MOSFET Sizing

Recently two approaches have become widely used as unified synthesis methodologies valid in all regions of operation for determining MOSFET sizing and are now described. The new approaches are based on analysis rather than tool-based synthesis related with the conventional analogue design methods which require complicated synthesis tools, SPICE like and simulators models, analytical or quick hand methods for analogue circuits synthesise.

3.6.1 The gm / IDmethodology

The gm/ID method for designing micro-power CMOS analogue circuits is proposed in [3.21] and valid for all regions of operation of the MOSFET. Heregmstands

CHAPTER THREE OTA Linearisation Techniques and the Proposed OTA

LOW POWER ELECTRONIC CIRCUITS FOR BIOMEDICAL APPLICATIONS Saad A. Hasan

is defined as the ratio of the MOSFET drain current to its aspect ratio. Therefore, the normalized current is given by





Both gm/ID and IN are independent of the transistor sizes, therefore the relation between the two is unique for all transistors of the same type for a given fabrication technology. It is worth noting that the validation of this methodology is evident for long-channels for L values in the range of (3-12) µm, while some revision is needed for short channel transistors [3.21]. The gm/ID versus IN relationship can be obtained either

by using transistor model equations or by experimentation. In the experimental case, the

gm/ID versus IN curves for many transistors needs to be obtained. Consequently, their

mean gm/IDversus IN curve used to consider the technology spreads [3.22].

The plot of the gm/ID ratio versus the normalized current, IN is used to calculate

MOSFET aspect ratios, W/L. Then by choosing the suitable length which represents the compromise between the transistor area and stability on the one hand and dc gain on the other hand, the MOSFET width, W can be found [3.23].

The gm/ID ratio in that plot is chosen according to the required region of

operation of the MOSFET. After making a projection of gm/ID on that plot, the normalised current is obtained. In other words for the given values for any two of gm/ID,

gm, ID variables; W/L is determined directly. Finally, equation (3.17) is used to find W/L

since the required value of IDis known. The gm/ID versus ID/(W/L) curve is obtained and shown in section 3.7 later. The total supply current is chosen and the drain of each transistor can then be found. Using the value of ID with an appropriate value of gm/ID

based upon the desired operating regime of the transistor, allows the W/L ratio to be determined. Therefore the primary variables in the synthesis process are the drain currents of each transistor and their preferred gm/ID ratios. The maximum value of gm/ID

CHAPTER THREE OTA Linearisation Techniques and the Proposed OTA

LOW POWER ELECTRONIC CIRCUITS FOR BIOMEDICAL APPLICATIONS Saad A. Hasan

is limited firstly, by the weak inversion maximum value of the technology (about 35V-1

in thin film fully-depleted SO1 MOS transistors and less than 30V-1 in bulk MOS transistors) and secondly, by the stability requirements because as gm/ID increases, with fixed current, ID the transistor sizes and parasitic capacitances are increased and the

phase margin is reduced [3.21]. It is important to mention that this methodology is adopted when sizing the MOSFETs in this work. The table containing the dimensions of the MOSFETs for the proposed OTA will be presented in the later sections. The MOSFETs dimensions are calculated by considering all MOSFETs to be operating in the weak inversion region.

3.6.2 The Inversion Coefficient Approach

This methodology is proposed in [3.24] and is based on the concept of „level of inversion‟. When the level of inversion is known, it can be used as the design variable for optimising circuit parameters [3.24], [3.25]. The design degree of freedom in this method is three, represented by the drain current ID, transistor length L, and so-called inversion coefficient, IC. The EKV MOS model is the most appropriate model to work with this approach. This model is continuous and valid in all regions of MOS operation, and can be used for correlating the three degrees of freedom. The inversion coefficient,

IC can be expressed as follows





where µOis the low-field mobility and kO=µOCOX. Hence, IC is as follows





where IOis a process dependent current equals to 2nkOUT2. The most convenient method for interpreting the inversion coefficient is by making use of the gm/ID ratio.

CHAPTER THREE OTA Linearisation Techniques and the Proposed OTA

LOW POWER ELECTRONIC CIRCUITS FOR BIOMEDICAL APPLICATIONS Saad A. Hasan