# CMOS Inverter. Performance Scaling

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1 Announcements Exam #2 regrade requests due today. Homework #8 due today. Final Exam: Th June 12, 8:30 10:20am, CMU 120 (extension to 11:20am requested). Grades available for viewing via Catalyst.

2 CMOS Inverter Performance Scaling State of the art short gate length technologies are hard to analyze Scaling can be used to properly set W/L for a given load capacitance relative to reference gate simulation with a reference load. P W / L W / L' C ' L C Lref or W Pr ef L ' W L Pr ef P C L ' C Lref Scaling allows us to calculate a new geometry (W/L)' in terms of a target load and delay. Microelectronic Microelectronic Circuit Circuit Design, Design 4E McGraw-Hill

3 CMOS Inverter Performance Scaling Consider a reference inverter with a delay of 3.16 ns. What is the delay if an inverter has a W/L 4x larger than the transistors of the reference inverter and twice the load capacitance. P 2/1 8/1' 2pF' 3.16 ns 1.58 ns 1pF Scaling allows us to calculate a new geometry (W/L)' or delay relative to a reference design.

4 CMOS Logic 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

5 CMOS Logic Delay of Cascaded Inverters (cont.) The simulated output of the previous circuit appears below, and it can be seen that the delay for the nonideal step input is approximately twice than the ideal case: PHL 2.4R onn C PLH 2.4R onp C t f 2 PHL t r 2 PLH

6 Cascade Buffers Driving Large Capacitances In some circuits, the logic must be able to drive large capacitances (10 to 50 pf) By cascading a number of increasingly larger inverters, it is possible to drive the loads

7 Cascade Buffers Inverter Sizing The taper factor determines the increase of the cascaded inverter s size in manner shown of the previous image. where C o is the unit inverter s load capacitance The delay of the cascaded buffer is given by the following: where o is the unit inverter s propagation delay

8 Cascade Buffers Optimum Design The following expressions can aid in the design of an optimum cascaded buffer

9 EE 331 Devices and Circuits I Chapter 8 MOS Memory

10 Random Access Memory Random Access Memory (RAM) refers to memory in a digital system that has both read and write capabilities and any location is directly accessible Static RAM (SRAM) is able to store its information as long as power is applied, and it does not lose the data during a read cycle Dynamic RAM (DRAM) uses a capacitor to temporarily store data which must be refreshed periodically to prevent information loss, and the data is lost in most DRAMs during the read cycle SRAM takes approximately four times the silicon area of DRAM

11 A 256 Mbit Memory Chip The memory block diagram contains 2 M+N storage locations (M columns x N rows) When a bit is selected, the set of sense amplifiers are used to read/write to the memory location Horizontal rows are referred to as wordlines, whereas the vertical lines are called bitlines

12 Static Memory Cells Inverters configured as shown in the above figure form the basic static storage building block (note the schematics represent two drawings of the same circuit) These cross coupled inverters are often referred to as a latch The circuit uses positive feedback

13 Static Memory Cells VTC The previous latch has only two stable states and is termed bistable However, it is possible for the circuit to be held at an unstable equilibrium point where slight changes in the voltage will cause it to latch in one of the stable states

14 Static Noise Margins Graphical Approach Butterfly diagram is produced by plotting v out vs. v in and v in vs. v O for the inverters. Noise shifts the characteristics.

15 Static Noise Margins Graphical Approach Butterfly diagram is produced by plotting v out vs. v in and v in vs. v o for a single inverter. Noise margins are defined by either the largest square or largest rectangle that can be placed between the two curves. Jaeger/Blalock 7/27/11 Microelectronic Circuit Design 4E McGraw Hill Chap 8 - UW 15 EE Chen/Dunham

16 Static Noise Margin Spice Simulation Circuit The opamp forces the output of the second inverter to equal the input of the first inverter.

17 The 6 T Cell Basic Circuitry With the addition of two control transistors, the 6 T cell is created that stores both the true and complemented values of the data

18 The 6 T Cell Read Operation Initial state of the 6-T cell storing a 0 with the bitlines initial conditions assumed to V DD /2 Conditions immediately after the WL transistors have been turned on

19 The 6 T Cell Read Operation (cont.) Final read state for the 6-T cell Waveforms of the 6-T cell read operation

20 The 6 T Cell Read Operation (cont.) Reading a 6 T cell that is storing a 1 follows the same concept as before, except that the sources and drains of the WL transistors are switched Note that the delay is approximately 20ns for this particular cell

21 The 6 T Cell Write Operation It can be seen that not much happens while writing a 0 into a cell that already stores a 0

22 The 6 T Cell Write Operation (cont.) While writing a 0 to a cell that is storing a 1, the bitlines must be able to overpower the output drive of the latch inverters to force it to store the new condition

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