Linearizing apparatus and method

A circuit to provide a substantially linear relationship between an input voltage and a frequency response of a capacitor, the circuit comprising:

• a voltage-to-current converter, the voltage-to-current converter capable of being coupled to receive the input voltage, the voltage-to-current converter capable of providing an input current substantially linearly proportional to the input voltage;
• a current mirror coupled to the voltage-to-current converter;
• a square root converter coupled to the current mirror to receive the input current, the square root converter capable of providing a first output voltage substantially proportional to a square root of a magnitude of the input current;
• and
• circuitry comprising a logarithmic generator coupled to the square root converter to receive the first output voltage and coupled to the current mirror to receive the input current, the circuitry adapted to provide a second output voltage substantially proportional to a sum or superposition of the first output voltage and a logarithm of the magnitude of the input current, the second output voltage capable of being coupled to the capacitor for a substantially linear frequency response to the input signal.

An apparatus to provide a substantially linear relationship between an input voltage and a predetermined circuit parameter, the apparatus comprising:

• a voltage-to-current converter, the voltage-to-current converter capable of being coupled to receive the input voltage, the voltage-to-current converter capable of providing an input current substantially linearly proportional to the input voltage;
• a current mirror coupled to the voltage-to-current converter;
• a square root converter coupled to the current mirror to receive the input current, the square root converter capable of providing a first output voltage substantially proportional to a square root of a magnitude of the input current;
• a logarithmic generator coupled to the current mirror to receive the input current, the logarithmic generator capable of providing a second output voltage substantially proportional to a logarithm of the magnitude of the input current;
• and
• a combiner coupled to the square root converter to receive the first output voltage and coupled to the logarithmic generator to receive the second output voltage, the combiner adapted to provide an applied signal substantially equal to a sum or superposition of the first output voltage and the second output voltage, wherein the applied signal has a substantially nonlinear relationship to the predetermined parameter.

A method of providing a substantially linear relationship between an input voltage and a predetermined circuit parameter, the method comprising:

• converting the input voltage to an input current, wherein the input current is substantially linearly proportional to the input voltage;
• generating a square root voltage from the input current, wherein the square root voltage is substantially proportional to a square root of a magnitude of the input current;
• generating a logarithmic voltage from the input current, wherein the logarithmic voltage is substantially proportional to a logarithm of the magnitude of the input current, and wherein the logarithmic voltage is substantially equal to a 3/2 power of the input current;
• and
• combining the square root voltage and the logarithmic voltage to form an applied signal substantially equal to a sum or superposition of the square root voltage and the logarithmic voltage, wherein the applied signal has a substantially nonlinear relationship to the predetermined parameter;
• and
• applying the applied signal to vary the predetermined circuit parameter substantially linearly with the input voltage.

A method to create a substantially linear relationship between an input signal and a selected parameter, comprising:

• (a) receiving the input signal;
• (b) determining a square root of a magnitude of the input signal to form a square root signal;
• (c) determining a logarithm of the magnitude of the input signal to form a logarithmic signal;
• (d) combining the square root signal with the logarithmic signal to form an applied signal, the applied signal having a substantially nonlinear relationship to the input signal;
• and
• (e) providing the applied signal for adjustment of the selected parameter substantially linearly with the input signal.

A method to create a substantially linear relationship between an input signal and a selected parameter, comprising:

• (a) receiving the input signal;
• (b) determining a square root of a magnitude of the input signal to form a square root signal;
• (c) determining a 3/2 power of the magnitude of the input signal to form a power signal;
• (d) combining the square root signal with the power signal to form an applied signal, the applied signal having a substantially nonlinear relationship to the input signal;
• and
• (e) providing the applied signal for adjustment of the selected parameter substantially linearly with the input signal.

An apparatus to provide a substantially linear relationship between an input signal and a selected parameter, the apparatus comprising:

• a voltage-to-current converter couplable to receive the input signal as an input voltage and adapted to provide an input current having a substantially linear relationship to the input voltage;
• a square root converter coupled to the voltage-to-current converter to receive the input current, the square root converter adapted to provide a square root signal, the square root signal substantially proportional to a square root of the input current;
• and
• circuitry comprising a logarithmic generator coupled to the voltage-to-current converter to receive the input current and coupled to the square root converter, the circuitry adapted to provide an applied signal substantially proportional to a sum or a superposition of the square root signal and a logarithm of the input signal.