Bandwidth enhancement of multi-stage amplifiers using active ...

BANDWIDTH ENHANCEMENT OF MULTI-STAGE
AMPLIFIERS USING ACTIVE FEEDBACK
M. Reza Samadi, AydÕn ø. KarúÕlayan and Jose Silva-Martinez
Texas A&M University
Department of Electrical Engineering
College Station, TX, 77843-3128, Email: samadi@ee.tamu.edu
ABSTRACT
A new topology for wideband multistage amplifiers (MA) is
introduced. The proposed method uses active negative feedback
in a chain of amplifiers to extend the bandwidth and improve
gain-bandwidth product. The topology has several advantages
such as having capability of widening bandwidth as the number
of stage increases and enhancing bandwidth by several times that
of the dominant pole of each stage. To verify the performance of
topology, an 8-stage amplifier in 0.35µm CMOS was designed,
where more than 2.8GHz bandwidth and 40dB gain were
obtained from simulations.
1. INTRODUCTION
For both data amplification and clock distribution, multistage
amplifiers (MA) must have high gain and wide bandwidth with
frequency response ranging from DC to multi-gigahertz-band
frequencies. A conventional MA is composed of n cascaded
amplifier stages such that each stage is presented as a transfer
function of g j (s) with a DC gain of G. To simplify, let us assume
ω G
p
g ( s)
=
j
s + ω
Then the overall DC gain and the bandwidth of the MA are
obtained by [1]
n
G
T
= G
2 1 / n
≈ −
bw
ω p
1
p
(1)
ω (2)
Increasing n decreases ω bw , whereas enlarging the bandwidth of
each stage increases the overall bandwidth of MA. Several
techniques have been used to increase the speed of amplifiers
[2]-[7]. One of the methods to improve bandwidth is using local
feedback [2]-[4]. Some techniques, such as capacitance and
inductance peaking, enhance the bandwidth by placing a peak in
the transfer function at high frequencies (these will be referred as
peaking techniques). Active feedback [2]-[3] uses peaking
technique to improve the bandwidth of the amplifier by reducing
feedback at high frequencies. In previously reported methods [2]-
[7], extending the bandwidth of one stage broadens the overall
bandwidth of MA. However, the combination of the poles of all
stages degrades the overall bandwidth such that ω bw is always
less than the bandwidth of each stage.
A meaningful definition for performance of an n-stage MA is the
gain-bandwidth product of a single stage [8] (GBP 1 ), which can
be written as:
1
( Overall Gain ) × (3 dB )
GBP1 = n − bandwidth (3)
The GBP 1 and total GBP (GBP T ) for an n-stage conventional
MA, when all stages are designed as in Eq. (1), are obtained by
2 1/
n
GBP=
Gω 1
(4)
−
1 p
n
2 1/
n
GBPT
= G ω
p
−1
(5)
If the number of stages (n) is increased, GBP 1 in Equation (4) is
decreased. Consider an n-stage conventional MA with passive
negative feedback within each stage as illustrated in Figure 1.
Assume each stage has a feedback of F (frequency independent)
and each forward gain stage can be presented as Equation (1).
Using feedback, the dominant pole of each stage is ideally shifted
to (1+GF)ω p . The overall bandwidth of an n-stage MA with
passive feedback can be written as:
V i
+
-f 1(s)
1/ n
ω ≈ ω (1 + GF ) 2 −1
(6)
bw
p
Figure 1. n-stage conventional MA with passive local
feedback
The GBP 1 of Figure 1 is obtained by Equation (4) and GBP T can
be written as:
GBP
-f j(s)
+
+
g 1(s) g j(s) g n(s)
n
G
1/ n
ω 2 −1
n 1 p
(1 + GF)
= T
−
-f n(s)
Equations (6) and (7) show that increasing feedback for having a
wider bandwidth decreases GBP T proportional to 1/(1+G×F) n-1 .
This paper introduces a new topology to build a multi-stage
wideband amplifier. It uses a chain of amplifiers with active
feedback to expand the bandwidth, and offers several advantages
such as:
• Improved bandwidth by several times that of the dominant
pole of each stage.
• Being capable of increasing bandwidth as n increases.
• Increased GBP 1 by several times that of the conventional
MA.
V o
(7)

• Being capable of increasing overall gain-bandwidth product
in comparison with the MA with local passive feedback for
the same bandwidth.
To validate the proposed topology, an 8-stage MA in 0.35µm
CMOS process was designed and simulated. Section II presents
the new topology or chained-feedback multistage amplifier
(CMA). Circuit simulation results are presented in Section III.
Finally, summary of the results and outline of the work are given.
2. CHAINED FEEDBACK TOPOLOGY
Figure 2 shows the proposed n-stage CMA topology, where
active feedback is used between stages. The overall structure is
composed of n amplifier stages g 1 (s) ,…, g n (s) with active
feedback gains f 1 (s) ,…, f n (s). The outputs of forward gain stages,
g j (s), and feedback stages, -f j (s), are added together. For
simplicity, assume that the amplifier blocks in Figure 2 have a
single dominant pole and can be represented as in Equation (1)
and feedback gains can be given as
V i
g 1(s)
f
ω F
p
( s) =
(8)
j
s + ωp
-f 2(s)
-f j(s) -f n(s)
-f 1(s) -f j-1(s) -f n-1(s) 0
+ + +
g 2(s) g 3(s)
g j(s)
+ + +
g j+1(s) g n(s)
Figure 2. Scheme of an n-stage CMA
V o
H
ω
2 2
dc n1
n2
2
1 n1
n1
2 n2
n2
2
2 2
2
( s + ζ ω s + ω )( s + 2ζ
ω s + ω )
where ω n1 , ω n2 , ζ 1 , ζ 2 and an overall DC gain are
ω
(12)
ω
n1 = ω
p
1+
0. 38GF
ω
n2 =ω
p
1+
2. 62GF
(13)
−0.
5
−0.
5
ζ = ( 1+
0. GF) = ( 1+
2. GF) 1
38
ζ
2
62
(14)
4
( G )
( )
[ 1 + 3GF
GF ]
2
H dc
=
+
(15)
Since ω n s and ζs are different for both sections, each 2 nd -order
transfer function has a peak at different frequencies. Matlab
simulation of the transfer function of 4-stage CMA and two 2 nd -
order functions (@ F=1) for Gs of 2.3 and 6.1, respectively, are
illustrated in Figure 3. The peak of one of the 2 nd -order functions
is placed where the other 2 nd -order function is decreasing. For
small Gs, the –3dB frequency of CMA is determined by the –3dB
frequency of the first 2 nd -order function. Increasing DC gain of
forward stages (G) increases the ripple of the overall function
and pushes the –3dB frequency to higher frequencies and extends
the bandwidth. Increasing DC loop gain widens the bandwidth
up to the point where the first 2 nd -order function produces a peak
of more than 1.5dB.
AC Response
G=6.1
To explain how CMA uses the peaking technique to widen the
bandwidth, let us consider n=2, so that there is only feedback
from the second amplifier to the first one. This two-stage CMA
has a 2 nd -order transfer function given by
s
2
+
H
ω
2
dc n
2
2ζω
s + ω
n n
where the natural frequency, damping factor, DC gain and
bandwidth are given by
−0.
5
ω = ω 1 GF
ζ = ( 1 + GF ) (10)
n p
+
2
G
H dc
= 1+
GF
ω
bw
2
4 2
= ω 1−
2ζ
+ 4ζ
− 4ζ
+ 2
n
(9)
(11)
For the underdamped case (ζ1) ω bw can be
improved up to 2.69ω p , while the peak gain is less than 1.5dB
(for GF≤ 3.34). In fact, using feedback mostly decreases H dc
rather than increasing the bandwidth, i.e., GBP T decreases more
as the bandwidth is widened.
2.1 Bandwidth of CMA
Transfer function of a 4-stage CMA is a 4 th -order function. It can
be presented as a product of two 2 nd -order transfer functions as:
Overall transfer function
First 2 nd -order
Second 2 nd -order .-.-
Frequency/ ω p
G=2.3
Figure 3. Matlab plot of magnitude of two 2 nd -order
transfer functions and the overall function of 4-stage
CMA
-f 2(s)
-f 4(s)
-f 1(s) 0 -f 3(s)
0
(a)
V i + + + + V o
g 1(s) g 2(s) g 3(s) g 4(s)
V i
g 1(s)
-f 1(s)
-f 2(s)
+ + +
g 2(s) g 3(s)
-f 3(s)
+
g 4(s)
-f 4(s)
Figure 4. The schemes of a) cascaded two 2-stage
CMAs, b) 4-stage CMA
0
V o
(b)

To clarify how much the feedback between stages improves the
bandwidth of a 4-stage CMA, consider two 2-stage CMAs in
cascade form (see Figure 4). It can be intuitively seen that
cascade combination of two 2-stage CMAs has a bandwidth less
than the single 2-stage CMA. Also Figure 5 shows the Matlab
plots of the magnitude of transfer functions of a 4-stage CMA
and two cascaded 2-stage CMAs for different Gs and F=1.
Indeed, a 4-stage CMA has one extra feedback path from the
output of the third stage to the second stage. For G>2.3 in two
cascaded 2-stage CMAs, there is a peak (>1.5 dB). The
maximum bandwidth in two cascaded 2-stage CMAs is 1.96ω p
that is about 71% of the bandwidth of one 2-stage CMA. Not
only did not the maximum achievable bandwidth of 4-stage
CMA decrease, but also it can reach up to 2.9ω p without
incurring a significant peak in transfer function. In this case the
maximum bandwidth is 6.7 times of the bandwidth of a 4-stage
conventional MA.
Increasing G
AC Response
have high loop gains due to passive feedback, which limits the
expansion of the bandwidth.
The ratio of GBP T of CMA and conventional MA shows how
much GBP T is decreased. Unfortunately, GBP T of CMA in
comparison with that of the conventional MA is decreased (as n
and DC loop gain are increased this ratio decreases further).
However, GBP T of CMA in comparison with that of other
structures (such as Figure 1) is much better. A simulation of the
ratio of GBP T of an n-stage CMA and an n-stage conventional
MA with passive feedback for n=2, 4, 6 and 8 for different DC
gain loops is shown in Figure 7. As it shows, increasing DC loop
gain increases CMA’s GBP T . As n is increased, this ratio also
increases. Another parameter is the ratio of GBP 1 of CMA and a
similar conventional MA that shows how much the GBP 1 is
improved. This ratio is simulated in Figure 8. It shows that GBP 1
of an n-stage CMA can be several times of GBP 1 of an n-stage
conventional MA and the structure shown in Figure 1.
Bandwidth
ω -3dB=2.91ω p
G=6.1
ω -3dB=1.96ω p
G=2.3
Cascaded two 2-stage CMAs -----
4-stage CMA
Bandwidth(×ωp)
8-Stage x
6-Stage o
4-Stage *
2-Stage +
Frequency/ω p
Figure 5. Matlab plot of magnitude of transfer functions
of schemes in Figure 4 for different Gs and F=1.
The transfer function of the CMA for n=6 and 8 can also be
written as a product of 2nd-order transfer functions. Figure 6
shows the bandwidth of n-stage CMA extracted from the
magnitude response simulation result for different DC loop gains
(GF) for n=2, 4, 6, and 8. The n-stage CMA for odd ns has a real
pole (@ ω p ) which limits the expansion of bandwidth to some
extent. Figure 6 shows that the CMA has two advantages. First,
its bandwidth can be several times of ω p (the bandwidth of one
stage); whereas for n-stage conventional MA, ω bw is always less
than ω p . Second, CMA can have more bandwidth as n increases.
As shown above, 4-stage CMA has more bandwidth than 2-stage
CMA. On the contrary, 4-stage conventional MA has less
bandwidth than 2-stage conventional MA. The maximum
bandwidth that can be obtained for n=8 is 4.51ω p . As F
decreases, a higher G is needed to have the same bandwidth.
Although as n increases CMA can have more bandwidth, it also
needs more GF. Figure 6 shows that if GF is constant, smaller n
gives more bandwidth.
To evaluate the performance of a wideband MA topology,
several parameters can be calculated. One of them is the
bandwidth of MA. It can be proven that for the same number of
stages and the same GF, both structures of CMA and Figure 1
have almost the same bandwidth and comparable group delay
variation. In contrast to CMA, the topology in Figure 1 cannot
dB
DC Loop Gain (G×F)
Figure 6. Matlab plot of the bandwidth of 2, 4, 6 and 8-
stage CMA in ω p for different DC loop gains (GF)
⎛
GBP
⎞
⎜
T of CMA
20log
⎝ GBPT
of Conventional MAwith PassiveFeedBack⎠
DC Loop Gain (G×F)
8-Stage x
6-Stage o
4-Stage *
2-Stage +
Figure 7. Matlab plot of the ratio of GBP T of n-stage CMA
and conventional MA with passive feedback for n=2, 4, 6 and
8.

3. TOPOLOGY VALIDATION
The proposed topology was validated through simulation an 8-
stage CMA in 0.35µm CMOS. A simple circuit was used as
forward and feedback stages to be easily modeled as Equations
(1) and (8). CMA was combined with a buffer to drive 50Ω in
series with 1pF capacitor at 3V single power supply. The circuit
of two stages of CMA is shown in Figure 9. To increase the gain
of forward and feedback stages, R l =1.8kΩ was chosen, where M l
was used for gain boosting. The M f and M g paired transistors
(feedback and forward transistors, respectively) are matched, so
the Miller effect of C gd is partially canceled. Because of low-DCgain
stage (