1. gm/ID Design Approach

2. Transconductance
As a voltage-controlled current source, a MOS transistor can be characterized by its transconductance:
It is important to know that

3. What Happens to gm/ID when W and ID are doubled?

4. Small Signal Model for NMOS Transistor

5. gm/ID Design Optimization
gm/ID Design Flow
Specs
Design
Equations
(Analytical)
gm/Id Data Set
(Emprical)
The gmoverid design flow is a technique that allows engineers to size up transistors quickly and accurately without using complicated transistor models.
It was published by Silveira and his colleagues back in 1996.
A typical gmoverid design flow goes like this:
You start with the specs. You express your specs in terms of a set of design equations, you then use query the gmoverid data base to obtain optimum W/L that satisfy the constraints.
gm/ID Design Optimization
(F. Silveira, JSSC, 1996.)
W/L Ratios

6. Intuition gm gds gm/ID gm/gds 2gm 2gds gm/ID gm/gds 2gm 2gds gm/ID
How does it work?
This figures shows a transistor which has a transconductance
(gm), a drain-to-source conductance (gds), and a current (I)
when biased at a gate-to-source voltage (VGS) and a drain-to-source
(VDS). If an identical device is connected in parallel
so that both devices are biased at the same VGS and VDS,
both devices have the the same gm, gds and the same ID.
Since the devices are connected in parallel, they can be treated
as one device with an aspect ratio of 2W=L. The effective
transconductance over current ratio is gm/ID for both the
merged device as well as the stand alone device because gm
and ID are doubled. The drain-to-source transconductance is
also doubled for the merged device. As a result, the intrinsic
gain (gm/gds) is identical for both the stand alone device and
the merged device. It can therefore be stated that as long as
transistors are biased at the same gm/ID, they will have the
same gm/gds. This observation is true for two small signal
parameters whose ratio depend solely on the gm/ID and not
on the width of a transistor.
Once a transistor of a given width (W) is characterized
over a range of gm/ID, the gm/ID based parameters can
be generalized to a transistor of an arbitrary width. gm/ID
methodology will hold as long as a parameter of interest scales
with W. gm
gds
gm/ID
gm/gds
2gm
2gds
gm/ID
gm/gds
2gm
2gds
gm/ID
gm/gds

7. Extended gm/ID Data Set
gm/gds
gm/gmbs
ID/W
Cgd/Cgg
Cgs/Cgg
….more
γ (thermal noise)
fco (flicker noise)
Distortion parameters
(F. Silveira, JSSC, 1996.)
What we have on this slide is a list of most commonly used gmoverid based parameters.
gmovergds, for example, is the self-gain of a transistor. ID/W is the current density. The list goes on and on.
How do we obtain the gmoverid data set?
The gmoverid data set is not part of the standard design kit. You have to create it yourself by running DC simulation.
You only have to generate the database once when you start a new design kit.
We have shown in a previous paper that we can include additional parameters to enable gmoverid based noise simulation.
We would like to add distortion parameters to enable nonlinear analysis.
(Ou, 2011.)

8. Small Signal Model of NMOS

9. Design Example

10. Calculation
(gm is determined)

11. gm/gds
(50)

12. Current Density