EE105 – Fall 2014
Microelectronic Devices and Circuits
Prof. Ming C. Wu
wu@eecs.berkeley.edu
511 Sutardja Dai Hall (SDH)
1
Ideal vs Non-ideal Op Amps
Ideal Op Amp
A=∞
Rid = ∞
Ro = 0
Non-ideal Op Amp
A<∞
Rid < ∞
Ro > 0
Other non-ideal characteristics:
•  Finite common-mode rejection ratio
(CMRR)
•  Output voltage is not just proportional to
the difference input voltage but also their
absolute values
•  Common-mode input resistance
•  dc error sources (offset voltage, input
bias current, offset current)
•  Output voltage, slew rate, maximum
current limits
2
1
Classic Feedback Systems
vd = vi − v f
vo = Avd
v f = βv o
Av =
# T &
vo
A
1 # Aβ &
Ideal
=
= %
(= A %
(
vi 1+ Aβ β $ 1+ Aβ '€ v $1+ T '
•  A = transfer function of open
-loop
€ amplifier or open-loop
gain.
•  T = loop gain = Aβ
–  For negative feedback: T(s) > 0
–  For positive feedback: T(s) < 0
•  β = transfer function of
feedback network.
3
Gain Error and Fractional Gain Error
•  Gain Error:
–  GE = (ideal gain) - (actual gain)
•  For non-inverting amplifier,
1 1 $ T ') 1 $& 1 ')
GE = − &&
=
β β %1+T )( β &%1+T )(
•  Fractional or
€ percentage error:
1# 1 &
%
(
β $1+ T '
GE
1
1
FGE = Ideal =
=
≅
1
1+ T T
Av
β
€
for
T >> 1
4
2
Gain Error Example: Noninverting Amplifier
•  Problem: Find actual gain and gain error for an amplifier
•  Given data: Ideal closed-loop gain of 200 (46 dB), open-loop gain of
op amp is 10,000 (80 dB).
•  Approach: Amplifier is designed to give ideal gain and deviations
from ideal case are determined.
•  Note: R1 and R2 are not normally designed to compensate for finite
open-loop gain of amplifier.
•  Analysis:
" T %
Av = AvIdeal $
'
# 1+ T &
AvIdeal =
1
= 200
β
Note : FGE ≅
" 1 %
T = Aβ = 10 4 $
' = 50
# 200 &
" 50 %
200 −196
Av = 200$
FGE =
= 0.02
' = 196
200
#1+ 50 &
with
1 1
=
= 0.02
T 50
5
€
Gain of Noninverting Amplifier
vo = Avid = A ( vi − v1 ) = A ( vi − β vo )
vo
A
1 " Aβ % 1 " T %
=
= $
'
'= $
vi 1+ Aβ β # 1+ Aβ & β # 1+ T &
T = Aβ is called the loop gain
For T >> 1
1
R
Av → AvIdeal = = 1+ 2
β
R1
Av =
For i− = 0,
β=
€
R1
R1 + R2
vid = vi − v1 = vi − β vo
R1
v1 =
v = βvo
R1 + R2 o
T
v
vi = i
1+ T
1+ T
Although no longer zero, vid is small
vid = vi −
Feedback factor
for large loop gain T.
6
3
Output Resistance
(Both Noninverting and Inverting Amplifiers)
The output terminal is driven by test source
vx and current ix is calculated to determine
output resistance (all independent sources
are turned off). Note that the equivalent
circuit is same for both inverting and non
-inverting amplifiers.
Rout =
vx
ix
7
€
Output Resistance (cont’d)
Analysis :
ix = io + i2
io =
v x − Avid
Ro
and i2 =
vx
R2 + R1
Also, vid = −v1 and v1 =
R1
v = βvx
R2 + R1 x
1
i
1+ Aβ
1
= x =
+
Rout vx
Ro
R2 + R1
Rout =
Ro
( R + R1)
1+ T 2
Thus, shunt feedback reduces R out .
Typically, Ro (1 + T) << ( R2 + R1 ) and Rout ≅
Ro
.
1+ T
For infinite T, Rout = 0.
8
€
4
Nonideal Op Amps
Open-loop Gain: Design Example
•  Problem: Design non-inverting amplifier and find the
required open-loop gain
•  Given Data: Av = 35 dB, Rout ≤ 0.2 Ω, Ro = 250 Ω
•  Analysis:
35dB
AvIdeal = 10 20dB = 56.2
Ro
≤ 0.2 Ω
1+ Aβ
+
1( R
∴ A ≥ * o −1- |
β ) Rout ,
|
β=
1
Ideal
v
A
=
1
56.2
Rout =
( 250 +
A ≥ 56.2*
−1- = 7.02x10 4 or 96.9 dB
) 0.2 ,
€
9
Input Resistance of Noninverting Amplifier
Assuming i− << i2 gives i1 ≅ i2
v1 =
R1
vo = β vo
R1 + R2
v1 = β ( Avid ) = Aβ ( vx − v1 )
Aβ
T
vx =
vx
1+ Aβ
1+ T
T
vx −
vx
vx − v1
vx
1+
T
∴ ix =
=
=
Rid
Rid
Rid (1+ T )
Test voltage source vx is applied to
v1 =
input and current ix is calculated:
v −v
ix = x 1
| v1 = i1 R1 ≅ i2 R1
Rid
€
Rin = Rid (1+ T )
10
5
Gain of Inverting Amplifier
i1 =
vi − (−vid )
R1
i2 = i1
(−vid ) − vo
and
i2 =
and
vo = Avid
R2
After some algebra,
" T %
v " R % Aβ
Av = o = $ − 2 '
= AvIdeal $
'
# 1+ T &
vi # R1 & 1+ Aβ
Let i1 be the current going from
the input source through R1 and
with
i2 be the current going through R2
β=
R1
R1 + R2
into the amplifier output.
11
Input Resistance of Inverting Amplifier
Rin =
R1 removed
vx ix R1 + v−
v
=
= R1 + −
ix
ix
ix
i 1 = i− + i2 =
∴ G1 =
! R $
R
Rin = R1 + Rid || # 2 & ≅ R1 + 2
" 1+ A %
1+ A
For large A, Rin ≅ R1
v1 v1 − vo v1 v1 + Av1
+
=
+
Rid
R2
Rid
R2
i1
1 1+ T
=
+
v1 Rid
R2
12
6
Nonideal Amplifier Summary
Inverting and Noninverting Amplifier
β=
R1
R1 + R2
and T = Aβ
€
13
Feedback Amplifier Categories
Voltage Amplifiers - Series-Shunt Feedback
•  A voltage amplifier should have a high input resistance to
measure the desired voltage and a low output resistance to
drive the external load. To achieve the desired behavior, the
input ports of the amplifier and feedback network are
connected in series, and the output ports are connected in
parallel (shunt).
14
7
Feedback Amplifier Categories
Transresistance Amplifiers - Shunt-Shunt Feedback
•  A transresistance amplifier converts an input current to an
output voltage. Thus it should have a low input resistance
to sink the desired current and a low output resistance to
drive the external load. To achieve the desired behavior, the
input ports of the amplifier and feedback network are
connected in parallel (shunt), and the output ports are
connected in parallel (shunt).
15
Feedback Amplifier Categories
Current Amplifiers - Shunt-Series Feedback
•  A current amplifier should provide a low resistance current
sink at the input and a high resistance current source at its
output. The input ports of the amplifier and feedback
network are connected in parallel, and the output ports are
connected in series.
16
8
Feedback Amplifier Categories
Transconductance Amplifiers - Series-Series Feedback
•  The transconductance amplifier converts an input voltage to
an output current. This amplifier should have a high input
resistance and a high output resistance. The input ports
and the output ports of the amplifier and feedback networks
are connected in series.
17
Feedback Amplifier Category Summary
18
9