Patent Publication Number: US-9887653-B2

Title: Sensorless brushless direct current (BLDC) motor position control

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     None. 
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     None. 
     BACKGROUND 
     Detecting when alternating current (AC) voltage and/or current waveforms cross through a zero current (or voltage) axis (e.g., “zero crossing”) is frequently performed, for example in electric motor control, lamp dimming, powerline communication and other applications. In motor control systems, a half-bridge circuit is frequently used to drive a switching node coupled to a load (e.g., the motor). There is difficulty in robustly detecting the zero-crossing when the switching node is noisy. 
     Switching node noise is a particular issue when MOSFETs are employed as power switches (e.g., in the half-bridge circuit) for a motor control. Motors tend to present an inductive load to the half-bridge circuit, and the combination of the inductive load with the capacitance of the MOSFETs can cause ringing on the switching node, making accurate detection of the zero crossing difficult. 
     Therefore, an improved zero crossing detector is envisioned to more reliably and accurately detect zero crossings of a current (or voltage) waveform of interest. 
     SUMMARY 
     This Summary is provided to introduce a selection of concepts in a simplified form that are further described in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. 
     One aspect provides an electronic circuit for controlling operation of a brushless direct current (DC) motor having a plurality of windings. The electronic circuit includes a gate driver for providing an associated control signal to each of one or more switching elements coupled to the electronic circuit. The one or more switching elements control a voltage applied to each of the plurality of windings of the motor. A controller generates a speed signal based upon a received frequency demand signal and provides the speed signal to the gate driver. A zero crossing detector detects a zero crossing of a voltage applied to at least one of the windings, and transitions a zero crossing signal between a first logic level and a second logic level based on the detected zero crossing. A position estimator estimates an angular position of the motor. The position estimator includes a counter configured to count in a first predetermined direction based on the first logic level of the zero crossing signal, and configured to count in a second predetermined direction based on the second logic level of the zero crossing signal. An observer determines a value of the counter after a predetermined elapsed time, and generates an angular position signal based, at least in part, upon the determined value of the counter. 
     In an embodiment, the one or more switching elements are coupled in a half-bridge circuit including at least one branch. Each branch is associated with a given one of the plurality of windings, and includes a first switching element coupled between a high supply voltage and a switching node of the given winding, and a second switching element coupled between the switching node and a low supply voltage. 
     In an embodiment, the gate driver receives the angular position signal from the observer, generates the control signal for each switching element based, at least in part, upon the angular position signal and the speed signal. 
     In an embodiment, the observer generates a frequency signal based, at least in part, upon the determined value of the counter and provide the frequency signal to the controller. 
     In an embodiment, the controller generates the speed signal based upon the received frequency demand signal and the frequency signal. 
     In an embodiment, the observer receives at least one adjustment parameter, and generates at least one of the angular position signal and the frequency signal based upon the determined value of the counter and the at least one adjustment parameter. 
     In an embodiment, the at least one adjustment parameter includes a frequency adjustment parameter, K I . The observer generates the frequency signal by multiplying the determined value of the counter by the frequency adjustment parameter, added to a previous value of the frequency signal. In an embodiment, the at least one adjustment parameter includes a position adjustment parameter, K P . The observer generates the angular position signal by multiplying the determined value of the counter by the position adjustment parameter, added to a previous value of the angular position signal and added to the frequency signal. 
     In an embodiment, the angular position signal is determined by: θ(n)=θ(n−1)+(K P ·ERROR)+FREQ(n), and the frequency signal is determined by: FREQ(n)=FREQ(n−1)+(K I ·ERROR), where θ(n) is a current value of the angular position signal, θ(n−1) is the previous value of the angular position signal, K P  is the position adjustment parameter, ERROR is the determined value of the counter, FREQ(n) is a current value of the frequency signal, FREQ(n−1) is the previous value of the frequency signal, and K I  is the frequency adjustment parameter. 
     In an embodiment, the frequency adjustment parameter adjusts a slope of the frequency signal, and the position adjustment parameter adjusts a slope of the angular position signal. 
     In an embodiment, the at least one adjustment parameter is determined based on one or more characteristics of the motor. In an embodiment, the one or more characteristics include a response time of the motor. 
     In an embodiment, the counter is an up/down counter to increment the value of the counter based on the first logic level of the zero crossing signal, and decrement the value of the counter based on the second logic level of the zero crossing signal. The first logic level is a logic high level, and the second logic level is a logic low level. 
     In an embodiment, if the determined value of the counter is non-zero, the observer adjusts the frequency signal. In an embodiment, if the determined value of the counter is a positive value, the frequency signal is increased, and if the determined value of the counter is a negative value, the frequency signal is decreased. 
     In an embodiment, the controller employs the frequency signal as a reference signal to compare to the received frequency demand signal to run the motor at a substantially constant frequency. 
     In an embodiment, the electronic circuit does not employ blanking time to determine the angular position of the motor. In an embodiment, the electronic circuit does not receive signals from one or more position sensors of the motor. 
     In an embodiment, the zero crossing detector detects a zero crossing of a voltage applied to all of the windings. 
     In an embodiment, the one or more switching elements each comprise a field effect transistor. In an embodiment, the electronic circuit is implemented in an integrated circuit. In an embodiment, the one or more switching elements are internal to the integrated circuit. In an embodiment, the one or more switching elements are external to the integrated circuit. 
     In an embodiment, the electronic circuit includes a center tap averaging block coupled to the zero crossing detector and a voltage applied to at least one of the windings. The center tap averaging block generates an approximate center tap voltage of the windings, and wherein the zero crossing detector detects a zero crossing based upon the approximate center tap voltage. 
     Another aspect provides an electronic circuit for driving a load. The electronic circuit includes a gate driver for providing an associated control signal to each of one or more switching elements coupled to the electronic circuit and the load. The one or more switching elements control a voltage applied to the load. A controller generates a speed signal based upon a received frequency demand signal and provides the speed signal to the gate driver. A zero crossing detector detects a zero crossing of a voltage applied to the load, and transitions a zero crossing signal between a first logic level and a second logic level based on the detected zero crossing. A position estimator estimates an angular position of the load, and includes a counter to count in a first predetermined direction based on the first logic level of the zero crossing signal, and to count in a second predetermined direction based on the second logic level of the zero crossing signal. An observer determines a value of the counter after a predetermined elapsed time, and generates an angular position signal based, at least in part, upon the determined value of the counter. The observer generates a frequency signal based, at least in part, upon the determined value of the counter and provides the frequency signal to the controller. The controller generates the speed signal based upon the received frequency demand signal and the frequency signal. 
     In an embodiment, the load comprises a brushless direct current (DC) motor having a plurality of windings. The one or more switching elements are coupled in a half-bridge circuit comprising at least one branch, each branch associated with a given one of the plurality of windings. Each branch includes a first switching element coupled between a high supply voltage and a switching node of the given winding, and a second switching element coupled between the switching node and a low supply voltage. The gate driver receives the angular position signal from the observer, and generates the control signal for each switching element based, at least in part, upon the angular position signal and the speed signal. 
     In an embodiment, the observer receives at least one adjustment parameter, and generates at least one of the angular position signal and the frequency signal based upon the determined value of the counter and the at least one adjustment parameter. 
     In an embodiment, the at least one adjustment parameter includes a frequency adjustment parameter, K I , and a position adjustment parameter, K P . The observer generates the frequency signal by multiplying the determined value of the counter by the frequency adjustment parameter, added to a previous value of the frequency signal. The observer generates the angular position signal by multiplying the determined value of the counter by the position adjustment parameter, added to a previous value of the angular position signal and added to the frequency signal. 
     In an embodiment, the angular position signal is determined by: θ(n)=θ(n−1)+(K P ·ERROR)+FREQ(n), and the frequency signal is determined by: FREQ(n)=FREQ(n−1)+(K I ·ERROR), where θ(n) is a current value of the angular position signal, θ(n−1) is the previous value of the angular position signal, K P  is the position adjustment parameter, ERROR is the determined value of the counter, FREQ(n) is a current value of the frequency signal, FREQ(n−1) is the previous value of the frequency signal, and K I  is the frequency adjustment parameter. 
     In an embodiment, the at least one adjustment parameter is determined based on one or more characteristics of the motor, and the one or more characteristics include a response time of the motor. 
     In an embodiment, the counter is an up/down counter configured to increment the value of the counter based on the first logic level of the zero crossing signal, and decrement the value of the counter based on the second logic level of the zero crossing signal. The first logic level is a logic high level, and the second logic level is a logic low level. 
     In an embodiment, if the determined value of the counter is a positive value, the frequency signal is increased, and if the determined value of the counter is a negative value, the frequency signal is decreased. 
     In an embodiment, the controller employs the frequency signal as a reference signal to compare to the received frequency demand signal to operate the load at a substantially constant frequency. 
     In an embodiment, the electronic circuit includes a center tap averaging block coupled to the zero crossing detector and a voltage applied to at least one of the windings. The center tap averaging block generates an approximate center tap voltage of the windings, and the zero crossing detector detects a zero crossing based upon the approximate center tap voltage. 
     Another aspect provides a method for controlling operation of a brushless direct current (DC) motor having a plurality of windings. The method includes providing an associated control signal to each of one or more switching elements coupled to the electronic circuit. The one or more switching elements control a voltage applied to each of the plurality of windings of the motor. A controller generates a speed signal based upon a received frequency demand signal and provides the speed signal to the gate driver. A zero crossing detector detects a zero crossing of a voltage applied to at least one of the windings, and transitions a zero crossing signal between a first logic level and a second logic level based on the detected zero crossing. A position estimator estimates an angular position of the motor. The position estimator includes a counter configured to count in a first predetermined direction based on the first logic level of the zero crossing signal, and configured to count in a second predetermined direction based on the second logic level of the zero crossing signal. An observer determines a value of the counter after a predetermined elapsed time, and generates an angular position signal based, at least in part, upon the determined value of the counter. 
     In an embodiment, the one or more switching elements are coupled in a half-bridge circuit including at least one branch. Each branch is associated with a given one of the plurality of windings, and includes a first switching element coupled between a high supply voltage and a switching node of the given winding, and a second switching element coupled between the switching node and a low supply voltage. 
     In an embodiment, the control signal for each switching element is generated based, at least in part, upon the angular position signal and the speed signal. 
     In an embodiment, a frequency signal is generated based, at least in part, upon the determined value of the counter and provide the frequency signal to the controller. 
     In an embodiment, the speed signal is generated based upon the received frequency demand signal and the frequency signal. 
     In an embodiment, at least one of the angular position signal and the frequency signal are generated based upon the determined value of the counter and at least one adjustment parameter. 
     In an embodiment, the at least one adjustment parameter includes a frequency adjustment parameter, K I , and a position adjustment parameter, K P . The frequency signal is generated by multiplying the determined value of the counter by the frequency adjustment parameter, added to a previous value of the frequency signal. The angular position signal is generated by multiplying the determined value of the counter by the position adjustment parameter, added to a previous value of the angular position signal and added to the frequency signal. 
     In an embodiment, a slope of the frequency signal is adjusted based upon the frequency adjustment parameter, and a slope of the angular position signal is adjusted based upon the position adjustment parameter. 
     In an embodiment, the at least one adjustment parameter is determined based on one or more characteristics of the motor. In an embodiment, the one or more characteristics comprise a response time of the motor. 
     In an embodiment, the value of the counter is incremented based on the first logic level of the zero crossing signal, and decremented based on the second logic level of the zero crossing signal. The first logic level is a logic high level, and the second logic level is a logic low level. 
     In an embodiment, if the determined value of the counter is a positive value, the frequency signal is increased, and if the determined value of the counter is a negative value, the frequency signal is decreased. In an embodiment, the frequency signal is compared to the received frequency demand signal, and, based upon the comparison, the motor is operated at a substantially constant frequency. 
     In an embodiment, an approximate center tap voltage of the windings is generated and a zero crossing is detected based upon the approximate center tap voltage. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING FIGURES 
       Other aspects, features, and advantages of the claimed subject matter will become more fully apparent from the following detailed description, the appended claims, and the accompanying drawings in which like reference numerals identify similar or identical elements. Reference numerals that are introduced in the specification in association with a drawing figure might be repeated in one or more subsequent figures without additional description in the specification in order to provide context for other features. 
         FIG. 1  is a schematic diagram showing a motor driver with a zero crossing detector in accordance with illustrative embodiments; 
         FIG. 2  is a block diagram of a position and speed sensing circuit of the motor driver of  FIG. 1  in accordance with illustrative embodiments; 
         FIGS. 3A and 3B  are timing diagrams showing illustrative signals of the motor driver of  FIG. 1  in accordance with illustrative embodiments; 
         FIGS. 4A, 4B, 4C and 4D  are timing diagrams showing illustrative signals of the position and speed sensing circuit of  FIG. 2  in accordance with illustrative embodiments; 
         FIG. 5  is a timing diagram showing illustrative signals of the position and speed sensing circuit of  FIG. 2  in accordance with illustrative embodiments; 
         FIG. 6  is a timing diagram showing illustrative signals of the position and speed sensing circuit of  FIG. 2  in accordance with illustrative embodiments; 
         FIG. 7  is a flow diagram showing an illustrative operating process of the motor driver of  FIG. 1  in accordance with illustrative embodiments; and 
         FIG. 8  is a flow diagram showing an illustrative process for adjusting phase control signals of the motor driver of  FIG. 1  in accordance with illustrative embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     Described embodiments provide circuits, systems and methods for controlling operation of brushless direct current motors that include a plurality of windings. A gate driver provides control signals to switching elements that control a voltage applied to each of the windings of the motor. A zero crossing detector detects zero crossings of a voltage applied to the windings and transitions a zero crossing signal between a first logic level and a second logic level based on the detected zero crossings. A position estimator estimates an angular position of the motor, and counts in a first direction based on the first logic level of the zero crossing signal, and in a second direction based on the second logic level of the zero crossing signal. An observer determines a value of the counter after an elapsed time, and generates an angular position signal based upon the value of the counter. 
     Referring to  FIG. 1 , a schematic of illustrative motor system  100  is shown. Motor system  100  includes motor driver  102  to control operation of multi-phase motor  104 . Although shown in  FIG. 1  as being a three-phase motor, in some embodiments, motor  104  could employ other numbers of phases, as would be understood by one of ordinary skill in the art. 
     When motor  104  is a three-phase motor, the motor includes three windings, shown as windings  122   a ,  122   b  and  122   c , each of which, as would be understood by one of skill in the art, can be depicted as an equivalent circuit having an inductor in series with a back electromotive force (EMF) voltage source. As shown in  FIG. 1 , each winding  122   a ,  122   b , and  122   c  is joined in a Y configuration at a common point shown as center tap  123 . The voltage of the back EMF voltage source is directly observable when the current through the associated motor winding is zero. Thus, zero crossing information might beneficially be employed to determine back EMF and, therefore, also a direction of motion and position of motor  104 . 
     Motor system  100  includes controller  126  coupled to receive frequency demand signal  131  from an external device coupled to motor system  100 . In various embodiments, controller  126  may be either internal or external to motor driver  102 . In general, frequency demand signal  131  is indicative of a requested speed of motor  104 . Frequency demand signal  131  may be provided in one of a variety of formats, for example, a Single Edge Nibble Transmission (SENT) format, a Serial Peripheral Interface (SPI) format, a Local Interconnect Network (LIN) format, a CAN (Controller Area Network) format, an Inter-Integrated Circuit (I 2 C) format, a pulse width modulated (PWM) signal, or other similar signal formats. 
     Controller  126  provides a frequency demand signal  133  to drive modulator  106 . Drive modulator  106  generates signals  135  to control gate driver  108  for each phase of motor  104 . In some embodiments, drive modulator  106  generates signals  135  with a modulation characteristic (i.e., a relative time-varying duty cycle). 
     Gate driver  108  receives signals  135  and generates transistor drive signals  137   a ,  137   b ,  137   c ,  137   d ,  137   e  and  137   f  (collectively, transistor drive signals  137 ) to drive corresponding switching elements, shown as field effect transistors (FETs) Q 1 , Q 2 , Q 3 , Q 4 , Q 5 , and Q 6 . Together, transistors Q 1  and Q 2  form a half-bridge circuit that generates motor control signal OUTA corresponding to a first phase, A, of motor  104 . Similarly, transistors Q 3  and Q 4  form a half-bridge circuit that generates motor control signal OUTB corresponding to a second phase, B, of motor  104 , and transistors Q 5  and Q 6  form a half-bridge circuit that generates motor control signal OUTC corresponding to a third phase, C, of motor  104 . 
     Although transistors Q 1 , Q 2 , Q 3 , Q 4 , Q 5  and Q 6  are shown as being an N-channel metal oxide semiconductor field effect transistors (MOSFETs), other types of switching elements may be employed, such as P-channel MOSFETs, bipolar junction transistors (BJTs), Silicon-Controlled Rectifiers (SCRs), thyristors, triacs, or other similar switching elements. When MOSFETs are employed, each transistor has a corresponding intrinsic body diode as shown in  FIG. 1 . Each body diode is arranged from drain (cathode) to source (anode) of the MOSFET, making the MOSFET able to block current in only one direction. The body diodes are thus frequently utilized as freewheeling diodes for inductive loads, such as motor  104 , for example when the MOSFET is used as a switch in a half-bridge circuit. 
     The six transistors Q 1 , Q 2 , Q 3 , Q 4 , Q 5  and Q 6  are synchronized to operate in saturation to provide three motor drive signals OUTA, OUTB and OUTC to motor  104 . In some embodiments, such as shown in  FIG. 1 , transistors Q 1 , Q 2 , Q 3 , Q 4 , Q 5  and Q 6  may be internal to motor driver  102 . In other embodiments, transistors Q 1 , Q 2 , Q 3 , Q 4 , Q 5  and Q 6  may be external devices coupled to motor driver  102 . 
     Motor driver  102  includes position and speed sensing circuit  112  to generate a position reference signal  139  indicative of a rotational reference position of motor  104 . In some embodiments, position and speed sensing circuit  112  includes, or is coupled to, zero crossing detector  116 . Zero crossing detector  116  is coupled to receive one or more center tap signals  143  from signal conditioning block  118 . Signal conditioning block  118  is coupled to receive at least one of the motor drive signals (e.g., at least one of OUTA, OUTB, and OUTC). Zero crossing detector  116  generates at least one signal indicative of a zero crossing of the voltage applied to one or more of the windings of motor  104 . As will be described, the zero crossing signal can be used by position and speed sensing circuit  112  to estimate a position and/or back EMF of motor  104 . Described embodiments do not employ Hall effect elements or other magnetic field sensing elements disposed within motor  104  to detect the rotational position of motor  104 . 
     Drive modulator  106  is coupled to receive a position reference signal  139  from position and speed sensing circuit  112 . Drive modulator  106  and position and speed sensing circuit  112  are also coupled to oscillator  110  to receive a local reference frequency signal  141 . In some embodiments, position and speed sensing circuit  112  generates a frequency reference signal  129  based upon zero crossings detected by zero cross detector  116  and local reference frequency signal  141 . Controller  126  is coupled to receive frequency reference signal  129 . 
     In some embodiments, drive modulator  106  can modify control signals  135  to gate driver circuit  108  based, at least in part, upon position reference signal  139  and frequency demand signal  133 . Thus, in some embodiments, motor driver  102  can automatically adjust a timing (i.e., a phase) of the transistor drive signals  137  in relation to a sensed rotational position and sensed rotational frequency of motor  104 . 
     For example, drive modulator  106  might control the speed, position and direction of motor  104  based upon position reference signal  139  and frequency demand signal  133 . Some embodiments of motor driver  102  might also provide for driving motor  104  in a phase advance mode to reduce a back electromotive force of the motor and align a phase of the current through motor  104  and a phase of a voltage applied to motor  104  (e.g., align a phase of the current of motor drive signals OUTA, OUTB and OUTC and a phase of the voltage of motor drive signals OUTA, OUTB and OUTC, respectively). 
     Motor driver  102  receives a power supply voltage VBB, which is also supplied to motor  104  through transistors Q 1 , Q 3  and Q 5  during times when transistors Q 1 , Q 3  and Q 5  are turned on. Motor driver  102  also receives a ground (or circuit common) supply voltage GND, which is supplied to motor  104  through transistors Q 2 , Q 4  and Q 6  during times when transistors Q 2 , Q 4  and Q 6  are turned on. It will be understood that there can be a small voltage drop (for example, 0.1 volts) through transistors Q 1 , Q 2 , Q 3 , Q 4 , Q 5  and Q 6  when they are turned on and supplying current to motor  104 . 
     Current is provided to motor  104  by turning on an upper transistor (e.g., one of transistors Q 1 , Q 3  and Q 5 ) in a given half-bridge circuit to couple supply voltage VBB though the upper transistor to motor  104 , and turning on a lower transistor (e.g., one of transistors Q 2 , Q 4  and Q 6 ) in another half-bridge circuit to couple ground voltage GND though the lower transistor to motor  104 , allowing current to flow through one or more corresponding windings of motor  104 . For example, if upper transistor Q 1  is turned on (e.g., control signal  137   a  is logic high), then one of lower transistors Q 4  and Q 6  could be turned on (e.g., one of control signals  137   d  or  137   f  is logic high) to allow a current to flow through associated windings of motor  104  (e.g., windings  122   a  and  122   b , or windings  122   a  and  122   c ). 
     To prevent short circuit (or “shoot through”) conditions, only one transistor in each half-bridge circuit can be turned on at a given time. As a precaution, gate driver circuit  108  might control transistor drive signals  137  such that for short periods of time after one of the transistors of a given half-bridge circuit turns off, the other transistor cannot turn on and, thus, both transistors are off. This time is commonly known as “dead time” of the half-bridge circuit. For the illustrative system shown in  FIG. 1 , during dead time for each half-bridge circuit, the upper transistor (e.g., transistors Q 1 , Q 3  and Q 5 ) and the lower transistor (e.g., transistors Q 2 , Q 4  and Q 6 ) are both off (e.g., transistor drive signals  137   a  and  137   b  are both logic low, transistor drive signals  137   c  and  137   d  are both logic low, and transistor drive signals  137   e  and  137   f  are both logic low). 
     Referring to  FIG. 2 , a block diagram showing additional detail of position and speed sensing circuit  112  and signal conditioning block  118  is shown. As shown in  FIG. 2 , the motor control signals (OUTA, OUTB, and OUTC, for a three phase motor  104 ) are provided to signal conditioning block  118 ′. In some embodiments, signal conditioning block  118 ′ may be implemented as an averaging block of resistors to approximate the center tap of a load structure (e.g., to approximate center tap  123  of motor  104 ). For example, as shown in  FIG. 2 , signal conditioning block  118 ′ includes resistors  202   a ,  202   b  and  202   c . One terminal of each of resistors  202   a ,  202   b  and  202   c  is coupled to motor drive signals OUTA, OUTB and OUTC, respectively. The other terminals of resistors  202   a ,  202   b , and  202   c  are coupled together to generate center tap signal  143 ′. 
     Position and speed sensing circuit  112 ′ includes zero cross detector  116 ′ and observer circuit  206 . Zero cross detector  116 ′ includes comparators  204   a ,  204   b  and  204   c . Center tap signal  143 ′ is provided to an input of each of comparators  204   a ,  204   b  and  204   c . In an illustrative embodiment, motor drive signal OUTA is provided to another input of comparator  204   a , motor drive signal OUTB is provided to another input of comparator  204   b , and motor drive signal OUTC is provided to another input of comparator  204   c . Although not shown in  FIG. 2 , each comparator  204  may also receive a power supply signal (e.g., VBB of  FIG. 1 ) and a ground signal (e.g., GND of  FIG. 1 ). For example, comparators  204  may be “rail-to-rail” comparators (e.g., from GND to VBB). 
     Thus, comparators  204   a ,  204   b , and  204   c  compare center tap signal  143 ′ to motor drive signals OUTA, OUTB, and OUTC, respectively. Thus, each comparator  204  is between a respective phase voltage (e.g., OUTA, OUTB, and OUTC) and the approximated center tap of motor  104  (e.g., center tap signal  143 ′). Comparators  204   a ,  204   b  and  204   c  generate zero cross output signals ZXA, ZXB and ZXC, respectively, which are collectively shown as zero cross signals  210 . In some embodiments, zero cross signals  210  output from comparators  204  are digital signals having a logic high value when the respective motor control signal (e.g., OUTA, OUTB or OUTC) is greater than center tap signal  143 ′, and having a logic low value when the respective motor control signal (e.g., OUTA, OUTB or OUTC) is less than center tap signal  143 ′. 
     By comparing motor control signals OUTA, OUTB, and OUTC with center tap signal  143 ′, a zero crossing point of the motor back EMF for each phase (e.g., each winding  122 ) can be determined. The back EMF for each winding is a voltage opposing the voltage of the motor control signals (e.g., OUTA, OUTB, and OUTC) that is proportional to the speed of the motor. Knowing when back EMF zero crossing points occur is indicative of an angular position of motor  104  (e.g., of a position of a moving element (rotor) of motor  104  relative to a stationary element (stator) of motor  104 ). 
     Observer circuit  206  is coupled to receive zero cross signals  210  from zero cross detector  116 ′. Observer circuit  206  also receives a frequency adjustment parameter, K I , and a position adjustment parameter, K P , collectively shown as adjustment signals  208 . Adjustment signals  208  may also be provided to controller  126 ′. Based upon zero cross signals  210 , observer circuit  206  determines an electrical frequency of motor  104  and an angular position of motor  104  (e.g., an angular position of a moving element (rotor) of motor  104  relative to a stationary element (stator) of motor  104 ). Once the frequency and angular position of motor  104  are determined, signals  135 ′ to control gate driver  108 ′ for each phase of motor  104  can be synchronized, for example to drive motor  104  at a substantially constant frequency, regardless of changes to supply voltage VBB. 
     Observer circuit  206  includes counter  212 , which generates an output value, COUNT. In some embodiments, zero cross signals  210  (e.g., the ZXA signal, the ZXB signal, and the ZXC signal) are provided to counter  212 . Alternatively, in some embodiments, each of the ZXA signal, the ZXB signal, and the ZXC signal may be provided to one or more separate counters included in counter  212 . In an illustrative embodiment, counter  212  is an up/down counter that counts up or down based upon the value of zero cross signals  210 . As will be described, when counter  212  is an up/down counter, the output value COUNT is incremented (e.g., counts up) when a respective one of zero cross signals  210  (e.g., ZXA) is a logic low value and the output value COUNT is decremented (e.g., counts down) when a respective one of zero cross signals  210  (e.g., ZXA) is a logic high value. As will be described, the output value, COUNT, may be determined for a given “count sector” during operation of motor driver  102 . 
     Observer circuit  206  may generate a frequency signal (FREQ)  129 ′ and angular position signal (θ)  139 ′ based upon zero cross signals  210 , adjustment signals  208  and COUNT. As will be described, frequency signal (FREQ)  129 ′ may correspond to a determined frequency of motor  104 , and angular position signal (θ)  139 ′ may correspond to a determined angular position of motor  104 . Frequency signal (FREQ)  129 ′ is provided to controller  126 ′ and an angular position signal (θ)  139 ′ is provided to drive modulator  106 ′. 
     In some embodiments, such as shown in  FIG. 2 , controller  126 ′ may generate frequency demand signal  133 ′ based upon received frequency demand signal  131 ′, adjustment signals  208 , and frequency signal (FREQ)  129 ′. Controller  126 ′ provides frequency demand signal  133 ′ to drive modulator  106 . Drive modulator  106  receives angular position signal (θ)  139 ′ and generates signals  135 ′ to control gate driver  108 ′ for each phase of motor  104 , for example, based upon frequency demand signal  133 ′ and angular position signal (θ)  139 ′. 
       FIGS. 3A-B ,  4 A-D,  5  and  6  show timing diagrams to aid in understanding operation of motor system  100 . As shown in  FIGS. 1 and 2 , described embodiments drive a brushless direct current (BLDC) motor (e.g., motor  104  of  FIG. 1 ) without having Hall elements or other sensors in motor  104  to determine the motor position (e.g., sensorless operation). Further, described embodiments do not employ sense resistors in the current path for each winding  122  of motor  104  (e.g., there are not resistors in series with one or more of windings  122  of motor  104  to generate a sense voltage). 
     For simplicity, the timing diagrams are shown for drive modulator  106  generating trapezoidal motor control signals (e.g., motor driver  102  operating in a trapezoidal mode with motor control signals OUTA, OUTB and OUTC being generally trapezoidal in shape), although other embodiments may employ other control schemes (e.g., motor driver operating in a sinusoidal mode with motor control signals OUTA, OUTB and OUTC being sinusoidal in shape, etc.). 
     Referring to  FIG. 3A , a timing diagram of zero cross signals  210  (e.g., ZXA, ZXB and ZXC) is shown in relation to motor control signals OUTA, OUTB and OUTC. An illustrative waveform of zero cross signal ZXA is shown as curve  302 , an illustrative waveform of zero cross signal ZXB is shown as curve  304 , and an illustrative waveform of zero cross signal ZXC is shown as curve  306 . An illustrative waveform of motor control signal OUTA is shown as curve  308 , an illustrative waveform of motor control signal OUTB is shown as curve  310 , and an illustrative waveform of motor control signal OUTC is shown as curve  312 . 
     As shown, one or more count sectors occur within time intervals between indicated times t 0 , t 1 , t 2 , t 3 , t 4 , t 5 , t 6 , t 7  and t 8 . As shown, at time t 0 , when a first count sector may start, motor control signal OUTA is logic low and zero cross signal ZXA, corresponding to motor control signal OUTA, is also logic low. Similarly, at time t 0 , motor control signal OUTB is nearly logic low, and zero cross signal ZXB, corresponding to motor control signal OUTB, is logic low, and motor control signal OUTC is logic high, and zero cross signal ZXC, corresponding to motor control signal OUTC, is also logic high. 
     At time t 1 , the first count sector may complete and a second count sector may start. At time t 1 , motor control signal OUTA has become logic high and zero cross signal ZXA, corresponding to motor control signal OUTA, is also logic high. Zero cross signal ZXA may transition between logic low and logic high during the count sector, for example at a time indicated by line  301 . For example, motor control signal OUTA may transition between approximately GND (e.g., approximately 0V) and approximately VBB, and zero cross signal ZXA may transition from logic low to logic high when OUTA is approximately VBB/2, as shown. At time t 1 , motor control signal OUTB is still logic low and motor control signal OUTC is still logic high, so zero cross signals ZXB and ZXC remain logic low and logic high, respectively. 
     At time t 2 , the second count sector may complete and a third count sector may start. At time t 2 , motor control signal OUTA and zero cross signal ZXA remain logic high. At time t 2 , motor control signal OUTB and zero cross signal ZXB remain logic low. Motor control signal OUTC has become logic low, and zero cross signal ZXC has also become logic low. Zero cross signal ZXC may transition between logic high and logic low during the count sector, for example at a time indicated by line  303 . For example, motor control signal OUTC may transition between approximately VBB and approximately GND (e.g., approximately 0V), and zero cross signal ZXC may transition from logic high to logic low when OUTC is approximately VBB/2, as shown. Operation of zero cross signals ZXA, ZXB and ZXC continues as described for one or more subsequent count sectors during operation of motor driver  102 . 
       FIG. 3B  shows a magnified view of a transition of a zero cross signal (ZXA) in relation to the corresponding motor control signal (OUTA). As shown by curve  302 ′, a given zero cross signal, zero cross signal ZXA in this example, may have one or more transition glitches or commutations, shown as glitches  314 , as motor control signal OUTA, shown by curve  308 ′, increases between low and high voltages (or vice versa). For example, when the voltage of OUTA is near the value of center tap signal  143 ′, the output of comparator  204   a , ZXA, may transition multiple times as OUTA passes the trigger point set by center tap signal  143 ′. Such glitches may be caused by, for example, PWM switching signals, ringing of motor windings, and other transient conditions of motor system  100 . Thus, in a given count sector, zero cross signal ZXA may have one or more transitions between logic levels. Such glitches could lead motor driver  102  to inaccurately determine the angular position and frequency of motor  104  and, in turn, inaccurately adjust frequency demand signal  133 . As will be described, observer circuit  206  employs the COUNT value generated by counter  212  to reduce, or ideally eliminate, the effect glitches in the zero cross signals have on determining the angular position and frequency of motor  104 . Employing the COUNT value may eliminate the need to use blanking time (e.g., time when all of switching elements  137  are off) to determine the back EMF of motor  104 . 
       FIGS. 4A-4D  show illustrative timing diagrams of a zero cross signal (e.g., ZXA) in relation to the COUNT value during an illustrative count sector. As described, the COUNT value is incremented or decremented during a count sector based upon the value of the zero cross signal (ZXA in the example shown in  FIGS. 4A-4D ). For example, a count sector may start during an un-driven portion of the associated phase (e.g., the associated motor control signal, OUTA in the example shown in  FIGS. 4A-4D , is a logic low value). A count sector has a predetermined time duration, indicated as the duration between time t 0  and time t 1 . In some embodiments, the time duration of a count sector may be set based upon the expected midpoints of the zero cross signals (e.g., an expected frequency of motor  104 ). Although shown in  FIGS. 4A-4D  as being related only to ZXA, some embodiments may employ a COUNT value related to ZXB or ZXC. Some embodiments may employ a plurality of COUNT values, for example a COUNT value associated with each zero cross signal ZXA, ZXB, and ZXC. Other embodiments may employ a single COUNT value for all zero cross signals ZXA, ZXB, and ZXC. 
     At the beginning of a count sector, the COUNT value is incremented or decremented from an initial value (e.g., 0) based upon the logic level of the zero cross signal (e.g., incremented when the zero cross signal is logic high, and decremented when the zero cross signal is logic low). At the end of the count sector, the COUNT value is determined. If the COUNT value has not returned to its initial value (e.g., 0), then the zero cross signal did not transition between logic levels in the center of the count sector and, thus, the estimated frequency and angular position of motor  104  are incorrect. The COUNT value at the end of the count sector is proportional to the number of up- and down-counts of the angle variable. The difference between the COUNT value at the end of the count sector and the initial COUNT value (e.g., 0) may be used as an ERROR value. The ERROR value may, in turn, be used by observer circuit  206  to adjust the estimated frequency and angular position of motor  104  (e.g., via frequency signal (FREQ)  129 ′ and angular position signal (θ)  139 ′). After the ERROR value is determined, the COUNT value may be reset to the initial value (e.g., 0) to start a subsequent count sector. 
     At the end of each count sector, the estimated frequency and angular position of motor  104  (e.g., via frequency signal (FREQ)  129 ′ and angular position signal (θ)  139 ′) are updated. Note that phase is the integral of frequency. In illustrative embodiments, the estimated frequency is equal to a previous estimated frequency value (e.g., for a previous count sector) plus the ERROR value. In some embodiments, the ERROR value may be multiplied by frequency adjustment parameter, K I , and the product may be added to the previous estimated frequency value. In illustrative embodiments, the estimated angular position is equal to the current estimated frequency value plus the ERROR value plus the previous estimated angular position. In some embodiments, the ERROR value may be multiplied by position adjustment parameter, K P , and the product may be added to the current estimated frequency value and the previous estimated angular position. For example, the current estimated frequency, FREQ(n), may be given by: FREQ(n)=FREQ(n−1)+(K I ·ERROR), and the current angular position, θ(n), may be determined by: θ(n)=θ(n−1)+(K P ·ERROR)+FREQ(n), and, where θ(n−1) is the previous value of the angular position and FREQ(n−1) is the previous value of the estimated frequency. 
     The frequency adjustment parameter, K I , and position adjustment parameter, K P , may be adjustable to accommodate a wide variety of loads (e.g., to accommodate different properties of motor  104 ). For example, properties of motor  104  may change based upon a size or type of motor  104 . For example, a high value of position adjustment parameter, K P , allows larger changes in the estimated angular position each count sector, which may allow the position to be accurately synchronized more quickly, for example at initial start-up of motor system  100 . Similarly, a high value of frequency adjustment parameter, K I , allows larger changes in the estimated frequency each count sector, which may allow the estimated frequency to be accurately synchronized more quickly, for example at initial start-up of motor system  100 . Some embodiments may adjust the values of frequency adjustment parameter, K I , and position adjustment parameter, K P , during operation of motor system  100 , for example to allow coarser adjustment of the estimated frequency and estimated angular position at initial start-up of motor system  100 , and then allow finer adjustment of the estimated frequency and estimated angular position after operating time of motor system  100 . Thus, frequency adjustment parameter, and position adjustment parameter, K P , are the steps by which to adjust the estimated frequency and angular position to correct for the ERROR value, and therefore adjust the convergence speed of the control loop of motor system  100 . 
       FIG. 4A  shows an illustrative timing diagram of the ZXA signal, shown as curve  402 , and an illustrative plot of the COUNT value, shown as curve  404 . As shown in  FIG. 4A , when a zero cross occurs in the center of the count sector (at time t cross ), the COUNT value returns to the initial value at the end of the count sector (at time t 1 ). As shown, at the start of the count sector (at time t 0 ), the COUNT value is decremented from an initial value while ZXA is logic low. At time t cross , a zero cross of OUTA is detected, and ZXA transitions from logic low to logic high, and the COUNT value is incremented until the end of the count sector at time t 1 . In the illustrative condition shown in  FIG. 4A , time t cross  occurs in the middle of the count sector and, thus, the COUNT value returns to the initial value at the end of the count sector at time t 1 . Thus, there is no ERROR value, and observer circuit  206  updates the estimated frequency and angular position of motor  104  (e.g., via frequency signal (FREQ)  129 ′ and angular position signal (θ)  139 ′) without making an ERROR adjustment. In other words, the estimated frequency and angular position of motor  104  was correct for the count sector. 
     The angular position variable changes even though ERROR=0 because the previous angular position value is summed with the previous frequency variable in order to determine the new angular position. In steady-state operation of motor  104 , the ERROR value is ideally 0 at the end of each count sector, since, at steady-state, the frequency remains substantially constant. The angular position is updated to reflect the rotation of motor  104  (e.g., the position of the moving rotor). Thus, for the illustrative conditions shown in  FIG. 4A , FREQ(n)=FREQ(n−1), and θ(n)=θ(n−1)+FREQ (n) since ERROR=0. 
       FIG. 4B  shows another illustrative timing diagram of the ZXA signal, shown as curve  406 , and an illustrative plot of the COUNT value, shown as curve  408 . As shown in  FIG. 4B , when a zero cross occurs before the center of the count sector (at time t cross ), the COUNT value exceeds the initial value at the end of the count sector (at time t 1 ). As shown, at the start of the count sector (at time t 0 ), the COUNT value is decremented from an initial value while ZXA is logic low. At time t cross , a zero cross of OUTA is detected, and ZXA transitions from logic low to logic high, and the COUNT value is incremented until the end of the count sector at time t 1 . In the illustrative condition shown in  FIG. 4B , time t cross  occurs earlier than the middle of the count sector and, thus, the COUNT value has a non-zero value at the end of the count sector at time t 1 , since the COUNT value is incremented for a longer portion of the count sector. Thus, the ERROR value has a positive value, shown as ERROR value  410 , which is the difference between the initial value of COUNT and the value of COUNT at the end of the count sector. Observer circuit  206  updates the estimated frequency and angular position of motor  104  (e.g., via frequency signal (FREQ)  129 ′ and angular position signal (θ)  139 ′), making an ERROR adjustment. In other words, the estimated frequency and angular position of motor  104  were inaccurate for the count sector, meaning the speed (e.g., frequency) of motor  104  changed from the previous count sector. 
     The angular position variable changes because the previous angular position value is summed with the previous frequency variable and summed with the ERROR value, adjusted by the position adjustment parameter, K P , in order to determine the new angular position. The angular position is updated to reflect the rotation of motor  104  (e.g., the position of the moving rotor). Thus, for the illustrative conditions shown in  FIG. 4B , the current frequency FREQ (n)=FREQ(n−1)+(K I ·ERROR), and the current angular position θ(n)=θ(n−1)+(K P ·ERROR)+FREQ(n), since ERROR≠0. 
       FIG. 4C  shows another illustrative timing diagram of the ZXA signal, shown as curve  412 , and an illustrative plot of the COUNT value, shown as curve  416 . As shown in  FIG. 4B , when a zero cross occurs after the center of the count sector (at time t cross ), the COUNT value does not reach the initial value at the end of the count sector (at time t 1 ). As shown, at the start of the count sector (at time t 0 ), the COUNT value is decremented from an initial value while ZXA is logic low. At time t cross , a zero cross of OUTA is detected, and ZXA transitions from logic low to logic high, and the COUNT value is incremented until the end of the count sector at time t 1 . In the illustrative condition shown in  FIG. 4C , time t cross  occurs later than the middle of the count sector and, thus, the COUNT value has a non-zero value at the end of the count sector at time t 1 , since the COUNT value is decremented for a longer portion of the count sector. Thus, the ERROR value has a negative value, shown as ERROR value  414 , which is the difference between the initial value of COUNT and the value of COUNT at the end of the count sector. Observer circuit  206  updates the estimated frequency and angular position of motor  104  (e.g., via frequency signal (FREQ)  129 ′ and angular position signal (θ)  139 ′), making an ERROR adjustment. In other words, the estimated frequency and angular position of motor  104  were inaccurate for the count sector, meaning the speed (e.g., frequency) of motor  104  changed from the previous count sector. 
     The angular position variable changes because the previous angular position value is summed with the previous frequency variable and summed with the ERROR value, adjusted by the position adjustment parameter, K P , in order to determine the new angular position. The angular position is updated to reflect the rotation of motor  104  (e.g., the position of the moving rotor). Thus, for the illustrative conditions shown in  FIG. 4C , the current frequency FREQ(n)=FREQ(n−1)+(K I ·ERROR), and the current angular position θ(n)=θ(n−1)+(K P ·ERROR)+FREQ(n), since ERROR≠0. 
       FIG. 4D  shows an illustrative timing diagram of the ZXA signal, shown as curve  418 , and an illustrative plot of the COUNT value, shown as curve  422 . Similarly as shown in  FIG. 4A ,  FIG. 4D  shows the condition where a zero cross occurs in the center of the count sector (at time t cross ). Thus, the COUNT value returns to the initial value at the end of the count sector (at time t 1 ), such that there is no ERROR value. As described in regard to  FIG. 3B , zero cross signal ZXA may have one or more transition glitches  420  as the OUTA signal passes the zero cross trigger point. Described embodiments reduce the effect of the glitches by integrating them via counter  212 , which averages the glitches and provides a robust zero cross detection without employing blanking time. 
       FIG. 5  shows an illustrative timing diagram showing the COUNT value (curve  508 ) in relation to zero cross signals ZXA (curve  502 ), ZXB (curve  504 ), and ZXC (curve  506 ), as well as the estimated frequency, FREQ (curve  512 ), and the estimated angular position, θ (curve  514 ). As can be seen from  FIG. 5 , the angular position signal, θ, corresponds to the integral of the frequency signal, FREQ, and the slope of the angular position signal, θ, corresponds to the speed of motor  104 . As shown in  FIG. 5 , the angular position signal, θ, measures the angular position of motor  104  from 0 degrees to approximately 360 degrees (e.g., a full rotation) based on a number of degrees corresponding to each count sector. 
     The illustrative operating conditions shown in  FIG. 5  correspond to six count sectors, shown as count sectors A-F. In count sectors A and D, zero cross signal ZXA is being monitored by observer circuit  206  (e.g., COUNT corresponds to ZXA). In count sectors B and E, zero cross signal ZXC is being monitored by observer circuit  206  (e.g., COUNT corresponds to ZXC). In count sectors C and F, zero cross signal ZXB is being monitored by observer circuit  206  (e.g., COUNT corresponds to ZXB). At the end of each count sector, the ERROR value is determined, and the COUNT value is reset to the initial value. 
     In count sector A, observer circuit  206  is monitoring zero cross signal ZXA for a rising edge. Thus, while zero cross signal ZXA is logic low, the value of COUNT is decremented (e.g., counter  212  counts down from the initial value). When zero cross signal ZXA transitions to logic high, the value of COUNT is incremented (e.g., counter  212  counts up until the count sector ends). At the end of the count sector, an ERROR value is generated based upon any difference between the final COUNT value and the initial COUNT value. For example, as shown in the illustrative timing diagram of  FIG. 5 , ERROR  510   a  may be generated for count sector A, since the transition of zero cross signal ZXA occurred after the midpoint of count sector A. At the end of count sector A, the angular position, θ, and frequency, FREQ, of motor  104  are updated based upon the ERROR value (and any adjustment parameters). For example, the current frequency FREQ(n)=FREQ(n−1)+(K I ·ERROR), and the current angular position θ(n)=θ(n−1)+(K P ·ERROR)+FREQ(n), where the value of ERROR is based upon the value of the counter. In count sector A, the FREQ signal has a first value as shown by curve  512 , and the angular position changes at a first rate (e.g., slope  516   a ) as shown by curve  514 . 
     In count sector B, observer circuit  206  is monitoring zero cross signal ZXC for a falling edge. Thus, while zero cross signal ZXC is logic high, the value of COUNT is decremented (e.g., counter  212  counts down from the initial value). When zero cross signal ZXC transitions to logic low, the value of COUNT is incremented (e.g., counter  212  counts up until the count sector ends). At the end of the count sector, an ERROR value is generated based upon any difference between the final COUNT value and the initial COUNT value. For example, as shown in the illustrative timing diagram of  FIG. 5 , ERROR  510   b  may be generated for count sector B, since the transition of zero cross signal ZXC occurred before the midpoint of count sector B. At the end of count sector B, the angular position, θ, and frequency, FREQ, of motor  104  are updated (e.g., from the values determined for count sector A) based upon the ERROR value (and any adjustment parameters). For example, the current frequency FREQ(n)=FREQ(n−1)+(K I ·ERROR), and the current angular position θ(n)=θ(n−1)+(K P ·ERROR)+FREQ(n), where the value of ERROR is based upon the value of the counter. In count sector B, the FREQ signal has a second value, lower than the value during count sector A, as shown by curve  512  (since the frequency was reduced in response to the ERROR value determined for count sector A), and the angular position changes at a first rate (e.g., slope  516   b ) as shown by curve  514 . 
     In count sector C, observer circuit  206  is monitoring zero cross signal ZXB for a rising edge. Thus, while zero cross signal ZXB is logic low, the value of COUNT is decremented (e.g., counter  212  counts down from the initial value). When zero cross signal ZXB transitions to logic high, the value of COUNT is incremented (e.g., counter  212  counts up until the count sector ends). At the end of the count sector, an ERROR value is generated based upon any difference between the final COUNT value and the initial COUNT value. For example, as shown in the illustrative timing diagram of  FIG. 5 , there is no ERROR value for count sector C, since the transition of zero cross signal ZXB occurred at the midpoint of count sector C. At the end of count sector C, the angular position, θ, and frequency, FREQ, of motor  104  are updated (e.g., from the values determined for count sector B). For example, the current frequency FREQ(n)=FREQ(n−1), and the current angular position θ(n)=θ(n−1)+FREQ(n), since ERROR=0. In count sector C, the FREQ signal has the same value as in count sector B, as shown by curve  512  (since ERROR=0), and the angular position changes at a rate (e.g., slope  516   c ) as shown by curve  514 . 
     In count sector D, observer circuit  206  is monitoring zero cross signal ZXA for a falling edge. Thus, while zero cross signal ZXA is logic high, the value of COUNT is decremented (e.g., counter  212  counts down from the initial value). When zero cross signal ZXA transitions to logic low, the value of COUNT is incremented (e.g., counter  212  counts up until the count sector ends). At the end of the count sector, an ERROR value is generated based upon any difference between the final COUNT value and the initial COUNT value. For example, as shown in the illustrative timing diagram of  FIG. 5 , there is ERROR value  510   c  for count sector D, since the transition of zero cross signal ZXA occurred before the midpoint of count sector D. At the end of count sector D, the angular position, θ, and frequency, FREQ, of motor  104  are updated (e.g., from the values determined for count sector B). For example, the current frequency FREQ(n)=FREQ(n−1)+(K I ·ERROR), and the current angular position θ(n)=θ(n−1)+(K P ·ERROR)+FREQ(n), where the value of ERROR is based upon the value of the counter. In count sector D, the FREQ signal has the same value as in count sector B and C, as shown by curve  512 , and the angular position changes at a rate (e.g., slope  516   d ) as shown by curve  514 . 
     In count sector E, observer circuit  206  is monitoring zero cross signal ZXC for a rising edge. Thus, while zero cross signal ZXC is logic low, the value of COUNT is decremented (e.g., counter  212  counts down from the initial value). When zero cross signal ZXC transitions to logic high, the value of COUNT is incremented (e.g., counter  212  counts up until the count sector ends). At the end of the count sector, an ERROR value is generated based upon any difference between the final COUNT value and the initial COUNT value. For example, as shown in the illustrative timing diagram of  FIG. 5 , ERROR  510   a  may be generated for count sector E, since the transition of zero cross signal ZXC occurred after the midpoint of count sector E. At the end of count sector E, the angular position, θ, and frequency, FREQ, of motor  104  are updated based upon the ERROR value (and any adjustment parameters). For example, the current frequency FREQ(n)=FREQ(n−1)+(K I ·ERROR), and the current angular position θ(n)=θ(n−1)+(K P ·ERROR)+FREQ(n), where the value of ERROR is based upon the value of the counter. In count sector E, the FREQ signal has a fourth value as shown by curve  512  (adjusted by error  510   c  from count sector D), and the angular position changes at a rate (e.g., slope  516   e ) as shown by curve  514 , which is increased due to ERROR  510   c.    
     In count sector F, observer circuit  206  is monitoring zero cross signal ZXB for a falling edge. Thus, while zero cross signal ZXB is logic high, the value of COUNT is decremented (e.g., counter  212  counts down from the initial value). When zero cross signal ZXB transitions to logic low, the value of COUNT is incremented (e.g., counter  212  counts up until the count sector ends). At the end of the count sector, an ERROR value is generated based upon any difference between the final COUNT value and the initial COUNT value. For example, as shown in the illustrative timing diagram of  FIG. 5 , there is no ERROR value for count sector F, since the transition of zero cross signal ZXB occurred at the midpoint of count sector F. At the end of count sector F, the angular position, θ, and frequency, FREQ, of motor  104  are updated (e.g., from the values determined for count sector E). For example, the current frequency FREQ(n)=FREQ(n−1), and the current angular position θ(n)=θ(n−1)+FREQ(n), since ERROR=0. In count sector F, the FREQ signal has is reduced from count sector E (e.g., due to ERROR  510   d ), as shown by curve  512 , and the angular position changes at a rate (e.g., slope  516   f ) as shown by curve  514 , which is reduced due to ERROR  510   d.    
       FIG. 6  shows a timing diagram of an illustrative relationship between the angular position, θ (curve  604 ), frequency, FREQ (curve  602 ), and the speed of motor  104 . For example, as shown in  FIG. 6 , when the speed of motor  104  is constant (shown as steady state period  606 ), the angular position, θ, increments from 0 to 359 degrees (and then restarting at 0 degrees) over a constant time period, T 1 . The frequency signal, FREQ, may adjust occasionally (e.g., adjustments  612 ) to maintain the speed of motor  104  as a constant. When motor  104  is accelerating, for example during time period  608 , the frequency signal, FREQ, may increase in one or more steps  614  as the speed of motor  104  increases. Similarly, as motor  104  increases in speed, the time period to complete a rotation decreases (e.g., as shown by time periods T 2 &gt;T 3 &gt;T 4 , and so on) and, thus, the slope of the angular position, θ, increases. When motor  104  is decelerating, for example during time period  610 , the frequency signal, FREQ, may decrease in one or more steps  616  as the speed of motor  104  decreases. Similarly, as motor  104  decreases in speed, the time period to complete a rotation increases (e.g., as shown by time periods T 5 &lt;T 6 , and so on) and, thus, the slope of the angular position, θ, decreases. 
       FIG. 7  shows a flow diagram of an illustrative process,  700 , for operating motor driver  102 . Process  700  starts at block  702 , for example at an initial power on of motor system  100 . At block  704 , counter  212  is set to an initial value (e.g., 0). Also at block  704 , frequency adjustment parameter, K I , and position adjustment parameter, K P , are set to initial values, for example based on one or more parameters of motor  104 . At block  706 , if a motor demand signal (e.g., frequency demand signal  131  of  FIG. 1 ) is not received, then motor  104  may be idle (e.g., stopped), and process  700  remains at block  706  until a motor demand signal is received to start motion of motor  104 . 
     At block  706 , if a motor demand signal (e.g., frequency demand signal  131  of  FIG. 1 ) is received, then at block  708 , motor driver  102  generates motor phase control signals OUTA, OUTB and OUTC. At block  710 , signal conditioning block  118  generates center tap signal  143 . At block  712 , zero cross detector  116  compares motor phase control signals OUTA, OUTB, and OUTC to center tap signal  143  to generate zero cross signals ZXA, ZXB, and ZXC. At block  714 , position and speed sensing circuit  112  generates signals to adjust motor phase control signals OUTA, OUTB and OUTC based upon zero cross signals ZXA, ZXB, and ZXC. Process  700  returns to block  706  to receive a motor demand signal. Process  700  may run continually while motor system  100  is powered. 
       FIG. 8  shows additional detail of block  714  of  FIG. 7 , shown as process  714 ′. Process  714 ′ may run continually while motor system  100  is powered, for example in parallel with process  700 . At block  802 , process  714 ′ starts. At block  804 , a count sector starts. At block  806 , observer circuit  206  monitors zero cross signals ZXA, ZXB, and ZXC for a transition (edge). If, at block  806 , observer circuit  206  is monitoring for a rising edge of a zero cross signal, at block  808  if the zero crossing signal is logic low, then at block  810  counter  212  is decremented. If, at block  806 , observer circuit  206  is monitoring for a rising edge of a zero cross signal, at block  808  if the zero crossing signal is logic high, then at block  812  counter  212  is incremented. If, at block  806 , observer circuit  206  is monitoring for a falling edge of a zero cross signal, at block  814  if the zero crossing signal is logic low, then at block  818  counter  212  is incremented. If, at block  806 , observer circuit  206  is monitoring for a falling edge of a zero cross signal, at block  814  if the zero crossing signal is logic high, then at block  816  counter  212  is decremented. After any of blocks  810 ,  812 ,  816  or  818 , process  714 ′ proceeds to block  820 . 
     At block  820 , the angular position, θ, and frequency, FREQ, of motor  104  may be determined, for example based upon the previous angular position and frequency, such as described in regard to  FIGS. 4A-4D and 5 . At block  822 , if the count sector has ended, then at block  824 , the ERROR value may be determined based upon the COUNT value at the end of the count sector. At blocks  826  and  828 , the angular position, θ, and frequency, FREQ, of motor  104  may be updated based upon the ERROR value (and any adjustment parameters). For example, the current frequency FREQ(n)=FREQ(n−1)+(K I ·ERROR), and the current angular position θ(n)=θ(n−1)+(K P ·ERROR)+FREQ(n), where the value of ERROR is based upon the value of the counter. At block  830 , controller  126  may optionally adjust the speed signal (e.g., frequency demand signal  133 ) to, in turn, adjust the motor phase control signals OUTA, OUTB and OUTC in response to the determined angular position, θ, and frequency, FREQ, of motor  104 . 
     At block  832 , counter  212  is reset to the initial value (e.g., the count sector has ended), and process  714 ′ returns to block  804  to start a subsequent count sector. 
     Thus, described embodiments provide hardware and/or software to control BLDC motors without the need for a complicated control processes, sense resistors in the motor current path, blanking time, or other similar complexities, while also being adjustable to operate a wide range of different motors. 
     As used herein, the term “processor” describes an electronic circuit that performs a function, an operation, or a sequence of operations. The function, operation, or sequence of operations can be hard coded into the electronic circuit or soft coded by way of instructions held in a memory device. A “processor” can perform the function, operation, or sequence of operations using digital values or using analog signals. In some embodiments, the “processor” can be embodied in an application specific integrated circuit (ASIC). In some embodiments, the “processor” can be embodied in a microprocessor with associated program memory. In some embodiments, the “processor” can be embodied in a discrete electronic circuit. The “processor” can be analog, digital or mixed-signal. 
     Illustrative embodiments may be implemented as a circuit, an integrated circuit, a multi-chip module, a single card, or a multi-card circuit pack. Various functions of circuit elements may also be implemented as processing blocks in a software program. Such software may be employed in, for example, a digital signal processor, microcontroller, or general purpose computer. Thus, described embodiments may be implemented in hardware, a combination of hardware and software, software, or software in execution by one or more processors. 
     Some embodiments may be implemented in the form of methods and apparatuses for practicing those methods. Described embodiments may also be implemented in the form of program code, for example, stored in a storage medium, loaded into and/or executed by a machine, or transmitted over some transmission medium or carrier, such as over electrical wiring or cabling, through fiber optics, or via electromagnetic radiation. A non-transitory machine-readable medium may include but is not limited to tangible media, such as magnetic recording media including hard drives, floppy diskettes, and magnetic tape media, optical recording media including compact discs (CDs) and digital versatile discs (DVDs), solid state memory such as flash memory, hybrid magnetic and solid state memory, non-volatile memory, volatile memory, and so forth, but does not include a transitory signal per se. When embodied in a non-transitory machine-readable medium, and the program code is loaded into and executed by a machine, such as a computer, the machine becomes an apparatus for practicing the method. 
     When implemented on a processing device, the program code segments combine with the processor to provide a unique device that operates analogously to specific logic circuits. Such processing devices may include, for example, a general purpose microprocessor, a digital signal processor (DSP), a reduced instruction set computer (RISC), a complex instruction set computer (CISC), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a programmable logic array (PLA), a microcontroller, an embedded controller, a multi-core processor, and/or others, including combinations of the above. Described embodiments may also be implemented in the form of a bitstream or other sequence of signal values electrically or optically transmitted through a medium, stored magnetic-field variations in a magnetic recording medium, etc., generated using a method and/or an apparatus as recited in the claims. 
     Various elements, which are described in the context of a single embodiment, may also be provided separately or in any suitable subcombination. It will be further understood that various changes in the details, materials, and arrangements of the parts that have been described and illustrated herein may be made by those skilled in the art without departing from the scope of the following claims.