeneration

Why do this?

Vout

  • Higher Linearity

  • Possible Stability

Vin

Circuit

Element

Why not do this? gm

GND

GND

  • Lower Bandwidth

  • Higher Noise / Df

Source Degeneration

Vout

Vin


Source degeneration1

GND

GND

Source Degeneration

Vout

Neglect VA of Q1 and assume matched devices:

Vout

I

Vin

I = Ieo e V1 /UT = Ieo e(Vin - V1 + Vout/Av )/UT

Vin

V1

2 V1 = Vin + Vout / Av

Q1

I = Ieo e(Vin + Vout/Av )/(2 UT)

A similar result for MOSFETs


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