Transistor Sizing

Thread Starter

thisonedude

Joined Apr 20, 2014
52
Hi everyone. I'm currently working on the following problem 2.JPG
So i am having trouble understanding what it means by worst-case equivalent resistance. I understand the following: The worst case path for the PUN is when only on path exists between the Output and Vdd. This occurs when EFGHIJ = 011011. For the PDN the worst case occurs again when only one path (longest) exists between the output and GND. Int his case it occurs when EFGHI = 111001. Okay so i understand this much. I also know that transistors in series are added and in parallel are halfed. so EF for PDN would be 2R and HI for PUN would be R/2 as an example. but how do i calculate the worst case resistance? How do i calculate the Width? I'm looking more to understand what it is asking me to find, than the final answer. how do i approach this problem?
 
Last edited:

WBahn

Joined Mar 31, 2012
25,907
What the picture tells me is that the resistance figures given are for minimum-length square transistors. But when the problem then states that Wn = 195 nm and that you are supposed to find Wp, that implies that the transistors used in the problem are not minimum-length square transistors.

But that should be okay because you are not asked to find the actual resistance, just to balance them.

So, assume that the transistors are all minimum-length square transistors and find the ratio of the worst case pull-up to the worse case pull-down resistance. What will that tell you about the needed ratio of Wp/Wn in order to make them equal?
 

Thread Starter

thisonedude

Joined Apr 20, 2014
52
What the picture tells me is that the resistance figures given are for minimum-length square transistors. But when the problem then states that Wn = 195 nm and that you are supposed to find Wp, that implies that the transistors used in the problem are not minimum-length square transistors.

But that should be okay because you are not asked to find the actual resistance, just to balance them.

So, assume that the transistors are all minimum-length square transistors and find the ratio of the worst case pull-up to the worse case pull-down resistance. What will that tell you about the needed ratio of Wp/Wn in order to make them equal?
I'm still confused but let me see if i understand this. So, the worst case pull-down would be, lets say if i take the worst path to be JEFG to Ground. This means that means i have 4Reqn. so if the transistor width Wp=195nm, then 4reqn = Reqn/4 -> Reqn = 195/8 ?

Does this mean that the ratio of Wp/Wn needs to be 1 in order to make them equal?
 

WBahn

Joined Mar 31, 2012
25,907
Nope.

The worst case resistance to ground is Rwcn = 4*Reqn.

What is the worst case resistance to Vdd, Rwcp, (in terms of Reqp)?
 

Thread Starter

thisonedude

Joined Apr 20, 2014
52
Nope.

The worst case resistance to ground is Rwcn = 4*Reqn.

What is the worst case resistance to Vdd, Rwcp, (in terms of Reqp)?
Ohh alright so I was right about my worst case for the pull down being 4Reqn? For the pullup the worst happens when I take either EH or FI or GI. So would it be Rwcp=Reqp/2?
 

WBahn

Joined Mar 31, 2012
25,907
Ohh alright so I was right about my worst case for the pull down being 4Reqn? For the pullup the worst happens when I take either EH or FI or GI. So would it be Rwcp=Reqp/2?
If k equal NFET resistances in series are k-times one NFET resistance, why would k equal PFET resistances in series be one PFET resistance divided by k?

Does that make sense to YOU?
 

Thread Starter

thisonedude

Joined Apr 20, 2014
52
If k equal NFET resistances in series are k-times one NFET resistance, why would k equal PFET resistances in series be one PFET resistance divided by k?

Does that make sense to YOU?
Ohhhhhhhhh yes sorry my mistake yes. Scratch my last response. Rwcp =2Reqp, since they are in series. Likewise worst case for the pull down would be the longest single path, JEFG: Rwcn=4Reqn since again they are in series. Alright but then how do I balance them? So you say that the ratio Wp/Wn would need to be one in order to make them equal?
 

WBahn

Joined Mar 31, 2012
25,907
Ohhhhhhhhh yes sorry my mistake yes. Scratch my last response. Rwcp =2Reqp, since they are in series. Likewise worst case for the pull down would be the longest single path, JEFG: Rwcn=4Reqn since again they are in series. Alright but then how do I balance them? So you say that the ratio Wp/Wn would need to be one in order to make them equal?
Where did I say that the Wp/Wn ratio needed to be one? YOU said that. I asked you what it NEEDED to be in order to make the resistances the same.

So set Rwcn equal to Rwcp. Then determine what Reqp/Reqn needs to be. Then determine what Wp/Wn needs to be.
 

Thread Starter

thisonedude

Joined Apr 20, 2014
52
Where did I say that the Wp/Wn ratio needed to be one? YOU said that. I asked you what it NEEDED to be in order to make the resistances the same.

So set Rwcn equal to Rwcp. Then determine what Reqp/Reqn needs to be. Then determine what Wp/Wn needs to be.
I think i misread one of your replies earlier.

Thank you for the help!
 
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