INF3410 — Fall 2013 · INF3410 — Fall 2013 Book Chapter 3: Basic Current Mirrors and Single-Stage Ampliﬁers. content Simple Current Mirror Common-Source Ampliﬁer Interrupt:

INF3410 — Fall 2013

Book Chapter 3: Basic Current Mirrors and Single-StageAmplifiers

contentSimple Current MirrorCommon-Source AmplifierInterrupt: A word on output resistanceCommon-Drain Amplifier with active load / Source FollowerCommon-Gate Amplifier with active loadSource-Degenerated Current MirrorsCascode Current MirrorsCascode Gain StageDiff Pair and Gain Stage

Book Chapter 3: Basic Current Mirrors and Single-StageAmplifiers 2

Simple Current Mirror

When will Iout Iin, Iout Iin, Iout � Iin, Iout � xIin?Book Chapter 3: Basic Current Mirrors and Single-StageAmplifiers 4

Diode Connected nMOS

Is the simplified small signal model very useful here? Forexample when you want to know the voltage when youapply a given current?


Current Mirror Small Signal Model

How do you describe the effect of different WL ratios of thetwo transistors in terms of the small signal model?


Current Mirror Small Signal Model, Example 3.1(1/2)

A detour solution (shorter in the book):

Veff Vin � Vt0 s

2�Iin

s

2

10�m=0:4�m� 190�A/V2� 100�A

205mV

Vin 205mV 570mV 775mV



Continued detour solution (shorter in the book):

Iout 12�V2eff

10�m=0:4�m� 190�A/V2 � 205mV2

2 100�A



Wrong (!!!) approach:

gm �� Veff 10�m=0:4�m� 190�A/V2 � 0:205V 974�A/V

That was still correct but ...

Iout Vin � gm 755�A

... is a wrong conclusion!!!



Continued correct detour solution:

rout 1

�Iout

L�LIout

0:4�m0:16�m=V � 100�A

0:025V/�A 25kÚBook Chapter 3: Basic Current Mirrors and Single-StageAmplifiers 10

Common-Source Amplifier with active load

Active: current mirror or FET with fixed gate voltage asloadPassive: a resistor to Vdd (normally lower outputimpedance or excessive voltage across resistor)

What are the conditions forthis circuit to work as anamplifier? When will it notwork?


Small Signal Model

AV voutvin

�gmR2 �gmrds1 k rds2

(Rin not well motivated in the book: makes only sense withincluding parasitic capacitances. It is actually attributed toa more reslistic voltage source, i.e. not the transistor.)


Example 3.2 (1/3)

g2m1 2�Ibias 2� 190�AV2� 12�m

0:5�m� ID=bias 9120

�AV2� ID=bias

rds1=2 L

�LID=bias 0:5�m

0:16�mV� 1ID=bias

3:125V� 1ID=bias


Example 3.2 (2/3)

A2V 152 �gm1 � rds1 k rds2

�2 �gm1 � rds12�2

9120�AV2� ID=bias � 3:125V2 �

1

2ID=bias

!2 22266�A� 1

ID=bias

ID=bias 22266�A

152 99�A


Example 3.2 (3/3)

Veff Vin=DC s

2ID�

vuut 2� 99�A

190�AV2� 12�m0:5�m

208:4mV

This Veff is the DC level (large signal value) of the input!For the Veff of the pFETs one would need to use adifferent �Cox resp. �!


Example 3.2 alternative

For Common-Source with active load where rds1 rds2:

AV Ai2 gm1rds1

2� 1�Veff

Veff 1�15

0:5�m0:16�mV 15

208:4mVID

12�V2eff 99�A


Output resistance

The output resistance of circuit’s output is the rate ofchange of output voltage when forcing an output current.

Rout @Vout@Iout

Consequently, an ideal voltage source has a zero outputresistance and an ideal current source has infinite outputresistance.


Output resistance, small signal model

Rout

Rout


Input resistance

equivalently the input resistance is the change in voltageseen when forcing a current into a circuit.

Rin @Vin@Iin

The small signal equivalent circuit is a resistance from theinput node to ground. If the input is a current signal, Rinshould be small. If the input is a voltage signal Rin shouldbe large.


What is a small signal analysis good for?

æ determine input and output resistances/impedances

æ determine gain (voltage or current), transconductance,transresistance, transadmittance, transimpedance


Source Follower

What are the conditions forthis circuit to work? Wouldyou call it an amplifier?


Small Signal Model


Simplified Small Signal Model

This circuit is used to follow avoltage but with an offset andsmall output resistance.

AV gm11gm1

k 1gs1

k rds1 k rds2

gm1gm1 gs1 1rds1

1rds2

� 1

(but actually somewhat smaller)


Common Gate Amplifier

Similar to common-sourceamplifier but with a less thaninfinite input resistance.Good for e.g terminatingresistance for input from a(e.g. 50Ú) cable or currentinput (transresistance).


Small Signal Model


Simplified Small Signal Model and AV

AV is approximately thesame as for the comonsource amplifier.

vout � vs1gds1 voutGL � vs1gm1 gs1 0

AV voutvs1

gm1 gs1 gds1GL gds1

� gm1GL gds1

gm1RL k rds1


Small Signal Model and rin (1/2)

iin vingm1 gs1� vout � vingds1 vingm1 gs1 gds1�

vingm1 gs1 gds1GL gds1

gds1

vingm1 gs1 gds1

1� gds1GL gds1

!

vingm1 gs1 gds1GL

GL gds1 vingm1 gs1 gds1

1

1 gds1GLBook Chapter 3: Basic Current Mirrors and Single-StageAmplifiers 31

Small Signal Model ans rin (2/2)

gin iinvin

gm1 gs1 gds11

1 gds1GL� gm1

1

1 gds1GL

rin �1gm1

1 gds1GL


A realistic voltage source at input

Since the input resistance is not infinit, one needs to becareful here: if considering a resistance RS between idealsource and common-gate amplifier, e.g. a 50Ú cable orsimply a realistic source with rout > 0, AV will appearsmaller! That is to say when you first meaure vin withoutconnecting your source to the amplifier, then connect theamp, and then measure vout, you will not see the AVcomputed before, but A0V (still called AV in the book)!

vs1vin

rinrin RS

) A0V AVrin

rin RS

A0V �gm1RL k rds1

1 RS gm1gs1gds11RL=rds1Book Chapter 3: Basic Current Mirrors and Single-StageAmplifiers 33

Source-Degenerated Current Mirror

A first attempt to providehigher output resistance (i.e.a better current source).Note: requires higher voltageat output to work at all!


Small Signal Model

Important point: tocompute small signalrout the input currentcan be consideredconstant and thus thesmall signal inputcurrent source is anopen circuit, i.e.vgs �vs .

rout rds2�1 RSgm2 gs2 gds2

�� rds2

�1 RSgm2 gs2

�Book Chapter 3: Basic Current Mirrors and Single-StageAmplifiers 36

Cascode Current Mirror

A second attempt to providehigher output resistance (i.e.a better current source).Note: also requires highervoltage at output to work atall but is less dependent on(large signal) current!


Small Signal routThe analysis is based on the source degenerated currentmirror where former RS is replaced by rds2

rout rds4�1 rds2gm4 gs4 gds4

�� rds4rds2gm4 3:37

VOUT!> 2Veff Vtn 3:42


Cascode Gain Stage

Offers large gain for a single stage (depends on quality ofcurrent source!) and limits voltage accross the input drivetransistor (e.g. avoiding short channel effects).Book Chapter 3: Basic Current Mirrors and Single-Stage

Amplifiers 41

Small Signal Model

The small signal analysismakes use of the previouscommon source andcommon gate analysis,simply multiplying theprvious two voltage gains:

voutvin

vs2vin

voutvs2

3:54

� �gm1gm2�rds1 k rin2rds2 k RL


Small Signal Model Folded Cascode

Similar to the telescopic cascode gain stage but noninverting and with an extra load resistor (current source)diminishing the gain:

voutvin

vs2vin

voutvs2

3:54 � gm1gm2rds1 k rin2 k RLrds2 k RL


Assuming High Quality Current Mirrors

voutvin

� �gm1gm2rds1 k rin2rds2 k RL � �12g2mr

2ds


Diff Pair

Realizes a differential inputfor most integratedamplifiers: immunity tonoise/offsets that affect bothinputs (e.g. pick-up noise ontwisted-pair cables etc.)


Small signal model

The book uses the T-model. Here comes an alternativededuction based on the ’normal’ model.

g vm +x

vx

g vm -xrds rds

i+ i-

i=� v=� � vxgm � vx1rds

i � i� v � v�gm 3:69Book Chapter 3: Basic Current Mirrors and Single-StageAmplifiers 47

Small signal model with resistive loads on eachbranch

g vm +x

vx

g vm -xrds rds

i+ i-

vout+ vout-

RL

RL

i=� �vout=�1RL v=� � vxgm vout=� � vx

1rds


Small signal model with resistive loads on eachbranch

g vm +x

vx

g vm -xrds rds

i+ i-

vout+ vout-

RL

RL

�vout=��

1RL 1rds

� v=�gm � vx

�gm

1rds

�

�vout � vout� v � v�gm

1RL

1rds

� v � v�gmRLBook Chapter 3: Basic Current Mirrors and Single-StageAmplifiers 49

Differential Gain Stage, Transcunductance Amp

The simple analysis: consider that thecurrent mirror faithfully copies thecurrent through the left branch andconsider a voltage source at theoutput, then the current into thatvoltage source is exactly the previousiout i � i�. With no voltage source,the difference in current has to flowtrough the output resistance )vout ioutrout. With (3.69) and (3.78)vout gmvinrout )AV � gmrds2 k rds4 which is (3.79).


More Careful Analysis for rout (1/4)

(different from the book)

-g vm1 2

v2

rds1 rds2

-g vm4 1 rds4

iouti1 vout

i2

-g vm2 2

1/gm3

v1

iout i2 � i1



-g vm1 2

v2

rds1 rds2

-g vm4 1 rds4

iouti1 vout

i2

-g vm2 2

1/gm3

v1

i1 �1rds4

vout � gm4v1

i2 1rds2

vout � v2� gm2v2

� 1rds2

vout � gm2v2

i2 v2 � v11rds1

gm1v2

� v11rds1

gm1v2

i2 v1gm3Book Chapter 3: Basic Current Mirrors and Single-StageAmplifiers 52


-g vm1 2

v2

rds1 rds2

-g vm4 1 rds4

iouti1 vout

i2

-g vm2 2

1/gm3

v1

Using 2. and 3. term on previous pagefor i2:

v2 �gm3gm1

v1

using 1. and 2. term on previous pagefor i2 and gm1 gm2

vout1rds2

� v11rds1

gm3v1 gm3gm2gm1

v1

� 2gm3v1

v1 � vout1

2gm3rds2Book Chapter 3: Basic Current Mirrors and Single-StageAmplifiers 53


-g vm1 2

v2

rds1 rds2

-g vm4 1 rds4

iouti1 vout

i2

-g vm2 2

1/gm3

v1

Finally substituting all into iout i2 � i1using the simplest expression for i2 (3rdon page (2/4))

iout vout1

2rds2 vout

12rds2

1rds4

vout

iout vout1rds2

1rds4


Simple Current MirrorCommon-Source AmplifierInterrupt: A word on output resistanceCommon-Drain Amplifier with active load / Source FollowerCommon-Gate Amplifier with active load Source-Degenerated Current MirrorsCascode Current MirrorsCascode Gain StageDiff Pair and Gain Stage

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INF3410 — Fall 2013 · INF3410 — Fall 2013 Book Chapter 3: Basic Current Mirrors and Single-Stage Ampliﬁers. content Simple Current Mirror Common-Source Ampliﬁer Interrupt: