ho6[1].l03 cs small signal

8/13/2019 Ho6[1].l03 Cs Small Signal

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Lecture 3Common Source Amplifier

Small-Signal Model

R. Dutton, B. Murmann

R. Dutton, B. Murmann 1EE114 (HO #6)

Stanford University

Let's Build Our Firs t Ampli fier

One way to amplify Convert input voltage to current using voltage controlled

current source (VCCS) Convert back to voltage using a resistor (R)

"Voltage gain" = Vout /Vin Product of the V-I and I-V conversion factors



2/12

Common Source Amplifier

MOS device acts as VCCS

T


( )22

1

t iox D V V

L

W C I = ( ) RV V

L

W C V V

t iox DDo = 2

2

1

Biasing

Need some sort of "battery" that brings input voltage into usefuloperating region

Define V =V -V " uiescent oint ate overdrive" V OV=VGS -Vt with no input signal applied

VoVi

VO

Vo


"Bias"

"Signal"

VI

i

VOV


3/12

Relationship Between Incremental Voltages

What is Vo as a function of Vi?

( ) +=+ iOV ox DDoO RV V W

C V V V 1 2

Note: V gs =Vi=(VI+Vi)

( )[ ][ ]

+=

+=

+=

OV

ii

OV

D

iiOV ox

OV iOV oxo

V V

V RV

I

V V V R LW

C

V V V R LW

C V

21

2

22

1

2

1

2

22


As expected, this is a nonlinear relationship

Nobody likes nonlinear equations; we need a simpler model Fortunately, a (1 st order) linear approximation to the above

expression is sufficient for 90% of all analog circuit analysis

Small Signal Approximation (1)

+=OV

ii

OV

Do V

V V R

V I

V 2

12

Assuming Vi


4/12

Small Signal Approximation (2)

Graphical illustration:

Notation:

VO

VOV

dVo/dV i = v o/vi = Av


I

The slope of the above tangent is the so called "small-signalvoltage gain" of our amplifier (A v)

Notation

Total quantityQuiescentpoint value

Incrementalchange

oOo vV V +=

Total quantityQuiescentpoint value

Incrementalchange

Alternatively:(IEEE standard)


oOO vV v +=


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Small Signal MOS Model

Fortunately we don't have to repeat this analysis for every singlecircuit we build

Instead, we derive a linearized circuit model for the MOSrans s or an p ug n o ar rary c rcu s


Transconductance

The parameter that relates small signal gate voltage to draincurrent is called transconductance (g m), or y 21 in two-portnomenclature

The transconductance is found by differentiating the large signalI-V characteristic of the transistor at its operating point

( )22

1t GS ox D V V L

W C I =

( ) OV oxt GS oxGS

D

s

d m V L

W C V V

LW

C V I

vi

g ====


OV

Dm V

I g

2=


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Small-Signal Equivalent of CS Amplif ier

Use large signal I-V law to compute operating point (I D, VO, g m)

R. Dutton, B. Murmann 11

Make sure device operates in proper region; considerdesired signal swing

Now perform rest of calculations in small-signal land Gain, bandwidth (more later),

EE114 (HO #6)

Example (1)

Given: V I=1.5V, W=20 m, L=1 m, R=5k , VDD=5V Technology parameters: C ox = 50 A/V2, V t=0.5V a cu a e: D, O, g m, v

I +i

VO+vo

VDD

R

( ) AV .V .V A

I D =

= 50050511

2050

2

1 22

V . Ak V V O 5250055 ==


vi

VI

SaturationV V V V V

V .V V

t I t GS

O DS

====

1

52


7/12

Example (2)

mS V .V .

AV I

gOV

Dm

15051

50022=

==

551 === k mS Rg A mv


Getting Started with HSpice

The above circuit was easy to analyze

In general, we want to be able to compute circuit characteristicsboth manually and by using a circuit simulator Both hand calculation and simulation is important; one does

not replace the other Double book keeping is important in design and analysis to

detect flaws in assumptions and understanding


Lets see how we can duplicate this result using HSpice

EE114 (HO #6)


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HSpice Input File (1)

* Common sour ce ampl i f i er* B. Murmann, Fal l 2008

ev c e mo e

. model my_ nmos nmos kp=50u vt o=0. 5

*** usef ul opt i ons

. opt i on post bri ef nomod

vdd vdd 0 5


*** i nput vol t age

vi vi 0 dc 1. 5 *** val ue f or . op anal ysi s

+ ac 0. 1 *** ampl i t ude f or . ac anal ysi s+ si n 1. 5 0.1 1k *** si newave f or . t r an: V_I =1. 5V, v_i =0.1V, f =1kHz

EE114 (HO #6)

HSpice Input File (2)

*** d g s b

mn1 vo vi 0 0 my_ nmos w=20u l =1u

R vdd vo 5k

*** cal cul ate operati ng poi nt

. op

*** l arge si gnal anal ysi s ( sweep Vi )

. dc vi 0 5 0. 01

*** smal l si gnal anal ysi s ( sweep fr equency)


. ac ec

*** t r ansi ent anal ysi s ( sweep t i me)

. t r an 1u 5m

. end

EE114 (HO #6)


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.op Output

** ** mosf etsel ement 0: mn1

model 0: nmos114_

r e i on Satu r at i

i d 500. 0000u

vgs 1. 5000

vds 2. 5000

vbs 0.

vt h 500. 0000m

vdsat 1. 0000

vod 1. 0000


e a . m

gam ef f 527. 6252m

gm 1. 0000m

gds 0.

EE114 (HO #6)

.dc Output

5

5.5

1.5

2

2.5

3

3.5

4

.

V o

[ V ]


0 1 2 3 4 50

0.51

Vi [V]


10/12

1

[ V ]

.ac Output

102

103

0

.

f [Hz]

| v o

|

300

v o ) [ V ]

Av = v o/vi

= -0.5V/0.1V

= -5


102

103

0

100

f [Hz]

p h a s e

(

EE114 (HO #6)

.tran Output

3

3.5

1

1.5

2

2.5

[ V ]


0 0.5 1 1.5 2 2.5 3

x 10-3

0

0.5

t [sec]

Vi

Vo


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Another Run

Now with the following stimulus

*** i nput vol t age

vi vi 0 dc 1. 5 *** val ue f or . op anal ysi s

+ ac 1000 *** ampl i t ude f or . ac anal ysi s

+ si n 1. 5 1000 1k ** * si newave f or . t ran: V_I =1.5V, v_i =0. 1V, f =1kHz

1000V input amplitude applied to the circuit!


.tran Output

5

6

1

2

3

4

[ V ]


0 0.5 1 1.5 2 2.5 3

x 10-3

-1

0

t [sec]

Vi

Vo


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9000

10000

.ac Output

3000

4000

5000

6000

7000

8000

| v o

| [ V ]

5000V output!


102

103

0

1000

2000

f [Hz]

EE114 (HO #6)

Important to Remember

Once a small-signal model of the circuit is constructed, all largesignal information is lost The small-signal (.ac) circuit transfer function is linear and

extends from to + Features such as finite voltage range, signal clipping, etc. are

lost and completely meaningless in a small-signal analysis (or.ac simulation)

The input amplitude in the .ac statement is irrelevant and can be


Best to use 1V, in which case the output amplitude

corresponds to the circuit gain

EE114 (HO #6)

ho6[1].l03 cs small signal

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