Modern Electronics: F7 Basic Amplifiers II 1
Basic Amplifier Stages II
• CS - Example
• Common Gate Amplifier
• Cascode Amplifier
• Transistor Frequency Response
Reading instructions: 185-187, 194-196, 205, 207-210, 214,
217-229,490-495
Modern Electronics: F7 Basic Amplifiers II 2
Basic Amplifier Stages II
VDD
vOUT
V(t)
RL
50W
VDD
RD
47W
R2
1MW
R1
3MWR
100kWC2
1mFC1
0.01mF
Parameters:
k’=0.0015 A/V2
W/L=100
VT=0.5V
VDD=5V
l=0.1
1) Calculate
bias points
2) What fraction
of the current
is ”used”?
3) Calculate
medium
frequency
voltage gain
Gate biasing
Modern Electronics: F7 Basic Amplifiers II 3
Common Gate Amplifier
𝐺𝑀 = 𝑔𝑚
𝑅𝑖 =1
𝑔𝑚
𝑅0 = 𝑅𝐷
vIN
VDD
vOUT
RD
An common gate stage has
• Low input resistance (transconductance)
• High Output resistance (saturation)
• Application: ”Current Buffer” io=ii
Drain
gmvsgvsg RD
vo1/gm
Source
Gate
Modern Electronics: F7 Basic Amplifiers II 4
Common Gate Amplifier
𝐺𝑀 = 𝑔𝑚
𝑅𝑖 =𝑟0 + 𝑅𝐷 𝑅𝐿
1 + 𝑔𝑚 𝑟𝑜
𝑅0 = 𝑅𝐷 𝑟0 + 𝑅𝑆 1 + 𝑔𝑚𝑟0
𝑅0 ≈ 𝑅𝐷 𝑔𝑚𝑟0𝑅𝑠
An common gate stage has
• Low input resistance (transconductance)
• High Output resistance (saturation)
• Application: ”Current Buffer” io=ii• Addition of ro makes the amplifier
”bilateral”
Drain
gmvinvi
ro
RDvo
1/gm
Source
Gate
RS
vIN
VDD
vOUT
RDRS
RL
RL
Modern Electronics: F7 Basic Amplifiers II 5
Common Drain Amplifier – Source Follower
𝐺𝑀 ≈ 𝑔𝑚
𝑅𝑖 = ∞
𝑅0 =1
𝑔𝑚 +1𝑟0+
1𝑅𝐿
𝐴𝑉 = 𝑔𝑚1
𝑔𝑚 +1𝑟0+
1𝑅𝐿
< 1
• Vout≈Vin-(VT+Vov)
• Level Shifter
• Voltage Buffer
• Output stage – low output
resistance
vIN
VDD
vOUT
RL
gmvgsvi ro RLvo
vgs
Modern Electronics: F7 Basic Amplifiers II 6
2 minute exercise I
vx
VDD
A diode connected FET can
operate as a small signal resistor
1) Draw the small signal model
of the circuit.
2) Calculate the equivalent
resistance. R=Vx/Ix
Ix
gm2, r02
Modern Electronics: F7 Basic Amplifiers II 7
2 minute exercise II
VDD • How do you use this to build a
CS-amplifier using only
transistors?
• What is the corresponding
voltage gain?
gm2
Modern Electronics: F7 Basic Amplifiers II 8
Cascode
VDD
vOUT
RD
vIN
M1
M2
𝐺𝑀 ≈ 𝑔𝑚1
𝑅𝑖 = ∞
𝑅0 = 𝑟01 + 𝑟02 + 𝑔𝑚2𝑟01𝑟02 ≈ 𝑔𝑚2𝑟01𝑟02
• Two stage amplifier
• Increases output resistance
• Good high frequency
properties
gm1vivi ro1
RD
gm2vgs2
=-gm2vds1
ro2
vo
Modern Electronics: F7 Basic Amplifiers II 9
Differential Amplifier
Vid/2
VDD
RD
VDD
vod
RD
ITAIL
-Vid/2
𝐴𝑑𝑚 =𝑣𝑜𝑑𝑣𝑖𝑑
≈ −𝑔𝑚𝑅𝐷
• Two input signals –
opposite phase
• Output signal –
differential
• Rejects common-
mode signals (eg.
supply noise)
• Amplifies differential
signals
Modern Electronics: F7 Basic Amplifiers II 10
2 minute problem – differential / single ended
Vid/2
RD
VDD
vod
RD
-Vid/2
VDD
RD
Vd
Vout
If VDD varies with DV – (l=0, transistors in saturation)
• How much does vod change?
• How much does Vout change?
Modern Electronics: F7 Basic Amplifiers II 11
High Frequency Transistors
• Rd and Rs are usually small
• Cgd<<Cgs
Cgs
r0gmv1
+
-
vin
CgdRG
+
-
vout
+
-
v1
• The Cgd feedback
capacitance complicates the
analysis
• We will use the Miller
approximation
Modern Electronics: F7 Basic Amplifiers II 12
Maximum current gain frequency: fT
Cgs
gmv1
+
-
vin
CgdRG
+
-
v1r0
iin iin
Maximum current gain (iout/iin) when
output is shorted to ground
𝑖𝑜𝑢𝑡𝑖𝑖𝑛
= ℎ21 =𝑔𝑚 − 𝑗𝜔𝐶𝑔𝑑
𝑗𝜔(𝐶𝑔𝑠 + 𝐶𝑔𝑑)≈
≈𝑔𝑚
𝑖𝜔 𝐶𝑔𝑠 + 𝐶𝑔𝑑
Unit current gain |h21|=1
when w=2p*fT
𝑓𝑇 ≈𝑔𝑚
2𝜋 𝐶𝑔𝑠 + 𝐶𝑔𝑑10
510
100
20
40
60
80
100
120
140
160
Frequency (Hz)
Curr
ent G
ain
(dB
)
fT
Modern Electronics: F7 Basic Amplifiers II 13
Current Best High Frequency Transistors
• fT ~ 500-800 GHz
• MSG/U: These are power gain curves. fmax ~ 1 THz
• More about this in FFF115 High Speed Devices
Modern Electronics: F7 Basic Amplifiers II 14
Miller Approximation
• A feedback capacitance can be approximated
as a larger capacitance at the input.
• This is useful for simplifying calculations of the
imput impedance / approximate transfer
function
• Not accurate for output impedance!
Cgs
r0gmv1
+
-
vin
CgdRG
+
-
vout
+
-
v1Cgs
r0
gmv1+
-
vinCM
RG
+
-
vout
+
-
v1
Modern Electronics: F7 Basic Amplifiers II 15
Frequency Dependent Voltage Gain
Cgs
gmv1
+
-
vin
CgdRG
+
-
vout
+
-
v1RL
𝐾 = −𝑔𝑚𝑅𝐿
𝐴𝑣 𝜔 ≈ 𝐾1
1 −𝑗𝜔𝑝1
𝑝1 =−1
𝑅𝐺(𝐶𝑔𝑠 + 𝐶𝑔𝑑(1 + 𝑔𝑚𝑅𝐿))
105
1010
0
5
10
15
20
25
Frequency (Hz)
Voltage G
ain
(dB
)
w-3dB=|p1|
• High gm
• Small Cgs, Cgd!
• Depends on RL
Modern Electronics: F7 Basic Amplifiers II 16
670 GHz Common Source Amplifier
Input
CS Amplifiers
Output
5x Common Source
Stages
