1

MOSFET Amplifiers and High-Frequency Performance

Small-Signal equivalent circuit:

■ In many applications, MOSFET is used as a linear (small-signal) amplifier

■ A small signal equivalent circuit for MOSFET is needed to analyze the MOSFET frequency performance.

■ The equivalent circuit is constructed from the basic MOSFET geometry

■ Resistance and capacitances are incorporated

Input and output signals are assumed small as compared to the steady-state DC current and voltage (operating point)

Operating point is based on the MOSFET I-Vs and circuit conditions

2

MOSFET amplifier: low operating frequencies

Simple FET amplifier circuit:Δ VL = Δ I × RL

Voltage gain KV = Δ VL / Δ VG = (Δ I × RL) / Δ VG

KV = (Δ I / Δ VG) × RL = gm × RL

The larger the transconductance gm = ΔI / ΔVG, the higher is the voltage gain KV

gm is maximal in the saturation regime, i.e. for VD > VD sat

In the amplifier circuits, FETs usually work in the saturation regime,

In this regime, current DOES NOT depend on drain voltage.

Current is the function of the GATE VOLTAGE ONLY.ΔI1

ΔIS

3

0 2 4 6 8 100

1

2

3

4

5

6

7

8

9

10

VG = 1 V

VG = 2 V

VG = 3 V

VG = 4 V

ID, m

A

VD, V

MOSFET operating point:Effect of Load Resistance on the output Current amplitude

1. Load resistance RL = 5 kOhm

Consider the circuit with the drain bias VDD= 10 V and the gate bias VGG = 3 V ;

10V

RL

3V

Op. point: VD ≈ 1.2 V; ID ≈ 1.8 mA; gm1 ≈ (2-1.5)mA/(4-2)V ≈ 0.25 mA/V;

2. Load resistance RL = 0.6 kOhmOp. point: VD ≈ 6.8 V; ID ≈ 4.5 mA; gm2 ≈ (7-2.4)mA/(4-2)V ≈ 2.3 mA/V;

In MOSFET amplifiers, the operating point is normally in the saturation region

4

MOSFET Transfer CharacteristicsIn saturation regime, the drain current does not depend on the drain voltage

-1 0 1 2 3 40123456789

10

VD > 7 V

Satu

ratio

n cu

rren

t, m

AVG, V

The dependence IDsat (VG) is called the TRANSFER CHARACTERISTIC of MOSFET

0 2 4 6 8 100

1

2

3

4

5

6

7

8

9

10

VG = 1 V

VG = 2 V

VG = 3 V

VG = 4 V

ID, m

A

VD, V

5

S G D

G

S

D

rs Source series resistance

CgsGate to source capacitance

rs

Cgs Cgd

Cgd

Gate to drain capacitance

gmVgs

gmVgs

rd Drain series resistance

rd

gds Slope of ID vs VdsInputsignal

Outputsignal

MOSFET amplifier: high operating frequencies

ΔI1

ΔIS

6

G

S

D

rs

Cgs

Cgd

gmVgs

rd

gds

Simplified equivalent circuit diagram

Cgd

Cgs

vgs gmvgs

+

––

++

–

vivodsg

Assuming

rd, rs=0

7

MOSFET Gain

• voltage gain Cgd

Cgs

vgs gmvgs

+

––

++

–

vivodsg

Input voltage vi = vgsOutput voltage vo = voltage across gds

vo can be found using superposition.1) Assume vi = 0. The output voltage component is v01

The output current id = i(gds)+i(Cgd)i(gds) = v01 ×gds; i(Cgd) = v01 ×jωCgd

From this, id = v01 ×(gds +jωCgd);On the other hand, id = - gmvgs

Substituting id , we obtain:- gmvgs = v01 ×(gds + jωCgd);

IdI(Cgd)

01m

gsds gd

gv vg j Cω

−=

+

8

MOSFET Gain

• voltage gain Cgd

Cgs

vgs gmvgs

+

––

++

–

vivodsg

2) Now, turn off the current gmvgs

The output voltage component is v02

The voltage across gds = 1/rds:

v02 = vi × rds/(rds + 1/jωCgd) =

vi × rdsjωCgd/(jωCgdrds + 1) =

vi × jωCgd/(jωCgd + 1/rds) =

vi × jωCgd/(jωCgd + gds);

02gd

gsds gd

j Cv v

g j Cω

ω=

+The total output voltage, v0 = v01 + v02:

01m

gsds gd

gv vg j Cω

−=

+ 0m gd

gsds gd

g j Cv v

g j Cωω

− +=

+

9

MOSFET Gain

• voltage gain Cgd

Cgs

vgs gmvgs

+

––

++

–

vivodsg

The voltage gain:

0 m gdv

gs ds gd

g j CvAv g j C

ωω

− += =

+The gate - drain capacitance is very lowin the saturation region. Hence,

0 mv

gs ds gd

v gAv g j Cω

−= ≈

+

The voltage gain decreases with frequency when ;gd dsC gω ≈

mv

gd

gAj Cω−

≈

Corresponding characteristic frequency:2

dsv

gd

gfCπ

≈

At frequencies f > fv

10

MOSFET Gain

Cgd

Cgsvgs

gmvgs

–

+ +

–vi

i L

• short circuit current gain

Ai =iLii

=−gm

jω Cgs + Cgd( )

Cgd

Cgs

vgs gmvgs

+

––

++

–

vivodsg

Output current, iL = i0 = - gmvgs

Input current, ii = i (Cgs)+ i(Cgs) =

= vi × jω Cgs + vi × jω Cgd =

= vi × jω (Cgs + Cgd);

Also note that vi = vgs;

Therefore: ii = vi × jω (Cgs + Cgd);

The current gain: Ai = i0/ii = iL/ii

11

MOSFET current cutoff frequency fT

fT is the frequency at which the modulus of the short circuit current gain is unity

fT =gm

2π Cgs + Cgd( )

Assume that Cgs + Cgd ~ Ci where Ci = εiWL/di is the gate oxide capacitance.

Transconductance, gm

Consider short-gate MOSFETs at high drain voltage.

In short-gate devices, the electron velocity is saturated: Id = q nsvsW

The transconductance: gm = dId/dVg

Ai =iLii

=−gm

jω Cgs + Cgd( )fT estimation

d sm s

g g

I ng q v WV V

∂ ∂= =

∂ ∂

From:

12

MOSFET current cutoff frequency fT

Induced sheet carrier density in MOSFETs (see lecture #18):

From this, d s im s s

g g

I n Cg q v W q v WV V qWL

⎧ ⎫∂ ∂= = = ⎨ ⎬∂ ∂ ⎩ ⎭

( ) ( )i is GS T GS T

c Cn V V V V

q qWL= − = −

i sm

C vgL

=

( ) 2 22m i s s

Tigs gd

g C v vfLC LC C π ππ

= = =+

where W is the MOSFET width and L is the gate length

The cutoff frequency becomes:

13

fT = 1/ 2πttr

Practical cut-off frequency must also include the parasitic and fringing capacitances, Cp, which add to the gate capacitance:

fT =gm

2π Cgs + Cgd + Cp( )

Note that, L/vs = ttr , the electron transit time under the gate

( ) 2 22m i s s

Tigs gd

g C v vfLC LC C π ππ

= = =+

Using this,

14

Maximum oscillation frequency, fmax

The cutoff frequency fT is a characteristic of the intrinsic transistor (without parasitic series resistances). fmax is the characteristic of the extrinsic device

(which includes series source, drain, input, and gate resistances, Rs, Rd, Ri, and Rgfmax is defined as the frequency at which the

power gain of the transistor is equal to unity under optimum matching conditions for the input and output impedances.Simplified expression for fmax is given by:

Cgd

Cgs

vgsgmvgs

+

–

i

dsg

R

Rs

Rg Rd

Gate Drain

Source

fmax ≈fT

r + fT τwhere r = gds Rs + Ri + Rd( )

In MOSFETs with small parasitic resistances, RS, Ri and Rd ≈ 0 2

T Tmax

g gdT

f ffR Cf πτ

≈ =

τ = 2π RgCgd.