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1770 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 9, SEPTEMBER 2010
Current-Mode, WCDMA Channel Filter With
In-Band Noise Shaping
Alberto Pirola, Student Member, IEEE, Antonio Liscidini, Member, IEEE, and Rinaldo Castello, Fellow, IEEE
Abstract—A novel class of filters (called pipe filters) that fea-
tures in-band noise reduction is presented and a current mode bi-
quad cell based on cross-connected cascoded devices is introduced.
The presented solution gives in-band high-pass noise shaping and
passive pre-filtering of out-of-band blockers. This results in both
low in-band noise and high out-of-band IIP3. A 4th-order low-
pass prototype in 90 nm CMOS for WCDMA application features
32 V in-band noise (when integrated over the 2 MHz bandwidth
as defined by the standard) and 36 dBm out-of-band IIP3 which
results in a 75 dB SFDR with 1.25 mW power consumption. Active
die area is 0.5 mm .
Index Terms—Continuous time filters, current filter, gm-C, high
linearity, low noise, noise shaping, pipe filters, WCDMA.
I. INTRODUCTION
THE main goal of a wireless receiver is the detection of a
low power signal among strong interferers present across
the spectrum. Such an operation requires filtering out-of-band
unwanted signals without deteriorating the desired signal
present in the band of interest. This results in a very challenging
spurious-free dynamic range (SFDR) requirement for the
channel-select filter that has to manage at the same time a small
signal and high level blockers. The core of a filter design is to
take advantage of the noise–power–area and linearity trade-off
to achieve the best match between the filter performance and
the system requirements [1].
The amount of noise introduced by standard filters is pro-
portional to kT/C and is concentrated in the filter passband,
for this reason, once the noise filter floor is set, the amount
of capacitance is roughly defined and, with it, a minimum in
terms of area and power consumption [2]. The presence of a
lower bound in the achievable in-band noise forces to have a
minimum amount of gain (to be achieved with a sufficient lin-
earity) before the filtering. This results in an increment of the
power consumption not only for the filter, but also for the pre-
ceding stage, that performs the linear amplification. The solu-
tion presented in this paper aims to break these trade-offs by
inserting an in-band zero in the transfer function for the input
noise sources. This shapes the noise spectrum allowing to re-
duce the filter noise floor without increasing power consumption
Manuscript received March 11, 2010; revised June 17, 2010; accepted June
21, 2010. Date of current version August 25, 2010. This paper was approved
by Associate Editor Andreas Kaiser. This work was supported by the Italian
National Program FIRB under Contract RBAP06L4S5.
The authors are with the Dipartimento di Elettronica, Università degli Studi
di Pavia, 27100 Pavia, Italy (e-mail: alberto.pirola@unipv.it; antonio.lisci-
dini@unipv.it; rinaldo.castello@unipv.it).
Digital Object Identifier 10.1109/JSSC.2010.2056831
and capacitance [3]. The concept of noise shaping was intro-
duced for the first time by Tekin et al. [4] where a frequency-de-
pendent negative resistance (FDNR) based active RC low-pass
filter implementing such a behavior was presented. However at
that time no experimental verification to prove its practical via-
bility was provided. The first integrated prototype implementing
a noise shaping filter that includes also a complete set of exper-
imental measurements on both its noise and linearity was re-
ported in [3] and it is the base for the present paper that fur-
ther expands that original contribution. This last design real-
izes a gyrator-based low-pass filter implemented using gm-C
techniques. Subsequently, a prototype implementing the FDNR-
based design was also reported by the same authors [5]. In ad-
dition to in-band noise shaping, both the above structures filter
a large amount of the out-of-band interferers before they enter
the active devices, with a benefit on the SFDR.
The paper is structured as follows. In Section II, the concept
of pipe filter is introduced and a first-order pipe filter topology is
analyzed in terms of noise and linearity. A current biquad cell,
based on the pipe filter concept, is proposed in Section III and
analyzed in Section IV in further details. The design of the 4th-
order WCDMA filter prototype is discussed in Section V and a
complete set of experimental measurements is finally reported
in Section VI.
II. PIPE FILTER
The current driven gm-C circuit shown in Fig. 1 implements
a first-order low-pass filter (with a single real pole located at
, assuming ). The key feature of this
filter is the fact of producing a high-pass shaped output current
noise spectrum due to the presence of an in-band zero
in the transfer function from the transistor noise source to the
output (Fig. 1). This behavior can be explained considering that,
at very low frequencies, capacitance C is a high impedance,
which forces the noise to re-circulate inside the transistor. On
the contrary, at high frequencies, when the capacitance becomes
a low impedance, all the current noise can flow to the output.
More generally, the impedance associated with input current
source creates an in-band degeneration for the transistor that
minimizes noise and increases linearity, as it will be seen later.
An interesting way to describe this low-pass current filter is
to consider it as a “pipeline” in which current is flowing and
where a signal attenuation (frequency dependent) corresponds
to a current loss through a leakage. Under this model, in the
passband, the filter works as a lossless pipe where the input cur-
rent is equal to the output one and thus no noise or distortion
can be added to it [Fig. 2(a)]. On the contrary, in the stop band,
the current leakage allows both noise and distortion component
0018-9200/$26.00 © 2010 IEEE
PIROLA et al.: CURRENT-MODE, WCDMA CHANNEL FILTER WITH IN-BAND NOISE SHAPING 1771
Fig. 1. First-order LP pipe filter.
Fig. 2. Pipe filters: noise behavior.
to enter the pipe and reach the output. This occurs for example
for the noise produced by the transistor when the capacitor is no
more an open circuit [Fig. 2(b)]. In general, any kind of opera-
tion performed on the current that flows in the pipe can perturb
the signal and introduce noise. An example is signal amplifica-
tion that is obtained by injecting in the pipe an extra current pro-
portional to the input current. For this reason, to ensure (at least
ideally) that no noise is introduced in the passband, such kind
of filter must have a unitary input to output transfer function. In
practice this condition can never be perfectly satisfied due to the
finite impedance associated with the signal source and with the
bias circuitry (e.g., , and in Fig. 1).
A. High-Pass Noise Shaping
The noise spectral density produced by the transistor at the
filter output is equal to
(1)
where is the gamma coefficient of the FET thermal noise
model. As expected, this expression displays a high-pass shape.
However, due to the finite driving impedance , the zero in
the noise transfer function is no located at DC but it is moved at
.
The effect of the finite driver impedance is the introduction
of an additional in-band loss that lets some extra noise to come
out also in the passband. To better understand the impact of the
zero on the total filter output noise, (1) can be rewritten as
(2)
where the total output noise is given by the sum of two terms:
one still proportional to and high-pass shaped, plus one in-
versely proportional to which does not take any advantages
from the zero introduced. The presence of a term inversely pro-
portional to sets a lower bound on the transconductance that
can be used to synthesized the filter for a given total integrated
output noise. In particular, integrating (2) in the filter passband
(i.e., from 0 to ) the second term exceeds the first one for
.
1772 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 9, SEPTEMBER 2010
In Appendix I it is shown that for the ideal case in which
the zero is located at DC, this approach increases the in-band
signal-to-noise ratio (SNR) by at least 5.6 dB compared to a
classic first-order LP filter without noise shaping.
B. Intermodulation Distortion Mechanisms
Due to the same reason that produces an in-band noise
shaping, no intermodulation product (IM) can be generated
in the filter passband as long as the output current is equal
to the input one (lossless-pipe). Notice that this is valid inde-
pendently of the location of the interferers with respect to the
filter passband. This mechanism can be verified evaluating the
in-band third order intermodulation product (IM3) generated
at (with located in the passband) by two tones
located out of the filter passband at and at .
Using Volterra’s series approach ([6], [7]) and assuming for
the transistor characteristic a Taylor expansion with as the
th order coefficients, the power of the intermodulation term
is given by
(3)
where and are two current rms values of the two inter-
ferers at and while is a factor which
depends only on the relative position between the first inter-
ferer and the filter pole.1Equation (3) displays the same zero at
as in the noise transfer function (1), showing that
noise and linearity are improved according to the same mecha-
nism. The amount of in-band intermodulation given by (3) and
that obtained using simulations are plotted in Fig. 3(a), as a func-
tion of (normalized to ), in the range between 0 and .
As can be seen, a good agreement is obtained over the entire fre-
quency range considered.
In addition to the “pipe” effect, the presence of the capac-
itor at the input of the stage is key to ensure a high linearity in
the presence of far out-of band blockers since it filters out the
input interferers before entering the nonlinear device. In par-
ticular, this effect is related to the capability of the interferers
to modulate the gate-source voltage of the input transistor (i.e.,
the nonlinear device). The magnitude of this effect can be esti-
mated calculating the IM3 at a fixed in-band frequency as
a function of the first blockers position . Choosing for sim-
plicity Hz (i.e., IM3 product falling at DC) it follows
that
(4)
The amount of IM3 obtained using (4) is plotted in Fig. 3(b)
versus (also in this case normalized to ). For ,
(4) can be approximated by the following expression:
(5)
where the IM3 product decreases as .
1For , , and the factor equal to
.
Fig. 3. First-order filter IM3 (a) versus , (b) versus ( ,
, , , and
). Formulas (line) and simulation (dots).
The above behavior confirms the intuition, i.e., thanks to the
filtering action provided by the input capacitance, the IM3 de-
creases rapidly when the two interferers are moved further away
from the cut-off frequency . When the interferers fall in the
passband the gate-source voltage swing is constant and with it
the IM3. This is consistent with the fact that in this region the
impedance at the input of the filter does not vary with frequency.
The presence of a passive blocker attenuation in front of the
filter is not common to other filter topologies. For example, in
standard op-amp RC structures, the current signal injected in the
virtual ground is not filtered (as opposed to the voltage output).
This forces the operational amplifier to sink or source the same
amount of current independently of the position in frequency of
the interferer signal with respect to the filter band edge.
III. BIQUAD PIPE FILTER CELL
High-order filters need both real and conjugate poles. The
latter cannot be created by simply cascading two of the struc-
ture reported in Fig. 1. For a given input current signal, a pair of
complex poles can be realized through the RLC network shown
in Fig. 4(a). In this case the current flowing out from the in-
ductor has a second order low-pass characteristic with a cut-off
frequency equal to the L-C resonance frequency and a quality
PIROLA et al.: CURRENT-MODE, WCDMA CHANNEL FILTER WITH IN-BAND NOISE SHAPING 1773
Fig. 4. Current biquad cell.
factor set by the shunt resistance . Integrated inductors are
generally avoided in baseband filters due to the unfeasible value
of the inductances required at such frequencies. For this reason,
active circuits with an inductive frequency behavior are used
(e.g., the gyrator [8]).
A. Active Inductor
In the proposed biquad cell reported in Fig. 4(b), the active
inductor is realized through the network formed by transistors
M1–M2 and capacitor C2. At DC, the feedback closed around
M1 forces the input small signal voltage at the source of M1 to
be equal to the difference between the gate-source small signal
voltages of M1 and M2, producing (with the use of two iden-
tical transistors) a virtual short between the input and the gate
of M2. Moving from DC toward higher frequency, the presence
of capacitance C2 reduces the amount of feedback around M1
and the input impedance rises as in an inductor. Computing the
impedance value of versus frequency under the assumption
of , the following result is obtained:
(6)
This behavior corresponds to that of an inductance
placed in shunt with a resistance . The circuit has
literally “gyrated” the impedance obtaining at its input
an inductance of value . It can be proved that, in the same
way, an inductance connected at the source of M2 would be
transformed into a capacitance at the input node.
B. Complex Poles
Thanks to its ability to implement an active inductor, the
structure of Fig. 4(b) realizes a second-order low-pass filter with
the following transfer function:
(7)
where is the transconductance of M1 and M2. The cell has an
in-band current gain equal to 1, therefore it is acting as a lossless
pipe where no additional current is injected into the signal path.
The frequency of the conjugates poles and their quality factor
are given by
(8)
Having chosen the same for the two transistors, the biquad
cut-off frequency depends only on and on the product of
the capacitances, while the quality factor depends only on the
ratio. While the filter transfer function has a low-pass
shape, the input impedance of the filter corresponds to that of
an LCR shunt resonator and is given by
(9)
The bandpass shape of the input impedance gives a very low
impedance (ideally zero) close to DC (due to the presence of
the active inductor) and at extremely high frequencies (due to
the capacitance C1). The maximum of the input impedance is
located at and corresponds to (i.e., the shunt loss re-
sistance of the active inductor).
IV. BIQUAD SPURIOUS-FREE DYNAMIC RANGE
The SFDR of the solution proposed in Fig. 4(b) was computed
valuating the total noise produced by the cell and the amount of
distortion generated in the filter passband by a couple of inter-
ferers located far away from the channel bandwidth. The sources
of noise considered were those associated with transistors M1
and M2 and the bias current generator and while
the distortion was evaluated assuming that the only nonlinear
elements are transistors M1 and M2.
1774 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 9, SEPTEMBER 2010
Fig. 5. Biquad cell noise transfer functions.
A. Noise
Under the assumption of white noise sources and a finite
driving resistance , the transfer functions from the
noise sources associated to transistors M1 and M2 to the output
are given by
(10)
(11)
where and are given by (8) and . Both noise
transfer functions displays a zero in the filter passband: the po-
sition of these two zero is different for the two transfer functions
being a function of for M1 and located in dc for M2.
Fig. 5 shows all noise transfer functions for the biquad cell,
providing a comparison between theory and simulations. The
main difference between the biquad and the first-order filter in
the transfer function for the noise of M1 is the presence in (10)
of two complex poles and one zero that produces a passband
characteristic instead of a high-pass one. This is explained by
the fact that the second capacitor C2 filters not only the signal
but also the noise injected by M1. On the other hand, a pure
high-pass transfer function is present for the noise of M2, since
at frequency higher than the poles, capacitor C2 becomes a short
and all the noise injected by M2 can flow to the output.
The noise associated with is injected at the input and
thus is processed as the input signal (i.e., without experiencing
any attenuation in the filter passband) while the transfer func-
tion of is flat in frequency since this noise is injected at
the output of the cell. In general, these latter contributions are
proportional to the transconductance of the transistors used to
synthesize the current generators.
The shape of the whole output noise spectrum is qualitatively
shown in Fig. 6. At low frequencies the main contributors are
Fig. 6. Output noise summary.
the bias generators where noise is not directly related to the
filter poles. On the contrary, moving toward the filter cut-off fre-
quency, the noise contributed by M1 and M2 increases reaching
its maximum at where their noise spectral density is close
to the one of classical filter topologies. Beyond the filter cut-off
frequency, the only noise components that are not filtered out
are those due to M2 and to the upper bias current generator. This
out-of-band noise, as it will be explained in Section V, must be
carefully considered because it can be folded in band when the
signal is sampled at the end of the analog receiver chain, typi-
cally by an ADC.
B. Intermodulation Phenomena
As seen in Section II, the pipe filters allow to obtain high lin-
earity taking advantage of two different mechanisms. The first is
PIROLA et al.: CURRENT-MODE, WCDMA CHANNEL FILTER WITH IN-BAND NOISE SHAPING 1775
Fig. 7. Biquad cell stage IM3 (a) versus , (b) versus ( ,
, , , ,
and ). Formulas (line) and simulation with
and without finite transistor output resistance (square and dots, respectively).
the same mechanism that produces the in-band high-pass noise
shaping while the second is the filtering action provided by the
input capacitance. As it was done for the first-order filter, these
two effects were studied also for the biquad cell, evaluating the
IM3 generated by two out-of band blockers and for two
different scenarios. In the first, the frequency of the intermod-
ulation product is made to vary within the passband by
placing at and at . In the second, intermod-
ulation product is made to always fall at DC placing
at and at , while is made to vary. Contrary to the
first-order filter, where the transistor output resistance is in shunt
with the transconductance and thus its impact on linearity is neg-
ligible, in this case the finite output resistance (not considered in
the Volterra’s analysis) affects the linearity of the cell by modi-
fying the behavior of the feedback loop used to realize the active
inductor. For this reason in Fig. 7, simulations with output resis-
tance were also reported. Analyzing the case in which the IM3
product is made to vary across the band [Fig. 7(a)], it can be seen
that in the frequency range for which the virtual ground pro-
vides a very low impedance almost all the input current flows to-
wards the output and low distortion is produced. This behavior is
equivalent to the one of the first-order filter reported in Fig. 3(a).
In Fig. 7(b), the IM3 is plotted as a function of the first blocker
position showing a passband behavior. As in the first-order
topology (Section II), the IM3 frequency behavior follows the
input impedance profile given by (9): rising up with frequency in
the filter passband (inductive behavior), and decreasing with fre-
quency out-of-band (capacitive behavior). The worst distortion
occurs at the corner frequency, where the input impedance and
the modulation across the input transistor reach their maxima.
C. Hard Distortions
To fully characterize the linearity of the biquad cell, also hard
distortions have to be analyzed. These nonlinearities can influ-
ence the 1 dB compression point of the cell and occur when the
signal current becomes comparable with the bias level. Thus, the
higher is the bias current, the higher is the capability to handle
large signal without a significant compression. Also in this case
the filtering action of input capacitance C1, plays an important
role and gives this filter an advantage with respect to other clas-
sical architectures. In fact, the current due to the largest input
signals, typically located outside the channel bandwidth, is pri-
marily absorbed by C1. This reduces the current entering in the
filter with a consequent enhancement of the 1 dB compression
point.
In conclusion, the current mode biquad cell proposed has two
important properties making it very suitable for use in a receiver
chain. First, it achieves low noise in the signal band, where a
high signal-to-noise ratio is the key target. Second, its linearity
increases as the input signal is moved far away from the band
edge. This latter behavior fits the linearity requirement of a typ-
ical wireless receiver where most of the input signal power is
located out-of-band (interferers) [9]. Furthermore the interferer
power tends to increase proportionally to its distance from the
filter band edge (channel bandwidth).
V. D ESIGN OF 4TH WCDMA CHANNEL SELECTION
BASEBAND FILTER
To validate the theory reported above, a 4th-order Butter-
worth filter intended to perform channel selection in a WCDMA
receiver was designed and integrated in 65 nm CMOS tech-
nology. The filter was implemented as the cascade of two cur-
rent biquad cells like the one of Fig. 4 (adopting a fully-dif-
ferential architecture to easily implement the sign inversion in
the feedback network). A complete scheme of the structure is
drawn in Fig. 8. The filter was designed to operate after a cur-
rent mixer that, for its nature, behaves as a current signal source.
In this case, however, for testing purpose, two resistances (R1)
were connected to the input to implement a V-I converter. This
was possible since this structure has a very low in-band input
impedance. Also for ease of testing, the output current was con-
verted to voltage on the differential resistor R2. The relative
noise contribution of R2 decreases as R2 is increased. In fact,
while the noise added by R2 is proportional to its value, all the
other contributes are amplified by the square of R2. The max-
imum feasible value for R2 is limited by the maximum swing
at the cell output. However, most of the input energy is located
out of band and it is filtered out before reaching R2. As a conse-
quence R2 can be chosen sufficiently high (20 k ) to make its
noise contribution negligible (less than 2% of the total).
1776 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 9, SEPTEMBER 2010
Fig. 8. Fourth-order filter schematic.
Fig. 9. Choice of cut-off frequency.
A. Design Strategies for Pipe Filter Cascade
One of the first steps in a filter design is the choice of the
cut-off frequency . In classic filters, where noise and
signal have roughly the same transfer function, this frequency is
generally minimized to maximize the blockers attenuation. In-
deed, a higher would not produce any benefit on the
in-band SNR, since both the noise and the signal are processed
by the same transfer function [10]. For a pipe filter however, the
presence of in-band noise shaping makes this choice less ob-
vious, as it is qualitatively shown in Fig. 9. If is moved
beyond the channel bandwidth, due to the difference in the noise
and signal transfer functions a significant improvement of SNR
is produced. However, this benefit trades off with the require-
ments of selectivity that depends on the position and on the
amplitude of the input interferers. In the case of a WCDMA
receiver, the scenario considered by the standard assumes the
presence of two interferers at 10 MHz and 20 MHz, with well
defined energies [9]. On the base of these requirements a com-
promise 2.8 MHz, that is 1.45 times the channel
bandwidth (i.e., 1.92 MHz), was chosen.
The second step in the filter design is the definition of the bias
current for each stage. This value must be greater or equal to the
largest between the minimum current necessary to handle the in-
terferers and the minimum current that allows to satisfy the con-
dition required for a proper operation of the filter
(see Section II). Although in general the first condition is the
more stringent, the use of a mixer as driving stage could require
a higher bias current to keep negligible the effect of the finite
impedance of the down-converter on the filter transfer function
[11]. In this design, since the input capacitance C1 attenuates
the blocker at 10 MHz by almost 10 dB and the one at 20 MHz
by almost 16 dB (being 2.8 MHz), the bias current
can be three time smaller than the one that would be required to
manage the full interferer. For the same reason, the bias current
of the second stage can be reduced by another factor of ten since
the 10 MHz blocker is attenuated by an additional 20 dB by the
first stage. The minimum bias current required by the second
stage is lower also because the first stage provides an output
impedance larger than (i.e., ).
The final step is to choose the transconductances and the ca-
pacitances of the cell that minimize the noise and maximize
the signal voltage swing compatibly with the supply voltage.
The impedance levels can be increased moving down the fil-
tering chain because each stage increases the driving impen-
dence for the following stage and contributes in the filtering
of out-of-band interferers. The impedance scaling gives also
a reduction of the silicon area since smaller capacitances are
needed. For the solution proposed, the transconductances of the
two stages have been set respectively to 3.3 mS for the first cell
and 330 S for the second one.
In Table I the design parameters for all transistors are re-
ported. Notice that the overdrive of the current generators is
PIROLA et al.: CURRENT-MODE, WCDMA CHANNEL FILTER WITH IN-BAND NOISE SHAPING 1777
TABLE I
FILTER PROTOTYPE TRANSISTORS PARAMETERS
much larger than that of M1–M2 to minimize their contribution
to the in-band noise.
B. Out-Band Noise Folding
The out-of-band noise present at the output of a pipe filter can
be folded down during the sampling phase that occurs within the
ADC. For this reason this noise has to be minimized to maintain
an advantage compared to traditional solutions, where most of
the noise lies in the filter passband.
The out-of-band noise in a pipe filter is contributed only by
the last stages of the filtering chain that have a high-pass transfer
function (e.g., the noise of M2 and of in Fig. 5). This
noise is proportional to the bias current that, as shown in the
previous section, is scaled down in the last stage. Finally, since
in general the current signal has to be converted to voltage before
entering the ADC, an additional pole can be added at the end
of the pipe filter, placing a capacitor in parallel with the load
resistance, providing a further attenuation of the out-of-band
noise. Introducing this additional pole does not require a large
capacitance since a large resistor can be used at the output where
most of the interferers are already filtered.
Due to the above, in the proposed design the out-of-band
noise (obtained integrating it from the filter corner to
“infinite”) is less than one third of the in-band noise This means
that, even sampling the output at the Nyquist rate, which is rarely
done, the in-band noise after sampling would increase less than
1 dB.
VI. EXPERIMENTAL RESULTS
The chip micrograph of the filter prototype, fabricated in a
90 nm CMOS process, is shown in Fig. 10. All pads are ESD
protected and the active die area is 0.5 mm . This area is dom-
inated by low-density MiM capacitors (210 pF), whose place-
ment could be further improved, resulting in a lower area oc-
cupation. Moreover, large on-chip MoM bypass capacitors are
used to filter the noise on the supply voltage with respect to
ground. The die was bonded on a dedicated double-side RF
board, realized on an FR4 substrate. Gold strip lines, optimized
to reduce their area occupation, carry the signals from the input
connectors to the die. As discussed in the previous section, the
voltage-to-current conversion is performed placing two resis-
tances (R1) of 1.66 in series with the input while the output
signal is sensed on a resistor (R2) of 20 k . The plot of the
filter frequency response versus frequency from DC to 20 MHz
is shown in Fig. 11 together with the response of the ideal 4th-
Fig. 10. Chip micrograph.
order Butterworth filter used for the design. The plot is obtained
de-embedding the effect of the parasitic pole caused by the ca-
pacitive load associated with the probe (about 5 pF). The DC
gain is about 15 dB, due to the ratio between the output and
the input resistors, and the filter cut-off frequency is close to
2.8 MHz as expected from the simulations. When the out-of-
band attenuation reaches about 55 dB the plot levels off due to
a parasitic leakage on the board. This was proved by measuring
the input to output transfer function with the filter powered off.
The output noise spectrum was measured shorting the dif-
ferential inputs of the die in front of the R1 resistance. In this
way the effect of the finite driving impedance (i.e., the output
resistance of the mixer in a receiver chain) on the filter output
noise is included. At the receiver output an active probe with
a 20 dB gain was used to raise the filter noise above the sensi-
tivity level of the spectrum analyzer. The measured output noise
spectrum is reported in Fig. 12 compared with the simulated
one. The noise transfer function has a bandpass shape as ex-
pected from the theory. The noise spectrum shows a minimum
equal to 128.5 dBm/Hz, located in the filter band, where the
main contributors are the bias generators. Below that 1/f noise
dominates while near the corner frequency, where the main con-
tributors are the filtering transistors, there is a local maximum
equal to 123 dBm/Hz. At higher frequencies the output noise
decreases because all contributors are filtered out by the filter it-
self and by the parasitic output pole. The 1/f corner is located at
25 kHz. This output noise frequency behavior is consistent with
the theory, as shown by the solid line in Fig. 12. The out-of-band
IIP3 is 35.6 dBm, and it has been measured with two tones, the
first placed at 10 MHz and the second at 19.5 MHz, that give a
third-order intermodulation product at 500 kHz. Fig. 13 shows
the simulated (dots) and measured (squares) filter IIP3, versus
the frequency of the IM3 product [Fig. 13(a)] and versus the
frequency of the first blocker [Fig. 13(b)]. These frequencies
are kept the same, with respect to the plots in Section IV. The
1778 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 9, SEPTEMBER 2010
Fig. 11. Measured output transfer function.
Fig. 12. Measured output noise function.
measurements fit very well with the simulations, confirming the
theory.
A summary of the most relevant measurements and a com-
parison with the state of art for filters designed for the same ap-
plications (WCDMA) is reported in Table II. In particular this
work has the lowest power consumption, equal to 1.26 mW, with
an SFDR higher than all but one of the other filters. The filter
cut-off frequency is set to 2.8 MHz, i.e., about 40% larger than
the UMTS bandwidth that is equal to 1.92 MHz. This gives a
significant in-band noise improvement while still providing suf-
ficient selectivity. Finally, the figure of merit (FoM) (based on
[1]) is almost 6 dB better than the next best one. Two more ver-
sions of the filter were also fabricated, where the capacitors are
scaled down by a factor of six (Table III). One of these scaled
filters (called filter 2) is operated from a 2.5 V supply while the
other (called filter 3) is operated from a 1.8 supply. Filter 2 uses
input resistors scaled up by a factor slightly higher than 6 and
has a slightly better FoM than the un-scaled filter. For the case
of filter 3, the input resistors are increased close to the maximum
feasible value which still allows to reach full scale swing at the
output without exceeding the supply with the input signal. In
this situation a much greater linearity is obtained together with
a relatively small increase in noise. This results in a further im-
provement of the FoM (2 dB with respect to filter 2, 6 dB with
respect to the unscaled filter and 12 dB with respect to the state
of the art).
PIROLA et al.: CURRENT-MODE, WCDMA CHANNEL FILTER WITH IN-BAND NOISE SHAPING 1779
Fig. 13 Fourth-order filter IIP3 (a) versus , (b) versus . Simulation (dots)
and measurements (squares).
TABLE II
FILTER PROTOTYPE MEASUREMENTS AND COMPARISON
WITH THE STATE OF THE ART
VII. CONCLUSION
A class of filters based on the concept of pipe filtering was
presented. In the filter passband, such kinds of structures be-
have like lossless pipes where no noise or distortion can be
added to the signal. This results in an in-band zero in both noise
TABLE III
2.5 V (FILTER 2) AND 1.8 V (FILTER 3) SCALED VERSIONS
and IM3 transfer functions. Furthermore, passive filtering action
provided by the capacitance at the input of the filter improves
linearity. Thanks to these properties, such filters consume less
area and power than the conventional ones, especially when op-
erating with strong interferers moderately far from the channel
band (as is the case of wireless receiver chains).
APPENDIX I
CURRENT VERSUS VOLTAG E OUTPUT
In the current-driven gm-C filter reported in Fig. 1, there are
two different ways to take the output: the first is to sense the
signal as a voltage across the capacitor , and the second
is to detect the current flowing out of the transistor .
Although in both cases the input–output transfer function is
a first-order low-pass filter (with a single real pole located
at ), the output noise is different. In the case
of a voltage output, the noise introduced by the transistor
is filtered according to the signal transfer function, while
in the current-mode approach (with ), the noise
transfer function has a zero at DC, leading to high-pass shaping
[Fig. 1(b)]. The difference between the two approaches is a
significant in-band noise reduction in favor of the current-mode
one. In particular, the output noise integrated from DC to the
filter cut-off frequency for the two cases is
(12)
(13)
where is the Boltzmann’s constant, is the temperature,
is the voltage noise power across the capacitance, and is
the current noise power flowing out of the transistor.
In terms of SNR, a comparison can be done assuming the
same in-band input signal, i.e., an input current power equal to
. This corresponds to an output voltage power
and an output current power . From (12) and (13), the
SNR for the two configurations becomes
(14)
1780 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 45, NO. 9, SEPTEMBER 2010
(15)
This corresponds to 5.6 dB better SNR in favor of the current-
mode one.
ACKNOWLEDGMENT
The authors thank Marvell for technology access, and Steve
Shia of TSMC for his support.
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Alberto Pirola (S’07) received the M.Sc. degree
(summa cum laude) in microelectronic engineering
from the University of Pavia, Italy, in 2007. Cur-
rently he is working towards the Ph.D. degree at
the University of Pavia in the Microelectronics
Laboratory.
His research interests are in the implementations of
analog RF front-end in CMOS technology, with par-
ticular focus on high SFDR current-driven baseband
filters.
Antonio Liscidini (S’99–M’06) received the Laurea
degree (summa cum laude) and the Ph.D. in electrical
engineering from the University of Pavia, Pavia,Italy,
in 2002 and 2006, respectively.
He was a summer intern at National Semiconduc-
tors, Santa Clara, CA, in 2003 studying poly-phase
filters and CMOS LNA. Currently he is an Assistant
Professor at the University of Pavia. His research
interests are in the implementations of analog RF
front-end in CMOS and BiCMOS technology, with
particular focus on the analysis and design of LNAs
for multi-standard applications, ultralow-power receivers and digital PLLs.
In addition to his academic activities, he has been acting as a consultant for
Marvell Semiconductors in the area of integrated circuit design.
Dr. Liscidini received the Best Student Paper Award at IEEE 2005 Sympo-
sium on VLSI Circuits. Since December 2007, he has served as an Associate
Editor of the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II: EXPRESS
BRIEFS and since 2010 he has been a member of the TPC of the European Solid
State Circuit Conference (ESSCIRC).
Rinaldo Castello (S’78–M’78–SM’92–F’99) grad-
uated from the University of Genova (summa cum
laude) in 1977 and received the M.S. and the Ph. D.
degrees from the University of California, Berkeley,
in 1981 and 1984.
From 1983 to 1985 he was Visiting Assistant
Professor at the University of California, Berkeley.
In 1987 he joined the University of Pavia, Italy,
where he is now a Full Professor. He consulted for
ST-Microelectronics, Milan, Italy, up to 2005 and
from 1998 to 2005 was the Scientific Director of a
joint research centre between the University of Pavia and ST. He promoted the
establishment of several design centers from multinational IC companies in the
Pavia area, including Marvell, for which he has been consulting since 2005.
Dr. Castello has been a member of the TPC of the European Solid State Cir-
cuit Conference (ESSCIRC) since 1987 and of the International Solid State Cir-
cuit Conference (ISSCC) from 1992 to 2004. He was Technical Chairman of
ESSCIRC ’91 and General Chairman of ESSCIRC’02, Associate Editor for Eu-
rope of the IEEE JOURNAL OF SOLID-STATE CIRCUITS from 1994 to 1996 and
Guest Editor of the July 1992 special issue. From 2000 to 2007, he was a Distin-
guished Lecturer of the IEEE Solid-State Circuits Society. He was named one
of the outstanding contributors for the first 50 years of the ISSCC and was a
co-recipient of the Best Student Paper Award at the 2005 Symposium on VLSI.
