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Miscellaneous. EE116B (Winter 2001): Lecture # Miscellaneous-1. Sizing PMOS/NMOS Inverters. Usual single unloaded inverter guideline: make PMOS and NMOS equal strength to make t pLH =t pHL (W/L) p = m n / m p * (W/L) n = e (W/L) n Situation different when inverters are cascaded.

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EE116B (Winter 2001): Lecture # Miscellaneous-1

sizing pmos nmos inverters
Sizing PMOS/NMOS Inverters
  • Usual single unloaded inverter guideline: make PMOS and NMOS equal strength to make tpLH=tpHL
    • (W/L)p = mn/mp * (W/L)n= e (W/L)n
  • Situation different when inverters are cascaded
sizing pmos nmos in identical cascaded inverters
Sizing PMOS/NMOS inIdentical Cascaded Inverters
  • Let (W/L)PMOS be a times larger than (W/L)NMOS
    • Cdp = aCdn, Cdp = aCdn
    • CL = (1+a)(Cdn+Cgn)+CW = (1+a) Cn+CW
  • Propagation delay
    • tp = (tpLH+tpHL)/2 = const * ((1+a) Cn+CW) * (1+ e/a)

where e = mn/mp

  • Optimal a when dtp/da = 0
    • aopt= (e(1+CW/Cn))0.5

= sqrt(e) when CW is neglible

Therefore, PMOS should be somewhat smallerthan the e ratio when chaining inverters!

using single inverter as buffer
Using Single Inverter as Buffer




Chip Core



  • Let
    • tp0 = delay of minimum size inverter when it drives one minimum size inverter
    • u = the strength of the buffer inverter (i.e. how much larger it is than the minimum)
  • What is the optimum u?






CL = xCi

input capacitance

Of minimum-size inverter

optimum u for single inverter buffer
Optimum u for Single Inverter Buffer
  • Total propagation delay

tp = utp0 + (x/u) tp0

  • Finding optimum u to minimize tp

dtp/du = 0

 tp0 - (x/u2) tp0 = 0

 uopt = sqrt(x)


tp,opt = 2tp0 sqrt(x)

It makes sense to introduce a bufferwhen xtp0 > 2tp0 sqrt(x)or, equivalently, when x > 4

multistage buffer n 1 inverters




Multistage Buffer: N-1 Inverters




Chip Core

  • Propagation delay
    • tp = u1tp0 + (u2/u1) tp0 + … + (CL/uN-1) tp










CL = xCi

optimum u 1 u 1 u n 1 for multi stage inverter buffer
Optimum u1, u1, … uN-1 forMulti-stage Inverter Buffer
  • Propagation delay

tp = u1tp0 + (u2/u1) tp0 + … + (CL/uN-1) tp0

  • Finding optimum u1, u1, … uN-1 to minimize tp

tp/ ui = 0 for i = 1, 2, … N-1

tp0 - (u2/u12) tp0 = 0 u2 = u12

(1/u1) tp0 - (u3/u22) tp0 = 0 u3 = u22/u1 = u13

(1/uN-3) tp0 - (uN-1/uN-22) tp0 = 0 uN-1 = uN-22/uN-3 = u1N-1

(1/uN-2) tp0 - (x/uN-12) tp0 = 0 x = uN-12/uN-2 = u1N

Optimum propagation delay is tp = Nu1tp0and, corresponding N = ln(x)/ln(u1)

optimum n and u 1 for multi stage inverter buffer
Optimum N and u1 for Multi-stage Inverter Buffer
  • Propagation delay

tp = Nu1tp0 = u1tp0 ln(x)/ ln(u1)

  • Finding optimum u1 to minimize tp

dtp/du = 0

 tp0 ln(x)/ ln(u1) - u1tp0 ln(x)/ u1(ln(u1))2

 uopt = e = 2.7182


tp,opt = e ln(x) tp0 = e ln(CL/Ci) tp0

Optimum buffer design scales consecutivestages in an exponential fashion

common vhdl issues combinational processes
Common VHDL IssuesCombinational Processes

process (A, B, SELECT)begin if (SELCT=‘1’) then OUT <= A; else OUT <= B; end if;end process;

  • Sensitivity list must consist of all signals that are read inside the process
    • Synthesis tools often ignore sensitivity list, but simulation tools do not… a forgotten signal will lead to difference in behavior of the simulated model and the synthesized design
common vhdl issues combinational processes1
Common VHDL IssuesCombinational Processes

process (A, B, SELECT)begin if (SELCT=‘1’) then OUT <= A; else OUT <= B; end if;end process;

processbegin if (SELCT=‘1’) then OUT <= A; else OUT <= B; end if; wait on A, B, SEL;end process;

  • Can use WAIT ON instead of sensitivity list
  • But not both!
common vhdl issues wait free paths
Common VHDL IssuesWait-free Paths

processbegin if (some condition) wait on CLK’event and CLK=1; X <= A + B;

end if;end process;

  • Every possible path that the code can take through the process body in a process without sensitivity list must have a WAIT
    • Otherwise the process can hang (feedback loop)
common vhdl issues mistakenly inferences latches
Common VHDL IssuesMistakenly Inferences Latches

process (A,B)begin if (cond1) X <= A + B; elseif (cond2)

X <= X – B;

end if;end process;

  • Remember, incomplete assignments imply latches
    • in the above example, if neither cond1 nor cond2 is true then X will retain its value … basically, X is stored in a latch
    • if you are writing combinational logic, make sure that every output gets assigned a value along each path (e.g. if statements, case statements) through the process body
    • in general, latches are not recommended any way in synchronous designs (not testable via scan paths)
common vhdl issues implicit register inference
Common VHDL IssuesImplicit Register Inference
  • Storage registers are synthesized for all signals that are driven within a clocked process
  • Storage registers are also synthesized for all variables that are read before being updated

processbegin wait until CLK’event and CLK=1;

if (COUNT >= 9) then COUNT <= 0; else COUNT <= COUNT +1;

end process;




common vhdl issues reset or set in synthesis
Common VHDL IssuesReset (or Set) in Synthesis

processbegin wait until CLK’event and CLK=1;

if (RST=‘1’) then -- synchronous reset else -- combinational stuff

end if;

end process;

process (CLK, RST)begin if (RST=‘1’) then -- asynchronous reset

elsif ( CLK’event and CLK=1) then

-- combinational stuff

end if;

end process;

  • Must reset all regsiters, other syntehsized chip won’t work
    • unlike simulation, you can’t set initial values in synthesis!
  • Asynchronous reset possible only with a process that ha sensitivity list
common vhdl issues coding style influence
Common VHDL IssuesCoding Style Influence

process(A, B, C, SEL)begin if (SEL=‘1’) then Z <= A + B; else

Z <= A + C

end if;end process;

process(A, B, C, SEL) variable TMP : bit;begin if (SEL=‘1’) then TMP := B; else

TMP := C; end if; Z <= A + TMP;end process;

  • Structure of initially generated hardware is determined by the VHDL code itself
    • Synthesis optimizes that initially generated hardware, but cannot do dramatic changes
    • Therefore, coding style matters!











common vhdl issues if vs case
Common VHDL IssuesIF vs CASE
  • IF-THEN-ELSIF-THEN-…-ELSE maps to a chain of 2-to-1 multiplexors, each checking for the successive conditions

…if (COND1) then OUT <= X1;elsif (COND2) then OUT <= X2;…else OUT <= Xn;…

  • CASE maps to a single N-to-1 multiplexor

…case EXPRESSION is when VALUE1 =>

OUT <= X1;

when VALUE2 =>

OUT <= X2;

when others =>

OUT <= Xn;

end case;…

common vhdl issues let the tool do the synthesis
Common VHDL IssuesLet the tool do the Synthesis
  • Don’t do synthesis by hand!
    • do not come up with boolean functions for outputs of arithmetic operator
      • let Synopsys decide which adder, multiplier to use
    • you will only restrict the synthesis process
    • Best to use IEEE signed and unsigned types, and convert to integers if needed (IEEE NUMERIC_STD and NUMERIC_BIT packages)






other vhdl issues
Other VHDL Issues
  • Let synthesis tool decide the numeric encoding of the FSM states
    • use enumerated type for state
  • Split into multiple simpler processes
  • Keep module outputs registered
    • simplifies timing constraints