EE105 – Fall 2014
Microelectronic Devices and Circuits
Prof. Ming C. Wu
wu@eecs.berkeley.edu
511 Sutardja Dai Hall (SDH)
Lecture 5: Op Amp Frequency Response
1
Op Amp Frequency Response
Single-pole Amplifiers
General purpose op amps are typically
low-pass amplifiers with high gain at
dc and a single-pole frequency
response.
Av ( s ) =
Aoω B
ωT
=
s + ωB s + ωB
A ( jω ) =
Aoω B
2
ω +ω
2
B
=
Ao
1+
ω2
ω B2
ωB = open loop bandwidth of the op
amp. ωT = unity gain frequency or gain
bandwidth product (frequency at
which magnitude of gain is unity).
Lecture 5: Op Amp Frequency Response
2
1
Op Amp Frequency Response
Single-pole Amplifiers (cont.)
For ω >> ω B ,
and
A ( jω ) =
Aoω B ωT
=
ω
ω
A ( jω ) ⋅ ω = ωT
For ω = ωT ,
A ( jω ) =
ωT
=1
ωT
For ω >> ωB, the product of
magnitude of amplifier gain
and frequency is a constant
value equal to the unity-gain
frequency.
Hence, ωT is also called the
gain-bandwidth product.
Lecture 5: Op Amp Frequency Response
3
Op Amp Frequency Response
Single-Pole Amplifier Example
Single-pole amplifier response:
Aω
ωT
Av ( s ) = o B =
s + ωB s + ωB
80dB
Ao = 10 20dB = 10 4
ω B = 10 3 rad/s
ωT = Aoω B = 10 7 rad/s
10 7
s +10 3
Frequency values are often expressed in Hz:
Av ( s ) =
•
Problem:
Find transfer function describing
frequency-dependent amplifier
voltage gain.
Lecture 5: Op Amp Frequency Response
fB =
ωB
= 159 Hz
2π
fT =
ωT
= 1.59 MHz
2π
4
2
Frequency Response of Noninverting
Amplifier
For a closed-loop feedback amplifier:
Av ( s ) =
A ( s)
Aoω B
=
1+ A ( s ) β s + ω B (1+ Ao β )
Ao
A (0)
1+ Ao β
Av ( s ) =
= v
s
s
+1
+1
ω B (1+ Ao β )
ωH
ω H = (1+ Ao β )ω B =
ωT
Av ( 0 )
At low frequencies, gain is set by
the feedback, but at high
frequencies, it follows the gain of
the amplifier.
For Ao β >> 1,
1
Av ( 0 ) ≅
and ω H ≅ βωT
β
Lecture 5: Op Amp Frequency Response
5
Frequency Response of Noninverting
Amplifier
•  Given data: Ao= 105 = 100 dB, fT = 10 MHz, desired Av = 1000 or 60 dB
•  Assumptions: Amplifier is described by a single-pole transfer function.
•  Analysis:
fT 10 7 Hz
=
= 100 Hz
Ao
10 5
!
! 10 5 $
A $
fH = fB (1+ Ao β ) = fB ##1+ o && = 100 #1+ 3 & = 10.1 kHz
" 10 %
" Av ( 0 ) %
fB =
Op amp transfer function: Av ( s ) =
ωT
2x10 7 π
=
s + ω B s + 200π
Close-loop amplifier transfer function: Av ( s ) =
Lecture 5: Op Amp Frequency Response
ωT
2x10 7 π
=
s + ω B (1+ Ao β ) s + 2.01x10 4 π
6
3
Frequency Response of Inverting Amplifier
" R %
A ( s) β
T
Av ( s ) = AvIdeal
= AvIdeal
= $− 2 '
1+ T
1+ A ( s ) β # R1 &
Ao β
1+ Ao β
s
+1
(1+ Ao β )ω B
For Ao β >> 1,
" R % 1
Av ( s ) ≅ $ − 2 '
# R1 & s +1
ωH
ωH =
Lecture 5: Op Amp Frequency Response
ωT
≅ βωT
Ao
1+ Ao β
7
Frequency Response of Inverting Amplifier
•  Given data: Ao = 2x105, fT = 5x105 Hz, desired Av = -100 or 40 dB
•  Assumptions: Amplifier is described by a single-pole transfer
function.
•  Analysis:
fB =
fT 5x10 5 Hz
=
= 2.5 Hz
Ao
2x10 5
β=
1
1
=
1+ Av ( 0 ) 101
! 2x10 5 $
fH = fB (1+ Ao β ) = 2.5Hz #1+
& = 4.95 kHz
101 %
"
ωT
10 6 π
=
s + ω B s + 5π
Inverting amplifier transfer function:
Op amp transfer function: Av ( s ) =
Av ( s ) = Av ( 0 )
βωT
9.9x10 5 π
=−
s + ω B (1+ Ao β )
s + 9.91x10 3 π
Lecture 5: Op Amp Frequency Response
8
4
Op Amp Frequency Response Summary
Lecture 5: Op Amp Frequency Response
9
Feedback Control of Frequency Response
Av ( s ) = Ao
ωH s
s 2 + !"ω L + (1+ Ao β )ω H #$ s + ω Lω H
ω H (1+ Ao β ) >> ω L :
For
ω LF ≅
ωL
1+ Ao β
ω HF ≅ ω H (1+ Ao β )
BWF ≅ ω H (1+ Ao β )
Av ( s ) =
Upper and lower cutoff frequencies
as well as bandwidth of amplifier
are improved, gain is stabilized at
A ( s)
1+ A ( s ) β
where A ( s ) = Ao
s
Aoω H s
=
!
s $ (s + ω L ) (s + ω H )
( s + ω L ) #1+ &
" ωH %
Lecture 5: Op Amp Frequency Response
Amid =
Ao
1+ Ao β
GBW = Amid ⋅ BWF = Aoω H
10
5
Large Signal Limitations
Slew Rate and Full-Power Bandwidth
•  Slew rate: Maximum rate of
change of voltage at the output
of an op amp. Typical values
range from 0.1V/µs to 10V/µs.
vO = VM sin ω t
dvO
dt
= VM ω ⋅ cosω t max = VM ω
max
For no signal distortion,
VM ω ≤ SR
•  For given frequency, slew rate
limits the maximum signal
amplitude that can be amplified
without distortion.
Lecture 5: Op Amp Frequency Response
→ VM ≤
SR
ω
Full-power bandwidth is
highest frequency at which a
full-scale signal can be
developed.
fM ≤
SR
2π VFS
11
Operational Amplifier
Macro Model for Frequency Response
•  Simplified circuit representations are available in most simulators
to model the terminal behavior of op amps that include all nonideal
limitations of op amps and a large number of parameters that can
be adjusted to model op amp behavior.
•  To model a single-pole roll-off, an auxiliary “dummy” loop (voltage
controlled voltage source v1 in series with R and C) is added to the
original two-port model.
Vo ( s ) Aoω B
Ao
1
=
=
ωB =
s
V1 ( s ) s + ω B
RC
+1
ωB
•  The RC product is chosen to give the desired -3dB point for the
open-loop amplifier.
Av ( s ) =
Lecture 5: Op Amp Frequency Response
12
6
General Purpose Op Amp Parameters
Sample Values
Note the fourpole frequency
response
Lecture 5: Op Amp Frequency Response
13
7