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### Chapter 7Complementary MOS (CMOS) Logic Design

Microelectronic Circuit Design

Richard C. JaegerTravis N. Blalock

Microelectronic Circuit Design

McGraw-Hill

Chapter Goals

- Introduce CMOS logic concepts
- Explore the voltage transfer characteristics CMOS inverters
- Learn to design basic and complex logic gates
- Discuss static and dynamic power in CMOS logic
- Present expressions for dynamic performance of CMOS logic devices
- Present noise margins for CMOS logic
- Introduce dynamic logic and domino CMOS logic techniques
- Introduce design techniques for “cascade buffers”
- Explore layout of CMOS logic gates
- Discuss the concept of “latchup”

Microelectronic Circuit Design

McGraw-Hill

CMOS Inverter Technology

- Complementary MOS, or CMOS, needs both PMOS and NMOS devices for their logic gates to be realized
- The concept of CMOS was introduced in 1963 by Wanlass and Sah, but it did not become common until the 1980’s as NMOS microprocessors were dissipating as much as 50 W and alternative design technique was needed
- CMOS still dominates digital IC design today

Microelectronic Circuit Design

McGraw-Hill

CMOS Inverter Technology

- The CMOS inverter consists of a PMOS stacked on top on a NMOS, but they need to be fabricated on the same wafer
- To accomplish this, the technique of “n-well” implantation is needed as shown in the figure which shows the cross-section of a CMOS inverter

Microelectronic Circuit Design

McGraw-Hill

CMOS Inverter

- Circuit schematic for a CMOS inverter
- Simplified operation model with a high input applied
- Simplified operation model with a low input applied

Microelectronic Circuit Design

McGraw-Hill

CMOS Inverter Operation

- When vI is pulled high (VDD), the PMOS inverter is turned off, while the NMOS is turned on pulling the output down to VSS
- When vI is pulled low (VSS), the NMOS inverter is turned off, while the PMOS is turned on pulling the output up to VDD

Microelectronic Circuit Design

McGraw-Hill

CMOS Inverter Layout

- Two methods of laying out a CMOS inverter are shown
- The PMOS transistors lie within the n-well, whereas the NMOS transistors lie in the p-substrate
- Polysilicon is used to form common gate connections, and metal is used to tie the two drains together

Microelectronic Circuit Design

McGraw-Hill

Static Characteristics of the CMOS Inverter

- The figure shows the two modes of static operation with the circuit and simplified models
- Notice that VH = 5V and VL = 0V, and that ID = 0A which means that there is no static power dissipation

Microelectronic Circuit Design

McGraw-Hill

CMOS Voltage Transfer Characteristics

- The VTC shown is for a CMOS inverter that is symmetrical (KP = KN)
- Region 1: vO = VH vI < VTN
- Region 2: |vDS| ≥ |vGS – VTP|
- Region 4: vDS≥ vGS – VTN
- Region 5: vO = VL vI > VDD – |VTP|

Microelectronic Circuit Design

McGraw-Hill

CMOS Voltage Transfer Characteristics

- The simulation result shows the varying VTC of the inverter as VDD is changed
- The minimum voltage supply for a certain MOS technology is 2VT∙ln(2)

Microelectronic Circuit Design

McGraw-Hill

CMOS Voltage Transfer Characteristics

- The simulation result shows the varying VTC of the inverter as KN/KP = KR is changed
- For KR > 1 the NMOS current drive is greater and it forces vI < VDD/2
- For KR < 1 the PMOS current drive is greater and it forces vI > VDD/2

Microelectronic Circuit Design

McGraw-Hill

Noise Margins for the CMOS Inverter

- Noise margins are defined by the regions shown in the given figure

Microelectronic Circuit Design

McGraw-Hill

Propagation Delay Estimate

- The two modes of capacitive charging that contribute to propagation delay

Microelectronic Circuit Design

McGraw-Hill

Propagation Delay Estimate

- If it is assumed the inverter in “symmetrical”, (W/L)P = 2.5(W/L)N, then τPLH = τPHL

Microelectronic Circuit Design

McGraw-Hill

Rise and Fall Times

- The rise and fall times are given by the following expressions:

Microelectronic Circuit Design

McGraw-Hill

Reference Inverter Example

- Design a reference inverter to achieve a delay of 250ps with a 0.1pF load given the following information:

Microelectronic Circuit Design

McGraw-Hill

Reference Inverter Example

- Assuming the inverter is symmetrical and using the values given in Table 7.1:

Microelectronic Circuit Design

McGraw-Hill

Reference Inverter Example

- Solving for RonN:
- Then solve for the transistor ratios:

Microelectronic Circuit Design

McGraw-Hill

Delay of Cascaded Inverters

- An ideal step was used to derive the previous delay equations, but this is not possible to implement
- By using putting the following circuit in SPICE, it is possible to produce more accurate equations

Microelectronic Circuit Design

McGraw-Hill

Delay of Cascaded Inverters

- The output of the previous circuit looks like the following an it can be seen that the delay for the nonideal step input is approximately twice than the ideal case:

Microelectronic Circuit Design

McGraw-Hill

Static Power Dissipation

- CMOS logic is considered to have no static power dissipation
- Since the ROFF of the two transistors is very large, the DC current driving a capacitive load is zero
- This is not completely accurate since MOS transistors have leakage currents associated with the reverse-biased drain-to-substrate connections

Microelectronic Circuit Design

McGraw-Hill

Dynamic Power Dissipation

- There are two components that add to dynamic power dissipation:
- Capacitive load charging at a frequency f given by: PD = CVDDf
- The current that occurs during switching which can be seen in the figure

Microelectronic Circuit Design

McGraw-Hill

Power-Delay Product

- The power-delay product is given as:

The figure shows a symmetrical inverter switching waveform

Microelectronic Circuit Design

McGraw-Hill

CMOS NOR Gate

CMOS NOR gate implementation

Reference Inverter

Microelectronic Circuit Design

McGraw-Hill

CMOS NOR Gate Sizing

- When sizing the transistors, it is ideal to keep the delay times the same as the reference inverter
- To accomplish this, the on-resistance on the PMOS branch of the NOR gate must be the same as the reference inverter
- For a two-input NOR gate, the (W/L)p must be made twice as large

Microelectronic Circuit Design

McGraw-Hill

CMOS NOR Gate Body Effect

- Since the bottom PMOS body contact is not connected to its source, its threshold voltage changes as VSBchanges during switching
- Once vO = VH is reached, the bottom PMOS is not affected by body effect, thus the total on-resistance of the PMOS branch is the same
- However, the rise time is slowed down due to |VTP| being a function of time

Microelectronic Circuit Design

McGraw-Hill

Three-Input NOR Gate Layout

- It is possible to extend this same design technique to create multiple input NOR gates

Microelectronic Circuit Design

McGraw-Hill

CMOS NAND Gates

CMOS NAND gate implementation

Reference Inverter

Microelectronic Circuit Design

McGraw-Hill

CMOS NAND Gates Sizing

- The same rules apply for sizing the NAND gate as the did for the NOR gate, except for now the NMOS transistors are in series
- The (W/L)N will be twice the size of the reference inverter’s NMOS

Microelectronic Circuit Design

McGraw-Hill

Complex CMOS Logic Gate Design Example

- Design a CMOS logic gate for (W/L)p,ref=5/1 and for (W/L)n,ref=2/1 that exhibits the function: Y = A + BC +BD
- By inspection (knowing Y), the NMOS branch of the gate can drawn as the following with the corresponding graph, while considering the longest path for sizing purposes:

Microelectronic Circuit Design

McGraw-Hill

Complex CMOS Logic Gate Design Example

- By placing nodes in the interior of each arc, plus two more outside the graph for VDD (3) and the complementary output (2’), the PMOS branch can be realized as shown on the left figure
- Connect all of the nodes in the manner shown in the right figure, and the NMOS arc that PMOS arc intersects have the same inputs

Microelectronic Circuit Design

McGraw-Hill

Complex CMOS Logic Gate Design Example

- From the PMOS graph, the PMOS branch can now be drawn for the final CMOS logic gate while once again considering the longest PMOS path for sizing

Microelectronic Circuit Design

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Complex CMOS Gate with a Bridging Transistor Design Example

- Design a CMOS gate that implements the following logic function using the same reference inverter sizes as the previous example: Y = AB +CE + ADE + CDB
- The NMOS branch can be realized in the following manner using bridging NMOS D to implement Y. The corresponding NMOS graph is shown to the right.

Microelectronic Circuit Design

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Complex CMOS Gate with a Bridging Transistor Design Example

- By using the same technique as before, the PMOS graph can now be drawn

Microelectronic Circuit Design

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Complex CMOS Gate with a Bridging Transistor Design Example

- By using the PMOS graph the PMOS branch can now be realized as the following (considering the longest path for sizing)

Microelectronic Circuit Design

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Minimum Size Gate Design and Performance

- With CMOS technology, there is a area/delay tradeoff that needs to be considered
- If minimum feature sized are used for both devices, then the τPLH will be decreased compared to the symmetrical reference inverter

Microelectronic Circuit Design

McGraw-Hill

Minimum Size Complex Gate and Layout

- The following shows the layout of a complex minimum size logic gate

Microelectronic Circuit Design

McGraw-Hill

Dynamic Domino CMOS Logic

- One technique to help decrease power in MOS logic circuits is dynamic logic
- Dynamic logic uses different precharge and evaluation phases that are controlled by a system clock to eliminate the dc current path in single channel logic circuits
- Early MOS logic required multiphase clocks to accomplish this, but CMOS logic can be operated dynamically with a single clock

Microelectronic Circuit Design

McGraw-Hill

Dynamic Domino CMOS Logic

- The figure demonstrates the basic concept of domino CMOS logic operation

Microelectronic Circuit Design

McGraw-Hill

Dynamic Domino CMOS Logic

- It should be noted that domino CMOS circuits only produce true logic outputs, but this problem can be overcome by using registers that have both true and complemented output to complete the function shown by the following

Microelectronic Circuit Design

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Cascade Buffers

- In some circuit, the logic must be able to drive large capacitances (10 to 50pF)
- By cascading an even number of increasing larger inverters, it is possible to drive the loads

Microelectronic Circuit Design

McGraw-Hill

Cascade Buffers

- The taper factor β determines the increase of the cascaded inverter’s size in manner shown of the previous image.

where Co is the unit inverter’s load capacitance

- The delay of the cascaded buffer is given by the following:

Where τo is the unit inverter’s propagation delay

Microelectronic Circuit Design

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Optimum Design of Cascaded Stages

- The following expressions can aid in the design of an optimum cascaded buffer

Microelectronic Circuit Design

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The CMOS Transmission Gate

- The CMOS transmission gate (T-gate) is one of the most useful circuits for both analog and digital applications
- It acts as a switch that can operate up to VDD and down to VSS

Microelectronic Circuit Design

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The CMOS Transmission Gate

- The main consideration that needs to be considered is the equivalent on-resistance which is given by the following expression:

Microelectronic Circuit Design

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CMOS Latchup

- There is one major downfall to the CMOS logic gate – Latchup
- There are many safeguards that are done during fabrication to suppress this, but it can still occur under certain transient or fault conditions

Microelectronic Circuit Design

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CMOS Latchup

- Latchup occurs due parasitic bipolar transistors that exist in the basic inverter as shown below

Microelectronic Circuit Design

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CMOS Latchup

- The configuration of these bipolar transistors create a positive feedback loop, and will cause the logic gate to latchup as shown to the left
- By using heavily doped material where Rn and Rp exist, there resistance will be lowered thereby reducing the chance of latchup occurring

Microelectronic Circuit Design

McGraw-Hill

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