# Variation in Tphl of MOS nand gate due to input patterns

I was studying the variation of propagation delays in CMOS NAND gate from Jan.M.Rabey Digital IC Design book. It has this table given for Tplh and Tphl for different input patterns applied at inputs A and B:

Consider first three rows of table for Tphl. In my spice simulations I have got delay for the [B=1,A=0->1] case (83 ps) case greater than that of [A=1, B=0->1] (79.5 ps) case, which contradicts with printed data. I am running my simulations on 180nm while the data is given for 0.25um scale.

for transition at input A

for transition at input B

My findings are backed by the VTC curve variations due to applied input patterns , that are given in same book and are in accordance with my spice simulations. Here when A 0->1, then it has higher threshold voltage due to body effect and takes more time to turn ON, hence shifting curve VTC curve to right and also should increase delay.

Please let me know what am I missing.

Edit:

I tried simulating the circuit as per the answers by varying slew rate of input signal and loading the output to input of similar NAND gate. The delays in now are in accordance with the trend printed in book. But now I am confused as how slew rate can affect propagation delays and what governs the delay of row2 be greater than row3 as it is opposite of that suggested by VTC curve ?

• I would like to know how you measured propagation delay. Any waveform to back up your measurement?? Commented Dec 10, 2021 at 19:31
• please refer to the screenshots for measurements of propagation delays Commented Dec 10, 2021 at 20:32
• Okay, I am not surprised. Why are you using 10F load capacitance? It's an unrealistic value, it should be of order of pFs. Commented Dec 10, 2021 at 20:50
• It's 10 femto-Farad, not 10F Commented Dec 10, 2021 at 21:07

Propagation delay of a cell in CMOS is modeled at different PVT corners (slow, typical, fast PVT corners).

Take any model from above three, again Propagation delay basically depends on two more factors, for different timing arcs (0-->1, 1-->0):

• Slew rate of the input signal.

So, if you really want to make a fair comparison of Propagation delays of two cells from two different processes from the same vendor (250 nm, 180 nm in your case), you have to assume similar VT (Voltage, Temperature) conditions, same input slew rate and load/parasitic capacitances for your test circuit.

As far as I see, we don't know whether Author and you are in agreement on all the above factors. If not, you don't have to be surprised on the 'discrepancies' between yours and Author's measurements.

• This means that the trend printed in book cannot be generalized for any load and input slew rate, right? Commented Dec 11, 2021 at 5:55
• And in addition, the VTC shown in question should also show deviations from it's proposed trend in book on changing the suggested values.. Commented Dec 11, 2021 at 6:07
• But we don't know the operating conditions in which that VTC was drafted. And yea, I don't think you can generalize like what author said for the given cell. As propagation delay depends on multiple factors. Commented Dec 11, 2021 at 9:09
• So what governs the delay of B 0->1 being greater than A 0->1 for small slew rate ? Commented Dec 11, 2021 at 9:12
• It can depend on how body is biased. To reduce body effect, body biasing is finely tuned for different MOSFETs in a cell during fabrication. In this way, in the end, either of your two cases can be better performing than the other. Commented Dec 11, 2021 at 12:37

There is no guarantee in a digital library that the A and B FETs are the same size; they can be optimized for different performance.

When you have a A=1; B 0->1 transition, the output may initially go slightly up due to gate-drain capacitive coupling; it will then fall to the final logic 0 value. This initial 'wrong direction' depends on supply voltage, input signal slew rate, and output loading (you should load with a similar logic gate, not a simple capacitor; similarly drive via a buffer to get a realistic input slew rate and drive strength).

At low supply voltages, and very fast input slew rates, this effect will be more noticeable.

• Does VTC of a given assembly depends upon it's load capacitance? Commented Dec 11, 2021 at 7:43
• No; VTC is a DC characteristic. In v. advanced process nodes, where gate leakage is not insignificant (although still quite small), it may have a small effect. Commented Dec 11, 2021 at 18:18