gm/ID Design Approach

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

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

Small Signal Model for NMOS Transistor

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

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

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.)

Small Signal Model of NMOS

Design Example

Calculation (gm is determined)

gm/gds (50)

Current Density