electronic devices and circuits - utcluj.ro · and the bandwidth in inverse ratio due to miller’s...
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Electronic Devices and Electronic Devices and
CircuitsCircuits
Frequency responseFrequency response
Cascode amplifiersCascode amplifiers
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medium frequency :– coupling capacitors coupling capacitors →→ shortshort--circuitscircuits
–– internal parasitic capacitances internal parasitic capacitances →→ openopen--circuitscircuits
low frequency:- coupling capacitors coupling capacitors →→ equivalent impedancesequivalent impedances
-- internal parasitic capacitances internal parasitic capacitances →→ openopen--circuitscircuits
high frequency : - coupling capacitors coupling capacitors →→ shortshort--circuitscircuits
-- internal parasitic capacitances internal parasitic capacitances →→ equivalent impedancesequivalent impedances
• must be taken inmust be taken intoto considerationconsideration::- output resistance of the signal sourceoutput resistance of the signal source
-- load resistanceload resistance
Frequency response of the CS and CE amplifiers
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PS
( )( )ω
ωω
jv
jvjA
i
ov =)(
CS amplifier
vo(jω)=Fo(jω)⋅id(jω);
id(jω)=Fs(jω)⋅vg(jω);
vg(jω)=Fi(jω)⋅vi(jω);
( ) ( ) ( )ωωω jFjFjFA osiv ⋅⋅=
Analysis in the low-frequency range
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( )( )( ) ( ) i
i
i
g
iCRRj
CRj
jv
jvjF
G
G
++==
ω
ω
ω
ωω
1
( ) ( ) CiiCi
LiCRRCRR
fG
+=
+=
ππ 2
1
2
1
HPF, introduces a pole at
the frequency of the pole:CCi multiplied by the total resistance seen by CCi
( )( )( )ω
ωω
jv
jijF
g
ds =
SS
m
Ls
CRg
f
=
||1
2
1
π
( )( )( )ω
ωω
ji
jvjF
d
oo =
( ) ( ) CoLoCoLD
LoCRRCRR
f+
=+
=ππ 2
1
2
1
• the dominant pole: the greater break frequency between fLi, fLs, fLo if the nearest pole or zero will be at least a decade away.
• usally given by fLs, for equal coupling capacitances
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Analysis in the high-frequency range
CCgdgd is reflected to the input according to
MillerMiller’’s theorems theorem ( ) gdLmgsi CRgCC '1++=
( )( )( ) ( ) iG
Lm
G
G
i
ov
CRRjRg
RR
R
jv
jvjA
||1
1'
ωω
ωω
+⋅⋅
+−==
Lm
G
Gvo Rg
RR
RA '⋅
+−=
( ) ( ) iiiG
HCRRCRR
f||2
1
||2
1
ππ==
Cds is not shown here because it generates a pole at a much higher frequency that the one generated by Cgs
and Cgd
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Numerical example
CCi=CCo=Cs=10µF, R=20KΩ, RG=2MΩ, RD=10kΩ, RL=20kΩ,
Rs=10KΩ, I=400µA.
K=100µA/V2, (W/L)=18, VA=100V. Cgs=Cgd= 1pF @ I=400µA
mS2.1=mgSolution: KΩ250=or
( )mHz8
1010102000202
163
≅⋅⋅+
=−π
Lif
Hz21
10101010||2.1
12
1
63
≅
⋅⋅
=
−πLsf
( )Hz5.0
10101020102
163
≅⋅⋅+
=−π
Lof
fL=21Hz
The output resistance of the signal source R does not affect fLi but affects fH
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( )[ ] ( )[ ] pF8.9120||10||2502.111||||1 ≅⋅++=++= gdLDomgsi CRRrgCC
( )KHz820
108.9102000||202
1123
=⋅⋅⋅
=−π
Hf
7.17)7.7log(20dB
==voA
7.75.62.1202.0
2−=⋅⋅
+−=voA
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The effect of each capacitor is found considering the othertwo capacitors with infinite capacity (zero equivalent impedance)
CE amplifier
Analysis in the low-frequency range
CibeB
LiCrRR
f)||(π2
1
+=
;π2
1
EE
LeCR
f′
=
1
||||
+
+=′
β
RRrRR Bbe
EE
CoLC
LoCRR
f)(π2
1
+=
21 || BBB RRR =
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Analysis in the high-frequency range
bcLmbei CRgCC )1( ′++=
ii
LCm
beB
beBv
CRRRg
rRR
rRA
′++=
ωω
j1
1)||(
||
||)j(
RRrR Bbei ||||=′
iBbe
HCRRr
f)||||π(2
1=)||(
||
||LCm
beB
beBvo RRg
rRR
rRA
+=
10/13
Cascode amplifiers
for the CS and CE amplifiers the absolute value of the gain and the bandwidth in inverse ratio due to Miller’s effect
when the gain increases, the parasitic capacitance reflected to the input also increases so the high cutoff frequency decreases
a technique to build wideband amplifiers
to reduce the multiplication effect of the parasitic capacitanceit is often use the cascodecascode configurationconfiguration::
- connection of a CS (CE) amplifier followed by aCG (CB) amplifier
Lm
G
Gvo Rg
RR
RA '
+−=
( ) )'1)(||||π(2
1
gdLmgsBbe
HCRgCRRr
f++
=
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The cascode configuration with MOSFET
−==
2
211
1
1||
m
om
i
ov
grg
v
vA
1
2
1o
m
rg
<< same current through T1, T2
medium frequency
21 mmm ggg == 11 −≅vA
CG
DmDm
o
ov RgRg
v
vA =≈= 22
1
21 vvv AAA ⋅=
Dmv RgA −=
GGGi RRRR == 21 ||
DoomooDo RrrgrrRR ≈++= )(|| 21221
CS
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High frequency
11111 2)1( gdgsgdvgsi CCCACC +=−+=
The multiplication factor of Cgd1 is 2, considerable smaller that the one in CS configuration . The value for Ci results much more reduced, that leads to a much higher value of the high cutoff frequency:
)1( 2Rgm′+
iG
HCRR
f)||(π2
1=
the other two poles due to Cgs2 and Cgd2 results to considerable higher frequency than fH
CCii introduces the dominant pole at high frequency and determines introduces the dominant pole at high frequency and determines the passthe pass--band of the amplifierband of the amplifier
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Numerical illustration
MΩ421 == GG RR Ω= K10DR
µA400=I
KΩ20=R KΩ20=LR
18)/( =LW V100=AV
2V
µA100=K
pF1== gdgs CC
mS 1,2µS 12004001810022 ==⋅⋅⋅== IL
WKgm
Ω=== M 24||4|| 21 GGG RRR
[ ] 9,7)20||10(2,1200020
20)||( −=⋅⋅
+−=−
+= LDm
G
v RRgRR
RA
pF 31212 =⋅+=+= gdgsi CCC
MHz 7,210310)2000||20(2
1
)||(2
1123
≅⋅⋅⋅
==−ππ iG
HCRR
f
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The cascode configuration with BJT
)||(1
||
||2
2
1
1
1LCm
m
m
beB
beB
i
ov RRg
gg
rRR
rR
v
vA
−
+==
21 || BBB RRR =
21 bebebe rrr ==
21 mmm ggg ==
)||(||
||LCm
beB
beBv RRg
rRR
rRA
+−=
)2)(||||(2
1
bcbeBbe
HCCRRr
f+
=π
For identical T1 and T2 transistors