lect13_disto_ann3
TRANSCRIPT
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Examples
Niknejad Distortion
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Distortion of BJT Amplifiers
+
vs
RL
vo
VCC
Consider the CE BJTamplifier shown. Thebiasing is omitted forclarity.
The output voltage is simply
Vo=VCC ICRC
Therefore the distortion is generated by ICalone. Recall that
IC =ISeqVBE/kT
Niknejad Distortion
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BJT CE Distortion (cont)
Now assume the input VBE =vi+VQ, where VQ is the biaspoint. The current is therefore given by
IC =ISeVQVT
| {z }IQe
viVT
Using a Taylor expansion for the exponential
ex = 1 +x+ 1
2!x2 +
1
3!x3 +
IC =IQ(1 + vi
VT+
1
2
vi
VT
2+
1
6
vi
VT
3+ )
Niknejad Distortion
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BJT CE Distortion (cont)
Define the output signal ic=IC IQ
ic= IQ
VTvi+
1
2
qkT
2IQv
2i +
1
6
qkT
3IQv
3i +
Compare to So=a1Si+a2S2i +a3S
3i +
a1=qIQ
kT =gm
a2=1
2 q
kT2
IQ
a3=1
6
qkT
3IQ
Niknejad Distortion
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Example: BJT HD2
For any BJT (Si, SiGe, Ge, GaAs), we have the followingresult
HD2=1
4
qvi
kT
where vi is the peak value of the input sine voltage
For vi= 10mV, HD2= 0.1 = 10%We can also express the distortion as a function of the outputcurrent swing ic
HD2=
1
2
a2
a21Som =
1
4
ic
IQ
For icIQ
= 0.4, HD2= 10%
Niknejad Distortion
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Example: BJT IM3
Lets see the maximum allowed signal for IM3 1%
IM3=
3
4
a3
a1S2
1 =
1
8 qvi
kT2
Solve vi = 7.3mV. Thats a pretty small voltage. For practicalapplications wed like to improve the linearity of this amplifier.
Niknejad Distortion
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Example: Disto in Long-Ch. MOS
vi
VQ
ID = IQ + io
ID= 12Cox
W
L (VGSVT)
2
io+IQ= 12Cox
W
L (VQ+viVT)
2
Ignoring the output impedance we have
= 12Cox
W
L
(VQ VT)
2 +v2i + 2vi(VQ VT)
= IQ|{z}dc
+ CoxWLvi(VQ VT)| {z }
linear
+ 12Cox
WLv2i| {z }
quadratic
Niknejad Distortion
S
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Ideal Square Law Device
An ideal square law device only generates 2nd order distortion
io=gmvi+ 12Cox
W
Lv2i
a1=gm
a2= 12CoxW
L = 12
gm
VQ VT
a3 0
The harmonic distortion is given by
HD2=12a2
a1vi =
14
gm
VQ VT
1gm
vi=14
vi
VQ VT
HD3= 0
Niknejad Distortion
R l MOSFET D i
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Real MOSFET Device
0
200
400
600
Effective Field
Mobility
Triode CLM DIBL SCBE
Rout
k
Vds(V)
2
4
6
8
10
12
14
0 1 2 3 4
The real MOSFET device generates higher order distortion
The output impedance is non-linear. The mobility is not aconstant but a function of the vertical and horizontal electricfield
We may also bias the device at moderate or weak inversion,where the device behavior is more exponential
There is also internal feedback
Niknejad Distortion