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Lecture 10
Frequency response
2
topics
• Bode diagram
• BJT’s Frequency response
• MOSFET Frequency response
3
Amplifier tVtv ii sin)( )sin()( tVtv oo
Magnitude: Phase:i
o
V
V
)(
)()(
)(
)()(
i
o
i
o
V
VT
sV
sVsT
jsjs
Magnitude: Phase:)(
)(
jV
jV
i
o
)(
)(
jV
jV
i
o
Steady-state response
4
dB (decibel)= Decimal + Bell
2
110
2
110
22
2
110
log20log20
log10
i
i
v
vdB
z
vzip
p
pdB
Human hearing frequency zone : 10Hz~24kHzMost Sensitive frequency zone : 2kHz~5kHz
5
1
210log
decDecade :1
22log
octOctave :
1 10 100
Logarithmic coordinate
2 3 4 20
dB
0
Log scale
6
Example(low pass)
oV
iVR
C
)(1
1
)(1
1)(
1
)(1
1)(
1
1
0
0
jRCjT
RClet
RCjTV
sCRsCV io
01
0
451tan0)(
2
1)(
T
Tif
7
Magnitude:
])(1log[10
)(1log20)1(
2
0
2
0
1
0
dB
j
01log10
00
0
dB
]log20log20[
log20
1
0
0
000
dB
dB
j
01.32log10110 dBj
)(1
1
)(1
1)(
00
js
T
0
10
0
tan0)1(
j
oT 00tan)(0 1
00
oT 90tan)( 1
00
Phase:
8
)()( dBT
)(T
0
1.0 1 10
0900180
090
01800
0 45
0
decadedB /20
dB0
sT
0
0)(
9
10
oV
iV RC
Example(high pass)
)(1
)(
)(1)(
1
)(1)(
1
0
00
j
j
RCj
RCjT
RClet
RCj
RCjTV
sCR
RV io
01
0
451tan90)(
2
1)(
T
Tif
11
Magnitude:
Phase:
]log[10log20
log20log20
20
2
20
2
0
dBj
j
oj
j
1
0
tan90
01log20
1log20
1
1log20
0
00
dB
j
j
201.0log201.0
log20log20
log20
0
0
00
dB
dB
dB
oT 0tan90)( 1
00
oT 900tan90)(0 1
00
01.32log2011
10
dB
j
00
)()(
j
jT
s
ssT
12
)()( dBT
)(T
0
1.0 1 10
0900180
090
01800
0 45
0
decadedB /20dB0
0
)(
s
ssT
13
14
dBT
Tif
T
32log10)(log20
2
1)(
)(log20
The bandwidth represents the distance between the two points in the frequency domain where the signal is of the maximum signal strength.
21
)(log20 TdB
2
1)(0 Tif
15
BJT high frequency model
Depletion capacitance
Emitter-base capacitance= diffusion capacitance + Base-Emitter junction capacitance
Splitting resistance (refinement the lumped-component circuit)
16
B
C
b
cfe I
I
I
Ih
sC1
)////(
)(1
CCr
VI
VsCg
sC
VVgI
b
mmc
rCCsrCCs
rgh
CCsr
sCg
I
Ih
mfe
m
b
cfe
)(1)(1
)(1
0
Low frequency ß
)(1
1)(
0
s
T
rCC )(
1
3-dB frequency
17
srCCsI
Ih
b
cfe
1
1
)(10
decadedB /201
)(1
0)(1log20log20
2
2
T
T
T
Unity-gain bandwidth
)(2
CC
gf
CC
g
mT
mT
18
CE Amplifier
19
)( HLHLH fffffBW
Parallel capacitors
Series capacitors
)////()//(
)//(LCom
sB
B
sig
oM RRrg
RrR
rR
v
vA
Midband amplitude
Bandwidth
20
High frequency response: The effect of parallel capacitors
)1(
)(
'
'
Lmeq
eq
Lmo
o
RgCC
vsCi
vRgv
vvsCi
21
)(1
1'
0
svv s
)(21
)(1
'
'0
eqsH
eqs
CCRf
CCR
)1( 'Lmeq RgCC
Miller multiplier
22
Example 5.18 Find the Midband gain and upper 3 dB frequency of CE amplifier.
Mhzf
rpFC
VV
kRkR
kRkR
mAI
VVV
T
x
A
Ls
CB
EECC
800
50,1
100,100
5,5
8,100
1
10
The parameters of Hybrid model
pFC
CpFg
CC
kI
Vr
kI
Vr
VmAV
Ig
T
m
C
Ao
B
T
T
Cm
7
18
100
5.2
/40
23
39)////()//(
LComxsBsB
B
sig
oM RRrg
rrRR
r
RR
R
v
vA
pFCCC
RgCC
eqin
Lmeq
128
)1( '
kCCR
f
CCR
eqsH
eqs
754)(2
1
)(1
'
'0
kRRrrR SBxs 65.1)]//(//['
24
Low frequency response: The effects of the series capacitors
25
Consider CC1
])//[(
1
}
])//[(1
{])//[(
)//()//(
1])//[(
)//()//(
)//(1)//(
)//(
)//(
1)//(
//
11
1
1
1
1
1
sBCp
sBCsB
BLCm
sBC
CBLCm
LCm
CsB
B
s
o
LCmo
CsB
Bs
RrRC
RrRCs
s
RrR
rRRRg
RrRsC
sCrRRRg
RRg
sCRrR
rR
v
v
RRvgv
sCRrR
rRvv
26
Consider CE
])1
//[(
1
}
])1
//[(
1{
)1()//(
)//(
)1)(1()//(
)//(
)//(
)1)(1()//(
1
2
esB
E
p
esB
E
esB
LC
sB
B
EesB
LC
sB
B
s
o
LCbo
EesBsB
Bsb
rRR
C
rRR
Cs
s
rRR
RR
RR
R
sCrRR
RR
RR
R
v
v
RRIv
sCrRRRR
RvI
27
Consider CC2
)(
1
)(1
)//()//(
)//(
1
)//(
//
23
2
2
LCCp
LCC
LCmsB
B
s
o
L
CLC
Cmo
sB
Bs
RRC
RRCs
sRRg
RrR
rR
v
v
R
sCRR
Rvgv
RrR
rRvv
28
))()((321 ppp
Ms
o
s
s
s
s
s
sA
v
v
decadedB /20
decadedB /40
decadedB /60
])//[(
1
11
sBCp RrRC
])
1//
[(
12
esB
E
p
rRR
C
)(
1
23
LCCp RRC
1CR 2CRER
%80%10%10
dominant
29
Example 5.19 Find the CC1, CC2 and CE the CE amplifier of the example 5.18.
hzf
kr
g
kRkR
kRkR
mAI
VVV
L
m
Ls
CB
EECC
100
5.2
40,100
5,5
8,100
1
10
])//[(
1
11
sBCp RrRC
])1
//[(
12
esB
E
p
rRR
C
)(
1
23
LCCp RRC
FCfrRR
C ELesB
E
6.2728.0])1
//[(
FCfRrRC CLsBC 1.221.0])//[( 11
FCfRRC CLLCC 2.12)( 22
30
MOSFET high frequency model
31
)(2
)(
)(
)(
gdgs
mT
gdgs
mT
gdgs
m
i
o
gdgs
igs
gsmgsgdgsmo
CC
gf
CC
g
CCs
g
I
I
CCs
Iv
vgvsCvgI
32
High frequency response: The effect of parallel capacitors
33
)( HLHLH fffffBW
)////( LDomsG
G
sig
oM RRrg
RR
R
v
vA
Midband amplitude
Bandwidth
34
)]1()[//(2
1
)]1()[//(
11
1
1
)1(
)1(
'
)(
'
'0
'
0
'
'
LmgdgssGH
LmgdgssG
LmsG
G
s
oM
ssG
Ggs
Lmgdeq
gseqgsLmgdgd
gsLmo
ogsgdgd
RgCCRRf
RgCCRRRC
RgRR
R
v
vA
sv
RR
Rv
RgCC
vsCvRgsCI
vRgv
vvsCI
35)]1()[//(2
1
)]1()[//(
11
'
'0
'
LmgdgssGH
LmgdgssG
LmsG
GM
RgCCRRf
RgCCRRRC
RgRR
RA
36
Example 4.12 Find the Midband gain and upper 3 dB frequency of CS amplifier.
pFCpFC
krg
kRkR
MRkR
mAI
gdgs
m
LD
GS
4.0,1
150,1
15,15
7.4,100
0
)]1()[//(2
1
)]1()[//(
11
'
'0
'
LmgdgssGH
LmgdgssG
LmsG
GM
RgCCRRf
RgCCRRRC
RgRR
RA
37
Low frequency response: The effects of the series capacitors
)(1
)(1
1
11
1
1
sGCp
sGCsG
Gsg
sC
G
Gsg
RRC
RRCs
s
RR
Rvv
RsCR
Rvv
38s
mp
s
mgm
sm
gd
Cg
Cgs
svg
sCg
vi
2
11
)(1
)(1
)//(
1
22
2
2
LDCp
LDC
LDdLoo
LC
D
Ddo
RRC
RRCs
sRRiRiv
RsCR
Rii
39
)(1
11
sGCp RRC
s
mp C
g2)(1
23
LDCp RRC
))()()(//(321 ppp
LDmsG
G
s
o
s
s
s
s
s
sRRg
RR
R
v
v
40
Example 4.13 Find the CC1, CC2 and Cs the CS amplifier of the example 4.12.
10
100
100
4.0,1
1
15,15
7.4,100
31
Hzff
Hzf
pFCpFC
g
kRkR
MRkR
mAI
pp
L
gdgs
m
LD
GS
nFRRfC
RRCHzf
sGpC
sGCp
3.3)(21
)(2110
11
11
FRRfC
RRCHzf
LDLC
LDCp
53.0)(21
)(2110
2
23
Ff
gC
gC
ff
L
ms
m
spL
6.12
)(2
12
