Miscellaneous active electrical nonlinear devices – circuits – and – Signal converting – shaping – or generating – Synchronizing
Reexamination Certificate
2002-12-23
2004-12-14
Callahan, Timothy P. (Department: 2816)
Miscellaneous active electrical nonlinear devices, circuits, and
Signal converting, shaping, or generating
Synchronizing
C327S163000, C327S147000, C375S376000
Reexamination Certificate
active
06831491
ABSTRACT:
TECHNICAL FIELD
The present invention is generally related to phase lock loop (PLL) devices and more particularly to systems and methods for addressing tracking error utilizing feed-forward phase modulation.
BACKGROUND OF THE INVENTION
Phase locked loops (PLLs) are devices that generate a signal and that lock the phase of the generated signal to the phase of an input reference signal. According to the prior art, as shown in
FIG. 1
, PLL
100
typically has three main components: voltage-controlled oscillator (VCO)
101
, phase detector
102
, and loop filter
103
. VCO
101
generates a signal that has a frequency proportional to the tuning voltage input. This proportionality is typically expressed as a VCO gain parameter (K
v
) denoted in units of radians/second per volt. Reference signal
104
may be provided at a reference frequency and phase. Phase detector
102
generates an output voltage proportional to the phase difference between the reference signal and the VCO signal. This proportionality is typically expressed as a phase detection gain parameter (K
d
) denoted in units of volts/radian. Thus, phase detector
102
generates a phase error signal (i.e., the phase tracking error). Loop filter
103
amplifies and filters this error signal, which is then fed back to VCO
101
. This feedback adjusts the phase of VCO
101
and causes VCO
101
to approximate the phase of the reference signal thereby minimizing the error.
PLL
100
as shown in
FIG. 1
is difficult to analyze on a mathematical basis, because the input and output of the loop filter are different types of variables (i.e., voltage proportional to phase and voltage proportional to frequency, respectively). By definition, phase is the time integral of frequency. Therefore, an ideal VCO
200
may be modeled as two mathematical blocks: ideal integrator
201
and ideal voltage to phase transducer
202
as shown in
FIG. 2
according to the prior art. Ideal VCO
200
may be incorporated in a PLL system to provide useable PLL model
300
as shown in
FIG. 3
according to the prior art. PLL model
300
may then be analyzed according to mathematical model
400
shown in
FIG. 4
according to the prior art. In mathematical model
400
, K
d
represents the phase detection gain parameter of phase detector
102
, F(s) represents the transfer function of loop filter
103
(expressed in Laplace transform notation), 1/s represents the transfer function of ideal integrator
201
(also expressed in Laplace transform notation), and K
v
represents the VCO gain parameter of VCO
101
. The loop gain is represented by the parameter G which equals K
d
K
v
F(s)/s. Moreover, &thgr;
vco
represents the phase of the signal produced by VCO
101
and &thgr;
ref
represents the phase of the reference signal. The relationship between &thgr;
vco
and &thgr;
ref
may be represented by the following equation: &thgr;
vco/&thgr;
ref
=G/(1+G). Thus, when the loop gain is relatively large (G>>1), &thgr;
vco
approximates &thgr;
ref
with a significant degree of accuracy.
Integrator
201
acts as a low pass filter and causes the loop gain to decrease with increasing frequency. Thus, tracking error increases with increasing frequency. At some frequency, the loop gain falls below unity. Above this frequency (which defines the loop bandwidth), the loop has relatively little response to the reference stimulus and, hence, limits the capacity of PLL
100
to continue accurately tracking the reference signal. Accordingly, this places a constraint upon the bandwidth of modulation that may be applied to the reference signal. Theoretically, the loop bandwidth can be increased by increasing the loop gain. However, in practice, implementations of VCO
101
have finite modulation bandwidth. The limited bandwidth of VCO
101
may be modeled in VCO
500
as a parasitic low pass filter
501
defined by transfer function P(s) as shown in
FIG. 5
according to the prior art. This has the effect of modifying the mathematical model by adding another low pass function to loop model
600
as shown in
FIG. 6
according to the prior art. As shown in
FIG. 6
, the loop gain (G) equals K
d
K
v
F(s)P(s)/s. This has the practical effect of limiting the loop bandwidth to a relatively small fraction of the VCO bandwidth. Because of numerous design constraints associated with implementations of VCO
101
, the VCO bandwidth cannot be made arbitrarily high. Accordingly, the VCO bandwidth often becomes a limiting factor on loop bandwidth. In addition to the VCO bandwidth, the loop filter may have its own bandwidth limitations, especially if it utilizes active circuitry. The effect of finite loop filter bandwidth is the same as VCO bandwidth in terms of limiting loop bandwidth.
PLLs are commonly utilized to build frequency or phase demodulators. A demodulator is a system driven by a modulated signal that produces an output voltage that is proportional to the modulation.
FIG. 7
depicts PLL frequency demodulator
700
according to the prior art. VCO
101
tracks the phase of the reference signal. Because of the close mathematical relationship between phase and frequency, VCO
101
also tracks the frequency of the reference. Since the tuning voltage applied to VCO
101
is proportional to the VCO frequency (and, hence, to the reference frequency), the tuning voltage is used directly as demodulated output
701
.
FIG. 8
depicts phase demodulator
800
according to the prior art. Phase demodulator
800
is substantially the same as frequency demodulator
700
except that leaky integrator
801
has been added to convert the tuning voltage (proportional to frequency) into a voltage (demodulated output
802
) proportional to phase. Since an ideal integrator is not physically realizable, a so-called “leaky” integrator
801
is shown. Specifically, leaky integrator
801
approximately acts as an ideal integrator above a specified minimum frequency (&ohgr;
1
). Below that frequency, leaky integrator
801
changes to a flat gain versus frequency characteristic. This imparts a low frequency cutoff to the frequency response of the demodulation output port.
BRIEF SUMMARY OF THE INVENTION
Embodiments in accordance with the invention adapt PLL devices to compensate for the tracking error of these devices. As previously mentioned, tracking error is the difference in the phase of the reference signal and the phase of the VCO signal. It shall be appreciated that addressing the tracking error of a PLL device with known techniques may be problematic for a number of factors. For example, VCOs are typically are non-linear frequency dependent devices. Accordingly, if the PLL device is incorporated into a system that is intended to be frequency-agile, tracking error compensation may become difficult. Moreover, the non-linearity and frequency dependence of VCOs generally have temperature-dependent gain drift as well thereby further complicating or prohibiting tracking error correction using known techniques for certain applications.
Embodiments in accordance with the invention address the tracking error of a PLL device without imposing a critical dependence on the vagaries of the VCO of the PLL device. Embodiments in accordance with the invention model the tracking error as a spurious phase modulation of the VCO signal. Accordingly, embodiments in accordance with the invention employ a phase modulator to correct the tracking error. The output of the phase detector is provided to the phase modulator to modulate the phase of the VCO signal. The phase and the gain of the phase modulator are calibrated such that approximately equal and opposite compensating phase modulation is added to the VCO signal. Addressing the tracking error in this manner is advantageous, because the accuracy associated with the method is determined by the accuracy of the phase detector and the phase modulator. Specifically, the characteristics of phase detectors and phase modulators are substantially improved as compared to the characteristics of VCOs. For example, many phase detectors have linear gain and have a fla
Agilent Technologie,s Inc.
Callahan Timothy P.
Nguyen Hai L.
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