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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 tpLH=tpHL
- (W/L)p = mn/mp * (W/L)n= e (W/L)n

- Situation different when inverters are cascaded

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

- tp = (tpLH+tpHL)/2 = const * ((1+a) Cn+CW) * (1+ e/a)
- 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!

- aopt= (e(1+CW/Cn))0.5

Using Single Inverter as Buffer

VDD

VDD

Buffer

Chip Core

a

ua

- 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?

Vout

Vin

Ci

1

u

CL = xCi

input capacitance

Of minimum-size inverter

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)

and

tp,opt = 2tp0 sqrt(x)

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

VDD

u2a

u2

Multistage Buffer: N-1 InvertersVDD

VDD

VDD

Chip Core

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

uN-1a

u1a

a

Vout

Vin

u1

uN-1

Ci

1

CL = xCi

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 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

and

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

Optimum buffer design scales consecutivestages in an exponential fashion

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 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 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 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 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;

‘1’

COUNT

CLK

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 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!

B C

A B A C

+

+

SEL

A

+

SEL

Z

Z

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 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)
example:

A_INT <= TO_INTEGER(A_VEC);

B_INT <= TO_INTEGER(B_VEC);

C_INT <= A_INT * B_INT;

C_VEC <= TO_UNSIGNED(C_INT, 4);

- do not come up with boolean functions for outputs of arithmetic operator

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

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