MOSFET Operation and Modeling

Posted on May 25, 2024 in Design and Engineering

MOSFET Operation

Accumulation

Negative voltage applied to the gate attracts mobile holes to the surface under the gate.

Depletion (weak inversion, subthreshold)

Small positive voltage applied to the gate repels free holes, not negative enough to attract holes, not positive enough to attract many electrons.

Inversion

Moderate positive voltage applied to the gate attracts free electrons from source and drain under the gate.

MOSFET Modeling

MOS Large Signal Model

In saturation, the drain current is basically constant for a large range of V_DS which makes the NFET good as a voltage controlled current source.

Small Signal MOS Models

At small signals, MOS acts like voltage controlled current source: signal v_gs between gate and source produces drain current g_mv_gs.

•Model includes transconductance and output resistance (dependence of drain current on drain voltage) 

•Output resistance r_o usually in range 10-1000kΩ

Small signal analysis 

–First, calculate the bias point using DC equations  

–Next, use the DC values to estimate small signal parameters –Next, create the small signal equivalent circuit:  

§Short DC voltage sources  

§Open DC current sources  

§Replace active elements by their small signal equivalent models  

–Transconductance is extremely important parameter  

–Relates AC gate voltage to AC drain current  

–Transconductance for a MOSFET increases with the square root of the drain current I_D and linearly with the excess gate voltage V_DSsat  

Output resistance depends on channel length L and V_DS,sat  

oAs L increases, drain current decreases and output resistance r_o increases  

oIf L is constant, decreasing V_DS,sat causes drain current to decrease and output resistance r_o to increase  

oHowever, increasing L causes inherent speed of MOSFET to decrease  

•Body Effect – As source-body potential increases, threshold voltage increasesoMatters whenever source  and body are NOT shorted  

Drain current

Mobility ↓ causes less current, threshold voltage ↓ causes more current

At low VGS, threshold changes dominate and current increases as T ↑ 

At high VGS, mobility changes dominate and current decreases as T ↑ 

At one special bias point, the effects cancel

Transition frequency

Frequency at which transistor stops amplifying

Inherent design tradeoff

– For high speed, need minimum channel length and high VDS,sat

– For high output resistance (and high gain), need long channel length

Constant gain-bandwidth product

– Higher speeds results in lower gain

– Transition frequency is inherently smaller for PMOS than NMOS due to lower hole mobility

Current Mirrors

Main design focus: achieving high output resistance

Steps to calculate output resistance

1 small signal model

Short dc voltages

Open circuit dc currents

Replace circuit components with small signal models

2 Ground the input

3 Apply small test voltage “vt” so that current “it” can flow through the circuit

4 Rout = vt /it