Highly linear-gain oscillator

Abstract

A variable frequency oscillator includes an inductance unit having a first inductance, a first variable capacitor coupled across the inductance unit, and a second variable capacitor coupled across a part of the inductance unit. The inductance of the part of the inductance unit coupled by the second variable capacitor is a proportion of the first inductance.

Claims

1. A variable frequency oscillator comprising: an inductance unit having a first inductance; a first variable capacitor coupled across the inductance unit; and a second variable capacitor coupled across a part of the inductance unit, the inductance of said part being a proportion of the first inductance; the oscillator having an operating frequency range and the proportion being such as to substantially minimise the variation of rate of change of an operating frequency of the oscillator with a variation of a capacitance of at least one of the first variable capacitor and the second variable capacitor.

2. A variable frequency oscillator as claimed in claim 1, the proportion being such as to substantially maximise the linearity of the rate of change of the operating frequency of the oscillator.

3. A variable frequency oscillator as claimed in claim 1, the proportion being such that the derivative of the rate of change of the operating frequency of the oscillator is substantially minimum at said proportion.

4. A variable frequency oscillator as claimed in claim 1, said part having a second inductance, the relationship between the first and second inductances being such as to substantially minimise the variation of rate of change of the operating frequency of the oscillator over the operating frequency range.

5. A variable frequency oscillator as claimed in claim 1, the rate of change of the operating frequency of the oscillator being dependent on the change in frequency of the oscillator with respect to the change in capacitance of the first and/or second variable capacitors.

6. A variable frequency oscillator as claimed in claim 1, the variance of the oscillator rate of change of operating frequency being dependent on the change in the rate of change of an operating frequency with respect to the change in the capacitance of the first and/or second variable capacitors.

7. A variable frequency oscillator as claimed in claim 1, the capacitance of the first and second variable capacitor being variable for varying the frequency of the oscillator.

8. A variable frequency oscillator as claimed in claim 1, the capacitance of the first and/or second variable capacitor being variable by means of the voltage applied to the capacitor(s).

9. A variable frequency oscillator as claimed in claim 1, the capacitance of the second variable capacitor being less than the capacitance of the first variable capacitor.

10. A variable frequency oscillator as claimed in claim 1, the inductance of said part being less than the first inductance.

11. A variable frequency oscillator as claimed in claim 1, further comprising a controller configured to select an operating frequency, the operating frequency being selectable over an operating frequency range.

12. A variable frequency oscillator as claimed in claim 1, the oscillator being a voltage controlled oscillator or a digitally controlled oscillator.

13. A variable frequency oscillator as claimed in claim 1, the oscillator further comprising a pair of cross coupled field effect transistors, one of said transistors being coupled to a terminal of the inductance unit and the other transistor being coupled to the other terminal of the inductance unit.

14. A phase-locked loop comprising a variable frequency oscillator as claimed in claim 1.

15. A variable frequency oscillator as claimed in claim 1, wherein the first inductance is fixed.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The present invention will now be described by way of example, with reference to the accompanying drawings, in which:

(2) FIG. 1 shows a conventional prior art LC tank;

(3) FIG. 2 shows a conventional prior art VCO core comprising the LC tank of FIG. 1;

(4) FIG. 3 shows a proposed LC tank according to an embodiment of the present invention;

(5) FIG. 4 shows a proposed oscillator comprising the LC tank of FIG. 3; and

(6) FIG. 5 shows an example of the gain variation verses =L/L.sub.t for the proposed DCO.

DETAILED DESCRIPTION OF THE INVENTION

(7) In general, an oscillator can be implemented around an oscillating circuit such as an LC resonator. The frequency of the oscillator can be a function of L and C. For example, in a LC based VCO the frequency of oscillation can be changed by changing the capacitance of the capacitor across the tank. This can lead to a non-linear dependence of the VCO gain on the frequency as explained below.

(8) For the sake of illustration, a DCO is used when describing the prior art and embodiments of the present invention. However, the same principles describing the prior art and the embodiments of the present invention also apply to analogue VCOs and other similar oscillators.

(9) The general structure of a prior art oscillator LC tank 10 is shown in the FIG. 1, which comprises an inductance source 11 and a variable capacitor 12 coupled across the inductance source 11. This LC tank 10 along with an active circuit builds a conventional VCO core 13 as shown in FIG. 2. The active circuit comprises a pair of cross coupled field effect transistors 14 and 15, a power supply 16 and a current source 17.

(10) In a conventional LC tank 10, as shown in FIG. 1, the oscillation frequency .sub.0 and its derivative with respect to the capacitance C is:

(11) $\begin{array}{cc}\begin{array}{c}{}_0=\frac{1}{\sqrt{{\mathrm{LC}}_t}}.Math.K_v\stackrel{}{=}\frac{{}_0}{C}\\ =-\frac{L}{2}{}_0^3\end{array}& \left(1\right)\end{array}$

(12) As can be seen in equation (1), K.sub.v, the gain of the oscillator, is dependent on cubic of .sub.0. This means that the gain varies over the tuning frequency range and the more the tuning range, the more gain variation. Intuitively this can be seen by observing that the gain is changed by adding/subtracting a C.sub.lsb, to the capacitance C.sub.t and as the result, the normalized capacitance change is C.sub.lsb/C.sub.t. Hence, for a higher C.sub.t (i.e. lower .sub.0), the normalized capacitance step is smaller (i.e. smaller K.sub.v) and vice versa.

(13) An embodiment of the present invention is shown in FIG. 3. In the LC tank 20 shown in FIG. 3, the capacitance is divided into two parts. A capacitance C.sub.t, which can be provided by a first variable capacitor 21, is connected across the whole of an inductance source L.sub.t, which can be provided by an inductance unit 22. The inductance unit 22 can comprise one or more inductors. The capacitance C.sub.t and inductance L.sub.t can be used to set the centre frequency of the oscillator. A capacitance C, which may be provided by a second variable capacitor 23, is connected across a part of the inductance source L.sub.t (i.e. a part of the inductance unit 22), the part being indicated by L. The capacitance C connected across the part of the inductance source L may be smaller than the capacitance C.sub.t connected across the whole inductance source L.sub.t.

(14) The second variable capacitor 23 can be coupled across a part of the inductance unit 22 such that the inductance of said part is a proportion of the whole inductance of the inductance unit 22. Thus the inductance L coupled to the second variable capacitor can be smaller than the whole inductance L.sub.t. The inductance unit 22 may comprise more than one inductor element connected in series or the inductance unit 22 can be a single inductor element. The second variable capacitor 23 can be connected, for example, at an end of an inductor element and/or at a point along an inductor coil of the element.

(15) The LC tank 20 shown in FIG. 3 along with an active circuit can be used to build an oscillator core 24 as shown in FIG. 4. The active circuit comprises a pair of cross coupled field effect transistors 25 and 26, a power supply 27 and a current source 28. Transistor 25 can be coupled to one terminal of the inductance unit 22 and transistor 26 can be coupled to the other terminal of inductance unit 22. The oscillator core 24 can be implemented in a VCO or DCO, for example. The frequency range at which the oscillator operates may be determined by the capacitance C.sub.t and inductance L.sub.t. The capacitance of the first and second variable capacitors can be varied by a controller. The controller can select an operating frequency by varying the capacitances of the first and/or second variable capacitors. The capacitances of the first and/or second variable capacitors can be varied by applying a voltage to the capacitors. The controller may determine the frequency range from which the operating frequency can be selected from. The smaller capacitance C (provided by the second variable capacitor 23) can be used for fine frequency tuning.

(16) In an example derivation, the small inner LC tank (i.e. the second variable capacitor 23 and the part of the inductance that the second variable capacitor 23 is coupled to) can be replaced by an effective inductance L.sub.e:

(17) $\begin{array}{cc}{L}_e=\frac{L}{1-{}_0^{2}LC}& \left(2\right)\end{array}$

(18) In this example derivation, the inner LC tank can be represented by an effective inductance L.sub.e as long as .sub.0LC<1. This is true as .sub.0 is the resonance frequency of the total circuit with the larger capacitance of L.sub.tC.sub.t>>LC.

(19) The derivative of the L.sub.e with respect to capacitance is:

(20) $\begin{array}{cc}\frac{L_e}{C}=\frac{L^2{}_0^2}{{\left(1-{}_0^{2}LC\right)}^2}& \left(3\right)\end{array}$

(21) On the other hand, the derivative of the resonance frequency .sub.0 with respect to inductance is:

(22) $\begin{array}{cc}\frac{{}_0}{L}=-\frac{C_t}{2}{}_0^3& \left(4\right)\end{array}$

(23) Using equations (3) and (4), the derivative of the resonance frequency .sub.0 with respect to capacitance for the tank circuit 20 is:

(24) $\begin{array}{cc}\begin{array}{c}{K}_v=\frac{{}_0}{C}\\ =-\frac{C_t}{2}{}_0^3\frac{L{}_0^2}{{\left(1-{}_0^{2}LC\right)}^2}\\ =-\frac{C_t}{2}\frac{L{}_0^5}{{\left(1-{}_0^{2}LC\right)}^2}\end{array}& \left(5\right)\end{array}$

(25) Reducing the nonlinearity can be achieved by minimising the DCO gain variation, i.e. d.sub.0 (.sub.0 step) variation with respect to dC (capacitance steps). In other words, an almost constant d.sub.0/dC is required. This may be done by finding the global minimum of function K.sub.v=d.sub.0/dC by solving d.sup.2.sub.0/d.sup.2C=0.

(26) For example, an improvement can be observed by comparing equation (1) and (5). In the conventional LC tank 10 represented by equation (1), K.sub.v=d.sub.0/dC is not constant and is changing with .sub.0.sup.3. This means for a fixed step size of dC, when capacitance C increases, K.sub.v is reduced with the factor of .sub.0.sup.3.

(27) For the LC tank 20 shown in FIG. 3 and its K.sub.v represented by equation (5), when capacitance increases (i.e. .sub.0 decreases), the numerator decreases by .sub.0.sup.5. In the denominator, when capacitance increases, .sub.0.sup.2LC term increases as the rate of capacitance increase is much higher than the rate of .sub.0.sup.2 decrease. Hence, the denominator is decreased. As a result, when capacitance is increasing both the numerator and denominator are decreasing with different rates. These different rates depend on the value of L, L.sub.t, C and C.sub.t. The value of C.sub.t and L.sub.t is determined by the required resonance frequency and the value of C and L is determined by the required d.sub.0(K.sub.v). The inventors have found that one way of changing the rates in the denominator and the numerator is to change the ratio of L to L.sub.t, or =L/L.sub.t.

(28) For a certain value of L/L.sub.t both the denominator and numerator decrease almost at the same rate and hence K.sub.v=d.sub.0/dC is almost constant with minimum variation. This can be seen in FIG. 5 which shows K.sub.v variation versus =L/L.sub.t for an example of the proposed circuit. There are 2 global minimums in K.sub.v variation function versus . The first minimum is when =L/L.sub.t=0 which means the inner LC tank is not present (and hence there is no gain in the system). The second global minimum is at a value of .sub.opt=L/L.sub.t. .sub.opt is the optimum point in which K.sub.v variation (i.e. d.sub.0/dC variation) is minimum. Thus, a proportion of L.sub.t can be selected or provided for L so as to substantially minimise the oscillator gain variation (or the nonlinearity of the gain). Thus such a relationship between L and L.sub.t can be used to substantially minimise the oscillator gain variation. This minimised gain variation may be across an operating frequency range.

(29) In an example comparison between the conventional and proposed circuits, the size of the inductor can be identical (L.sub.t in FIGS. 1-4). The size of the total capacitance (C+C.sub.t) in the proposed circuit (shown in FIGS. 3 and 4) can be bigger than the capacitance of the conventional circuit (shown in FIGS. 1 and 2) to achieve the same K.sub.v gain. This capacitance increase is not a problem for several reasons: 1. The total size of the LC tank is almost determined by the size of the inductors and the proposed circuit has the same size of inductor as the conventional circuit. 2. The increase in capacitance size is negligible. This is due to the fact that the total capacitance is dominated by C.sub.t which is much bigger than C. 3. An increase in C can lead to an increase in C.sub.lsb. In some applications for fine tuning, the size of C.sub.lsb is small and it creates matching issues. In the proposed circuit, as C.sub.lsb is bigger (in order to achieve the same K.sub.v), matching between the capacitors is better and it gives even more linearity.

(30) In terms of power consumption, both conventional and proposed circuits are similar.

(31) The proposed circuit provides a simple linearization technique with no extra power consumption penalty. It can also be used along with other techniques for even more improvement in oscillator gain linearity.

(32) Providing a small inner LC tank can increase the linearity of the oscillator gain. The inventors have found that the improvement in linearity is optimal when the inductance of the inner LC tank is a certain proportion of the total inductance of the outer LC tank. The optimal proportion (i.e. .sub.opt) can vary for different oscillators having different specifications. For example, an oscillator required to operate within a frequency range may comprise an inner and outer LC tank with different variable capacitance and inductance values to that of an oscillator required to operate within a different frequency range. The optimal proportion may be that at which the oscillator gain variation is minimum or that at which the linearity of the oscillator gain is maximum. Such properties may vary between different oscillators. Similarly, the optimal proportion at which the derivative of the oscillator gain is minimum may vary between different oscillators. The optimal proportion for differing oscillators can be obtained by performing various analysis such as the analysis described above to locate the global minimum on K.sub.v variation function versus .

(33) The applicant hereby discloses in isolation each individual feature described herein and any combination of two or more such features, to the extent that such features or combinations are capable of being carried out based on the present specification as a whole in light of the common general knowledge of a person skilled in the art, irrespective of whether such features or combinations of features solve any problems discloses herein, and without limitation to the scope of the claims. The applicants indicate that aspects of the present invention may consist of any such feature or combination of features. In view of the foregoing description it will be evident to a person skilled in the art that various modifications may be made within the scope of the invention.