# Whats the difference with those two representation

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#### AMSA84

Hi guys,

I was reviewing some basic concepts of MOSFET transistors and I have a doubt.

What's the difference representing for example the output resistance by Ro or ro? The same goes for the gain, for example the transconductance as gm and Gm?

#### KlausST

##### Super Moderator
Staff member
Hi,

With capital letters it is referenced to zero, with lower case letters it is referenced to a specific operting area.

Example: a zener diode maybe has the folowing points on a graph.
3.30V at 0.9 mA, and 3.35 V at 1.1mA.
So R at 3.3V is 3.3V/0.9mA = 3.7 kOhms
But r at about 1mA is (3.35 - 3.30)V/(1.1-0.9)mA = 0.05V/0.2mA = 0.25 kOhms

Klaus

#### AMSA84

It is referenced to zero? What you mean?

#### KlausST

##### Super Moderator
Staff member
Hi,

So R at 3.3V is 3.3V/0.9mA = 3.7 kOhms
So R at 3.3V is (3.3 - 0)V / (0.9 - 0) mA= 3.7 kOhms

R is like a line through points (0 , 0) and (3.3, 0.9)
While r is like a tangent to the graph at the point where thr graph meets 1.0mA.

Klaus

Klaus

#### AMSA84

But the same goes for the gm? For example, I saw a statement in a ppt slide where they say:

"If both M1 and M2 operate in saturation, then Gm ≈ gm1 and (...)" - Why they are using the Gm? Why not only gm1 and its done? What's the different between saying in one way or in the other?

I have read in sedra's book (5th ed) for example, in page 302 that the Gm is the short circuit transconductance. However, in the same sedra's book (5th edition) in page 616, he has an example of a cascode where he says:

"We are now in position to derive an expression for the short-circuit transconductance Gm (...)"

I can't understand this.

#### LvW

AMSA84 - it is simply the difference between (a) STATIC values (DC currents and voltages, capital letters ) and (b) differential (dynamic) values (small ac values, small letters).
Examples:
* An (idealized) ohmic resistor has a linear I-V characteristic. Hence, there is no difference between R1 and r1
* Diodes, transistors,.. have non-linear current-voltage relationships. Hence, the SLOPE of the characteristic depends on the bias conditions (DC operating point) and , thus, determines the differential values (written in small letters).
* For my opinion, the transconductance of such a device (BJT,FET) should always be written with small letters (gm) because it always is a differential quantity.

It is rather important to distinguish between static and dynamic values - otherwise one cannot understand the meaning of some quantities.
Example: In some books, instead of the transconductance gm its inverse value is used ro=1/gm (in some cases it is even written as Ro). I think, such a terminology is not correct because this quantity is not a resistive value because it connects an output current with an input voltage.

AMSA84

### AMSA84

Points: 2

#### AMSA84

Hi LvW, Thanks for the answer. However, I didn't understood yet what means this: "We are now in position to derive an expression for the short-circuit transconductance Gm (...)"

Why in some cases the Gm = gm1 and in other they have another expressions and is called like that?

#### LvW

Hi LvW, Thanks for the answer. However, I didn't understood yet what means this: "We are now in position to derive an expression for the short-circuit transconductance Gm (...)"
Why in some cases the Gm = gm1 and in other they have another expressions and is called like that?

I really dont know. As I have mentioned, for my opinion and according to my understanding the transconductance of a transistor is ALWAYS a differential quantity (gm).
Please, can you copy the relevant section of Sedras book?

#### AMSA84

Hi LvW, from what I read the Gm is the short-circuit transconductance. We make a short-circuit at the input of the amplifier and then derive the short-circuit transconductance.

From my understanding (after reading more carefully and reading another sources) the Gm could be a way to the the total transconductance of the circuit so that in the end we can represent the equivalent circuit of the amplifier by only a gm (a total gm called Gm) and an output resistance (a total ro callend Ro)? Is that it?

If not, well, I still don't get why they compute the so called Gm (short-circuit transconductance) and for it is for.

Regards.

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