# Speaking of units - and beta

#### KevinEamon

Joined Apr 9, 2017
284
So we've been talking about units recently...
Now i'm studying Mosfets as part of an exam on Monday. Here's a strange outcome in relation to units...

Beta for a Mosfet which I shall define as = B

B(Vgs-VT)Vds = i

So what's the units of B here...? Now please resist the temptation to go into great detail on what exactly it is. There seems to be a whole lot of disagreement about that and I'm just looking for a very simple answer.

It looks to me like it's R/V

Similiary 1/(B(Vgs-VT) ) = omhs

Right?

Joined Mar 10, 2018
4,057
B = 1 / RV

To convert to current -

I = V / R
BV**2 = I = V/R
BV = 1 / R
B = 1 / RV

Regards, Dana.

#### WBahn

Joined Mar 31, 2012
30,295
So we've been talking about units recently...
Now i'm studying Mosfets as part of an exam on Monday. Here's a strange outcome in relation to units...

Beta for a Mosfet which I shall define as = B

B(Vgs-VT)Vds = i

So what's the units of B here...? Now please resist the temptation to go into great detail on what exactly it is. There seems to be a whole lot of disagreement about that and I'm just looking for a very simple answer.

It looks to me like it's R/V
Can you explain why it looks like that to you?

Well, let's see.

Resistance has units of (voltage)/(current), so R/V would have units of 1/(current).

But if we then put that back into the original expression, we would have V²/A on the left and A on the right.

So we know this is wrong.

Similiary 1/(B(Vgs-VT) ) = omhs

Right?
By "omhs" do you mean 'ohms' or 'mohs'? I can't tell because either is just a transposition of two adjacent letters.

If you mean 'ohms', then yes.

This would then mean that B would have to have units of 1/(Ω·V)

The equation tells us directly that the units are

(current)/(voltage-squared) or A/V².

Now, this can be written a number of ways and which is most useful depends on what you are doing.

Since resistance is (voltage)/(current), equivalent units would be 1/(Ω·V) or A/Ω².

Of course, you can also write it in SI base units or in terms of other derived units such as newtons and joules.

#### KevinEamon

Joined Apr 9, 2017
284
Thanks Dana and Wbahn. Lul for the ohms... smh... sigh

R/V = 1/I
Of course it makes perfect sense, but I never even thought of it before now. I like it...

I've seen that designation A/V² - Usually beside the B of course. 10^-4 A/V².
Do you know I looked at that many a time and never thought about it being the units of beta. The V is right there... wth? ...sigh

Anyways just cause I can't find it on google I'm going to take the plunge here and ask one of my stupid questions...

A/V² - wouldn't that give 1/R ? or better again 1/RV

#### WBahn

Joined Mar 31, 2012
30,295
Thanks Dana and Wbahn. Lul for the ohms... smh... sigh

R/V = 1/I
Of course it makes perfect sense, but I never even thought of it before now. I like it...

I've seen that designation A/V² - Usually beside the B of course. 10^-4 A/V².
Do you know I looked at that many a time and never thought about it being the units of beta. The V is right there... wth? ...sigh

Anyways just cause I can't find it on google I'm going to take the plunge here and ask one of my stupid questions...

A/V² - wouldn't that give 1/R ? or better again 1/RV
Your wording makes it sound like you think that 1/R is correct (possibly) but that 1/RV would be even more so. However, 1/R and 1/RV are simply not the same. If either of them is correct, the other is flat wrong. It's possible that they are both wrong, it is simply impossible for them to both be correct.

A/V would be 1/R

A/V² would be 1/(RV)

Technically, 1/RV would be (1/R)V = V/R = I due to order of operations (according to most conventions).