MOSFET Amplifiers and High-Frequency Performance
■ 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.
Small-Signal equivalent circuit:
■ The equivalent circuit is constructed from the basic MOSFET geometry
■ Resistance and capacitances are incorporated
ƒ 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
1
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
ΔIS
ΔI1
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.
2
MOSFET operating point:
Effect of Load Resistance on the output Current amplitude
10
9
8
VG = 4 V
7
RL
3V
ID, mA
10V
6
5
VG = 3 V
4
3
VG = 2 V
2
Consider the circuit with the drain bias
VDD= 10 V and the gate bias VGG = 3 V ;
VG = 1 V
1
0
0
2
4
6
8
10
VD, V
1. Load resistance RL = 5 kOhm
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 kOhm
Op. point: VD ≈ 6.8 V; ID ≈ 4.5 mA;
gm2 ≈ (7-2.4)mA/(4-2)V ≈ 2.3 mA/V;
3
In MOSFET amplifiers, the operating point is normally in the saturation region
MOSFET Transfer Characteristics
In saturation regime, the drain current does not depend on the drain voltage
10
Saturation current, mA
9
8
VG = 4 V
7
ID, mA
6
5
VG = 3 V
4
3
2
VG = 2 V
1
VG = 1 V
0
0
2
4
6
8
10
10
9
8
7
6
5
4
3
2
1
0
-1
VD > 7 V
0
1
VD, V
2
VG, V
3
4
The dependence IDsat (VG) is called
the TRANSFER CHARACTERISTIC of MOSFET
4
MOSFET amplifier: high operating frequencies
S
D
G
Cgd
Cgs
rs
rd
gmVgs
ΔIS
ΔI1
Gate to drain
capacitance
G
D
Cgd
rd Drain series
Cgs
Gate to source
capacitance
Input
signal
S
resistance
gmVgs
gds
rs Source series
resistance
Slope of ID vs Vds
Output
signal
5
G
D
Cgd
rd
Cgs
gds
gmVgs
rs
S
Simplified equivalent circuit diagram
Cgd
+
+
+
vi
–
v gs
–
g
C
gs
ds
vo
Assuming
rd, rs=0
gm v gs
–
6
MOSFET Gain
• voltage gain
Cgd
Id
I(Cgd)
+
+
+
vi
–
Input voltage vi = vgs
Output voltage vo = voltage across gds
v gs
–
g
C
gs
ds
vo
gm v gs
–
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);
− gm
v01 =
vgs
g ds + jωCgd
7
MOSFET Gain
2) Now, turn off the current gmvgs
• voltage gain
The output voltage component is v02
The voltage across gds = 1/rds:
Cgd
+
+
vi
v gs
–
–
g
C
gs
ds
+
v02 = vi × rds/(rds + 1/jωCgd) =
vo
vi × rdsjωCgd/(jωCgdrds + 1) =
vi × jωCgd/(jωCgd + 1/rds) =
gm v gs
–
vi × jωCgd/(jωCgd + gds);
v02 =
jωCgd
g ds + jωCgd
vgs
The total output voltage, v0 = v01 + v02:
− gm
v01 =
vgs
g ds + jωCgd
v0 =
− g m + jωCgd
g ds + jωCgd
vgs
8
MOSFET Gain
• voltage gain
The voltage gain:
Cgd
+
+
+
vi
–
v gs
–
g
ds
C
gs
vo
gm v gs
–
v0 − g m + jωCgd
Av =
=
vgs
g ds + jωCgd
The gate - drain capacitance is very low
in the saturation region. Hence,
v0
−gm
Av =
≈
vgs g ds + jωCgd
The voltage gain decreases with frequency when
Corresponding characteristic frequency:
At frequencies f > fv
−gm
Av ≈
jωCgd
fv ≈
ωCgd ≈ g ds ;
g ds
2π Cgd
9
MOSFET Gain
•
short circuit current gain
Output current, iL = i0 = - gmvgs
Cgd
+
+
+
vi
–
g
v gs
vo
ds
C
gs
–
gm v gs
–
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);
Cgd
+
vi
–
+
v gs
–
The current gain: Ai = i0/ii = iL/ii
gm v gs
Cgs
iL
iL
− gm
Ai =
=
ii
jω Cgs + Cgd
(
)
10
MOSFET current cutoff frequency fT
fT is the frequency at which the modulus of the short circuit current gain is unity
From:
iL
− gm
Ai =
=
ii
jω Cgs + Cgd
(
)
fT =
(
gm
2π C gs + Cgd
)
fT estimation
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
∂I d
∂ns
gm =
=q
vsW
∂Vg
∂Vg
11
MOSFET current cutoff frequency fT
Induced sheet carrier density in MOSFETs (see lecture #18):
ci
Ci
ns = (VGS − VT ) =
(VGS − VT )
q
qWL
where W is the MOSFET width and L is the gate length
From this,
⎧ Ci ⎫
∂I d
∂ns
gm =
vsW = q ⎨
=q
⎬ vsW
∂Vg
∂Vg
⎩ qWL ⎭
Ci vs
gm =
L
The cutoff frequency becomes:
fT =
gm
Ci vs
v
=
= s
2π ( Cgs + Cgd ) 2π LCi 2π L
12
gm
Ci vs
vs
fT =
=
=
2π ( Cgs + Cgd ) 2π LCi 2π L
Note that, L/vs = ttr , the electron transit time under the gate
Using this,
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 C gs + Cgd + C p
)
13
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 Rg
fmax 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:
fmax ≈
fT
r + fT τ
where
In MOSFETs with small parasitic resistances,
RS, Ri and Rd ≈ 0
R
R
d
C gd
g
+
Gate
v
gs
–
g
C
Drain
ds
gs
gm v gs
R
i
R
s
Source
r = gds (Rs + Ri + Rd )
f max ≈
τ = 2π RgCgd.
fT
fT
=
2π Rg Cgd
f Tτ
14