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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.