__BACKGROUND OF THE INVENTION__
This invention relates generally to continuous-time filters
and, more particularly, to resonators that are critical components in continuous-time
filters. A continuous-time filter operates on continuously varying (analog) signals
rather than discrete digital signal samples. Although digital signal processing
is widely used in communication systems and other applications, there is still a
need for continuous-time filters to perform certain critical functions, such as
at the point of analog-to-digital (A/D) conversion. One specific area in which the
accurate tuning of active filters is important is the world of continuous-time delta-sigma
analog-to-digital converters. This type of A/D converter contains at its core a
continuous-time "loop filter." A loop filter is typically composed of a number of
resonators that create transfer function "poles" at specific frequencies. The pole
frequency (resonant frequency) and Q (quality) value of each resonator are critical
factors in ensuring that that the overall closed loop A/D converter is stable and
subject to only low noise in a frequency band of interest.

By way of further background, it is worth noting that although
filter circuits are often characterized in terms of their frequency response and
their characteristics in the time domain, they are typically analyzed and designed
in terms of their characteristics in the "s-domain" or "s-plane," a plane in which
a time-domain signal *x*(*t*) can be represented as an s-domain signal,
which is a function of s, where s is a complex variable in the well known Laplace
transform that relates any time-domain signal to its corresponding s-domain form.
One of the advantages of representing a continuous-time filter in the s-domain is
that the characteristics of the filter can be depicted In the s-plane as points
known as poles and zeros. In such a "pole-zero plot," as it is known, each pole
is a point in the s-plane at which the transfer function of the filter becomes very
large, and each zero is a point in the s-plane at which the transfer function of
the filter falls to near zero. The frequency response of the filter is represented
in the s-plane by the variation of the transfer function along the imaginary axis
of the s-plane. Therefore, for a resonator circuit a pole on the imaginary axis
of the pole-zero plot corresponds to a resonant frequency in the frequency response
of the circuit.

The design of continuous-time filters is complicated by
the fact that integrated circuit process variations and other factors can skew the
filter's most important figures of merit (e.g. the center frequency, bandwidth,
and Q factor) such that the constructed end product does not meet the design specification.
For example, the accuracy of an integrated filter designed using active-resistor-capacitor
(active-RC) techniques depends greatly on the accuracy of the resistors and capacitors
available. These components commonly vary by as much as 10-20% from their nominal
values in an integrated circuit (IC) environment. There is a need, therefore, for
a tuning technique that can compensate for these inaccuracies so that the finished
filter can meet the design criteria. The present invention is directed to this end.

__SUMMARY OF THE INVENTION__
The present invention resides in a tunable resonator of
which certain parameters adversely affected by integrated-circuit (IC) fabrication
processes may be corrected after fabrication. Briefly, and in general terms, the
invention is embodied in a tunable resonator for use in RC (resistance-capacitance)
continuous-time filters, comprising a pair of integrator circuits interconnected
in a loop to provide resonance at a selected resonance frequency. Each of the integrator
circuits comprises an operational amplifier (often abbreviated to "opamp") with
feedback capacitors, and with resistors for coupling output signals from one opamp
to input lines of the other opamp. The integrator circuits are implemented in integrated
circuit (IC) form and the resonator further comprises means for tuning the selected
resonance frequency after fabrication of the resonator, and means for tuning the
Q (quality) factor of the resonator after fabrication.

More specifically, preferably the means for tuning the
selected resonance frequency comprises means for adjusting at least one of either
capacitor values or resistor values in each of the integrator circuits. In the embodiment
of the invention disclosed by way of example, the means for tuning the selected
resonance frequency comprises a variable capacitance component coupled to each of
the feedback capacitors and means for applying a tuning signal to the variable capacitance
component to vary the total capacitance value and thereby tune the resonance frequency.
The variable capacitance component may be a varactor diode, in which case the tuning
signal is applied to the varactor diode to change a reverse-bias voltage applied
to the diode.

in the disclosed embodiment of the invention, the means
for tuning the Q factor of the resonator comprises means for adding capacitance
to the coupling resistors between the pair of integrator circuits and means for
adjusting the amount of added capacitance and, therefore, the degree to which a
phase adjustment is made to the signals coupled from one of the integrator circuits
to the other. In particular, the means for adding capacitance to the coupling resistors
comprises at least one varactor diode included in an RC network coupling one of
the integrator circuits to the other. The means for adjusting the amount of added
capacitance is a variable source of bias voltage applied to the varactor diode or
diodes to vary their capacitance value.

The invention may also be defined as a method for making
and tuning a resonator circuit in a continuous-time filter fabricated as an integrated
circuit (IC). Briefly, the method comprises the steps of forming a resonator circuit
from a pair of integrator circuits connected in a continuous loop to provide a total
of 180° of phase shift; forming a plurality of feedback capacitors for each
of the integrator circuits to include a variable capacitance; applying a tuning
signal to the variable capacitance to tune the circuit to a selected resonance frequency;
forming a resistance-capacitance (RC) network between a first of the integrator
circuits and the second of the integrator circuits, to include at least one additional
variable capacitance; applying a second tuning signal to the additional variable
capacitance, to apply a phase shift to signals coupled from the first of the integrator
circuits to the second, and thereby adjusting the Q factor associated with the resonator
circuit. The method may further comprise the step of adding a resistance value to
at least one of the feedback capacitors, to apply a phase shift to signals in the
resonator circuit.

It will be appreciated from the foregoing that the present
invention represents a significant advance in the field of continuous-time filters.
In particular, the invention allows for post-fabrication tuning of filters implemented
in integrated-circuit form, and thereby eliminates possible filter performance degradation
as a result of fabrication processes. Other aspects and advantages of the invention
will become apparent from the following more detailed description, taken in conjunction
with the drawings.

__BRIEF DESCRIPTION OF THE DRAWINGS__
FIG. 1 is a schematic diagram of an active-RC resonator
of the prior art.

FIG. 2 is a schematic diagram of a tunable active-RC resonator
in accordance with the present invention.

__DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION__
As shown in the drawings for purposes of illustration,
the present invention is concerned with active-RC resonators, which may be advantageously
used in continuous-time filters. As briefly discussed above, active filters are
important components in continuous-time delta-sigma analog-to-digital (A/D) converters.
This type of A/D converter contains a continuous-time loop filter that is typically
composed of a number of resonators, each of which is made up of circuit components
selected to provide desired resonator parameters, such as Q factor and center frequency.
When these resonators are fabricated in integrated-circuit (IC) form, the circuit
components may vary as much as 10-20% from their nominal values and, in prior art
resonators of this type, there was no way to tune the resonator parameters after
fabrication.

A prior-art active-RC resonator is shown in FIG. 1 as including
two operational amplifiers (opamps), indicated generally by reference numerals 10
and 12, configured as integrators connected in a feedback loop. Those skilled in
the art will understand that one way to create a pole on the imaginary axis is to
connect two integrator blocks in a feedback loop such that the phase shift around
the loop is as close as possible to 180°. Integrator blocks ideally have a
constant 90° of phase shift. Therefore, two Integrators in cascade produce
a constant 180° of phase shift. The integrator blocks in FIG. 1 are composed
of the fully differential opamps 10 and 12, together with various resistors and
capacitors.

More specifically, opamp integrator block 10 receives a
differential input signal V_{ln} over input lines 14, through input resistors
R_{in} connected in series with the input lines. Opamp 10 has two feedback
capacitors C_{1} coupling the opamp 10 output lines 16 to its input lines
14. The output lines 16, with output voltage V_{o1} are also coupled through
resistors R_{2} to Input lines 18 of opamp 12, which has output lines 20
with output voltage V_{o2}. Opamp 12 also has feedback capacitors C_{2}
between its output lines 20 and its input lines 18. To complete the loop, the output
lines 20 of opamp 12 are coupled through resistors R_{1} to the input lines
14 of opamp 10.

It can be shown that the center frequency of the resonator,
assuming that R_{1}=R_{2}=R and C_{1}=C_{2}=C is
1/(2&pgr;RC). It is obvious then, that the tuning of the resonator is highly dependent
on the accuracy of the realized resistor and capacitor values. If either R or C
can be made electrically adjustable post-fabrication, the resonator center frequency
can be tuned to any desired frequency within some preferred range.

Another important way in which the resonator may deviate
from ideal is that the integrator blocks are typically not perfect 90° phase
shifters. The actual phase shift may be in error by as much as a few degrees in
either direction. In addition, the integrator phase shift my have a slight variation
with frequency. This Inaccuracy in the integrator phase response will degrade the
quality factor, Q, of the resonator. Generally, a high-Q resonator will peak more
sharply at resonance than a low Q one. Ideally, the pole created by the resonator
lies exactly on the imaginary axis of the s-domain representation of the resonator
characteristics. When the phase shift around the resonator loop is not exactly 180
degrees, the pole moves to the left or to the right of the imaginary axis. If the
pole moves to the right of the imaginary axis, the circuit is mathematically unstable
and will oscillate. If the pole moves to the left of the imaginary axis, the circuit
is stable but the peak value at resonance will decrease. In a continuous-time delta-sigma
A/D converter, a minimum level of resonance is required for the overall data converter
to meet the effective number of bits (ENOB) design specification. Therefore, in
addition to being able to tune the resonator center frequency, it is also necessary
to tune the resonator Q factor by incorporating some electrically adjustable lead
or lag compensation.

FIG. 2 shows a resonator configured in accordance with
the invention, including modifications that allow both the resonance frequency and
the Q factor to be electrically tuned post-fabrication. Two separate tuning operations
are performed in the circuit of FIG. 2: frequency tuning and Q tuning.

First, frequency tuning is effected by varying the integrator
capacitance values rather than the resistance levels, Each capacitor C_{1}
of FIG. 1 is replaced by series-connected capacitors C_{1A} and C_{1B}
in FIG. 2. Each capacitor C_{1A} has a varactor diode 24 connected across
it in parallel, with the cathode of the varactor diode being connected to the junction
between capacitors C_{1A} and C_{1B}. A selectable DC bias voltage
tuning signal V_{tune_f} is applied to the cathode of the varactor diode
24 through a large resistance R_{big}. Varactor diodes have inherent capacitance
that can be varied by changing the reverse-bias voltage applied across the diode.
Thus the varactor diode 24 functions to vary the total capacitance provided by the
capacitors C_{1A} and C_{1B} and the varactor diode 24. Given that
varactor diodes are often available in commercial IC processes, varying the integrator
capacitance rather than the resistance is the presently preferred technique to effect
frequency tuning. Similarly, in the other opamp circuit 12 each capacitor C_{2}
of FIG. 1 is replaced by series-connected capacitors C_{2A} and G_{2B}
in, FIG. 2, and each capacitor C_{2A} has a varactor diode 24 connected
across it in parallel. The tuning voltage signal V_{tune_f} is also applied
to the cathode of the second varactor diode 24 through a large resistance R_{big}.
Varactors are useful variable capacitance elements that are commonly used in voltage
controlled oscillator (VCO) circuits. Varactors are basically specialized diodes
whose capacitance is designed to vary significantly with reverse bias voltage, Varying
the tuning voltage V_{tune_f} changes the net capacitance of the network,
altering the integrator RC time constants, changing the resonance frequency of the
entire circuit.

The frequency tuning circuit has the advantage that it
allows the varactor DC bias voltage to be applied without disturbing the AC behavior
of the rest of the circuit. In preferred embodiments of this invention, the varactor
anode is connected to the opamp input, which is a virtual ground node. The frequency
tuning voltage is applied to the varactor cathode through a large resistor R_{big}.
This DC tuning voltage cannot affect the AC behavior of the rest of the resonator
circuit because the DC cannot pass through the two fixed capacitors C_{1A}
and C_{1B} or C_{2A} and C_{2B}.

Resonator Q factor tuning is effected by the network in
FIG. 2 composed of the four resistors R_{2}/2, capacitor C_{3},
another large resistor R_{big}, and two additional varactor diodes 26. This
network takes the place of the two resistors R_{2} in the prior-art circuit
of FIG. 1. Specifically, each of the original resistors R_{2} is replaced
by two resistors R_{2}/2 connected in series. The capacitor C_{3}
is connected between the common junctions of each pair of resistors R_{2}/2.
Also connected between these two junctions are the two additional varactor diodes
26, with their anodes connected to the respective resistor junctions and their cathodes
connected in common to a tuning voltage V_{tune_q}, through large resistor
R_{blg}. The capacitor C_{3} and the varactor diodes 26 together
form a tunable capacitance network. When the varactor diodes 26 are adjusted by
the tuning voltage V_{tune_q}, the capacitance network provides a small
phase shift In the signal coupled from the output of opamp 10 to the input of opamp
12. This small amount of tuning allows the overall phase shift of the loop to approximate
180° more closely, which is the condition for good resonance. Since the tuning
voltage V_{tune_q} is applied at a virtual ground node, the DC does not
affect the normal AC operation of the rest of the resonator circuit. It should be
noted that this circuit can only provide a phase delay, and will only allow the
Q factor to be improved only if the nominal loop phase shift is less than 180°.
If it is expected that the nominal phase shift will be greater than 180°, small
fixed resistors can be inserted in series with capacitors C_{1B} and C_{2B}
to bring the nominal loop phase shift back to something less than 180°, so
that the phase delay added by the tuning circuit will improve the Q.

It will be appreciated from the foregoing that the present
invention represents a significant improvement in continuous-time resonators. In
particular, providing for post-fabrication tuning can eliminate the potential inaccuracies
and uncertainties resulting from integrated circuitry (IC) fabrication processes.
It will also be appreciated that placing varactor diodes in the resonator circuit
is not the only way to adjust resonance frequency and Q. It is also possible to
make all of the capacitors fixed and incorporate some form of tunable resistance,
since it is the RC product that determines the resonance frequency. This tunable
resistance could take the form of a metal oxide semiconductor (MOS) transistor biased
in the triode region. Unfortunately, the resistance provided by an MOS device in
triode is very non-linear and may unacceptably distort any signal that passes through
it. It is also possible to fabricate a binary array of fixed capacitors that can
be switched in and out with MOS devices, but this technique uses a lot more IC "real
estate" than the presently preferred approach described here.

It will be understood, therefore, that although a preferred
embodiment of the invention has been described in detail for purposes of illustration,
various modifications may be made without departing from the scope of the invention.
Accordingly, the invention should not be limited except as by the appended claims.