JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B. Tech IV Year ANALOG CMOS IC DESIGN Previous Question Paper (September - 2020 - R16)

A MOS transistor can be configured to act as a resistor by operating it in the triode (linear) region. This is achieved by ensuring the drain-to-source voltage is small compared to the overdrive voltage, specifically V_DS < V_GS - V_TH.

The drain current in the linear region is given by:

For small values of V_DS, the quadratic term (V_DS²/2) becomes negligible, simplifying the expression to:

The equivalent resistance R_on is defined as V_DS/I_D:

To implement this in circuits:

• Voltage-Controlled Resistor: The resistance is controlled by the gate voltage V_GS. Increasing V_GS reduces the resistance.
• Linearity: To maintain high linearity, V_DS must be kept very small.
• Applications: These are commonly used in continuous-time filters, automatic gain control circuits, and as load elements in CMOS amplifiers.

When the gate-source voltage V_GS is less than the threshold voltage V_TH, the transistor is in the sub-threshold (weak inversion) region. In this regime, the channel is not fully formed, and conduction occurs primarily through diffusion rather than drift.

The drain current in the sub-threshold region is exponentially dependent on V_GS, similar to a BJT:

Where:

• I₀ is a process-dependent constant.
• V_T is the thermal voltage (kT/q ≈ 26 mV at room temperature).
• n is the sub-threshold swing parameter (typically 1 < n < 2), representing the capacitive voltage divider between the gate oxide and the depletion region.

For V_DS > 3V_T, the term [1 - exp(-V_DS / V_T)] approaches unity, and the current becomes independent of V_DS, showing a saturation-like behavior. This model is critical for low-power, low-speed CMOS design, such as in watch circuits or medical implants.