Systems and methods for correcting gain error due to transition density variation in clock recovery systems

In one embodiment, the present invention is directed to a system for processing a data stream. The system comprises: a voltage controlled oscillator (VCO) that generates a VCO signal in response to a tuning signal; a phase detector that generates an error signal that is indicative of a phase difference between a data signal and the VCO signal; a first filter that filters a reference signal that is indicative of an occurrence of a data transition; a second filter that filters the error signal, wherein the first filter and second filter are low-pass filters that possess a bandwidth that approximately equals one half of the reciprocal of: a unit interval multiplied by a maximum run length; and a divider circuit that divides the filtered error signal by the filtered reference signal.

RELATED APPLICATIONS

The present application is related to concurrently filed, co-pending, and commonly assigned U.S. patent application Ser. No. 10/328,304, entitled “SYSTEM AND METHOD FOR DESIGNING AND USING ANALOG CIRCUITS OPERATING IN THE MODULATION DOMAIN;” U.S. patent application Ser. No. 10/328,363, entitled “PHASE LOCKED LOOP DEMODULATOR AND DEMODULATION METHOD USING FEED-FORWARD TRACKING ERROR COMPENSATION;” and U.S. patent application Ser. No. 10/328,358, entitled “SYSTEMS AND METHODS FOR CORRECTING PHASE LOCKED LOOP TRACKING ERROR USING FEED-FORWARD PHASE MODULATION;” the disclosures of which are hereby incorporated herein by reference.

TECHNICAL FIELD

The present invention is directed to processing a data stream that includes an embedded clock and, more particularly, to operating a phase locked loop (PLL) that exhibits predictable phase demodulation sensitivity in response to variation in symbol transition density.

BACKGROUND OF THE INVENTION

Non-return-to-zero (NRZ) signaling refers to a binary encoding scheme in which there is no return to a reference voltage between encoded bits. Instead, the signaling remains at a “high” voltage for consecutive “ones” and remains at a “low” voltage for consecutive “zeros.” In data transmission systems that utilize NRZ signaling, it is necessary to recover the clock based on the timing of the data transitions. In general, the clock associated with a data stream is recovered utilizing a phase locked loop (PLL). By comparing the timing of data transitions in the NRZ data stream to the phase of a voltage controlled oscillator (VCO) of the PLL, the phase error of the VCO may be determined. The VCO signal is adjusted thereto thereby locking the VCO to the embedded clock of the data. Specifically, the phase error may be “servo'd” to zero utilizing closed-loop feedback via the PLL design.

FIG. 1depicts clock recovery loop100according to the prior art. Clock recovery loop100comprises continuous phase detector104, VCO105, and loop filter106. Data101to be measured is received by continuous phase detector104. VCO105generates a VCO signal (which is provided as recovered clock102) that is controlled by tuning voltage107. When a data transition occurs, continuous phase detector104compares the timing of the data transmission to the phase of the VCO signal. Continuous phase detector104is referred to as “continuous,” because it produces phase error103that is proportional to the difference between the timing of the data transition and the phase of the VCO signal (as opposed to a quantized or binary output that merely indicates “early versus late” but not by how much). Phase error103is filtered by loop filter106to generate tuning voltage107to provide the closed-loop feedback.

However, for random data, the transition from “one” to “zero,” or vice versa, is a random event. Thus, there is some uncertainty whether and when a transition will occur. For example, if the data is “01010100000000001,” for the first six bits, there will be a transition at every opportunity, because no two consecutive bits are the same. However, the next ten consecutive bits are all “zero.” A “run length” refers to the number of consecutive bits or symbols that occur without a transition. Accordingly, the example data stream has a run length of ten “zeros.” During the run length of symbols or bits, no transition occurs from “zero” to “one.” Since there is no transition during the period, there is no phase information available from the data to correct any phase error in the VCO. Furthermore, data may be communicated in a “run length limited” manner (e.g., for jitter measurements). Specifically, the permissible run length of applied data patterns must be less than some predetermined number. A typical run length limit applied to data for which the jitter is measured is 31 bits.

In general, phase detectors work by outputting phase information only when there is a transition. When there is no transition in the data (at least two consecutive symbols that are the same), known phase detectors output a zero (i.e., meaning there is no detected phase error). This characteristic has the effect of making the phase detector gain (e.g., radians/volt), a function of the transition density of the data pattern. Thus, the phase detector gain is high during the “010101” portion of the example data stream and the phase detector gain is low during the “00000000001” portion of the example data stream.

Unpredictable phase detector gain has at least two important deleterious effects. First, the PLL bandwidth becomes unpredictable, because the PLL bandwidth is directly proportional to the phase detector gain. This degrades loop performance (e.g., tracking error), which makes the loop more difficult to design. Secondly, in jitter measurements, the calibration factor is directly proportional to the phase detector gain. Thus, the accuracy of the jitter measurement is questionable, when the data being measured does not have a predictable transition density. However, it is typically advantageous to utilize a wide variety of data patterns with appreciable variation in transition density in jitter measurements.

BRIEF SUMMARY OF THE INVENTION

In embodiments in accordance with the invention, a PLL is adapted such that the resulting phase error generated by the PLL is independent of the transition density of a data stream provided to the PLL. Specifically, the data stream may be considered to be a stream of symbols or bits that transition from one state to another according to a random sequence. Symbols or bits of the data stream are communicated in discrete intervals of time (“unit intervals”). Also, the data stream is communicated according to a run length limit that places an upper limit upon the number of consecutive symbols or bits that occur without a transition to another symbol or bit. The PLL may be adapted by filtering the phase error from a continuous phase detector of the PLL utilizing a first filter. A reference signal that is indicative of whether data transition has just occurred may be filtered by a second filter. The first and second filters may be advantageously implemented as low-pass filters that have a bandwidth that approximately equals one half of the reciprocal of the unit interval multiplied by the maximum run length. The output of the first and second filters may be provided to a divider circuit to produce a signal that is indicative of the phase error independent of the data transition density.

DETAILED DESCRIPTION OF THE INVENTION

Before discussing embodiments in accordance with the invention in greater detail, a discussion of Nyquist's sampling theorem is presented for the convenience of the reader. The Nyquist sampling theorem is related to the problem of reconstructing a continuous analog waveform utilizing only discrete samples of that waveform's voltage taken at uniform time intervals. In Nyquist's sampling theorem, an assumption is made that the continuous analog waveform is bandlimited, meaning that there are no frequencies contained in the waveform that exceed an upper bound frequency (which defines the Nyquist bandwidth). Utilizing this assumption, Nyquist was able to prove that the continuous analog waveform can be perfectly reconstructed from these samples, if and only if the sampling rate is at least twice the Nyquist bandwidth. This sampling rate is referred to as the Nyquist rate. In practice, a phenomenon known as “aliasing” requires the sampling rate to be slightly higher than Nyquist's theoretical minimum rate.

A familiar example is the digital audio compact disc (CD) format. Analog audio is typically filtered by a low-pass filter such that the analog audio does not possess a frequency component that is greater than 20 kHz. The analog audio is then sampled at a rate of 44,100 samples per second. This sampling rate is slightly (˜10%) greater than the Nyquist rate of 40,000 samples/per second.

As previously noted, Nyquist's sampling theorem assumes a uniform sampling rate. Embodiments in accordance with the invention extend Nyquist's sampling theorem to non-uniform sampling. For the convenience of further discussion, the term “pseudo-rate” shall be used to refer to the minimum sampling rate (as defined by the maximum time between consecutive samples) in a sampling set having a variable rate. It is submitted that perfect reconstruction of a continuous analog waveform is possible from samples taken at a variable rate, if the pseudo-rate is at least as high as the Nyquist rate (which is twice the highest frequency component of the continuous analog waveform). In a sense, in a variable sampling application that satisfies this criterion, there are “surplus” samples (e.g., samples taken at a rate higher than the Nyquist rate) available to facilitate recovery of the continuous analog waveform. These surplus samples may average out any non-systematic errors made by the sampling functionality.

A specific example may illustrate the concept of the pseudo-rate. Suppose a data transmission system with a data rate of 40 gigabits/sec (40 Gb/s) is tested for jitter using a data pattern with a run length limit of 32 (chosen for mathematical simplicity). Each bit occupies 25 ps which is referred to as the “unit interval” (UI). Since at least one data transition must occur every 32 symbols, the maximum time between samples of a phase error signal from a phase detector is 32×25 ps or 800 ps. A time interval of 800 ps corresponds to a pseudo-rate of 1.25 gigasamples/sec (which is the reciprocal of 800×10−12sec). Thus, the pseudo-rate supports a bandwidth of 625 MHz according to the present extension of the Nyquist sampling theorem. The bandwidth supported by the pseudo-rate will be referred to as the pseudo-Nyquist bandwidth.

FIG. 2depicts system200that is adapted according to the pseudo-Nyquist bandwidth according to embodiments in accordance with the invention. System200comprises conventional clock recovery loop210. Conventional clock recovery loop210is almost the same as conventional clock recovery loop100except continuous phase detector211is modified. Continuous phase detector211comprises a first port to output phase error103and, additionally, a second port to output reference signal201that is indicative of a data transition. In embodiments in accordance with the invention, continuous phase detector211produces a pulse of one UI duration each time a data transition occurs on the second port. As shown inFIG. 2, the functionality that produces the pulse during a data transition is implemented integrally with continuous phase detector211. However, this functionality may be implemented as a discrete circuit element if desired.

Reference signal201is provided to filter202. Filter202filters reference signal201to produce signal204which is approximately proportional to the transition density associated with data101. Filter202may be implemented as a low-pass filter that integrates the pulses generated by phase detector211. In embodiments in accordance with the invention, filter202may be implemented as a low-pass filter that possesses a cut-off frequency that approximately (considering aliasing effects) equals the pseudo-Nyquist bandwidth. As previously noted, the pseudo-Nyquist bandwidth is defined by the maximum time between samples which, in turn, may be defined by the run length limit associated with data101. Also, in embodiments in accordance with the invention, filter202may be advantageously implemented to possess well-behaved time domain characteristics (i.e., low under/overshoot). Suitable filters include Bessel filters and Gaussian filters. Similarly, phase error103from continuous phase detector211is provided to filter203. Filter203may be implemented in the same manner as filter202.

The outputs (signal204and signal205) from filters202and203are provided to divider206(which may be an analog or digital circuit element). Divider206divides the filtered phase error signal (signal205) by the filtered reference signal202to produce corrected phase error207. This configuration has an advantage in terms of utilizing a PLL as a phase demodulator to recover and measure jitter. Corrected phase error207has ajitter sensitivity that is independent of data transition density or run length. In contrast, raw phase error103has a sensitivity that is directly proportional to transition density.

Although system200has been described as generating a VCO signal, the present invention is not so limited. Embodiments in accordance with the invention may be implemented in a system in which the VCO signal is independently available and the phase detector with gain correction is used in an open loop.

Also, for the convenience of the reader, a mathematical analysis of system200is provided. Let Dma(t) (which corresponds to signal204) be defined as a moving average consisting of the number of transitions occurring in a length of time equal to the pseudo-Nyquist period (the reciprocal of the pseudo-Nyquist rate). Then, it follows from the definition of the pseudo-Nyquist period, that Dma(t) has a minimum value of 1 and a maximum value equal to the run length limit. Let Φma(t) denote a similar moving average of the phase error, where the moving averages are over the same time interval. Then, the filtered phase error (phase error203) is given by Φma(t) Dma(t). Thus, dividing Φma(t) Dma(t) by Dma(t) gives Φma(t) which is the desired result (i.e., the phase error independent of transition density). System200does not strictly function utilizing moving averages, because the filtering may typically be performed using Bessel or Gaussian filters. However, the operational principle remains the same. Additionally, it is noted that embodiments in accordance with the invention may advantageously implement filters202and203as 3rdorder Bessel filters, because the resulting impulse response is positive for times of interest. This is advantageous, because other filter shapes typically have an impulse response with a significant negative region, from which it follows that the output must approach and cross through zero. Divider206will not function properly if its divisor is equal to or approximately equal to zero, because the required output voltage will exceed the dynamic range of divider206.

It shall be appreciated that the implementation of a high speed divider (such as an analog divider) can be challenging, especially when the dynamic range of the divider is increased for a particular application. If an ideal moving average were utilized, the dynamic range would be equal to the run length limit. The dynamic range exhibited by an implementation that uses Bessel filters is somewhat less than the dynamic range of an ideal moving average, although the dynamic range is still relatively substantial. The difficulty associated with implementation of a divider may be mitigated if the dynamic range were reduced.FIG. 3depicts system300which reduces the dynamic range according to embodiments in accordance with the invention.

System300ofFIG. 3is similar to system200except that system300includes automatic gain control (AGC) block305. AGC block305is disposed after filters202and203which provide reference signal201and phase error signal103. Matched multipliers301and302are inserted after filters202and203and before divider206. The first input of multiplier301is the filtered reference signal from filter202and the first input of multiplier302is the filtered phase error signal from filter203. The second input of each multiplier is driven by a servo-loop that uses the output (the multiplied filtered phase error signal) from multiplier302as an error signal. The multiplied filtered phase error signal may be advantageously provided to servo-amplifier303and exponentiator304. By including exponential circuit element304, the servo-loop may be linearized thereby making the loop gain independent of the incoming signal levels. Although exponentiator304is shown as a separate element, in practice, exponentiator304may be combined with each of multipliers301and302. A commonly available 2-quadrant multiplier circuit consists of a differential pair biased by a current mirror. Adding an exponentiation function involves replacing the current mirror with a single transistor thereby resulting in reduced complexity.

At first glance, it may appear that the modification shown inFIG. 3has merely traded off the difficulty in implementing a divider for the equally difficult task of implementing the multipliers. However, there is actually a net decrease in difficulty. The total dynamic range may be partitioned between the AGC block305and divider206. Accordingly, neither of these elements are required to handle the entire dynamic range. Additionally, the implementation of multipliers301and302need not cause multipliers301and302to be especially accurate. Servo-loop errors are common mode, and, hence do not affect the ratio of the multiplied signals. Specifically, if multipliers301and302are matched, then any multiplication errors drop out after the operation of divider206. Furthermore, it is relatively straight-forward to obtain matching between multipliers301and302by monolithically integrating these elements on a single integrated circuit.

FIG. 3further depicts the output of multiplier302connected to provide feedback to the PLL of system300. This stabilizes the loop gain and the loop bandwidth of the PLL (which, otherwise, would be affected by the transition density associated with data101). In another embodiment of the present invention, additional stabilization of the loop gain and loop bandwidth may be achieved by providing corrected phase error signal207to loop filter106as shown in system400ofFIG. 4.