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ELE 2110A Electronic Circuits
Week 9: Multivibrators,
MOSFET Amplifiers
ELE2110A © 2008
Lecture 09 - 1
Topics to cover …
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Multivibrators
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Single-stage MOSFET amplifiers
– Common-source amplifier
– Common-drain amplifier
– Common-gate amplifier
Reading Assignment:
Chap 14.1 - 14.5 of Jaeger and Blalock or
Chap 4.6 - 4.7 of Sedra & Smith
ELE2110A © 2008
Lecture 09 - 2
Multivibrators
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A multivibrator is used to implement simple two-state
systems such as oscillators, timers and flip-flops.
Three types:
– Astable – neither state is stable.
Applications: oscillator, etc.
– Monostable - one of the states is stable, but the other is not;
Applications: timer, etc.
– Bistable – it remains in either state indefinitely.
Applications: flip-flop, etc.
Reference: http://en.wikipedia.org/wiki/Multivibrator
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Lecture 09 - 3
Astable Multivibrator
Redrawn
Circuit in Experiment A4
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Consists of two amplifying devices cross-coupled by resistors and
capacitors.
Typically, R2 = R3, R1 = R4, C1 = C2 and R2 >> R1.
The circuit has two states
– State 1: VC1 LOW, VC1 HIGH, Q1 ON (saturation) and Q2 OFF.
– State 2: VC1 HIGH, VC2 LOW, Q1 OFF and Q2 ON (saturation).
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It continuously oscillates from one state to the other.
ELE2110A © 2008
Lecture 09 - 4
Basic Mode of Operational
State 1:
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VB1 charges up through R3 from below ground towards VCC.
When VB1 reaches VON (of VBE, ≈1V), Q1 turns on and pulls VC1 from
VCC to VCESat ≈ 0V.
Due to forward-bias of the BE junction of Q1, VB1 remains at 1V.
ELE2110A © 2008
Lecture 09 - 5
Basic Mode of Operational
1V Æ1V-VCC
VCC Æ 0V
VCC
State 1 (cont’d):
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As C1’s voltage cannot change instantaneously, VB2 drops by VCC.
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Lecture 09 - 6
Basic Mode of Operational
0V
1V
State 1 (cont’d):
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Q2 turns off and VC2 charges up through R4 to VCC (speed set by the
time constant R4C2).
VB2 charges up through R2 towards VCC (speed set by R2C1, which is
slower than the charging up speed of VC2).
ELE2110A © 2008
Lecture 09 - 7
Basic Mode of Operational
VCC Æ 0V
1V
State 2:
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When VB2 reaches VON, Q2 turns on and pulls VC2 from VCC to 0V.
VB2 remains at VON.
ELE2110A © 2008
Lecture 09 - 8
Basic Mode of Operational
1VÆ1V-VCC
VCC
VCC Æ 0V
1V
State 2 (cont’d):
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As C2’s voltage cannot change instantaneously, VB1 drops by VCC.
ELE2110A © 2008
Lecture 09 - 9
Basic Mode of Operational
0V
1V
State 2 (cont’d):
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Q1 turns off and VC1 charges up through R1 to VCC, at a rate set by
R1C1.
VB2 charges up through R3 towards VCC, at a rate set by R3C2, which
is slower.
ELE2110A © 2008
Lecture 09 - 10
Basic Mode of Operational
Back to state 1:
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When VB2 reaches Von, the circuit enters state 1 again, and the
process repeats.
ELE2110A © 2008
Lecture 09 - 11
Initial Power-Up
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When the circuit is first powered up, neither transistor is ON.
Parasitic capacitors between B and E of Q1 and Q2 are charged up
towards VCC through R2 and R3. Both VB1 and VB2 rise.
Inevitable slight asymmetries will mean that one of the transistors is
first to switch on. This will quickly put the circuit into one of the
above states, and oscillation will ensue.
ELE2110A © 2008
Lecture 09 - 12
Multivibrator Frequency
t=0
T/2
0V
v B1 = (VON − VCC ) + (2VCC − Von )(1 − e − t / R C )
3 2
≈ −VCC + 2VCC (1 − e −t / R C )
3 2
At t = T/2, vB1=VON:
ELE2110A © 2008
for VON << VCC
VON = −VCC + 2VCC (1 − e −T / 2 R3C2 )
Lecture 09 - 13
Multivibrator Frequency
VON = −VCC + 2VCC (1 − e −T / 2 R C )
3 2
∴VCC ≈ 2VCC (1 − e −T / 2 R C )
3 2
for VON << VCC
∴1 = 2(1 − e −T / 2 R C )
3 2
∴ e −T / 2 R C = 0.5
3 2
∴ e −T / 2 R3C2 = 0.5
T
∴−
= − ln 2
2 R3C 2
∴ T = 2(ln 2) R3C 2
or
1
f =
2(ln 2) R3C 2
ELE2110A © 2008
For the above component values,
f =1.53kHz.
Lecture 09 - 14
Supply Voltage Limit
VON − VCC
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When VB1 is negative, BE junction of Q1 is reverse-biased.
Suppose the breakdown voltage of this junction is Vbreak (positive).
then to avoid breakdown,
VON − VCC > −VBreak
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⇒ VCC < VON + VBreak
Lecture 09 - 15
Mono-stable Multivibrator
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Capacitive path between VC2 and VB1
removed.
Stable for one state (state 1 here)
– Q1 ON and Q2 OFF
– VC1 LOW, VC1 HIGH
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When VB2 is momentarily pulled to ground
by an external signal
– VC2 rises to VCC
– Q1 turns on
– VC1 pulled to 0V
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When the external signal goes high
–
–
–
–
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VB2 charges up to VCC through R2
After a certain time T, VB2=VON, Q2 turns on
VC2 pulled to 0V, Q1 turns off
Enters state 1 and remains there
Can be used as a timer
Lecture 09 - 16
Bi-stable Multivibrator
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VCC
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Vout
–
–
–
–
–
–
Vout
Q1
Q2
VB1
set
VB2
reset
Both capacitors removed
Stable for either state 1 or 2
Can be forced to either state by Set or
Reset signals
If Set is low,
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Q1 turns off
VC1 (Vout) and VB2 rises towards VCC
Q2 turns on
VC2 (/Vout) pulled to 0V
VB1 is latched to 0V
Circuit remains in state 2 until Reset is low
If Reset is low
– Similar operation
– Circuit remains in state 1 until Set is low
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ELE2110A © 2008
Behave as an RS flip-flop
Lecture 09 - 17
Topics to cover …
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Multivibrators
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Single-stage MOSFET amplifiers
– Common-source amplifier
– Common-drain amplifier
– Common-gate amplifier
ELE2110A © 2008
Lecture 09 - 18
Common-Source Amplifier
Input
Source
Output
Load
AC ground
AC Equivalent:
ELE2110A © 2008
Lecture 09 - 19
CS Amplifier With Source Resistor
Input
Output
Load
Source
AC ground
AC Equivalent
Also named Source Degenerated Common Source Amplifier
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Lecture 09 - 20
Common-Drain Amplifier/Source Follower
Input
AC ground
Output
RG = R1 || R2
Source
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Load
RL = R4 || R7
AC equivalent
Lecture 09 - 21
Common Gate Amplifier
Output
AC ground
Load
RL = R3 || R7
Source
AC equivalent
Input
ELE2110A © 2008
Lecture 09 - 22
Topics to cover …
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Multivibrators
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Single-stage MOSFET amplifiers
– Common-source amplifier
– Common-drain amplifier
– Common-gate amplifier
ELE2110A © 2008
Lecture 09 - 23
Common-Source Amplifier
nMOS small-signal model
R
L
= ro R R
D 3
AC Equivalents
ELE2110A © 2008
Lecture 09 - 24
Voltage Gain
Terminal voltage gain from gate and drain is:
v
v
Avt = v d = v o = − g m R
L
g
gs
Overall voltage gain from source vi to vo:
⎛v
v gs ⎞⎟
⎜ gs
⎟= A
vt ⎜⎜ v
v ⎟
i ⎠
i
⎝
⎡
⎤
R
⎢
⎥
G
⎢
⎥
∴ Av = − g m R ⎢
L ⎢ R + R ⎥⎥
⎢⎣
I
G ⎥⎦
v o ⎛⎜ v o
Av = v = ⎜ v
i ⎜⎝ gs
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⎞⎛
⎟⎜
⎟⎜
⎟⎜
⎠⎝
⎞
⎟
⎟
⎟
⎠
Lecture 09 - 25
Input Resistances
Rin2
v x = ix R
G
R =R
G
in
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Input resistance (Rin2)
looking into the gate
terminal is infinite.
Input resistance (Rin)
looking into the
Lecture 09 - 26
coupling capacitor
Output Resistance
vgs=0.
Output resistance looking into the
output coupling capacitor:
R
ELE2110A © 2008
out
=
v
x =R r ≅R
D o
D
i
x
As ro>> RD.
Lecture 09 - 27
C-S Amplifier With Source Resistor
AC Equivalents
ELE2110A © 2008
Lecture 09 - 28
Terminal Voltage Gain
Terminal voltage gain:
id = g m v gs
v gs = v g − id RS
id = g m (v g − id RS ) ⇒ id =
vo = −id RL ⇒ AvtCS ≡
g mvg
1 + g m RS
vo
g R
=− m L
vg
1 + g m RS
Voltage gain is less sensitive to
gm after adding RS.
Note: body effect and ro have been ignored.
ELE2110A © 2008
Lecture 09 - 29
Input Signal Range
Q id =
g mvg
1 + g m RS
v gs = v g − id RS = v g −
∴ v gs =
g m RS v g
1 + g m RS
vg
1 + g m RS
Input signal range: magnitude of vgs must be less than 0.2(VGS - VTN)
v gs =
vg
≤ 0.2(V −V )
GS TN
1+ g m R
S
vg ≤ 0.2(V −V )(1+ gm R )
S
GS TN
Presence of RS increases input range.
ELE2110A © 2008
Lecture 09 - 30
Rin and Overall voltage gain
Input resistance looking into the gate terminal:
CS = ∞
Rin
Overall voltage gain:
⎡
⎢
⎢
⎢
⎢
⎢⎣
⎤
R
⎥
CS
CS
G
⎥
Av = Avt
R + R ⎥⎥
I
G ⎥⎦
ELE2110A © 2008
Lecture 09 - 31
Output Resistance
+
vgs
-
gmvgs
ro
vd
id
RS
Include ro in the model
Output resistance:
vs = id RS
vd = vs + ro [id − g m (−vs )]
vd = id RS + ro (id + g mid RS )
vd
= RS + ro + ro g m RS ≅ ro (1 + g m RS )
id
for RS << ro
CS = r ⎛⎜1+ g R ⎞⎟
∴Rout
o ⎜⎝
m S ⎟⎠
ELE2110A © 2008
Lecture 09 - 32
Summary of Common Source Amplifier
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Large and Inverting voltage gain
Infinite input resistance looking into the Gate terminal
Large output resistance
Input signal voltage range depends on source resistance
Suitable for internal voltage gain stage
– Need a voltage buffer to drive low load resistance.
ELE2110A © 2008
Lecture 09 - 33
Topics to cover …
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MOSFET circuits DC analysis
Building small signal model for MOSFET
Single-stage MOSFET amplifiers
– Common-source amplifier
– Common-drain amplifier
– Common-gate amplifier
ELE2110A © 2008
Lecture 09 - 34
CD Amplifier / Source Follower
AC equivalent:
RG = R1 || R2
RL = R4 || R7
nMOS small-signal model
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Lecture 09 - 35
Small Signal Analysis
Input resistance looking into Gate:
=∞
RCD
in
Overall voltage gain:
vo = g m (v g − vo ) RL
Terminal voltage gain:
gm R
vo
CD
L
∴ Avt = = +
vg
1+ g m R
L
For most cases, gmRL>>1 , terminal
voltage gain is close to 1. Hence the
name source follower.
ELE2110A © 2008
⎡
⎢
⎢
⎢
⎢
⎣⎢
⎤
R
⎥
CD = CD
G
⎥
Av
Avt
⎥
R +R ⎥
I
G ⎦⎥
Input signal range:
v gs =
vg
≤ 0.2(V −V )
GS TN
1+ g m R
L
vg ≤ 0.2(V −V )(1+ gm R )
L
GS TN
Lecture 09 - 36
Output Resistance
(ignore the ro)
ix
Output resistance:
ix = − g m v gs = − g m (−v x ) = g m v x
Rout
vx
1
= =
ix g m
Note: in the analysis for CD amplifier the body effect has be ignored.
More accurate analysis should include the body effect.
ELE2110A © 2008
Lecture 09 - 37
Summary of Source Follower
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Unity voltage gain
Infinite input resistance (excluding the bias resistors)
Low output resistance (=1/Gm)
Large input signal voltage range
Suitable for voltage buffer
ELE2110A © 2008
Lecture 09 - 38
Topics to cover …
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z
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MOSFET circuits DC analysis
Building small signal model for MOSFET
Single-stage MOSFET amplifiers
– Common-source amplifier
– Common-drain amplifier
– Common-gate amplifier
ELE2110A © 2008
Lecture 09 - 39
Common Gate Amplifier
RL = R3 || R7
AC equivalent
nMOS small-signal model
ELE2110A © 2008
Lecture 09 - 40
Small Signal Analysis
Input resistance looking into Source:
1
=
RCG
(same as the Rout of CD)
in
gm
Overall voltage gain:
Terminal voltage gain:
vo = − g m v gs RL
= − g m RL (−vs )
ACG
vt = + gm RL
The gain is non-inverting
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⎤
CG
⎥
R R
vg
v
v
⎥
in
CG
4
= ACG
⎥
Av = o = o
vt
⎞⎥
⎛
vg v
v
R + ⎜⎜ R R CG ⎟⎟ ⎥
i
i
I ⎝ 4 in ⎠ ⎥⎦
⎛
⎞
⎜
⎟
R
gm R
⎜
4 ⎟⎟
L
=
⎜
1+ g m ( R R ) ⎜⎜ R + R ⎟⎟
4⎠
I 4 ⎝ I
⎛
⎜
⎜
⎜
⎜
⎜
⎝
For RI >> R4,
⎞⎛
⎟⎜
⎟⎜
⎟⎜
⎟⎜
⎟⎜
⎠⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎠
CG
Av ≅
⎡
⎢
⎢
⎢
⎢
⎢
⎢⎣
gm R
L
1+ g m R
I
Lecture 09 - 41
Input Signal Range
Input signal range:
− v gs =
≅
R4 || (1 / g m )
vi
RI + R4 || (1 / g m )
1/ gm
vi
RI + 1 / g m
for 1/gm >> R4
1
=
vi
1 + g m RI
v ≤ 0.2(V −V )(1+ gm R )
i
I
GS TN
Relative size of gm and RI determine signal-handling limits.
ELE2110A © 2008
Lecture 09 - 42
Output Resistance
Output resistance:
ix = g m v gs = g m (− Rthix )
ix = 0 and thus Rout = ∞
Rth = RI || R4
Including the ro in the transistor,
ix = g m (−vs ) + (v x − vs ) / ro
= −vs ( g m + 1 / ro ) + v x / ro
vs = Rthix
Rout ≡
vx
= ro (1 + Rth ( g m + 1 / ro ) )
ix
≅ ro (1 + g m Rth )
ELE2110A © 2008
Lecture 09 - 43
Current Gains
Terminal current gain:
Since ID=IS, the terminal current is unity.
Overall current gain:
R4
AI =
≅1
R4 + 1 / g m
ELE2110A © 2008
Lecture 09 - 44
Summary of Common Gate Amplifier
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Unity Current Gain
Large Non-inverting voltage gain
Low input resistance (=1/Gm)
Large output resistance
Input voltage range depends on gmRI
Suitable for current buffer
ELE2110A © 2008
Lecture 09 - 45