AdvancedAnalog Building Blocks Two Stage amplifiers Fully … · 2017. 7. 7. · Two Stage Ampli ers Fully Di erential ampli er Schematic CMFB Fully Di erential - Common mode equivalent

AdvancedAnalog Building Blocks

Two Stage amplifiers

Fully Differential amplifiers

Albert Comerma (PI)([email protected])

Course web

SoSe 2017

http://www.kip.uni-heidelberg.de/~shen/Advanced_Analog_Building_Blocks/

IntroductionTwo Stage Amplifiers

Fully Differential amplifierOTA and OPAmp

OTA and OPAmp

• OTA: Operational Transconductance AmplifierVoltage input → Current output• OPAmp: Operational Amplifier

Voltage input → Voltage output (buffered)

OTA OTA+buffer OPAmp

Key parameters;

• Gain Bandwidth Product

• DC Gain

• Stability (Phase margin)

• Biasing (symmetry and matching)c©[email protected] AABB: Two Stage / Fully Differential amplifiers 1 / 14


Fully Differential amplifierOTA and OPAmp

General OPAmp model

General model

• First stage OTA; i1 = (v+ − v−)× gm = vdiff × gm

• Virtual short circuit in v1;→ voi1

= − 1sCc

• Thus; |Av (f )| = gm

2π×f×Cc

• GBW = Av (f )fT =1 = gm

2π×Cc

c©[email protected] AABB: Two Stage / Fully Differential amplifiers 2 / 14


Fully Differential amplifier

Miller OTA - schematicMiller OTA - analysisDesignCharacteristics

Miller OTA - Circuit

Two stage amplifier;

• Fist stage: OTA• Second stage: Inverter• Miller capacitance between first and second stage





Miller OTA - Circuit nodes

• 3-node for analisys (3 virtually grounded in ac)

• Load affects stability!

(WL

)8

=(

WL

)7(

WL

)5>>

(WL

)7

(Typically x10)





Miller OTA - Circuit DC gain

• Small-signal model (node 2 is low-resistance node).

go2,4 = go2 + go4

G ′L = GL + go5 + go6

C ′L = CL + C4

Av = vovin

= vivin

vovi

=(

gm1go2,4

)(gm6

G ′L

)= Av1Av2





Miller OTA - Pole splitting effect





Miller OTA - Circuit poles

• Circuit poles without Cc

• fp1 =go2,4

2πC1→ C1 = CGD2 + CDB2 + CGD4 + CDB4 + CGS6

• fp4 =G ′

L

2π(CL+C4) → C4 = CGD5 + CDB5 + CDB6

• fp2 = gm3

2πC2→ C2 = CGS3 +CDB3 +CGS4 +CGD4 +CGD1 +CDB1

• fp2 goes to high frequency forming a pole-zero pair, so can beneglected.

• Adding Cc the dominant pole becomes more dominant;BW ≈ fd =

go2,4

2πAv2Cc(applying Miller effect)

GBW ≈ gm12πCc

• Non-dominant pole, assuming C1 << Cc ,C′Landgm6 >> G ′L;

fnd ≈ gm6

2πC ′L

• PM ≈ 90◦ − arctg GBWfnd→ fnd = 3GBW (PM ≈ 70◦)





Miller OPamp - Cc and GBW,PM

• Variation of poles and zeros with Cc

• Cc value is fundamental to achieveenough GBW and PM

• GBW ≈ gm12πCc

• PM ≈ 90◦ − arctg GBWfnd

• fnd ≈ gm6

2πC ′L, gm = 2ID

(VGS−VT )

• fnd = 3GBW (PM ≈ 70◦)





Miller OTA - Steps for design

• Take a value for ID6 = ID5

• For M6;

1. Choose the overdrive voltage (ex. VGS − VT = 0.2).2. Obtain gm6 = 2.ID6

VGS6−VTand

(WL

)6

= gm6

K ′(VGS5−VT

3. Use minimum L6 to get W6

• Repeat for M5 (now use VGS − VT = 0.5 for better matching,reduced swing)

• Calculate Cc for desired Av .

• Use around a factor 10 between M5 and first stage bias.

• Iterate on simulation to fine tune values.





Miller OTA - characteristics

• Common mode input:VCMinMAX = VDD − VGS1 − VDS7

VCMinMIN = VSS + VGS3 − VDS1 − VGS1

• Output voltage range, with no RL rail-to-rail with somedistortion due to MOS linear operation close to rails.• Slew rate, non linear effect. Maximum rate output voltage

variation. SR =Ibias1st stage

Cc

• Output impedance: (will limit output voltage when RL)




SchematicCMFB

Fully Differential - schematic

Fully differential amplifiers show excellent CMRR and PSRR whichmake them very useful for mixed-signal design.

• No current mirror as load,just current sources.

• Nodes 1 and 2 becomesymmetric.

• GBW ≈ gm12πCL

Problem

Keep all transistors saturated,regulation of VB1,2




SchematicCMFB

Fully Differential - CMFB

• The common-mode output voltage is sensed and fed back toload sources (CMFB: Commmon-Mode FeedBack).




SchematicCMFB

Fully Differential - CMFB

• More usual implementation




SchematicCMFB

Fully Differential - Common mode equivalent circuit

• Open loop gain:AvCM = B1B2gm6RL

GBWCM = B1B2gm62πCL

• GBW can be madehigh with morepower.

• Condition:GBWCM > GBWDIFF

• The CMFB increasesthe CMRR.


Exercise 1: Miller OTA

Design a Miller OTA with the following specifcations:

• AvDC = 100

• BW = 100MHz

• PM > 70◦

• Try to minimize power consumption.

Use RL = 1M, CL = 1pF .

Exercise 2: Fully differential amplifier

Design a Fully differential amplifier with CMFB with the followingspecifcations:

• AvDC = 100

• BW = 100MHz

• PM > 70◦

• Try to minimize power consumption.

Use RL = 1M, CL = 1pF .

AdvancedAnalog Building Blocks Two Stage amplifiers Fully … · 2017. 7. 7. · Two Stage Ampli ers Fully Di erential ampli er Schematic CMFB Fully Di erential - Common mode equivalent

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