The present invention relates generally to a Wien-bridge oscillator and a circuit arrangement.
In many electric circuits including so-called integrated circuits, i.e., ICs, a fully integrated oscillator is needed for generating a reference clock signal with high frequency accuracy and with very low temperature and long-term drift. Clock signal generators are known to be used for a variety of applications, for example, for digital signal processing circuits. Highly accurate clock signal generators are typically used in analog-to-digital devices, i.e., for sampling an analog signal to produce a corresponding digital signal.
In conventional applications and for this purpose relaxation oscillators have been used, which exhibit low complexity and can be easily adjusted or programmed. However, a drift in frequency typically does not only originate from parameter changes of the primary passive frequency determining components like resistors and capacitors. Also active circuit components such as transistors in current mirrors, switches and comparators may cause a drift in frequency effectuated by temperature influence or stress on the components.
To a large extent this additional drift in frequency effectuated by parameter changes of active circuit components can be avoided through use of a harmonic oscillator comprising a resonator having a high quality factor wherein it is assumed that the active circuit portion fulfills some minimum requirements. In the case of a Wien-bridge oscillator and when operated at oscillation frequency the amplifier stage must comply with a minimum amplification and a maximum phase shift, in order to stay below a predefined maximum frequency drift of, for example, ±1%. As long as the minimum requirements are fulfilled the high quality factor of the resonator provides for corresponding high frequency stability. The quality of an open oscillatory circuit system is a measure of the capability of the closed oscillatory to suppress variations in the oscillation frequency. Then the drift in frequency is substantially independent of parameter changes of the active components and is caused primarily by temperature variations of the passive circuit devices.
In the following and with reference to
The resonant frequency ωr of the Wien-bridge is determined by resistors R1, R2 and capacitors C1, C2 as
wherein in many applications the values of the components is chosen as R1=R2=R and C1=C2=C. Consequently the resonant frequency is determined by
The complex transfer function normalized to the resonant frequency is
wherein
and wherein variable ε is a positive number, ε<1, and that describes the detune of the bridge circuit.
From equation (1) the frequency response Φ of the phase shifting follows as
a and 2b depict the frequency response of the amplitude (magnitude) and of the phase shifting (phase) for ε= 1/15.
As shown in
In a non-detuned Wien-bridge circuit, i.e., ε=0, the differential output signal would be zero. As a consequence the Wien-bridge necessarily must be detuned slightly in order to comply with the requirement of oscillating with constant amplitude.
The quality factor of a resonant circuit is
Note that generally the quality of a resonant circuit is defined as partial derivative of amplitude and phase at oscillation frequency. Since in the case considered here the partial derivative of the amplitude is zero at resonant frequency, the partial derivative of the phase remains.
Accordingly the correlation between detune and quality, i.e., stability in frequency, of a resonant circuit can be characterized in that the lower the detune, the higher is the quality, i.e., stability in frequency, of the resonant circuit.
The oscillator circuit comprising the Wien-bridge and the amplifier as depicted in
T(s)=A(s)·└Fp(s)−Fn(s)┘=A(s)·F(s)
wherein A(s) is the gain of the amplifying element in the circuit and
describes the transfer function of the feedback path.
The Barkhausen criterion is a (mathematical) condition to determine when a linear electronic circuit will oscillate and provides the necessary—but not sufficient—conditions for a stable oscillation. More precisely the Barkhausen criterion consists of two conditions, namely:
1. The absolute value of the loop gain in an amplifier with feedback path as depicted in
|T(s=jω0)=1|
2. The phase shift at the oscillating frequency must have a positive feedback. This condition is satisfied when the phase shift is an integer multiple of 360°:
∠T(s=jω0)=z·360° wherein z=0, 1, 2, . . .
In this embodiment a phase shift of z=0, i.e., 0° phase shift is considered.
It follows from the amplitude condition, i.e., the first of the above mentioned conditions, that the necessary gain A is higher when the detune is lower.
It can be shown that in a stable oscillating state it follows from the Barkhausen criteria that an amplification of A=(9/ε)+3 is required at the resonant frequency.
As a consequence in Wien-bridges the requirements for the amplifier stage are high, i.e., the amplifier stage must exhibit a high gain while at the same time exhibiting a low phase shift. In one embodiment the absolute value of the phase shift should be below 10° since in this range only a high quality and frequency stability can be achieved, i.e., the frequency response of the phase shift of the Wien-bridge is steep. Consequently the amplifier stage is a crucial component of the oscillator. Drift caused by temperature variation and process parameter variation may have significant influence on the accuracy of the oscillation frequency, as these typically cause significant variations in gain and phase shift in amplifier circuits.
With respect to the quality factor, i.e., stability in frequency, optimum solutions can be achieved by adjusting the detune ε of the Wien-bridge to a value high enough so that the oscillation amplitude exhibits a sufficient high value.
The achieved solution furthermore shall effectuate that the drift in frequency caused by temperature variations as far as possible depends on the temperature coefficients of the resistors in the Wien-bridge instead of depending on any semiconductor component as known from conventional circuits.
Embodiments of the invention provide an oscillator circuit comprising a Wien-bridge wherein a first feedback signal portion of zero detune and a second feedback signal portion exhibiting detune are coupled to the Wien-bridge. In one embodiment the first and second portion of the feedback signal are furthermore weighted before being coupled to the Wien-bridge.
The present invention will be understood more fully from the detailed description given below and from the accompanying drawings of the invention, which, however, should not be taken to limit the invention to the specific embodiments, but are for explanation and understanding only and wherein.
a, 2b, and 2c depict a frequency response of amplitude (magnitude), of phase shifting (phase) and the relation of phase shifting and detune of a Wien-bridge oscillator;
Reference numeral 420 depicts a Wien-bridge that acts as a resonator. The Wien-bridge comprises in its one path, shown on the left hand side, a series of resistor R1 and capacitor C1 being in series with parallel arrangement of C2 and R2. The other path, shown on the right hand side of the Wien-bridge, comprises a first ohmic resistor R3 in series with ohmic resistors R4, R5.
In a non-limiting embodiment the circuit components may be dimensioned as:
resistors: R1=R2=R=50 kΩ, R3=250 kΩ, R4=5 kΩ, R5=120KΩ
capacitors: C1=C2=C=5 pF
resonant frequency fosc_ideal=1/(2·π·R·C)≈125 kHz
detune values ε1=⅛, ε2=0
bias current Ib=7.5 μA.
In the depicted circuitry the implementation of amplifying and adding the signals is implemented differentially, since differential circuits basically are less sensitive to variations in supply voltage than single-ended implementations. Further, also effectuated by the fully differential implementation using two transistor pairs, there is almost no additional temperature drift due to the amplitude stabilization. Both aspects are of particular advantage in integrated circuits.
As discussed before the frequency of the oscillation in the Wien-bridge must be prevented from matching exactly the resonant frequency of the circuit, since then the voltage between the taps of the path, which is coupled to the comparator, would drop to zero. As a result, the Barkhausen criterion 1 would not be fulfilled. Consequently, the feedback signal coupled to the Wien-bridge must effectuate a sufficient detune of the oscillating frequency.
This is achieved by coupling a feedback signal to the Wien-bridge comprising a weighted and amplified detuned signal portion and a weighted non-detuned signal portion wherein the weighting of these two portions depends on the amplitude of the oscillation voltage Vosc. The detuned signal portion may be based on voltage Vfb1 exhibiting a non-zero detune of, for example, ε=⅛ and which may be tapped from the Wien-bridge between resistors R4 and R5 as illustrated in the figure. The non-detuned signal portion, i.e., the signal portion exhibiting a detune of ε=0, may be based on voltage Vfb2.
For amplifying the oscillating voltage Vfb1 the circuit comprises a first amplification means 430-1, which in the depicted embodiment may be implemented by a differential amplifier comprising a pair transistors controlled by voltage Vfb1. Similarly, for amplifying oscillation voltage Vfb2, the circuit comprises second amplification means 430-2 that in the depicted embodiment is implemented by a differential amplifier comprising another pair of transistors. Note that any suitable amplification means for amplifying the voltages can be used here as a replacement of the differential amplifiers comprising the transistors. The disclosed invention shall not be limited in this regard. Furthermore, when implementing the amplifier means by differential amplifiers, the differential amplifiers can be implemented using any suitable circuitry, but shall not be limited to the depicted circuitry based on P-MOS transistors.
First amplification means 430-1 accordingly outputs amplified voltage Vfb1 and second amplification means 430-2 outputs amplified voltage Vfb2. The output signals of the first and second amplification means are added, which in this embodiment is achieved by connecting the drains of the transistors of the differential amplifiers. The resulting signal may then be forwarded a buffer stage 440 that amplifies and couples the resulting signal, i.e., the oscillating voltage Vosc to comparator 410. Buffer stage 440 decouples the high-impedance output of the amplifier from the Wien-bridge and typically exhibits a gain of 1.
First amplification means 430-1 is supplied by a first current source 450-1, which provides a portion (1−k) of a bias current Ib, i.e., a portion (1−k)·Ib, to the first amplification means 430-1, wherein k with 0≦k≦1 is a weighting factor. Second amplification means 430-2 is supplied by a second current source 450-2 that provides a portion k with 0≦k≦1 of bias current Ib, i.e., k·Ib, to the second amplification means 430-2. Accordingly with decreasing k the portion of bias current Ib provided by the first current source 450-1 to the first differential amplifier 430-1 increases and the port of the bias current provided by the second current source 450-2 to the second differential amplifier decreases. As a consequence, for k being small, i.e., for 0≦k<½, the detuned signal Vfb1 is amplified more than the non-detuned signal Vfb2. Conversely, i.e., with increasing k, the portion of bias current Ib provided by second current source 450-2 to the second differential amplifier increases and the portion of bias current Ib provided by the first current source 450-1 decreases. Hence, for k being large, i.e., for ½<k<1, the non-detuned signal Vfb2 is amplified more than the detuned signal Vfb1. So by controlling the value of k the mixture of the added signal the amplification effectuated by the first and second differential amplifier can be controlled, consequently the ratio of the amplified detuned signal portion as output by the first differential amplifier 430-1 to the amplified non-detuned signal portion in the resulting signal provided to buffer 440 can be controlled.
The resulting effective detune εeff can be calculated as
In case differential amplifiers are of identical dimensions, i.e., exhibit identical amplification, then the amplification is gm1=gmmax·(1−k) and gm2=gmmax·(1−k). As mentioned above, weighting factor k may take values in the range 0≦k≦1. In order to increase the detune of Vosc the amplification of the detune signal portion Vfb1 must be increased and the amplification of the non-detuned signal portion Vfb2 must be decreased correspondingly, i.e., k must be decreased. Vice versa, i.e., to decrease the detune of Vosc, the amplification of the detuned signal Vfb1 may be reduced and the amplification of the non-detuned signal Vfb2 may be increase, which can be achieved by increasing the value of weighting factor k. Accordingly, maximum detune can be achieved by setting weighting factor k to zero, and minimum detune can be achieved by setting weighting factor k to 1.
In this way the detune of voltage Vosc can be controlled by setting weighting parameter k. Since the detune correlates with the amplitude of voltage Vosc, the detune serves as means for controlling Vosc so that its amplitude triggers comparator 410.
Weighting factor k is controlled by amplitude detector 460, which takes voltage Vosc as input signal. By comparing the amplitude of Vosc to a predefined threshold value, amplitude detector 460 may set weighting factor k. If amplitude detector 460 detects that the voltage amplitude of Vosc is way above its predetermined threshold value, it may set the weighting factor k to a value of ½<k<1 for decreasing the detune and thus decreasing the amplitude of Vosc in order to prevent an overshooting voltage Vosc. Vice versa, i.e., if amplitude detector 460 detects a situation wherein the amplitude of Vosc is below the predetermined threshold then it may set the weighting factor k to a value of 0<k<½ in order to increase the amplification of detuned signal Vfb1 by increasing the amplitude of bias current Ib. As indicated in
In this way, i.e., by monitoring the amplitude of voltage Vosc, the amplitude detector 460 may set weighting factor k correspondingly and thus may control the amplitude of Vosc to a desired range.
At operation startup of the circuit, i.e., if there is no oscillation, the value of weighting factor k is set to a value of k=0 in order achieve maximum detune of the circuit to start the oscillation. Bias current Ib in this situation accordingly entirely flows through differential amplifier 450-1 thus providing a maximum amplification of Vfb1. Then, as soon as oscillation has started and the amplitude of Vosc has reached a predefined level, the amplitude detector 460 may route a portion of bias current Ib to differential amplifier 450-2 by increasing the value of weighting factor k to a value above zero. By increasing the amplification of non-detuned voltage Vfb2, i.e., decreasing to the same extent detuned voltage Vfb1, the detune of Vosc is reduced.
The effective detune that takes weighting factor k into account can be described by
For ε2=0 follows
For k=½ the bias current flowing through the first differential amplifier 450-1 is equal to that flowing through second differential amplifier 450-2, so that the resulting effective detune is
The circuit as depicted in
Note that resistors 480-1 and 480-2 respectively reflect the drain-source resistance of the transistors used in the current source 480-1 and 480-2 respectively.
In an alternative embodiment, i.e., alternative to operating the Wien-bridge oscillator with a variable detune and amplitude control, the Wien-bridge can be operated with a constant detune, once the oscillator has started oscillating. In particular this approach can be of advantage for reference clock signal generators, since an additional temperature drift might be caused by variations of components in the amplitude control circuitry that can extend the temperature drift of the passive components in the Wien-bridge itself. In one embodiment a Wien-bridge oscillator has been realized exhibiting a constant detune of ε= 1/15. Measured results show that these match the simulation pretty exact. The temperature drift of the oscillation frequency does not extend the specified temperature drift of the resistors in the Wien-bridge. Since the amplitude of the oscillation, i.e., the voltage amplitude, is not controlled, this voltage amplitude varies heavily in this alternative depending on process parameters and temperature. However, this is not a major drawback when the oscillator is used for generating a reference clock signal. In addition the deployed amplifier circuit effectuates a decrease of the amplification when the oscillation amplitude increases and thus causes a limitation of the amplitude. A potentially critical point when operating the circuit is the condition for starting the oscillation, i.e., when powering up the circuit. In case the detune is too small there will be no oscillation. To achieve an optimal adjustment of the detune, the detune can be implemented digitally programmable and the amplitude detector can be used for determining the adjustment, which causes the oscillator to start oscillating safely. As depicted in
Note that in
The circuitry 500 depicted in
In view of the above mentioned requirements to the amplifier, i.e., small phase shift, high amplification and small current consumption preferably below 30 μA, a comparatively low basic, i.e., resonant frequency, of the Wien-bridge oscillator of 125 kHz is chosen in one embodiment. Higher frequencies, for example system clock frequencies, e.g., at around 40 MHz as used in many integrated circuits, can be generated by deploying frequency synthesizer PLLs.
For the sake of completeness the circuitry 600 of
Current mirror 620, which forms part of the common mode control, provides a current that is proportional to the output common mode voltage Vcm, which is Vcm=Vo_p+Vo_m. When balanced this current must correspond to current Ib. In case Vcm increases the current in the current mirror increases and the voltage at nodes g_p and g_m correspondingly decrease. Source followers M7/M8 transfer the voltage decrease level-shifted to outputs Vo_p and Vo_m and thus counteract an increase of the common mode output voltage. The value of Vcm can be adjusted by dimensioning transistors M3-M6 and resistors R7-R8.
In the depicted embodiment the common mode output voltage Vcm is adjusted by a voltage divider comprising transistors M1 and M2, which due to their long channel act approximately like highly-resistive ohmic resistors.
Whereas many alterations and modifications of the present invention will become apparent to a person of ordinary skill in the art after having read the foregoing description, it is to be understood that any particular embodiment shown and described by way of illustration is in no way intended to limit the scope of the claims which themselves recite only those features regarded as essential to the invention.
Number | Name | Date | Kind |
---|---|---|---|
4339829 | Dimon | Jul 1982 | A |
20040041599 | Murphy | Mar 2004 | A1 |
Entry |
---|
De Smedt, V. et al., “A 66 μW 86 ppm/°C Fully-Integrated 6 MHz Wienbridge Oscillator With a 172 dB Phase Noise FOM,” IEEE Journal of Solid-State Circuits, vol. 44, No. 7, Jul. 2009, pp. 1990-2001. |
Number | Date | Country | |
---|---|---|---|
20140285274 A1 | Sep 2014 | US |