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Static and Dynamic CMOS Design• Basic Considerations• Important Technical Concepts

– Transfer (DC) Characteristic and Switching Point – Transient (AC) Characteristic as well as Rise-Time, Fall-Time and Delay Time– Fan-In and Fan-Out

• Static CMOS-Logic– Conventional Complementary MOS Logic– Pseudo n-MOS Logic– Pass-Transistor Logic

• Dynamic CMOS-Logic– Precharge-Evaluate (PE) Logic

– NP Domino Logic– CMOS Domino Logic

CMOS Logic Circuit Designhttp://www.rcns.hiroshima-u.ac.jp

Link（リンク）: センター教官講義ノート の下 CMOS論理回路設計

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Basic Considerations

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Meaning of Static and Dynamic CMOS Logic

LogicOutput

VDD(1)

VSS(0)

Noise Noise Noise

Dynamic Logic

Static Logic

Time

Static CMOS logic actively restores the logic output values,while dynamic CMOS logic does not.

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Advantages of Static and Dynamic CMOS Design

- high functional reliability

- easy circuit design

- unlimited validity of logic outputs

The most important design goals determine, whether a static or a dynamic design technology is chosen.

dynamic design

- high switching speed

- small area consumption

- low power dissipation

static design

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Important Technical Concepts- Transfer (DC) Characteristic and

Switching Point

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Transfer (DC) Characteristic(Example Inverter)

Inverter Circuit Inverter Transfer Characteristic

VOH = “high” output voltageVOL = “low” output voltageVIL = max. “low” input voltageVIH = min. “high” input voltageVIL -VSS =“low” noise marginVDD - VIH = “high” noise margin

The transfer characteristic of CMOS logic is analog. The region between points A and B (slope = 1) is logically invalid.

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Switching Point VSP(Example Inverter)

At the switching point both transistors M1 and M2 are in the saturation region and have equal conductance.

Switching-Point Definition Switching-Point Condition

VSP =

βn

β p

⋅ VTH, n + (VDD − VTH, p )

1+βn

βp

ID, n− MOS = ID, p−MOS

βn

2VSP − VTH, n( )2

=β p

2VDD − VSP − VTH ,p( )2

β p ≈ βn ; VTH , p ≈ VTH, n VSP ≈VDD

2

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Transfer Characteristic and Transistor-Size (Example Inverter)

p- and n-MOS transistor design influences the transfer characteristic

Correlation between β and MOS-transistor parameters

The choice of MOS-transistor length L and width W is a major design freedom in CMOS circuit design.

β =µ ⋅ε ⋅ W

tox ⋅ L

µ = carrier mobilityε = gate-insulator permittivitytox = gate-insulator thicknessW = MOS transistor widthL = MOS transistor lengthµn ≈ 3µ p

β p ≈ βn Wp ≈ 3Wn

SP3

SP2

SP1

<<1

>>1

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Transfer Characteristic of NAND Gates

VSP =

βn

Nmβp

⋅VTH ,n + (VDD − VTH , p )

1+βn

N mβ p

; m = 1~2

N-input NAND Gate Switching-point N-input NAND Gate

N

,inv

, N-NAND

SPinv

SPN-NAND

<<1

To keep the switching point of the N-input NAND gate at about VDD/2, it is necessary to choose Wn~NWp/3.

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Transfer Characteristic of NOR Gates

To keep the switching point of the N-input NOR gate at about VDD/2, it is necessary to choose Wp~3NWn.

VSP =

Nmβn

βp

⋅ VTH, n + (VDD − VTH, p )

1+N mβn

β p

; m = 1~2

N-input NOR Gate Switching-point N-input NOR Gate

N

,inv

, N-OR

SPinv

SPN-OR

>>1

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Important Technical Concepts- Transient (AC) Characteristic as well as

Rise-Time, Fall-Time and Delay Time

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Rise-, Fall- and Delay-Time of Logic Circuits

Rise-, fall and delay time are the main quantities for characterizing the performance of a logic CMOS circuit.

50% (VDD/2)

VDD

VDD

Logic Gate Transient Input and Output Rise-, Fall- and Delay-Time

Rise-Time trTime for a transient waveform to rise from 10% to 90% of its steady state values.

Fall-Time tfTime for a transient waveform to fall from 90% to 10% of its steady state values.

Delay-Time tdTime difference from the 50% transition level of the input waveform to the 50% transition level of the output waveform.

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Simple AC Model/Equations for CMOS Logic

Pull-down, pull-up network and the load capacitance CLdetermine the AC-performance of the CMOS logic circuit.

VDD

VSS

VDD

VSS

t f = kf

CL

β pd,eff ⋅ VDDtdf ≈ 1

2 tf;VDD

Ckt

effpu

Lrr ⋅

=,β

tdr ≈ 12 tr;

rise time: pull-up networkfall time: pull-down network

td,av ≈tdr + tdf

2; kf and kr depend on fabrication technology (~2-4)

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Important Technical Concepts- Fan-In and Fan-Out

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Definition of Fan-In and Fan-Out for Logic Gates

The fan-in of a logic gate is the number of its inputs.The fan-out of a logic gate is the number of its output

connections to other gates.

fan-in = m fan-out = k

123

m-1m

2

1

3

k

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Delay-Time Effect of Fan-In (m) and Fan-Out (k) (Constant n-MOS and p-MOS transistor W/L-ratios, respectively)

The fan-in has a quadratic impact on NAND-Gate fall times as well as NOR-Gate rise times.

)k(mm fexfindf,NAND ttt ⋅+⋅⋅=

rexrindr,NAND ttt ⋅+⋅= km

NAND-Gate

)k(mm rexrindr,NOR ttt ⋅+⋅⋅=

fexfindf,NOR ttt ⋅+⋅= km

NOR-Gate

tfin and trin are internal fall- and rise-time of a minimum sized inverter, due to its own gate and drain capacitances, respectively.

tfex and trex are external fall- and rise-time of a minimum sized inverter, due the external load of a minimum sized inverter with typical routing capacitance, respectively.

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Static CMOS-Logic - Conventional Complementary MOS(CMOS) Logic

- Pseudo n-MOS Logic- Pass-Transistor Logic

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Conventional Static CMOS Logic

Conventional CMOS logic is static because 1 and 0 are restored by pull-up and pull-down network, respectively.

Conventional CMOS principle Example with fan-in equal 5

A

B

Pull-UpNetwork

Fu (A , B , ⋅ ⋅ ⋅, N )

Fd (A,B,⋅ ⋅ ⋅,N)

Pull-DownNetwork

N

Fd (A,B,⋅ ⋅ ⋅,N)

= Fu (A , B , ⋅ ⋅ ⋅, N )

Pull-UpNetwork

Z = A • (E + D) + (B • C) • (E + D)

Pull-DownNetworkZ = A• (B+ C) + (D• E)

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Pseudo n-MOS Logic

Advantage: Less transistors and lower input capacitance. Disadvantage: High power dissipation and low pull-up speed.

Principle:Use only the pull-down network.Chose pull-up strength of p-MOS smallerthan pull-down strength of network.

Pull-DownNetworkZ = A• (B+ C) + (D• E)

Example with fan-in equal 5

A

B

Fd (A,B,⋅ ⋅ ⋅,N)

Pull-DownNetwork

N

Fd (A,B,⋅ ⋅ ⋅,N)

VSS

VDD

VSS

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Pass-Transistor Logic

Any logic function FP can be constructed by controlling a set of pass signals Pi by another set of control signals Vi.

V1 V2 Vk

P1

P2

Pk

FP =P1(V1) + P2(V2 ) + ⋅⋅⋅ +Pk (Vk )

Pass-Transistor Logic Gate

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Operation P1 P2 P3 P4

NOR(A,B) 0 0 0 1

XOR(A,B) 0 1 1 0

NAND(A,B) 0 1 1 1

AND(A,B) 1 0 0 0

OR(A,B) 1 1 1 0

Realization Table of 2-Input Gates

Implementation with n-MOS transistors(Disadvantage: Noise-margin of “high” level reduced by Vth,n)

2-Input Pass-Transistor Gate Example

The pass-transistor logic has a good implementation density, but may have slow switching speed.

Implementation with n-MOSand p-MOS transistors

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Dynamic CMOS-Logic - Precharge-Evaluate (PE) Logic- NP Domino Logic- CMOS Domino Logic

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Precharge-Evaluate (PE) Logic

Advantage: Low power dissipation and high speed. Disadvantage: Low reliability and difficult design.

clock

VSS

AB

Fd (A,B,⋅ ⋅ ⋅,N)

Pull-DownNetwork

N

Fd (A,B,⋅ ⋅ ⋅,N)

VDD

Principle: Use only the pull-down network.clock=0: Precharge output to 1.clock=1: Evaluate pull-down network.

Example with fan-in equal 5

Pull-DownNetwork

Z = A• (B+ C) + (D• E)

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NP Domino Logic

Low power and high speed, but difficult to design.

VDD

VSS

clock

VDD

VSS

clock

VDD

VSS

clock

AB

N

Pull-DownNetwork

F1

Pull-UpNetwork

F2Pull-DownNetwork

F3

Alternating cascade of PE-logic with pull-up/pull-down networks.

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CMOS Domino Logic Gate

CMOS domino logic achieves a good balance of switching speed, area/power consumption and design reliability.

VDD

VSS

clock

Pull-DownNetwork

Fd (A,B,⋅ ⋅ ⋅,N)

Fd (A,B,⋅ ⋅ ⋅,N)

AB

N

Buffer and “high” level restoring elements

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CMOS Domino Logic Circuit

A CMOS domino logic circuit uses only pull-down networks.

VDD

VSS

clock

Pull-DownNetwork

Fd1

AB

N

VDD

VSS

clock

Pull-DownNetwork

Fd 2

VDD

VSS

clock

Pull-DownNetwork

Fd 3