IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 44, NO. 5, MAY 1997
A
-Enhanced Active-
341
Bandpass Filter
Ralph Duncan, Kenneth W. Martin, Fellow, IEEE, and Adel S. Sedra, Fellow, IEEE
Abstract—A fully differential high-Q bandpass filter that uses
lossy integrated inductors is presented. The circuit is implemented
in a 0.8 m BiCMOS technology and realizes a center frequency
of 750 MHz with a Q-factor that is tunable from 10 to 490
while dissipating 80–100 mW from a single 5 V supply. Since
the objective of the prototype was to explore the proposed Qenhancement technique, the dynamic range is limited to 25 dB
for Q = 20.
(a)
I. INTRODUCTION
Fig. 1.
T
HE PROLIFERATION of gigahertz-band communication
(direct broadcast satellite, cellular, and digital radio) has
heightened the need for single-chip realizations of the receiver
or, at the very least, the radio-frequency (RF) front-end, so as
to reduce size, power consumption, and cost. A fully integrated
receiver front-end effectively eliminates the bulky ceramic,
crystal, or SAW filters currently used, thereby reducing power
consumption, area, and assembly cost. This implies that all RF,
and subsequent intermediate-frequency (IF), filtering should
be integrated, without sacrificing dynamic range or receiver
sensitivity, and, necessarily, the RF must employ continuoustime filters. This is because digital filters and DSP engines are
relatively slow and power-hungry, and second-order effects
in switched-capacitor circuits, such as clock feedthrough and
poor amplifier settling, are exacerbated at high frequencies.
Integrated active bandpass filters exhibit a dynamic range
which, at best, is inversely proportional to their quality factor [1]–[5]. This is the result of active devices unwittingly
introducing and amplifying noise, and this limitation makes
designing for wide dynamic range and high difficult. Moreover, when high-frequency operation is required too, power
dissipation rapidly escalates. Yet, continuous-time bandpass
filters are indispensable in transceivers, and the increasing use
of portable communication devices makes integration of the
radio-frequency bandpass filter quite attractive.
To this end, we discuss the use of lossy monolithic inductors
to design a selective high-frequency bandpass filter. The role
of the RF bandpass filter in a radio receiver is to provide
coarse frequency selectivity; it favors the desired channel
while attempting to reject large out-of-band signals. Although
the required selectivity depends on the receiver architecture,
this frequency discrimination must be done without adding a
significant amount of noise so as not to reduce the sensitivity of
the receiver. Controlled active feedback is used to compensate
Manuscript received September 7, 1995; revised November 18, 1996. This
work was supported by the Micronet program. This paper was recommended
by Associate Editor L. A. Akers.
The authors are with the Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ont., Canada M5S 1A4.
Publisher Item Identifier S 1057-7130(97)02968-6.
(b)
Q-enhanced active-RLC circuits.
for the losses in the inductors, thus enhancing the
of the
approach has the potential
filter. We show that this activeto produce less noise than other active filter design approaches,
without excessive demands on the requisite amplifier. The
approach, and
following section introduces the activeanalyzes the circuit to define its dynamic range performance
and intermodulation properties. In Section III, the design of
the filter is discussed. Experimental results from a prototype
circuit are presented in Section IV.
II. THE ACTIVE-
APPROACH
The idea of activeis to realize high- natural modes
tank in a feedback loop containing an
by placing a passive
amplifier so as to partially compensate for the losses resulting
from the inductor. Typically, these inductors exhibit quality
factors of 3–8 in the low gigahertz range, but a -factor as
high as 10 is also possible [6]–[9]. The controlled positive
is equivalent
feedback required to increase the circuit
to adding a variable negative resistance into the loop. This
facilitates the design for a desired -factor.
approaches are shown in Fig. 1. In
Two activeFig. 1(a), the inductor current is sampled, and a voltage
proportional to this current is fed back by the currentcontrolled voltage source [10]. In a dual manner, in Fig. 1(b),
the capacitor voltage is sampled and a proportional current is
fed back by a voltage-controlled current source [11], [12].
The controlled source in Fig. 1(a) can be realized with
a transimpedance amplifier, and the controlled source in
Fig. 1(b), with a transadmittance amplifier. In either circuit,
and
are resistive, only the quality factor is
as long as
affected. As expected, the resonant frequency is unchanged.
It is straightforward to show that the -factor is increased
according to
1057–7130/97$10.00  1997 IEEE
(1a)
342
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 44, NO. 5, MAY 1997
variables, the intermediate transfer functions are found from
(3)
The elements
of the vector
represent the transfer
functions from the circuit input to each state (the signal transfer
of
is the transfer function
functions), while each
from each noise source to the output (a noise transfer function).
and an
Assuming that the amplifier has a dc gain
models its finite
ostensible single-pole response (
bandwidth), the response of the amplifier is
Fig. 2. A realization of Fig. 1(a).
(4)
(1b)
is the -factor of the inductor at the center frequency
where
of the filter. As seen, the quality factor of the filter, in both
cases, is increased by the loop gain at resonance, and the is
tunable via the variable gain of the amplifiers.
A possible realization of the circuit in Fig. 1(a)—the approach adopted for this paper—is shown in Fig. 2. Although
the input signal can be injected anywhere in the loop of
Fig. 1(a) to realize a filter with an enhanced -factor,1 feeding
the signal through a capacitor allows a bandpass response
to be taken from the low-impedance output of the amplifier.
Referring to Fig. 1(a), observe that -enhancement will still be
) is connected to
realized if only part of the capacitor (say
, while the other part of the capacitor
the feedback voltage
is connected to ground. This makes the other portion
of the tuning capacitor available to apply the input. Thus, in
Fig. 2, the inductor current is sampled at the low-impedance
, converted to a
input of the transimpedance amplifier,
voltage, and the output signal fed-back through part of the
tuning capacitor. The input voltage is then fed through the
other portion of the tuning capacitor.
The filter in Fig. 2 can be conveniently analyzed when statespace notation is used to represent it. This facilitates the use of
intermediate transfer-function analysis [13], [14] to describe
network behavior. One suspects at the outset that the noise
performance and sensitivities should be better than for
filters: the role of the amplifier in activeis only to
enhance the quality factor of natural modes that are already
(or active)
complex. This should be contrasted to
filters where poles have to be moved from the real axis into
the complex -plane.
For a system represented in state-space [13] by
(2)
and
where , , , and are real-valued matrices,
are the system input and output, and
contains the state
1 The point of signal-injection determines the type of transfer function
realized. The circuit in Fig. 1(a) is capable of realizing high- bandpass,
lowpass, and highpass transfer functions.
Q
For the state assignment shown in Fig. 2, the state-space
description of the circuit is
(5)
The transfer function can be shown to be
(6)
where
, the natural-mode polynomial, is
(7)
For an ideal amplifier
, we see that the nominal center
frequency and 3 dB bandwidth are given by
(8)
to denote the inductor
Again, using
frequency, we get
at the nominal center
(9)
which is similar to (1).
Including the finite bandwidth of the amplifier, and assum, (7) can be rewritten as
ing
(10)
DUNCAN et al.: A Q–ENHANCED ACTIVE-RLC BANDPASS FILTER
343
where
is the realized center frequency,
is the realized
is the closed-loop parasitic pole. By
quality factor, and
comparing (10) with (7), the parameters in (10) are
(11)
(12)
(13)
Not surprisingly, these equations suggest that the amplifier’s
bandwidth should be considerably larger than the desired
center frequency in order to get a small deviation from the
ideal parameters. They also show that a large inductor quality
factor is useful. This should be intuitive, since for a large
starting quality factor a smaller loop gain is required to achieve
a desired quality factor in the filter.
An important nonideality is the finite input impedance of the
transimpedance amplifier. It can be accounted for by extracting
the parasitic from the nonideal circuit and lumping it together
to reflect this
with the nominal inductor. By redefining
nonideality, all of the above equations are still applicable.
A. Noise and Dynamic Range
The intermediate transfer functions can be computed to be
(14)
of
The significance of the noise transfer functions—
—deserves special attention. Circuit noise sources can be
regarded as auxiliary inputs to the system, and, thus, simply
augment the state equations. Consequently, if we add a current
noise source to each node for which a KCL equation was
written, and a voltage noise source to each loop for which a
KVL equation was written, the following relationships ensue
[14]:
noise gain of a current noise source at node : in an
IC realization this noise source may be the result of
substrate coupling via parasitics;
noise gain of a current noise source at the input of
the amplifier;
noise gain of a voltage noise source at the input of
the amplifier;
noise gain of a voltage noise source at the circuit
input: this could be the result of the source resistance
or input buffers (if used).
In order to evaluate the output noise of the filter, we first
define a measure for signal magnitudes. We choose the
norm [13]. For a transfer function , this can be computed
using
(15)
is the noise bandwidth of the specified transfer
where
is the peak transfer function gain. Since
function, and
the noise bandwidth of a second-order bandpass filter is
, the -norm is easily computed.2
Suppose that
has input-referred voltage noise density
and input-referred current noise density
.
, the voltage noise resistance of the amplifier, is the value
of a resistor that produces the same thermal voltage noise
is defined similarly. The output
power as the amplifier.
noise power of the filter is, therefore,
(16)
and
are the
-norms of the noise transfer
where
functions for voltage noise and current noise at the input
of the amplifier. This result suggests that large inductances
are favored, and inductors like those in [8] can be used to
advantage.
From a distortion point of view, the critical signal-handling
path is the input of the amplifier for it is the amplitude of
its input current that sets the distortion in the amplifier. The
amplifier’s input current is also the inductor current, hence the
inductor current sets the maximum output voltage swing. This
maximum is obtained from the norm of the signal transfer
of
. If
denotes the rms value of
function
the inductor current when the amplifier is at the threshold of
distorting unacceptably, the dynamic range of the filter is
DR
(17)
The first quotient in (17) represents the dynamic range of a
passive series LC tank carrying a current equal to the maximum inductor current in the active realization. It is therefore a
convenient metric for assessing the performance of the active
circuit. In the active realization, this metric is reduced by two
factors: one is the amount of -enhancement, and the other
depends on the amplifier’s noise contribution. If inductor noise
dominates, then the dynamic range is inversely proportional
to -enhancement; if voltage noise in the amplifier dominates
(poor design or a high inductor is used), the dynamic range
is inversely proportional to the , as observed in other active
filter realizations [1]–[5].3 This last quotient makes sense: if
one already has a high- inductor, using an active realization
leads to an increase in circuit noise, and a reduction in the
available dynamic range.
Q
2 A highsecond-order low pass filter exhibits virtually the same noise
bandwidth as a second-order bandpass filter.
3 This is because
1=r.
1
Q /
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 44, NO. 5, MAY 1997
the current source
and the MOSFET current mirror
, while current sources bias the emitter followers. Each of
the MOS-FET transistors has an aspect ratio of 320/2, and
each of the bipolar transistors, except the buffers and
(which is a single 4 device), is a dual 4 device.4 The
buffers are relatively large 15 transistors. The large baseemitter capacitance of the buffers is of little concern due to
the large amount of series feedback provided by the current
source loads. Degeneration resistors are used to linearise the
current–voltage relationship of the current sources and to
reduce the noise contribution from the base resistances of the
ensure that
operates in the
transistors. Diodes
by
active mode, and positive feedback is effected through
interchanging the output nodes of the amplifier.
This circuit uses two 5 nH inductors, with a measured
of about 2 at 1 GHz (
16 ), a nominal 1 pF tuning
0.6. The capacitors were implemented
capacitance, and
using double polysilicon layers. No allowance was made for
tuning the center frequency of filter, although this can be
accomplished using an impedance multiplier as discussed in
[12] and [18].
Fig. 3. The
Q-enhanced bandpass filter.
A. Amplifier Noise
B. Intermodulation Distortion
The choice of amplifier directly impacts the dynamic range
of the filter since the amplifier is the dominant source of both
noise and distortion. Suppose that the amplifier in Fig. 2 is
ideal except for being weakly nonlinear. For a given choice
of amplifier, distortion of the filter is related to that of the
amplifier in a simple manner. Because the gain of the bandpass
filter is relatively constant for frequencies close to the center
frequency, the filter behaves as a simple positive-feedback
amplifier for in-band signals. So we should expect the filter’s
third-order intermodulation distortion to be worse than that of
the amplifier, and it can be shown to be
(18)
This is not a surprising result, albeit an unattractive one. It
speaks directly to the required linearity of the amplifier, and
to the need for low circuit noise if high dynamic range is to
be realized along with a high quality factor.
III. THE FILTER
To investigate the utility of the proposed -enhancement
scheme, a simple prototype circuit was designed and fabricated
using a 0.8 m BiCMOS technology [15], [16]. The circuit is
shown in Fig. 3, and is a direct implementation of the circuit
in Fig. 2. The amplifier is a resistively loaded Gilbert quad,
[17], with the output nodes buffered by the emitter
followers , . Thus, the midband gain resistance is defined
by the 180 load resistors and the ratio of the collector current
and
. By varying either of
or
, -control
of
can be effected. Biasing for the input diodes is provided by
The (differential) input-referred noise of the amplifier, together with the appropriate noise gains, determine the output
noise contribution of the filter. Referring to Fig. 3, we see that
for a balanced circuit the noise contribution from the current
is common-mode, and is rejected by the circuit, so
source
and
we will ignore it. Similarly, noise resulting from
establishes a common-mode component on the gates of
and
which, ultimately, is rejected by the circuit.
The equivalent voltage noise power spectral density at the
input of the amplifier can be shown to be
(19)
, and
are the base resistance, collector
where ,
is the
resistance, and transconductance of the devices, and
current-gain of the quad. Due to the large transconductance of
, as compared to
[the ratio is
], the
noise contribution of the MOSFET’s is minuscule. From (19),
for a low-noise filter it is imperative that the base resistance of
the input transistors be minimized. In the BiCMOS technology
used by us, the bipolar base resistance was quite high (
100 ) as the bases were not realized using self-aligned
polysilicon, so appreciable noise resulted. In addition, the
input-referred current noise power is easily found, and is
(20)
where is the collector current in each transistor comprising
the input diodes.
4 The
unit BJT is 4
2 0.8 m2 .
DUNCAN et al.: A Q–ENHANCED ACTIVE-RLC BANDPASS FILTER
345
Fig. 5. A high-
Q bandpass filter.
ratios, the simulated value was used to deduce internal signal
levels.
IV. MEASURED RESULTS
Fig. 4. Layout plot of the bandpass filter.
B. Distortion in the Amplifier
Distortion in this amplifier arises mostly from device mismatches and the presence of parasitic base and emitter resistances. These nonidealities result in parabolic and cubic
nonlinearities [17], respectively, but even-order distortion is of
secondary concern in a fully balanced configuration. Parasitic
base and emitter resistances are more troublesome because
they affect the third-order intermodulation distortion. If these
in
resistances are modeled as a single resistor
the emitter of each transistor, the third-order intermodulation
distortion can be expressed as
(21)
,
, and
where is the amplitude of the signal current in
is emitter–area ratio of
to
. As seen, intermodulation
distortion depends on three factors: the first is the voltage
modulation at the input of the amplifier; the second is the
current modulation of the diodes; and the third is the current
density in the devices. That is, if the current gain is equal to
the emitter-area ratio of the devices (the devices are operating
with equal current densities), no distortion is introduced by
the finite emitter resistances. This latter condition is unlikely
to occur since the variable current gain is used to tune the factor of the filter. Thus, good linearity comes at the expense
of increased power and circuit area.
The layout of the circuit is shown in Fig. 4. The active
740 m. The
area of the circuit is approximately 860 m
inductors are readily apparent at the left of the figure, with
the amplifier and capacitors occupying much of the central
portion of the picture.
A.
Tuning
180
The test setup comprised the filter, a pair of 50
power splitters, and four 100 k potentiometers that allowed
external control of the bias current of every transistor in the
signal path. One power splitter was used at the input to achieve
single-ended-to-differential conversion, and the other at the
output to provide differential-to-single-ended conversion.
A very high- response is shown in Fig. 5. The measured
center frequency and were 740 MHz and 494, respectively.
The relatively low center frequency is, in a large part, caused
by significant parasitic wiring inductance (a layout error) introduced by the connection from the inductors to the amplifier.
This parasitic increased the nominal circuit inductance by
approximately 20%.
Fig. 6 illustrates the tuning of the -factor, and also the
second-order dependence of the center frequency on the is tuned from 20 to about 120, the
factor. In the plot, as
center frequency decreases from 768 to 741 MHz. This is
attributed to the change in the operating point of the amplifier
(and hence its frequency response) as the bias currents change
to tune the quality factor. The flattening of the responses away
from the center frequency is attributed to a combination of
noise from the test setup and the input-signal coupling through
the circuit board.
C. The Output Driver
B. Linearity and Dynamic Range
driver is a Darlington, emitter-degenerated difThe 50
ferential pair. It nominally dissipates 55 mW, and supports
an output swing of 400 mV. The driver exhibited a simulated
insertion loss of 18 dB, and since this is defined by resistor
20, used equalAn intermodulation distortion test, for
amplitude signals placed at 765.1 and 775.3 MHz. The output
response is plotted in Fig. 7. For an input of 40 dBm,
the filter exhibited a signal-to-distortion ratio of 36 dB. The
346
Fig. 6. Tuning the
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 44, NO. 5, MAY 1997
Q-factor.
Fig. 8. Jump resonance for
Q
= 32.
V. CONCLUSION
A high-frequency, high- bandpass filter operating at 750
MHz was designed and implemented using inductors with factors of 2 at 1 GHz. The circuit was fabricated in a 0.8
m BiC-MOS technology and demonstrates the potential of
integrating a low-noise, high- 1 GHz bandpass filter.
Although the dynamic range of the filter was rather limited,
this was primarily due to the linearity limitations of the amplifier used. As discussed, the linearity of the requisite amplifier
deserves careful attention, but for a fixed- application, the
Gilbert amplifier can still be used to advantage. The noise
performance of the amplifier as well needs to be improved.
ACKNOWLEDGMENT
Fig. 7. Intermodulation distortion for
Q
= 20.
poor distortion behavior is attributed to the nonlinearity of
the amplifier. Noise from the circuit board, coupled with the
low gain of the output drivers ( 18 dB when driving 50
), resulted in the test setup dominating the output noise.
In spite of this limitation, the spurious-free dynamic range
for this experiment was estimated as 25 dB, with an internal
third-order intercept point of 8 dBm.
C. Jump Resonance
The folding of intermodulation distortion products back
on the fundamental typically results in gain-compression in
amplifiers. In a bandpass filter, however, the phase of the
cubic with respect to the fundamental changes as the input
frequency is swept through resonance [19], [20]. This gives
rise to gain-expansion (larger gain) below resonance and gaincompression above resonance. This increase in gain below
resonance potentially leads to instability and is illustrated in
Fig. 8. In the filter, it is speculated that it is caused by the
strong cubic nonlinearity of the amplifier. For the response
shown, the filter- is set to 32 and the input power increased
from 50 to 20 dBm. This phenomenon severely limited the
signal handling capability of the filter.
The authors are indebted to M. Snelgrove for the use of
the resources at Carleton University, and to P. Lauzon for the
layout of the circuit board. Discussions with J. Long and M.
Copeland were much appreciated.
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[9] K. Negus et al., “Highly-integrated transmitter RFIC with monolithic
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[10] R. Duncan, K. Martin, and A. Sedra, “A Q-enhanced active-RLC
filter,” in Proc. ISCAS, 1993, pp. 1416–1419.
[11] Y. Tsividis, “Integrated continuous-time filter design,” in Proc. CICC,
1993, pp. 6.4.1–6.4.7.
[12] S. Pipilos and Y. Tsividis, “Design of active RLC integrated filters with
application in the GHz range,” in Proc. ISCAS, 1994, pp. 645–648.
[13] W. M. Snelgrove and A. S. Sedra, “Synthesis and analysis of state-space
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[14] G. W. Roberts, “Generalization and applications of the intermediate
function technique,” Ph.D. dissertation, Elect. Eng. Dept., Univ. Toronto,
Canada, 1989.
[15] R. Hadaway et al., “A sub-micron BiCMOS technology for telecommunications,” J. Microelec. Eng., vol. 15, pp. 513–516, 1991.
[16] “Design rules and process parameters for CMC 0.8-m BiCMOS, a
version of NTE BAT-MOS,” Rep. ICI-040R0, Canadian Microelectron.
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[17] B. Gilbert, “A new wideband amplifier technique,” IEEE J. Solid-State
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[18] R. Duncan, “Active-RLC filters in silicon,” Ph.D. dissertation, ECE
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[19] M. Snelgrove, private communication.
[20] J. Cherry, “Distortion analysis of weakly nonlinear filters using Volterra
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Ralph Duncan received the B.A.Sc., M.A.Sc., and
Ph.D. degrees in electrical engineering from the
University of Toronto, Toronto, Canada, in 1989,
1991, and 1995, respectively.
He is currently with Maxim Integrated Products,
Sunnyvale, CA, as member of the technical staff in
the Signal Processing and Converters group.
347
Kenneth W. Martin (F’91) received the B.A.Sc.,
M.A.Sc., and Ph.D. degrees from the University of
Toronto, Canada, in 1975, 1977, and 1980, respectively.
From 1977 to 1978, he was a member of the
Scientific Research Staff at Bell Northern Research,
Ottawa, Canada, where he conducted some of the
early research in integrated switched-capacitor networks. Between 1980 and 1992 he was, consecutively, an assistant, associate, and full professor at
UCLA. In 1992, he accepted the endowed “Stanley
Ho Professorship in Microelectronics” at the University of Toronto. He has
also been a consultant to many high technology companies including Xerox
Corp., Hughes Aircraft Co., Intel Corp., and Brooktree Corp. in the areas
of high-speed analog and digital integrated circuit design. He has ongoing
research programs in the areas of analog CMOS and BiCMOS systems,
high-speed GaAs MESFET and HBT circuits, and digital-signal-processing
algorithms for fixed and adaptive filters.
Professor Martin was appointed as the Circuits and Systems IEEE Press
representative (1985 to 1986). He was selected by the IEEE Circuits and
Systems Society for the Outstanding Young Engineer Award that was presented at the IEEE Centennial Keys to the Future Program in 1984. He was
elected by the Circuits and Systems Society members to their administrative
committee (ADCOM 1985–1987). He served as an Associate Editor of the
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS from 1985 to 1987, and has
served on the technical committee for many International Symposia on Circuits
and Systems. He is currently an Associate Editor for the PROCEEDINGS OF
THE IEEE, chairman of the IEEE CAS Guillemin–Cauer Best Paper Awards
Committee, and a member of the IEEE Circuits and Systems Board of
Governors (1995 to 1997). He was awarded a National Science Foundation
Presidential Young Investigator Award that ran from 1985 to 1990. He was a
corecipient of the Beatrice Winner Award at the 1993 ISSCC.
Adel S. Sedra (M’66–SM’82–F’84), photograph and biography not available
at the time of publication.