Compensation technique for the nonlinear behavior of digitally-controlled oscillator (DCO) gain
Systems and methods are provided for hopping a digitally controlled oscillator (DCO) among a plurality of channels, wherein a gain of the DCO K DCO is a nonlinear function of frequency. A first normalized tuning word (NTW) corresponding to a first channel of the plurality of channels is generated. A first normalizing gain multiplier X is generated based on the nonlinear function of frequency, on an estimate of the nonlinear function of frequency, at a first frequency corresponding to the first channel. The first NTW is multiplied by the first X to obtain a first oscillator tuning word (OTW). The first OTW is input to the DCO to cause the DCO to hop to the first channel. A system for hopping among a plurality of channels at a plurality of respective frequencies comprises a phase-locked loop (PLL), a digitally controlled oscillator (DCO), a multiplexer, and an arithmetic module.
1 . A method for controlling a digitally controlled oscillator (DCO), the method comprising:
fitting a respective polynomial approximation to each of multiple segments of a nonlinear function of frequency; and
generating a first control signal based on the polynomial approximation of one of the segments, wherein the DCO is configured to receive a first oscillator tuning word (OTW) generated based on a received tuning word and the first control signal.
2 . The method of claim 1 , wherein the tuning word is a first normalized tuning word (NTW), the method further comprising:
multiplying the first NTW by the first control signal to obtain the first OTW; and
inputting the first OTW to the DCO to cause the DCO to hop to a first channel corresponding to the first NTW and the first control signal, wherein the first control signal is generated based on a reference frequency and a linear interpolation of the nonlinear function at a first frequency, and the first frequency corresponds to the first channel.
3 . The method of claim 2 , wherein the reference frequency is the frequency of a second channel.
4 . The method of claim 1 , wherein the respective polynomial approximation to each of the multiple segments of the nonlinear function of frequency is a linear approximation.
5 . The method of claim 2 , further comprising:
generating a second NTW corresponding to a second channel;
generating a second control signal based on the nonlinear function of frequency at a second frequency corresponding to the second channel or based on an estimate of the nonlinear function of frequency at the second frequency;
multiplying the second NTW by the second control signal to obtain a second OTW; and
inputting the second OTW to the DCO to cause the DCO to hop to the second channel.
6 . The method of claim 1 , wherein at least part of the method is performed in an all-digital phase locked loop (ADPLL).
7 . The method of claim 2 , wherein the linear interpolation is based on a center point of the nonlinear function of frequency.
8 . The method of claim 1 , wherein the nonlinear function of frequency is a cubic function of frequency.
9 . The method of claim 2 , wherein the linear interpolation is based on:
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0
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f
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f
0
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=
0
(
1
-
3
f
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in which y corresponds to a change in DCO gain variation, f0 corresponds to a frequency at which the DCO gain variation is 100%, and y0 corresponds to the value of the change in DCO gain variation at which the gain variation is 100%.
10 . A system for controlling a digitally controlled oscillator (DCO), the system comprising:
a circuit configured to fit a respective polynomial approximation to each of multiple segments of a nonlinear function of frequency, and to generate a plurality of control signals, each control signal being based on the polynomial approximation at a respective frequency,
wherein the DCO is configured to receive a plurality of oscillator tuning words (OTWs) and each OTW is generated based on one selected from the control signals being stored and a respective tuning word and a respective control signal.
11 . The system of claim 10 , further comprising:
the DCO; and
an arithmetic module configured to generate the plurality of OTWs, wherein the first circuit is a phase-locked loop (PLL) and each control signal is also based on a reference frequency.
12 . The system of claim 11 , wherein at least one of the circuit and the arithmetic module is provided as part of a normalized DCO comprising the DCO, wherein the DCO is configured to hop among a plurality of channels based on the plurality of OTWs.
13 . The system of claim 10 , wherein each control signal is based on a linear interpolation of a nonlinear function of frequency at a respective frequency and the linear interpolation is based on a center point of the nonlinear function of frequency.
14 . The system of claim 10 , wherein the nonlinear function of frequency is a cubic function of frequency.
15 . The system of claim 13 , wherein the linear interpolation is based on:
=
0
+
d
0
df
(
f
-
f
0
)
=
0
(
1
-
3
f
-
f
0
f
0
)
in which y corresponds to a change in DCO gain variation, f0 corresponds to a frequency at which the DCO gain variation is 100%, and y0 corresponds to the value of the change in DCO gain variation at which the gain variation is 100%.
16 . The system of claim 13 , wherein the linear interpolation is based on a value of a change in DCO gain variation.
17 . The system of claim 13 , wherein the linear interpolation is based on at least one of a frequency at which DCO gain variation is 100% and a value of a change in DCO gain variation at which the DCO gain variation is 100%.
18 . A system configured to be coupled to a digitally controlled oscillator (DCO), the system comprising:
a circuit configured to fit a respective polynomial approximation to each of multiple segments of a nonlinear function of frequency, and to generate a plurality of control signals, each control signal being based on the polynomial approximation at a respective frequency,
wherein the DCO is configured to receive a plurality of oscillator tuning words (OTWs) and each OTW is generated based on a respective tuning word and a respective control signal.
19 . The system of claim 18 , further comprising:
the DCO; and
an arithmetic module configured to receive a plurality of the tuning words each corresponding to a respective channel, and further configured to generate a respective OTW based on each control signal, wherein each control signal is based on a reference frequency and a linear interpolation of the nonlinear function of frequency at the respective frequency.
20 . The system of claim 19 , wherein the linear interpolation is based on a center point of a frequency range.