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# which one among the two will be fastest??

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#### balavinayagam

##### Member level 3
hi all!

this was a question that i got in my interview. i do not know the exact answer.
which one will be the fastest among the two??

what is that 1X or 2X denote-the amount of cap loading or its sizing?
pls clarify this

---------- Post added at 21:56 ---------- Previous post was at 21:56 ----------

#### sudheepsrc

##### Junior Member level 3
plz refer VLSI text books...................

#### john blue

I guess it is the propagation delay to cross the inverter.

Last edited:
balavinayagam

### balavinayagam

Points: 2

#### lostinxlation

X1, X2 etc. are drive strengths if following the standard convention that we usually use.

Which one is faster is difficult to answer from that pic. Higher X means higher input cap, but on resistance is smaller. Lower X is opposite. But I'd say the 2nd is most probably faster to charge/discharge the capacitor.

balavinayagam

### balavinayagam

Points: 2

#### nitin2

##### Newbie level 4
Lets make an assumption: the delay for each stage be RC where C is only the load.
For the first circuit: delay1 = Rinv*Cinv + Rinv*C
For second circuit: delay2 = Rinv*2.5*Cinv + (Rinv/2.5)*C

If you equate the two delays it will give a critical value of C which is 2.5*Cinv.

Hence delay for ckt 1 is smaller for C < 2.5 Cinv and larger for C > 2.5*Cinv. Both circuits will have equal delay for C = 2.5*Cinv

balavinayagam

### balavinayagam

Points: 2

#### balavinayagam

##### Member level 3
thanks nitin

but still i am not very clear..Pls post references or links

thanks all

#### nitin2

##### Newbie level 4
A more precise computation:

Delay of any stage is the product of the resistance of the device and the sum of self and load capacitance. Generally the PMOS and NMOS of an inverter are sized to have equal resistance. Hence rising and falling delays are equal.

Circuit 1:

stage I: resistance = Rinv; capacitance = drain capacitance of first inverter + gate capacitance of second inverter. Assume Cgate = Cdrain. Then,
delay1_stage1 = Rinv*2*Cgate (since Cgate + Cdrain = 2*Cgate)
stage II: resistance = Rinv; capacitance = Cgate + C (here C is the load shown in the problem statement)
delay1_stage2 = Rinv*(Cgate + C)

Total delay of circuit1 = delay1_stage1 + delay2_stage2 = Rinv(3*Cgate + C)

Circuit2:
Stage1: resistance = Rinv; Capacitance = Cgate + 2.5*Cgate = 3.5 Cgate.
delay2_stage1 = Rinv*3.5*Cgate
Stage2: resistance = Rinv/2.5 (since size is 2.5x) and capacitance = 2.5*Cgate + C
delay2_stage2 = Rinv*(2.5*Cgate+C)/2.5

Total delay of circuit2 = Rinv(4.5*Cgate + C/2.5)

Equating the delays of the two circuits, we get Ccritical = 2.5*Cgate

Hence delay for ckt 1 is smaller for C < 2.5 Cgate and larger for C > 2.5*Cgate. Both circuits will have equal delay for C = 2.5*Cgate

balavinayagam

Points: 2