This document discusses MOSFETs as linear amplifiers. It explains that MOSFETs can act as voltage controlled current sources in saturation and be used as transconductance amplifiers. For linear amplification, a MOSFET is DC biased at a certain VGS and a small AC signal is superimposed. A common-source amplifier circuit is shown, where the input voltage VGS causes a change in drain current ID through load resistor RD, producing the output voltage VO. The document analytically derives the transfer characteristics of a MOSFET in cutoff, saturation, and triode regions. It also discusses operating a MOSFET as a switch by biasing it at the extremes of the transfer curve and establishing an appropriate

1. Microelectronic Circuits
Nithin Kumar N.R.
Assistant Professor, NHCE, Bengaluru

2. MOSFET as Linear Amplifier
• In Saturation region, MOSFET acts as voltage controlled current source and
can be used to implement a transconductance amplifier.
• Id & VGS are non-linearly related to each other.
• 𝑖𝑑 =
1
2
𝜇𝑛𝐶𝑜𝑥
𝑊
𝐿
(𝑉𝐺𝑆 − 𝑉𝑡)2
-Square Law
• To obtain linear amplification
• DC Biasing is done with MOSFET to operate at a certain VGS and then superimposing
a small vgs.
• superimposing a small AC voltage vgs to be amplified on DC bias Voltage VGS
• For this purpose, the transfer characteristics of the MOSFET is derived as
large signal operation.
• For all MOSFET is studied as a switch and then as an amplifier,

3. MOSFET as an Amplifier
• The figure shows the basic structure (skeleton) of the most
commonly used MOSFET amplifier, the common-source (CS)
circuit.
• The name common source arises because when the circuit is
viewed as two port network, the grounded source terminal is
common to both the input port (gate and source) and output
port (drain and source).
• Change in input voltage (Vgs ) gives rise to change in drain
current (id) by using a resistor RD to obtain output voltage (vo).
• 𝑣0 = 𝑉𝑑𝑠 = 𝑉𝐷𝐷 − 𝑖𝑑𝑅𝐷
• Thus transconductance amplifier is converted into a Voltage
amplifier.
• A DC supply is required to turn ON the device and supply
necessary power to operate.

4. Graphical Derivation of VTC-Load Line Analysis
• Relationship between id-Vds is given
by
• 𝑣0 = 𝑉𝑑𝑠 = 𝑉𝐷𝐷 − 𝑖𝑑𝑅𝐷
• 𝑖𝑑 = 𝑉𝐷𝐷/𝑅𝐷 − 𝑉𝑑𝑠/𝑅𝐷
• This straight line has a slope of -1/RD
• RD is load resistor of amplifier –
Resistance across output.
• The line called as load line.
• vo=VDS for vi=VGS
Id
Vds
VDD
VDD /RD

5. Graphical Derivation of VTC-Load Line Analysis

6. Graphical Derivation of VTC-Load Line Analysis

7. Analytical Expression
• 3 region of operation
• Cutoff Region Segment XA
• 𝑣𝑖 ≤ 𝑉𝑡, and 𝑣𝑜 ≤ 𝑉𝐷𝐷
• Saturation Region segment AQB
• 𝑣𝑖 ≥ 𝑉𝑡, and 𝑣𝑜 ≥ 𝑣𝑖 − 𝑉𝑡
• Triode region segment BC
• 𝑣𝑖 ≥ 𝑉𝑡, and 𝑣𝑜 ≤ 𝑣𝑖 − 𝑉𝑡

8. Analytical Expression
Cutoff Region Segment XA
• 𝑣𝑖 ≤ 𝑉𝑡, and 𝑣𝑜 ≤ 𝑉𝐷𝐷
The device will be off

9. Analytical Expression
• Saturation Region segment AQB
• 𝑣𝑖 ≥ 𝑉𝑡, and 𝑣𝑜 ≥ 𝑣𝑖 − 𝑉𝑡
• 𝑖𝑑 =
1
2
𝜇𝑛𝐶𝑜𝑥
𝑊
𝐿
(𝑣𝑖 − 𝑉𝑡)2
• 𝑣0 = 𝑉𝐷𝐷 − 𝑖𝑑𝑅𝐷
• 𝑣𝑜 = 𝑉𝐷𝐷 −
1
2
𝑅𝐷𝜇𝑛𝐶𝑜𝑥
𝑊
𝐿
(𝑣𝑖 − 𝑉𝑡)2
To obtain voltage gain
𝐴𝑣 =
𝑑𝑣0
𝑑𝑣𝑖
• At operating point

10. Analytical Expression
Triode region segment BC
• 𝑣𝑖 ≥ 𝑉𝑡, and 𝑣𝑜 ≤ 𝑣𝑖 − 𝑉𝑡
• 𝑖𝑑 = 𝜇𝑛𝐶𝑜𝑥
𝑊
𝐿
𝑣𝑖 − 𝑉𝑡 𝑣𝑜 −
1
2
𝑣𝑜
2
• 𝑣0 = 𝑉𝐷𝐷 − 𝑖𝑑𝑅𝐷
• 𝑣𝑜 = 𝑉𝐷𝐷 − 𝜇𝑛𝑅𝐷𝐶𝑜𝑥
𝑊
𝐿
𝑣𝑖 − 𝑉𝑡 𝑣𝑜 −
1
2
𝑣𝑜
2
• Vo is small and thus approximated as
• 𝑣𝑜 = 𝑉𝐷𝐷 − 𝜇𝑛𝑅𝐷𝐶𝑜𝑥
𝑊
𝐿
𝑣𝑖 − 𝑉𝑡 𝑣𝑜
• Reduced to
• 𝑣𝑜 = 𝑉𝐷𝐷 /(1 + 𝜇𝑛𝑅𝐷𝐶𝑜𝑥
𝑊
𝐿
𝑣𝑖 − 𝑉𝑡 )
• 𝑟𝑑𝑠 = 1/(1 + 𝜇𝑛𝐶𝑜𝑥
𝑊
𝐿
𝑣𝑖 − 𝑉𝑡 )

11. Operation as Switch
• As a switch it is operated at extreme points
of transfer curve
• The device is turned off
• vi<Vt operated in segment XA with vo=VDD
• The device is turned on
• By applying a voltage close to VDD with vo very
small
• As a switch it is operated in Points A and C
in VTC.

12. Biasing in MOS amplifier Circuits
• To design MOSFET as amplifier circuit we need to establish an
appropriate DC operating point for the MOSFET.

13. Biasing by fixing Vgs
• To fix the gate to source voltage to the value required to provide the
desired Ids.
• Vgs can be derived from VDD through an appropriate Voltage devider
or suitable reference voltage.

14. Biasing by fixing Vgs and connecting a
resistance in the source
• To fix the gate to source voltage to the value required to provide the
desired Ids.
• Vgs can be derived from VDD through an appropriate Voltage devider
or suitable reference voltage.