# US 2014/0191810 A1 · Systems and methods for synthesizer locking using iterative numerical techniques > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2014/0191810 A1 - Document ID: US20140191810A1 - Status: Published application - Kind: A1 - Application number: 13/738,903 - Filed: 2013-01-10 - Published: 2014-07-10 - Earliest claimed: 2013-01-10 - Assignees: QUALCOMM Incorporated - Applicants: Qualcomm Incorporated - Inventors: Justin A. HWANG - Web page: https://patentgrep.com/patent/US20140191810A1 ## CPC - H03L 7/10: for assuring initial synchronisation or for broadening the capture range - H03B 5/1212: {the amplifier comprising a pair of transistors, wherein an output terminal of each being connected to an input terminal of the other, e.g. a cross coupled pair} - H03B 5/1228: {the amplifier comprising one or more field effect transistors} - H03B 5/1265: {switched capacitors} - H03L 7/00: Automatic control of frequency or phase; Synchronisation - H03L 7/099: concerning mainly the controlled oscillator of the loop - H03L 7/16: Indirect frequency synthesis, i.e. generating a desired one of a number of predetermined frequencies using a frequency- or phase-locked loop - H03L: AUTOMATIC CONTROL, STARTING, SYNCHRONISATION OR STABILISATION OF GENERATORS OF ELECTRONIC OSCILLATIONS OR PULSES (generation of oscillations H03B) - H03B: GENERATION OF OSCILLATIONS, DIRECTLY OR BY FREQUENCY-CHANGING, BY CIRCUITS EMPLOYING ACTIVE ELEMENTS WHICH OPERATE IN A NON-SWITCHING MANNER; GENERATION OF NOISE BY SUCH CIRCUITS (generators adapted for electrophonic musical instruments G10H; masers or lasers H01S; generation of oscillations in plasma H05H) ## Abstract This disclosure includes systems and methods for frequency synthesis using a voltage-controlled oscillator (VCO) with a programmable array of capacitors. A suitable setting for the capacitor array may be derived through a non-successive iterative numerical technique. In one aspect, the iterative numerical technique may apply Newton's method to an equation relating frequency generated by the VCO and the capacitor setting of the first programmable array of capacitors. In another aspect, a secant method may be applied to determine a capacitor array setting based on previously and currently applied capacitor settings and the corresponding measured frequencies. ## Claims ### Claim 1 A method for operating a frequency synthesizer with a voltage-controlled oscillator (VCO) having a first programmable array of capacitors comprising: applying an initial setting to the first programmable array of capacitors; measuring an initial frequency generated by the VCO at the initial setting; determining a next setting for the first programmable array of capacitors using a non-successive iterative numerical technique; applying the next setting to the first programmable array of capacitors; measuring a frequency generated by the VCO at the next setting for the first programmable array of capacitors; and repeating the determination of the next setting for the first programmable array of capacitors, the application of the next setting for the first programmable array of capacitors and the measurement of the generated frequency until the current frequency is within a first desired threshold of a target frequency. ### Claim 2 (depends on 1) The method of claim 1, wherein the non-successive iterative numerical technique comprises an equation relating frequency generated by the VCO and the capacitor setting of the first programmable array of capacitors. ### Claim 3 (depends on 2) The method of claim 2, wherein the equation is based on Newton's Method. ### Claim 4 (depends on 3) The method of claim 3, wherein the equation comprises vcocap n + 1 = vcocap n + 2   F vco  ( vcopcap n ) - F target F vco  ( vcocap n )  ( C FIXED C LSB + vcocap n ) , wherein CFIXED is a fixed capacitance of an inductance-capacitance (LC) resonant tank of the VCO, CLSB is an effective unit capacitance in the first programmable array of capacitors, vcocapn is a current setting of the first programmable array of capacitors, vcocapn+1 is the next setting, Fvco(vcocapn) is the current frequency generated by the VCO at the current setting and Ftarget is the target frequency. ### Claim 5 (depends on 1) The method of claim 1, wherein the non-successive iterative numerical technique comprises an equation depending upon a previously applied capacitor setting and measured frequency and a currently applied capacitor setting and measured frequency. ### Claim 6 (depends on 5) The method of claim 5, wherein the equation is based on a secant method. ### Claim 7 (depends on 6) The method of claim 6, wherein the equation comprises vcocap n + 1 = vcocap n - [ F vco  ( vcopcap n ) - F target ]  vcocap n - vcocap n - 1 F vco  ( vcocap n ) - F vco  ( vcocap n - 1 ) , wherein vcocapn−1 is a previous setting of the first programmable array of capacitors, vcocapn is a current setting of the first programmable array of capacitors, vcocapn+1 is the next setting, Fvco(vcocapn−1) is a frequency generated by the VCO at the previous setting, Fvco(vcocapn) is a frequency generated by the VCO at the current setting and Ftarget is the target frequency. ### Claim 8 (depends on 1) The method of claim 1, wherein applying the initial setting comprises estimating the initial setting based upon the target frequency. ### Claim 9 (depends on 1) The method of claim 1, wherein the first programmable array of capacitors comprises a coarse sub-array and wherein the VCO comprises a second programmable array of capacitors comprising a fine sub-array, further comprising: applying an initial setting to the second programmable array of capacitors; measuring the initial frequency generated by the VCO at the initial setting; determining a next setting for the second programmable array of capacitors using the non-successive iterative numerical technique; applying the next setting for the second programmable array of capacitors to the second programmable array of capacitors; measuring the frequency generated by the VCO at the next setting for the second programmable array of capacitors; and repeating the determination of the next setting for the second programmable array of capacitors, the application of the determined setting for the second programmable array of capacitors and the measurement of the generated frequency at the next setting for the second programmable array of capacitors until the generated frequency is within a second desired threshold of the target frequency. ### Claim 10 (depends on 1) The method of claim 1, wherein the first programmable array of capacitors comprises a coarse sub-array and a fine sub-array, further comprising: determining a positive slope between a frequency generated at a previous setting of the first programmable array of capacitors and a frequency generated at a current setting of the first programmable array of capacitors; and adjusting the next setting of the first programmable array of capacitors by selecting a setting that generates a frequency corresponding to the frequency generated at the previous setting. ### Claim 11 A frequency synthesizer comprising: a voltage-controlled oscillator (VCO) having a first programmable array of capacitors; and a programming module, wherein the programming module is configured to: apply an initial setting to the first programmable array of capacitors; measure an initial frequency generated by the VCO at the initial setting; determine a next setting for the first programmable array of capacitors using a non-successive iterative numerical technique; apply the next setting to the first programmable array of capacitors; measure a current frequency generated by the VCO at the next setting; and repeat the determination of the next setting for the first programmable array of capacitors, the application of the next setting for the first programmable array of capacitors and the measurement of the generated frequency until the current frequency is within a first desired threshold of a target frequency. ### Claim 12 (depends on 11) The frequency synthesizer of claim 11, wherein the non-successive iterative numerical technique comprises an equation relating frequency generated by the VCO and the capacitor setting of the first programmable array of capacitors. ### Claim 13 (depends on 12) The frequency synthesizer of claim 12, wherein the equation is based on Newton's Frequency synthesizer. ### Claim 14 (depends on 13) The frequency synthesizer of claim 13, wherein the equation comprises vcocap n + 1 = vcocap n + 2   F vco  ( vcopcap n ) - F target F vco  ( vcocap n )  ( C FIXED C LSB + vcocap n ) , wherein CFIXED is a fixed capacitance of an inductance-capacitance (LC) resonant tank of the VCO, CLSB is an effective unit capacitance in the first programmable array of capacitors, vcocapn is a current setting of the first programmable array of capacitors, vcocapn+1 is the next setting, Fvco(vcocapn) is the current frequency generated by the VCO at the current setting and Ftarget is the target frequency. ### Claim 15 (depends on 11) The frequency synthesizer of claim 11, wherein the non-successive iterative numerical technique comprises an equation depending upon a previously applied capacitor setting and measured frequency and a currently applied capacitor setting and measured frequency. ### Claim 16 (depends on 15) The frequency synthesizer of claim 15, wherein the equation is based on a secant method. ### Claim 17 (depends on 16) The frequency synthesizer of claim 16, wherein the equation comprises vcocap n + 1 = vcocap n - [ F vco  ( vcopcap n ) - F target ]  vcocap n - vcocap n - 1 F vco  ( vcocap n ) - F vco  ( vcocap n - 1 ) , wherein vcocapn−1 is a previous setting of the first programmable array of capacitors, vcocapn is a current setting of the first programmable array of capacitors, vcocapn+1 is the next setting, Fvco(vcocapn−1) is a frequency generated by the VCO at the previous setting, Fvco(vcocapn) is a frequency generated by the VCO at the current setting and Ftarget is the target frequency. ### Claim 18 (depends on 11) The frequency synthesizer of claim 11, wherein the programming module applies the initial setting by estimating the initial setting based upon the target frequency. ### Claim 19 (depends on 11) The frequency synthesizer of claim 11, wherein the first programmable array of capacitors comprises a coarse sub-array, wherein the VCO comprises a second programmable array of capacitors comprising a fine sub-array, and wherein the programming module is further configured to: apply an initial setting to the second programmable array of capacitors; measure the initial frequency generated by the VCO at the initial setting; determine a next setting for the second programmable array of capacitors using the non-successive iterative numerical technique; apply the next setting for the second programmable array of capacitors to the second programmable array of capacitors; measure the frequency generated by the VCO at the next setting for the second programmable array of capacitors; and repeat the determination of the next setting for the second programmable array of capacitors, the application of the determined setting for the second programmable array of capacitors and the measurement of the generated frequency at the next setting for the second programmable array of capacitors until the generated frequency is within a second desired threshold of the target frequency. ### Claim 20 (depends on 11) The frequency synthesizer of claim 11, wherein the first programmable array of capacitors comprises a coarse sub-array and a fine sub-array and wherein the programming module is further configured to: determine a positive slope between a frequency generated at a previous setting of the first programmable array of capacitors and a frequency generated at a current setting of the first programmable array of capacitors; and adjust the next setting of the first programmable array of capacitors by selecting a setting that generates a frequency corresponding to the frequency generated at the previous setting. ### Claim 21 A wireless communications device comprising a voltage controlled oscillator (VCO) having a first programmable array of capacitors and a programming module, wherein the programming module is configured to: apply an initial setting to the first programmable array of capacitors; measure an initial frequency generated by the VCO at the initial setting; determine a next setting for the first programmable array of capacitors using a non-successive iterative numerical technique; apply the next setting to the first programmable array of capacitors; measure a current frequency generated by the VCO at the next setting; and repeat the determination of the next setting for the first programmable array of capacitors, the application of the next setting for the first programmable array of capacitors and the measurement of the generated frequency until the current frequency is within a first desired threshold of a target frequency. ### Claim 22 (depends on 21) The wireless communications device of claim 21, wherein the non-successive iterative numerical technique comprises an equation relating frequency generated by the VCO and the capacitor setting of the first programmable array of capacitors. ### Claim 23 (depends on 22) The wireless communications device of claim 22, wherein the equation is based on Newton's Wireless communications device. ### Claim 24 (depends on 23) The wireless communications device of claim 23, wherein the equation comprises vcocap n + 1 = vcocap n + 2   F vco  ( vcocap n ) - F target F vco  ( vcocap n )  ( C FIXED C LSB + vcocap n ) , wherein CFIXED is a fixed capacitance of an inductance-capacitance (LC) resonant tank of the VCO, CLSB is an effective unit capacitance in the first programmable array of capacitors, vcocapn is a current setting of the first programmable array of capacitors, vcocapn+1 is the next setting, Fvco(vcocapn) is the current frequency generated by the VCO at the current setting and Ftarget is the target frequency. ### Claim 25 (depends on 21) The wireless communications device of claim 21, wherein the non-successive iterative numerical technique comprises an equation depending upon a previously applied capacitor setting and measured frequency and a currently applied capacitor setting and measured frequency. ### Claim 26 (depends on 25) The wireless communications device of claim 25, wherein the equation is based on a secant method. ### Claim 27 (depends on 26) The wireless communications device of claim 26, wherein the equation comprises vcocap n + 1 = vcocap n - [ F vco  ( vcopcap n ) - F target ]   vcocap n - vcocap n - 1 F vco  ( vcocap n ) - F vco  ( vcocap n - 1 ) , wherein vcocapn−1 is a previous setting of the first programmable array of capacitors, vcocapn is a current setting of the first programmable array of capacitors, vcocapn+1 is the next setting, Fvco(vcocapn−1) is a frequency generated by the VCO at the previous setting, Fvco(vcocapn) is a frequency generated by the VCO at the current setting and Ftarget is the target frequency. ### Claim 28 (depends on 21) The wireless communications device of claim 21, wherein the programming module applies the initial setting by estimating the initial setting based upon the target frequency. ### Claim 29 (depends on 21) The wireless communications device of claim 21, wherein the first programmable array of capacitors comprises a coarse sub-array, wherein the VCO comprises a second programmable array of capacitors comprising a fine sub-array, and wherein the programming module is further configured to: apply an initial setting to the second programmable array of capacitors; measure the initial frequency generated by the VCO at the initial setting; determine a next setting for the second programmable array of capacitors using the non-successive iterative numerical technique; apply the next setting for the second programmable array of capacitors to the second programmable array of capacitors; measure the frequency generated by the VCO at the next setting for the second programmable array of capacitors; and repeat the determination of the next setting for the second programmable array of capacitors, the application of the determined setting for the second programmable array of capacitors and the measurement of the generated frequency at the next setting for the second programmable array of capacitors until the generated frequency is within a second desired threshold of the target frequency. ### Claim 30 (depends on 21) The wireless communications device of claim 21, wherein the first programmable array of capacitors comprises a coarse sub-array and a fine sub-array and wherein the programming module is further configured to: determine a positive slope between a frequency generated at a previous setting of the first programmable array of capacitors and a frequency generated at a current setting of the first programmable array of capacitors; and adjust the next setting of the first programmable array of capacitors by selecting a setting that generates a frequency corresponding to the frequency generated at the previous setting.