Temperature compensated oscillator

Abstract

Temperature compensated oscillators are provided. The oscillator comprises an oscillator circuit and a temperature compensation module. The temperature compensation module reduces temperature induced errors in the frequency of oscillation of the oscillator by providing a temperature compensation signal to the oscillator circuit based on a temperature sensor output. The temperature compensation module comprises a low pass filter configured to reduce noise in the temperature compensation signal. The low pass filter is such that, using Laplace representations of transfer functions, the transfer function H(s) of the filter is equivalent to the transfer function of a closed loop configuration in which a module having an open loop transfer function G(s) is configured to generate an output from the closed loop configuration by applying the open loop transfer function G(s) to an error between an input to the closed loop configuration and the output from the closed loop configuration.

Claims

1. A temperature compensated oscillator, comprising: an oscillator circuit; and a temperature compensation module configured to reduce temperature induced errors in the frequency of oscillation of the oscillator by providing a temperature compensation signal to the oscillator circuit based on an output from a temperature sensor, wherein the temperature compensation module comprises a low pass filter configured to reduce noise in the temperature compensation signal, the low pass filter being such that, using Laplace representations of transfer functions, the transfer function H(s) of the filter is equivalent to the transfer function of a closed loop configuration in which a module having an open loop transfer function G(s) is configured to generate an output from the closed loop configuration by applying the open loop transfer function G(s) to an error between an input to the closed loop configuration and the output from the closed loop configuration, wherein G(s) comprises at least one pole at the origin and at least one pole that is not at the origin.

2. The oscillator of claim 1, wherein the low pass filter comprises said closed loop configuration.

3. The oscillator of claim 1, wherein the low pass filter is configured to implement H(s) without comprising said closed loop configuration.

4. The oscillator of claim 1, wherein G(s) comprises at least two poles at the origin.

5. The oscillator of claim 4, wherein G(s) comprises at least four poles in total.

6. The oscillator of claim 1, wherein G(s) comprises at least one zero.

7. The oscillator of claim 1, wherein G(s) comprises m poles at the origin and at least m−1 zeros, wherein m is an integer equal to or greater than 2.

8. The oscillator of claim 1, wherein $G\left(s\right)=\frac{k}{s^m}\frac{{\Pi }_{i=1}^{\left(m-1\right)}\left(s-z_i\right)}{{\Pi }_{j=1}^{\left(n-m\right)}\left(s-p_j\right)}$ wherein k is a constant, m is an integer representing the number of poles at the origin, n is an integer representing the number of poles in total, z.sub.i represents the position of each zero, and p.sub.j represents the position of each pole that is not at the origin.

9. The oscillator of claim 1, wherein the temperature compensation module further comprises a temperature compensation signal generation unit configured to generate the temperature compensation signal, and the low pass filter is positioned between the temperature sensor and the temperature compensation signal generation unit, such that the temperature compensation signal generation unit uses a filtered output from the temperature sensor to generate the temperature compensation signal that is provided to the oscillator circuit.

10. The oscillator of claim 1, wherein the temperature compensation module further comprises a temperature compensation signal generation unit configured to generate a first temperature compensation signal and the low pass filter is positioned between the temperature compensation signal generation unit and the oscillator circuit, such that the first temperature compensation signal is filtered by the low pass filter to generate a second temperature compensation signal that is provided to the oscillator circuit.

11. The oscillator of claim 1, wherein the low pass filter is implemented in the analogue domain.

12. The oscillator of claim 1, wherein the low pass filter is implemented in the digital domain.

13. The oscillator of claim 1, wherein the oscillator comprises a piezoelectric resonator coupled to the oscillator circuit.

14. The oscillator of claim 1, wherein the piezoelectric resonator comprises a quartz crystal.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

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

(2) FIG. 1 depicts an example configuration for a temperature compensated quartz crystal oscillator according to the prior art;

(3) FIG. 2 depicts an example configuration of a temperature compensated oscillator in which a temperature compensation module comprises a low pass filter configured to filter an output from the temperature sensor before generating a temperature compensation signal;

(4) FIG. 3 depicts an example configuration of a temperature compensated oscillator in which a temperature compensation module comprises a low pass filter configured to filter a temperature compensation signal that has already been generated;

(5) FIG. 4 depicts a closed loop configuration comprising a module having an open loop transfer function G(s);

(6) FIG. 5 depicts an implementation of a first example filter in the digital domain; and

(7) FIG. 6 depicts an implementation of a second example filter in the digital domain.

DETAILED DESCRIPTION OF THE INVENTION

(8) As mentioned above, noise in an output from a temperature sensor can degrade the quality of an output from a temperature compensated oscillator. The temperature sensor noise causes frequency noise at the oscillator output, which becomes phase noise (as phase is the time integral of frequency).

(9) Phase noise is a critical parameter of oscillators. The oscillator has its own intrinsic phase noise, which sets the limit for phase noise performance. Any additional noise added by the temperature sensor should be reduced as far as possible. In embodiments of the present disclosure, phase noise is reduced by filtering.

(10) Example configurations for a temperature compensated oscillator 1 using filtering to reduce phase noise are depicted in FIGS. 2 and 3. In these configurations (and others), the oscillator 1 comprises a piezoelectric resonator 5 coupled to an oscillator circuit 4. The piezoelectric resonator 5 optionally comprises a quartz crystal. The oscillator 1 further comprises a temperature compensation module 3. The temperature compensation module 3 reduces temperature induced errors in the frequency of oscillation of the oscillator 1 by providing a temperature compensation signal to the oscillator circuit 4 based on an output from a temperature sensor 2. The temperature compensation module 3 comprises a filter 31 that reduces noise in the temperature compensation signal. The temperature compensation module 3 further comprises a temperature compensation signal generation unit 32. The filter 31 may be positioned before the temperature compensation signal generation unit 32, as depicted in FIG. 2, such that the output from the temperature sensor 2 is filtered before the temperature compensation signal is generated. Alternatively, the filter 31 may be positioned after the temperature compensation signal generation unit 32, as depicted in FIG. 3, such that the temperature compensation signal is generated using an unfiltered output from the temperature sensor 2 and is then filtered before being supplied to the oscillator circuit 4. In other embodiments, filters may be provided both before and after the temperature compensation signal generation unit 32.

(11) The basic aim of the filter 31 (or filters) is to reduce noise relative to signal. As described below, however, achieving this noise reduction in a way which contributes optimally to improvement of the oscillator output is challenging. Embodiments of the present disclosure specifically address these challenges.

(12) In many filter designs there is a trade-off between achieving good noise rejection and good tracking. A low filter bandwidth, for example, will favor removal of more noise, allowing the overall phase noise performance to improve, but will tend to have a negative effect on tracking. This is because a low filter bandwidth will normally increase lag, which is typically inversely proportional to the filter bandwidth. The result of lag is that the temperature compensation being applied at any given time is based on the temperature at an earlier time. This is not a problem when the temperature is static but will cause errors when the temperature is changing. The lag is reduced by choosing a higher filter bandwidth.

(13) As a specific example of the problem, consider a standard 1.sup.st order low pass filter with bandwidth ω.sub.o, which has the following transfer function (using a Laplace representation):

(14) $H\left(s\right)=\frac{1}{1+s/{\omega }_o}$
The group delay (lag) of this filter is given by:

(15) $\tau \left(\omega \right)=\frac{1}{{\omega }_o}\left(\frac{1}{1+{\left(\omega /{\omega }_o\right)}^2}\right)$
It can be seen that the delay through the filter is inversely proportional to the bandwidth.

(16) Similar issues exist for higher order filters, be they a series of buffered lower order stages, or single stage high order filters. Attempts have been made to counter the measurement lag problem by using the first differential of the temperature as an additional input to the temperature compensation, but the differential of the temperature is a noisier signal than the current temperature, and is therefore likely to degrade oscillator noise performance further.

(17) In an embodiment, the filter 31 is a low pass filter. This is appropriate because noise from the temperature sensor 2 is generally wideband while the signal is usually confined to a certain bandwidth.

(18) In an embodiment, the filter 31 is configured such that, using Laplace representations of transfer functions, the transfer function H(s) of the filter is equivalent to the transfer function of a closed loop configuration 10 such as that depicted schematically in FIG. 4. The closed loop configuration 10 comprises a module 11 having an open loop transfer function G(s) and is configured to generate an output Y from the closed loop configuration 10 by applying the open loop transfer function G(s) to an error E between an input X to the closed loop configuration 10 and the output Y from the closed loop configuration 10, wherein G(s) comprises at least one pole at the origin and at least one pole that is not at the origin.

(19) The inventors have found that using a filter 31 having this specific design allows the relationship between noise rejection and good tracking to be decoupled to a greater extent than is achieved using standard filters used in the context of temperature compensated oscillators, thereby allowing the performance of the filter 31 to approach more closely that of an ideal filter (which would reject all noise and track the input signal perfectly as it changes over time) in this context.

(20) The feedback in the closed loop configuration 10 attempts to keep the input X and the output Y identical. The ability of the system output to correctly track the input depends on: 1) the open loop transfer function G(s); and 2) the nature of the applied input X.

(21) In the context of temperature compensated oscillators, it has been found that the applied input X is typically such that arranging for G(s) to have at least one pole at the origin and at least one pole that is not at the origin provides improved performance relative to conventional alternatives.

(22) In the case where the input X is static, if the open loop transfer function G(s) is simply a gain term, then there will be a constant error between the input X and the output Y that is dependent on the magnitude of the gain. Introducing an integrator (origin pole) into the open loop transfer function G(s) integrates the error between the input X and output Y. Thus, when the output Y is stable, the error is zeroed and the input/output tracking is therefore ideal (after initial settling). Where variation in time exists, input/output tracking may be less than ideal (but still acceptable) depending on the degree of variation and the number of origin poles that are provided. The filter design allows flexibility in that tracking can be enhanced where a higher degree of variation in time is expected by adding further origin poles. In the case where the input X has an nth order polynomial variation in time, for example, n integrators in the open loop transfer function would achieve ideal tracking (after initial settling). In an embodiment, G(s) comprises at least two poles at the origin.

(23) The additional one or more poles that are not at the origin in G(s) provide the low pass functionality (a low pass signal transfer function from input to output). In an embodiment, at least two poles are provided that are not at the origin. In an embodiment, G(s) comprises at least two poles at the origin and at least two poles that are not at the origin, optionally exactly two poles at the origin and/or exactly two poles that are not at the origin.

(24) A closed loop system with several poles in the open loop transfer function G(s) as described will have phase shift in the feedback path, which in the absence of zeros can be excessive, resulting in a feedback system with no phase margin, or instability, or positive feedback.

(25) In an embodiment, one or more zeros are provided in the open loop transfer function G(s) to stabilize the loop. The pole and zero locations are selected appropriately to give the desired low pass filter bandwidth whilst maintaining stability.

(26) In an embodiment, G(s) comprises m poles at the origin and at least m−1 zeros (optionally exactly m−1 zeros), wherein m is an integer equal to or greater than 2. In an example of such an embodiment, G(s) is given as follows:

(27) $G\left(s\right)=\frac{k}{s^m}\frac{{\Pi }_{i=1}^{\left(m-1\right)}\left(s-z_i\right)}{{\Pi }_{j=1}^{\left(n-m\right)}\left(s-p_j\right)}$
wherein k is a constant, m is an integer representing the number of poles at the origin, n is an integer representing the number of poles in total, z.sub.i represents the position of each zero, and p.sub.j represents the position of each pole that is not at the origin. The transfer function shown is of type ‘m’ (m poles at origin), and order ‘n’ (n total poles). The corresponding closed loop transfer function H(s) is given as follows:

(28) $\begin{array}{c}H\left(s\right)=\frac{Y\left(s\right)}{X\left(s\right)}\\ =\frac{G\left(s\right)}{1+G\left(s\right)}\\ =\frac{k{.Math.}_1^{\left(m-1\right)}\left(s-z_m\right)}{s^m{.Math.}_1^{\left(n-m\right)}\left(s-p_m\right)+k{.Math.}_1^{\left(m-1\right)}\left(s-z_m\right)}\end{array}\hspace{1em}$
An advantage of this filter transfer function H(s) relative to conventional filters used in the context of temperature compensated oscillators is that the presence of the one or more origin poles within G(s) provides enhanced tracking of a range of input classes. This ability can be analyzed by looking at the tracking error transfer function—the ability of the output to track the input, which can be defined as:

(29) $\begin{array}{c}\mathrm{TETF}\left(s\right)=\frac{E\left(s\right)}{X\left(s\right)}\\ =\frac{X\left(s\right)-Y\left(s\right)}{X\left(s\right)}\\ =\frac{1}{1+G\left(s\right)}\\ =\frac{s^m{.Math.}_1^{\left(n-m\right)}\left(s-p_m\right)}{s^m{.Math.}_1^{\left(n-m\right)}\left(s-p_m\right)+k{.Math.}_1^{\left(m-1\right)}\left(s-z_m\right)}\end{array}\hspace{1em}$
The ability of the filter transfer function to track inputs in the time domain can be analyzed as follows:

(30) $\underset{t.fwdarw.\infty }{\mathrm{Lim}}e\left(t\right)=\underset{s.fwdarw.0}{\lim }\mathrm{sE}\left(s\right)=\underset{s.fwdarw.0}{\lim }\mathrm{sX}\left(s\right)\mathrm{TETF}\left(s\right)$
Some example input waveforms are analyzed in the table below, respectively for: 1) a static input, x(t)=a; 2) a 1.sup.st order ramp, x(t)=at; 3) an m.sup.th order ramp, x(t)=at.sup.m; and 4) an (m+1).sup.th order ramp, x(t)=at.sup.(m+1).

(31) TABLE-US-00001 x(t) X(s) =  (x(t)) sE(s) = sX(s)TETF(s) Steady State e(t) a a/s $\frac{{\mathrm{as}}^m\underset{1}{\overset{\left(n-m\right)}{.Math.}}\left(s-p_m\right)}{s^m\underset{1}{\overset{\left(n-m\right)}{.Math.}}\left(s-p_m\right)+k\underset{1}{\overset{\left(m-1\right)}{.Math.}}\left(s-z_m\right)}$ 0 at a/s.sup.2 $\frac{{\mathrm{as}}^{\left(m-1\right)}\underset{1}{\overset{\left(n-m\right)}{.Math.}}\left(s-p_m\right)}{s^m\underset{1}{\overset{\left(n-m\right)}{.Math.}}\left(s-p_m\right)+k\underset{1}{\overset{\left(m-1\right)}{.Math.}}\left(s-z_m\right)}$ 0 (m ≥ 1) at.sup.m (m − 1)! a/s.sup.(m+1) $\frac{\left(m-1\right)!a\underset{1}{\overset{\left(n-m\right)}{.Math.}}\left(s-p_m\right)}{s^m\underset{1}{\overset{\left(n-m\right)}{.Math.}}\left(s-p_m\right)+k\underset{1}{\overset{\left(m-1\right)}{.Math.}}\left(s-z_m\right)}$ 0$a\frac{\left(m-1\right)!}{k}\frac{\underset{1}{\overset{\left(n-m\right)}{.Math.}}\left(-p_m\right)}{\underset{1}{\overset{\left(m-1\right)}{.Math.}}\left(-z_m\right)}$ at.sup.(m+1) m! a/s.sup.(m+2) $\frac{m!a\underset{1}{\overset{\left(n-m\right)}{.Math.}}\left(s-p_m\right)}{s\left(s^m\underset{1}{\overset{\left(n-m\right)}{.Math.}}\left(s-p_m\right)+k\underset{1}{\overset{\left(m-1\right)}{.Math.}}\left(s-z_m\right)\right)}$ ∞

(32) This demonstrates that a type ‘m’ open loop transfer function G(s) can implement a closed loop filter that can track an (m−1).sup.th order ramp with no static error, and an m.sup.th order ramp with a fixed static error. Many other input waveform types can also be tracked with zero error.

(33) In an embodiment, G(s) comprises a type 2, 4.sup.th order transfer function, which has been found to provide a particularly good balance of performance and stability.

(34) In an embodiment, the filter 31 comprises the closed loop configuration described above. Alternatively, the filter 31 may be configured such that the transfer function H(s) is achieved without actually providing the closed loop configuration (i.e. by providing the same transfer function H(s) using other components and/or circuit layouts).

(35) The filter 31 of the above embodiments may be implemented in the analogue or digital domains.

DETAILED EXAMPLES

(36) Two example implementations in the digital domain are described, each comprising open loop transfer functions with feedback.

(37) A digital, discrete time implementation of the open loop transfer function has the following form (in Z transform representation):

(38) $G\left(z\right)\approx \left(\frac{T^3}{2}\right)\left(\frac{\left(1+2z^{-1}+z^{-2}\right)}{\begin{array}{c}1-\left(2-\frac{1}{Q_p}\left(T{\omega }_p\right)+\left(\frac{1-2Q_p^2}{2Q_p^2}\right){\left(T{\omega }_p\right)}^2\right)z^{-1}+\\ \left(1-\frac{1}{Q_p}\left(T{\omega }_p\right)+\left(\frac{1}{2Q_p^2}\right){\left(T{\omega }_p\right)}^2\right)z^{-2}\end{array}}\right)\left(\frac{\left(1-z^{-1}\left(1-T{\omega }_1\right)\right)}{\left(1+z^{-1}\right)}\right)\frac{1}{{\left(1-z^{-1}\right)}^2}$
with a simplifying assumption being made that Tω.sub.z, Tω.sub.p<<1. The full expression can also be derived but is considerably more complex.

(39) In Example 1, Q.sub.p=0.5 (real poles). In example 2, Q.sub.p=1 (complex poles).

(40) Example 2 has better roll-off characteristics than Example 1, but is more costly to implement in terms of area and power.

(41) Define:
Tω.sub.z′=2.sup.k.sup.z,k.sub.z is an integer
Tω.sub.p=2.sup.k.sup.p,k.sub.p is an integer

(42) Note: in the following expressions, int(x) means the integer part of x.

Example 1—Real Poles Implementation

(43) The circuit for Example 1 is depicted in FIG. 5. The open loop transfer function G(z) has the following form (in Z transform representation):

(44) $G\left(z\right)=\left[\frac{2^{\left(k_p-1\right)}\left(1+z^{-1}\right)}{\left(1-z^{-1}\left(1-2^{k_p}\right)\right)}\right].Math.\left[\frac{2^{\left(k_p-1\right)}\left(1+z^{-1}\right)}{\left(1-z^{-1}\left(1-2^{k_p}\right)\right)}\right].Math.\left[\left(\frac{2^{\left(k_p-3\right)}}{\left(1-z^{-1}\right)}\right)\right].Math.\hspace{1em}\left[\left(\frac{2^{\left(k_p+\mathrm{int}\left(\left(k_z-k_p-1\right)/2\right)\right)}}{\left(1-z^{-1}\right)}\right)\right].Math.\left[\frac{2^{\left(3-k_p\right)}\left(1-z^{-1}\left(1-2^{k_z}\right)\right)}{\left(1+z^{-1}\right)}\right]$

Example 2—Complex Poles Implementation

(45) The circuit in Example 2 is depicted in FIG. 6. The open loop transfer function G(z) has the following form (in Z transform representation):

(46) $G\left(z\right)=\left[\frac{2^{\left(2k_p-2\right)}\left(1+2z^{-1}+z^{-2}\right)}{\left(1-\left(2-2^{k_p}-2^{\left(2k_p-1\right)}\right)z^{-1}+\left(1-2^{k_p}+2^{\left(2k_p-1\right)}\right)z^{-2}\right)}\right].Math.\hspace{1em}\left[\left(\frac{2^{\left(k_p-2\right)}}{\left(1-z^{-1}\right)}\right)\right].Math.\hspace{1em}\left[\left(\frac{2^{\left(k_p+\mathrm{int}\left(\left(k_z-k_p-1\right)/2\right)\right)}}{\left(1-z^{-1}\right)}\right)\right].Math.\left[\frac{2^{\left(3-k_p\right)}\left(1-z^{-1}\left(1-2^{k_z}\right)\right)}{\left(1+z^{-1}\right)}\right]$

(47) Examples 1 and 2 both use implementations in which every multiplication is arranged to be a power of 2, which means that no multiplying hardware is involved.