Phase-locked loop having improved locking capabilities
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates generally to phase-locked loops for locking the phase of a variable-frequency output signal to the phase of an input signal, and specifically to such phase-locked loops capable of performing this locking function for any input signal having a frequency within a predetermined limit of a reference frequency. 
     2. Description of the Prior Art 
     Phase-locked loops are well known in the prior art. A phase-locked loop (hereinafter PLL) is used to synchronize, or lock, the phase and frequency of a locally produced variable-frequency output signal to the phase and frequency of an input signal. Typically, a PLL includes a phase comparator and a low-pass filter in a forward signal path, and a voltage-controlled oscillator (hereinafter VCO) for generating the output signal in a feedback path. The phase comparator is reponsive to the input and output signals. With no input signal present the phase comparator output is zero allowing the VCO to operate at a set frequency known as its free-running frequency. When an input signal is applied to the PLL, the phase comparator compares the phase and frequency of the input signal with the phase and frequency of the output signal and produces an error signal in response thereto. The error signal is filtered, amplified, and applied to the VCO. Since the frequency of the VCO signal is dependent on the voltage input thereto, the error signal forces the output signal frequency to vary in a direction to reduce the frequency difference between the input signal and the output signal. 
     Choosing the bandwidth of a PLL represents a critical design decision due to the significant effect of bandwidth on performance. Decreasing the PLL bandwidth slows the capture process, i.e., more time is required for the output signal to lock to the input signal. Also, the frequency range of input signals to which the output signal will lock decreases. However, a decreased bandwidth improves noise rejection characteristics of the PLL. Thus, the bandwidth chosen must represent a compromise between a narrow bandwidth providing high noise rejection and a wide bandwidth offering fast synchronization over a wide range of input frequencies. 
     U.S. Pat. No. 4,365,211 assigned to the assignee of the present invention, discloses means for overcoming this bandwidth choice dilemma. This patent discloses a phase-locked loop having two feedback loops: an initialization feedback loop for synchronizing a variable-frequency output signal to a reference signal, and a primary feedback loop for synchronizing the output signal to an input signal after the first-mentioned synchronization has been accomplished. A VCO, in cooperation with an integrator, produces the variable frequency output signal. The VCO and integrator are common components to both the primary and initialization loops. The primary loop has a narrow bandwidth and the initialization loop has a wide bandwidth; the reference signal has a frequency approximately equal to the frequency of the input signal. In operation, in the initialization loop the frequency of the reference signal is compared to the frequency of the output signal and an error signal is produced. An off-frequency detector is responsive to the error signal for producing a switching control signal having two states; the state of the switching control signal is dependent on the error signal. A switch, responsive to the switching control signal, selectively connects the initialization loop to the integrator and the VCO when the difference between the frequencies of the reference signal and the output signal is large. When this difference is small, the switch selectively connects the primary loop components to the integrator and the VCO. Thus, the wide bandwidth initialization loop adjusts the frequency of the output signal until it equals the frequency of the reference signal at which time the frequency of the output signal will be close to the frequency of the input signal. When this has been achieved, the primary loop with its narrow bandwidth is activated. Now the error signal represents the difference between the frequencies of the input signal and the output signal. The VCO is responsive to this error signal thereby allowing the output signal to precisely track the input signal. By providing dual operational modes, the invention offers the advantages of both a wide and a narrow-bandwidth PLL. 
     In actual operation it was discovered that the off-frequency detector of U.S. Pat. No. 4,365,211 sometimes improperly reactivated the initialization loop when the primary loop was operating, i.e., when the output signal was already locked to the input signal. This, of course, caused deactivation of the primary loop and loss of synchronism between the input and output signals. This problem occurred when the input signal was buried in noise. Phase jitter of the output signal, caused by the noise, falsely triggered the off-frequency detector, thereby activating the initialization loop. The present invention overcomes this problem, thus providing a phase-locked loop with improved locking capabilities for noisy input signals. 
     SUMMARY OF THE INVENTION 
     A phase-locked loop provides improved locking capabilities for a noisy input signal. The objective of the phase-locked loop is to synchronize the phase of a variable-frequency output signal to the phase of an input signal. Synchronization of the phase insures that the input and output signals have identical frequencies. A voltage-controlled oscillator produces the variable frequency output signal in cooperation with a primary feedback loop having a narrow bandwidth or an initialization feedback loop having a wide bandwidth. A reference signal has a frequency approximately equal to the frequency of the input signal. In the initialization feedback loop the frequency of the output signal is compared to the frequency of the reference signal for producing an error signal. The voltage-controlled oscillator is responsive to the error signal via a switch. The error signal causes the frequency of the output signal to change such that the frequency of the output signal equals the frequency of the reference signal. When the frequencies of the output signal and the reference frequency differ by less than a predetermined limit, an off-frequency detector causes the switch to change states. Now the voltage-controlled oscillator is responsive to a phase detector of the primary feedback loop. The phase detector compares the frequencies of the output signal and the input signal to produce a signal representative of the difference between the frequencies of the output signal and the input signal. The output signal is input to the voltage-controlled oscillator, via the switch, for precisely locking the frequency and phase of the output signal to the frequency and phase of the input signal. The off-frequency detector will not erroneously reactivate the initialization loop (and deactivate the primary loop) when the output signal experiences phase jitter caused by a noisy input signal. The present invention can therefore produce an output signal which accurately tracks an input signal even if the latter is buried in noise. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a first embodiment phase-locked loop constructed according to the teachings of the present invention; 
     FIG. 2 is a block diagram of a second embodiment of a phase-locked loop constructed according to the teachings of the present invention; 
     FIG. 3 is a timing diagram showing the temporal relationships of the various signals depicted in FIG. 1; and 
     FIG. 4 is an electrical schematic illustrating selected portions of the phase-locked loop of FIG. 2. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Positive logic and a positive ground are utilized throughout the descriptions of FIGS. 1, 2, 3, and 4. Thus a binary one is represented by ground potential and a binary zero is represented by a negative potential. 
     Referring to FIG. 1, there is shown a phase-locked loop 10 for producing an output signal, V out , having a phase (and therefore frequency) locked to the phase of an input signal, V in . V out  is produced by a voltage-controlled oscillator 12 wherein the frequency and phase of V out  are determined by a control voltage applied to an input terminal 13 of the voltage-controlled oscillator 12. The control voltage is provided by the selective operation of one of two feedback loops: a primary feedback loop, consisting of a first phase detector 14, and an initialization feedback loop, consisting of a second phase detector 28. In response to an off-frequency detector 32 which is responsive to the second phase detector 28, a switch 34 determines which of the two feedback loops is operative to control the voltage-controlled oscillator 12 at the input terminal 13 thereof. The initialization feedback loop operates when the frequency difference between V out  and V in  is above a predetermined limit. The initialization feedback loop has a wide bandwidth to provide a broad capture range, i.e., the range of frequencies over which V out  can be locked to a reference frequency approximating V in . The primary feedback loop has a narrow bandwidth to provide improved noise rejection for the phase-locked loop 10 and operates when the frequency difference between V out  and V in  is below the predetermined limit. 
     As can be seen in FIG. 1, in the primary feedback loop V out  is input to the first phase detector 14. The first phase detector 14 is also responsive to V in  to detect a phase difference between V out  and V in . The first phase detector 14 produces a difference signal in response to the phase difference; the difference signal is selectively input to the voltage-controlled oscillator 12 at the input terminal 13, via the switch 34, for controlling the frequency and phase of V out  only when the difference between the frequency of V out  and the frequency of V in  is below the predetermined limit. Operation of the switch 34 will be discussed in greater detail hereinafter. 
     In the initialization feedback loop V out  is input to the second phase detector 28. Within the second phase detector 28, V out  is input to a first mixer 16 and a delay circuit 18. A second mixer 20 is responsive to the delay circuit 18. The first mixer 16 and the second mixer 20 are also responsive to a first reference signal designated V ref1 . The first mixer 16, the delay circuit 18, and the second mixer 20 constitute the second phase detector 28. 
     The second phase detector 28 detects a phase difference between V out  and V ref1  ; the frequency of V ref1  is approximately equal to the frequency of V in . The second phase detector 28 produces a signal V e1  (see FIG. 1) representative of the difference between the frequency of V ref1  and the frequency of V out . V e1  is selectively input to the voltage-controlled oscillator 12 at the input terminal 13, via the switch 34, for controlling the frequency and phase of V out  when the disparity between the frequency of V out  and the frequency of V ref1  is above the predetermined limit. 
     The operation of the second phase detector 28 is as follows. The first mixer 16 determines the frequency difference between V ref1  and V out  and produces the first error signal, V e1 , representative of the frequency difference between the mixed signals. The delay circuit 18, which is responsive to V out , slightly delays and inverts V out . The delayed and inverted V out  signal and V ref1  are mixed in the second mixer 20 producing a second error signal, V e2 , representative of the frequency difference between the mixed signals. The signals V e1  and V e2  are both low frequency slightly distorted sine waves representative of the frequency difference between V ref1  and V out . V e2  is approximately 180 degrees out of phase with V e1 . V e1  and V e2  are illustrated in FIG. 3. 
     In one embodiment of the present invention V in  has a frequency close to 5.2 MHz; V ref1  has an extremely precise frequency of 5.2 MHz. Also, note that the delay circuit 18 functions solely to impart a phase difference and inversion between V e1  and V e2 . Therefore, in another embodiment the delay circuit 18 can be repositioned such that V ref1  is input thereto and the first mixer 16 is responsive to the output of the delay circuit 18. In this embodiment the second mixer 20 is responsive to V out . 
     Continuing with a description of the off-frequency detector 32 in FIG. 1, a level detector 36 is responsive to V e1  and produces a square wave signal V sq1  ; a level detector 38 is responsive to V e2  and produces a square wave signal V sq2 . V sq1  and V sq2  are combined in a logic circuit 40 which produces two output signals, V L1  and V L2 . The level detectors 36 and 38 and the logic circuit 40 constitute a logic means 41. An inverting set input terminal of a flip-flop 42 is responsive to V L1  ; an inverting reset input terminal of the flip-flop 42 is responsive to V L2 . The flip-flop 42 produces a square wave designated V ff . V ff  is input to a differentiator/rectifier 43. An integrator 44 is responsive to an output terminal of the differentiator/rectifier 43, and a Schmitt trigger 46 is responsive to an output terminal of the integrator 44. The Schmitt trigger 46 produces the switching signal, V sw , for controlling the switch 34. The differentiator/rectifier 43 and the integrator 44 constitute a frequency detector 45. The level detectors 36 and 38, the logic circuit 40, the flip-flop 42, the differentiator/rectifier 43, the integrator 44, and the Schmitt trigger 42 constitute the off-frequency detector 32. 
     Operation of the off-frequency detector 32 is as follows. The level detector 36 converts the sine wave signal V e1  to a square wave signal V sq1 . V sq1  may have chatter on the leading and trailing edges of each pulse if V out  is distorted by phase jitter. The phase jitter is present when V in  is noisy. Both signals V e1  and V sq1  are illustrated in FIG. 3. The level detector 38 produces a square wave signal V sq2  in response to V e2 . Like V sq1 , V sq2  may have jitter on the leading and trailing edges of each pulse; V sq2  is also shown in the FIG. 3 timing diagram. The phase difference between V e1  and V e2  in maintained in processing through the level detectors 36 and 38, but the inverse relationship is lost. Therefore, V sq1  is only slightly out of phase with V sq2 . 
     As discussed above, the chatter associated with the pulses of V sq1  and V sq2  can cause improper operation of the off-frequency detector 32 by causing the switching signal V sw  to change states incorrectly. For example, the chatter can cause activation of the initialization loop, and deactivation of the primary loop when V out  is already synchronized with V in . The logic circuit 40 and the flip-flop 40 eliminate this problem. 
     Within the logic circuit 40, V L1  and V L2  are produced by arithmetic operations on V sq1  and V sq2 . V L1  is the logical sum of V sq2  and the inverse of V sq1 . V L1  is present at the first output terminal of logic circuit 40 and input to the inverting set input terminal of the flip-flop 42. V L2  is the logical sum of V sq1  and the inverse of V sq2 . V L2  is provided at the second output terminal of logic circuit 40 and input to the inverting reset terminal of the flip-flop 42. Both V L1  and V L2  are shown in FIG. 3. Through the action of the flip-flop 42, V L1  and V L2  are converted to a square wave signal (V ff ) having no chatter on either the leading or the trailing edges. See FIG. 3. Once a transition of V ff  has occurred, V ff  cannot make a subsequent transition unless V out  undergoes an additional 180° phase shift (either plus or minus). Phase jitter on V out , induced by leading-edge and trailing-edge chatter in V sq1  and V sq2  has, therefore, been eliminated because it is unlikely V out  will contain jitter components with magnitude sufficient to cause a 180° phase shift. 
     The frequency of V ff  represents the difference between the frequency of V out  and the frequency of V ref1 . In response to V ff  the differentiator/rectifier 43 produces a current pulse for each positive transition of V ff  ; the integrator 44 integrates the current pulses. The integrator 44 is a frequency-to-voltage converter circuit that is insensitive to noise because the integrator 44 integrates over a long period. Occasional false transitions in V ff  do not significantly contribute to the long-term average and will therefore not cause erroneous state changes in V sw . An output signal of the integrator 44 is input to the Schmitt trigger 46. When the output signal of the integrator 44 exceeds the trip voltage threshold of the Schmitt trigger 46 V sw  goes high. When the frequency of V out  is made equal to the frequency of V ref1  the output signal of the integrator 44 is below the trip threshold of the Schmitt trigger 46 and V sw  will fall to a low state. 
     A first input terminal of the switch 34 is responsive to V e1 . A second input terminal of the switch 34 is responsive to the output signal from the first phase detector 14. An output terminal of the switch 34 is selectively responsive to V e1  and the output signal from the first phase detector 14. The input terminal 13 of the voltage-controlled oscillator 12 is responsive to the output terminal of the switch 34. The switching signal, V sw , produced by the off-frequency detector 32 and input to the switch 34 at a third input terminal thereof determines which of the two input signals to the switch 34 is connected to the output terminal thereof. When V sw  is in the high state the first input terminal (i.e., V e1 ) of the switch 34 is connected to the output terminal thereof. The high state of V sw  indicates a divergence between the frequency of V out  and the frequency of V ref1  in excess of the predetermined limit. This causes the initialization feedback loop to be operative. In this mode V e1  is input to the voltage controlled oscillator 12, via the switch 34, to equalize the frequency of V out  to the frequency of V ref1 . When V sw  is in the low state the second input terminal (i.e., the output signal from the first phase detector 14) of the switch 34 is connected to the output terminal thereof. The low state of V sw  indicates that the frequency of V out  equals the frequency of V ref1  such that the primary feedback loop can be activated to precisely synchronize V out  with V in . Now, the output signal from the first phase detector 14 is input to the voltage-controlled oscillator 12, via the switch 34, to perform the synchronization of V out  with V in . 
     In another embodiment of the present invention the output signal of the first phase detector 14 can be permanently connected to the voltage-controlled oscillator 12. Because the output signal of the first phase detector 14 is at a lower level than V e1 , the former does not interfere with the initialization process. In this embodiment the switch 34 is utilized only to connect and disconnect V e1  from the input terminal 13 of the voltage-controlled oscillator 12. 
     Turning to FIG. 2, there is shown a second embodiment of a phase-locked loop 10 constructed according to the teachings of the present invention. The components of FIG. 2 are identical in structure and function to the components bearing identical reference characters in FIG. 1. The embodiment of FIG. 2 includes a signal processing circuit 15 disposed between the voltage controlled oscillator 12 and the first mixer 16. A third mixer 22 is disposed between the first mixer 16 and the level detector 36; a fourth mixer 24 is disposed between the second mixer 20 and the level detector 38. A frequency divider 26 is also responsive to V ref1  for producing a second reference signal designated V ref2 . In the embodiment of FIG. 2, the signal processing circuit 15, the first mixer 16, the third mixer 22, the delay circuit 18, the second mixer 20, the fourth mixer 24, and the frequency divider 26 constitute the second phase detector 28. 
     The second phase detector 28 detects a phase difference between V out  and V ref1  plus V ref2  ; the frequency of V ref1  plus the frequency of V ref2  is approximately equal to the frequency of V in . The second phase detector 28 produces the signal V e1  representative of the difference between the frequency of V ref1  l plus the frequency of V ref2  and the frequency of V out . Like the embodiment of FIG. 1, signal V e1  is selectively input to the voltage-controlled oscillator 12 at the input terminal 13, via the switch 34, for controlling the frequency and phase of V out  when the disparity between the frequency of V out  and the frequency of V ref1  plus the frequency of V ref2  is above the predetermined limit. 
     Note that the embodiment of FIG. 2 utilizes four mixers, rather than two mixers as shown in the FIG. 1 embodiment. This is due to the availability of an extremely precise frequency of 5 MHz for V ref1  when V in  is approximately 5.2 MHz. V ref2  is obtained by dividing V ref1  by twenty-five (in the frequency divider 26) producing V ref2  with a frequency of 200 kHz. Thus, the frequency of V ref1  plus V ref2  equals V in . The mixing of V out  and the reference signal is performed in two stages (i.e., the first stage consisting of the first mixer 16 and the second mixer 20, the second stage consisting of the third mixer 26 and the fourth mixer 24) due to the availability of an extremely accurate 5 MHz source. The result obtained is identical to mixing V in  with a signal of 5.2 MHz in a single mixing stage. In other embodiments, more than two mixing stages or a single mixing stage (see FIG. 1) may be used depending on the frequencies involved and the availability of accurate frequency sources. 
     The operation of the second phase detector 28, as depicted in FIG. 2, is as follows. Note first that the frequency of V ref1  is divided by the frequency divider 26 to produce V ref2 . The first mixer 16 determines the frequency difference between V ref1  and V out  and produces an output signal representative thereof. In the third mixer 22, V ref2  and the output signal from the first mixer 16 are mixed to produce the first error signal, V e1 , representative of the frequency difference between the mixed signals. The delay circuit 18, slightly delays and inverts V out . The delayed and inverted V out  signal and V ref1  are mixed in the second mixer 20 producing an output signal representative of the frequency difference between the mixed signals. The fourth mixer 24 produces a second error signal, V e2 , representative of the difference between the frequency of the signal from the second mixer 20 and V ref2 . The signals V e1  and V e2  are both low frequencies slightly distorted sine waves representative of the frequency difference between V ref1  pus V.sub. ref2 and V out . V e2  is approximately 180° out of phase with V e1 . V e1  and V e2  are illustrated in FIG. 3. From this point, operation of the phase-locked loop 10 of FIG. 2 is identical to that described in conjunction with FIG. 1. 
     Turning now to FIG. 4, there is shown a schematic diagram of the second phase detector 28 (as illustrated in FIG. 2) and the off-frequency detector 32. A first terminal of a capacitor 48 is responsive to V out  ; a second terminal of the capacitor 48 is connected to an input terminal of an inverter 50. An output terminal of the inverter 50 is connected to an input terminal of an inverter 56 via a capacitor 54. The output terminal of the inverter 50 is also connected to the input terminal thereof via a resistor 52. An output terminal of the inverter 56 is connected to an input terminal of an inverter 60. The output terminal of the inverter 56 is also connected to the input terminal thereof via a resistor 58. The inverters 50, 56 and 60, and the associated resistors and capacitors constitute the signal processing circuit 15 of the second phase detector 28. The signal processing circuit 15 converts the analog signal V out  to a digital signal suitable for processing through the digital circuitry of the phase-locked loop 10. An output terminal of the inverter 60 is connected to an input terminal of an inverter 62. The inverter 62, which constitutes the delay circuit 18, not only delays V out , but also inverts V out . The result, as previously noted, is that V e2  is approximately 180 degrees out of phase with V e1 . As will be explained subsequently, a re-invention occurs within the level detector 38 to impart the proper polarity relationship to V sq1  and V sq2 . 
     The output terminal of the inverter 60 is connected to a first input terminal of an EXCLUSIVE OR gate 64. A second input terminal of the EXCLUSIVE OR gate 64 is responsive to the first reference signal V ref1 . The EXCLUSIVE OR gate 64 constitutes the first mixer 16. An output terminal of the inverter 62 is connected to a first input terminal of an EXCLUSIVE OR gate 66; a second input terminal of the EXCLUSIVE OR gate 66 is responsive to V ref1 . The EXCLUSIVE OR gate 66 constitutes the second mixer 20 of the second phase detector 28. Since the output signal of an EXCLUSIVE OR gate is a binary one only if the input signals are unequal, an EXCLUSIVE OR gate can be utilized as a detector whereby the EXCLUSIVE OR gate output signal&#39;s frequency equals the difference between the frequencies of the signals at the input terminals thereof. EXCLUSIVE OR gates 64 and 66 are used in this manner. 
     An output terminal of the EXCLUSIVE OR gate 64 is connected to a first input terminal of an EXCLUSIVE OR gate 68. A second input terminal of the EXCLUSIVE OR gate 68 is responsive to V ref2 , produced by the frequency divider 26. An output terminal of the EXCLUSIVE OR gate 66 is connected to a first input terminal of an EXCLUSIVE OR gate 70. A second input terminal of the EXCLUSIVE OR gate 70 is responsive to V ref2 . EXCLUSIVE OR gates 68 and 70 also function as frequency detectors. 
     An output terminal of the EXCLUSIVE OR gate 68 is connected to a non-inverting input terminal of an operational amplifier 88 via a series combination of a resistor 72 and a resistor 74. An output terminal of the EXCUSIVE OR gate 70 is connected to an inverting input terminal of an operational amplifier 90 via a series combination of a resistor 84 and a resistor 86. The junction between the resistor 72 and the resistor 74 is connected to ground via a capacitor 76; the junction between the resistor 84 and the resistor 86 is also connected to ground via a capacitor 80. The junction between resistor 74 and the non-inverting input terminal of the operational amplifier 88 is connected to ground via a capacitor 78; the junction between the resistor 86 and the inverting input terminal of the operational amplifier 90 is connected to ground via a capacitor 82. The EXCLUSIVE OR gate 68 and the resistors and capacitors associated therewith constitute the third mixer 22. The EXCLUSIVE OR gate 70 with the associated resistors and capacitors constitute the fourth mixer 24. 
     Note that the signal supplied to the non-inverting input terminal of the operational amplifier 88 is V e1  discussed in conjunction with FIGS. 1 and 2, and the signal applied to the inverting input terminal of the operational amplifier 90 is V e2  discussed in conjunction with FIGS. 1 and 2. Since V e2  is applied to the inverting input terminal of the operational amplifier 90 and V e1  is applied to the non-inverting input terminal of the operational amplifier 88, V e2  is inverted with respect to V e1 . This inversion compensates for the previously discussed inversion associated with the inverter 62 (i.e., the delay circuit 18). 
     An inverting input terminal of the operational amplifier 88 is connected to a power supply voltage V s  via a resistor 92 and connected to ground via a resistor 94. The junction between the resistor 94 and the inverting input terminal of the operational amplifier 88 is connected to a non-inverting input terminal of the operational amplifier 90. The operational amplifier 88 and the resistor associated therewith constitute the level detector 36. The level detector 38 is comprised of the operational amplifier 90 and the resistor 94. 
     The signal V sq1  is present at an output terminal of the operational amplifier 88; a first input terminal of a NAND gate 96 is responsive to V sq1 . A second input terminal of the NAND gate 96 is connected to ground. The first input terminal of the NAND gate 96 is also connected to ground via a resistor 100 and is connected to an anode terminal of a diode 108. 
     The operational amplifier 90 produces a signal V sq2  at an output terminal thereof. A first input terminal of a NAND gate 98 is responsive to V sq2 . A second input terminal of the NAND gate 98 is connected to ground. The first input terminal of the NAND gate 98 is also connected to ground via a resistor 102 and is connected to an anode terminal of a diode 106. 
     An output terminal of the NAND gate 96 is connected to an anode terminal of a diode 104; a cathode terminal of the diode 104 is connected to a cathode terminal of the diode 106. An output terminal of the NAND gate 98 is connected to an anode terminal of a diode 110; a cathode terminal of the diode 110 is connected to a cathode terminal of the diode 108. The junction between the diodes 104 and 106 is connected to the power supply voltage V s  via a resistor 112. A junction between the diodes 108 and 110 is connected to the power supply voltage V s  via a resistor 114. The NAND gates 96 and 98, the diodes 104, 106, 108, and 110, and the associated resistors constitute the logic circuit 40 of the off-frequency detector 32. The signal at the junction between the diodes 104 and 106 is referred to as V L1  in FIGS. 1 and 2. The signal at the junction between the diodes 108 and 110 is referred to as V L2  in FIGS. 1 and 2. 
     A first input terminal of a NAND gate 116 is responsive to V L1 , and a first input terminal of a NAND gate 118 is responsive to V L2 . A second input terminal of the NAND gate 116 is connected to an output terminal of the NAND gate 118. A second input terminal of the NAND gate 118 is connected to an output terminal of the NAND gate 116. The NAND gates 116 and 118 constitute the flip-flop 42 of the off-frequency detector 32. The first input terminal of the NAND gate 116 is referred to as the inverting set input terminal of the flip-flop 42 in FIGS. 1 and 2; the first input terminal of the NAND gate 118 is referred to as the inverting reset input terminal of the flip-flop 42 in FIGS. 1 and 2. 
     The signal at the output terminal of the NAND gate 116 is designated V ff  in FIGS. 1 and 2. A first terminal of capacitor 120 is responsive to V ff . A second terminal of the capacitor 120 is connected to the power supply voltage V s  via a parallel combination of a resistor 122 and a diode 124 such that the cathode terminal of the diode 124 is connected to the power supply voltage V s . The second terminal of the capacitor 120 is also connected to a base terminal of a transistor 126. A collector terminal of the transistor 126 is connected to the power supply voltage V s  via a resistor 128. An emitter terminal of the transistor 126 is connected to ground via a parallel combination of a capacitor 130 and a resistor 132. The capacitor 120, the resistor 122 and the diode 124 constitute the differentiator/rectifier 43; the transistor 126 and the associated resistors and capacitor constitute the integrator 44. 
     The emitter terminal of the transistor 126 is also connected to an inverting input terminal of an operational amplifier 134. A non-inverting input terminal of the operational amplifier 134 is connected to ground via a resistor 140 and is connected to the power supply voltage V s  via a resistor 136. An output terminal of the operational amplifier 134 is connected to the non-inverting input terminal thereof via a resistor 138. The switching signal V sw  discussed in detail in conjunction with FIGS. 1 and 2 is provided at the output terminal of the operational amplifier 134. The Schmitt trigger 46 of the off-frequency detector 32 comprises the operational amplifier 134 and the associated resistors. As discussed in conjunction with FIG. 2, when the output terminal of the operational amplifier 134 is in a high state, the initialization feedback loop is operative to equalize the frequency of V out  to the sum of the frequencies of V ref1  plus V ref2 . When the output terminal of the operational amplifier 134 is in a low state, the primary feedback loop will be operative to precisely synchronize the phase of V out  to the phase of V in .