DE3725732C1 - PLL with variable oscillator - has control circuit with filter using low cut=off amplifier to attenuate phase noise - Google Patents

Abstract

An oscillation producer has a controlled oscillator, and a regulator circuit with a phase comparator and an active filter for attenuating phase noise. The poles and zeros of the filter are so selected that for disturbance frequencies it has a first amplitude rise in the lowest frequency zone, and under the actual oscillator frequency, there is a pole which adjusts the disturbance frequency response in the high frequencies after a second rise at lower frequencies to a constant value. The filter is of second order, at least, and between the lowest and high frequencies is first at least one pole and then at least one zero such that in the mid-range the response is clearly under the value which would be extrapolated from the first rise, around the zero point. The complex frequencies of poles and zeros have real parts, and the loop gain satisfies the criteria for asymptotic stability of the control loop. ADVANTAGE - Good attenuation of h.f. noise.

Description

The invention is based on an electrical vibration generator the preamble of claim 1, known as a phase lock oscillator.

Fig. 1 shows the basic structure of such a vibration generator. The oscillator is labeled VCO . It provides the actual frequency F _a = Ω _a / 2 π . This is divided using a frequency divider N and fed to a phase comparator P , which carries out a phase comparison with a reference frequency F _r = Ω _r / 2 π . A filter with the transfer function F (s) is connected downstream of the phase comparator and is connected upstream of the control input of the oscillator VCO ; where s is the complex frequency of the filter input signal. The interference phase Φ _a (error angle) is determined in the phase comparator by comparing the actual phase Φ _i with the reference phase Φ _r .

In practice, filters of different orders, for example second orders, have been used as filters in this control loop, as shown in FIG. 2. This is an active low-pass filter with an operational amplifier OP .

Since the phase comparator P in FIG. 1 works digitally, voltage peaks occur at its output, which can overdrive the operational amplifier in the filter. In order to avoid this effect, an RC element is connected upstream of this operational amplifier. A corresponding arrangement for earth-symmetrical filter input is shown in FIG . A similar filter is known from "The Electronics Technician" No. 8, 1985, pp. 44-49, Fig. 2.

It has been shown that when using an inexpensive operational amplifier in the filter this is not able to phase noise of the To suppress vibration generator to a sufficient extent, the z. B. at a reference frequency of 1 MHz in the frequency range from 1 kHz to 100 kHz occurs.

The object of the invention is to provide a vibration generator at the noise component of a higher frequency (but still below that, if applicable divided oscillator frequency) are well damped despite use an amplifier in the filter that has a relatively low upper Has limit frequency.

This object is achieved with the means specified in claim 1. Advantageous further developments are specified in the subclaims.

The invention is based on the following considerations:
The frequency responses of a phase lock loop circuit are described using the following equations:

Open loop reinforcement:

A ₀ (s) = K ₀ F (s) / s (Eq. A)

Oscillator interference frequency response:

A ₁ (s) = Φ _a (s) / Φ _r (s) = s / [sK ₀ · (-F (s))] (Eq. B).

Mean

K ₀ the total loop gain,
F (s) the frequency response of the filter used,
s corresponds to jw (w = angular frequency),
Φ _a (s) the error angle corresponding to the output signal of the phase comparator P in Fig. 1,
Φ _r (s) the phase of the reference oscillation with the reference frequency F _r .

The following applies: Φ _a (s) = Φ _r (s) - Φ _i (s) with Φ _i = actual phase of the oscillator VCO .

A ₀ (s) describes the frequency response of the open loop and gives information about the stability of the control loop.
A ₁ (s) describes the frequency response when a disturbance variable is fed into the oscillator and gives a statement about the damping of the phase noise, which is caused by the oscillator.

A high attenuation of the oscillator noise and a good suppression of the reference frequency are to be achieved with the filter shown in FIG. 3, but at the same time the good stability of the control loop is to be maintained. Not all of these goals are achieved equally well, as a consideration of the oscillator interference frequency response A ₁ (s) shows, but in which it is assumed from Fig. 2, but with an upstream RC element. The transfer function of such a filter is:

F (s) = - (1+ sT ₂) / 2 · sT ₄ (1+ sT ₃) (1+ sT ₁ / 2)

with T ₁ = R ₁ C ₁;
T ₂ = R ₃ (C ₂ + C ₃);
T ₃ = R ₃ C ₃;
T ₄ = R ₁ C ₂.

The oscillator interference frequency response is:

This relationship is shown in FIG. 4 in a schematic floor diagram approximated by asymtotes as a function of the technical frequency f = w / 2π . The "technical frequency" f (hereinafter only referred to as "frequency") is the imaginary part of the complex frequency (s) . In the low frequency range, the term s ²2 T ₄ / K ₀ results in a 40 dB increase. The fourth-order denominator, depending on T ₃ and T ₁ / 2 at higher frequencies, reduces the rise to a horizontal course at 0 dB.
The basic frequency is designated f _n = 1/2 π T _n . In the example shown, it corresponds to the frequencies 1 / π T ₁ and 1/2 f T ₃, which are approximately f _n for stability reasons or must form f _n .

It can be seen that the interference or noise frequency response shown drops to low frequencies, so there the noise is suppressed. It would be desirable to shift the rising asymtote downwards and thus the cut-off frequency f _n in the direction of high frequencies in order to achieve a special noise suppression there as well. For this it would be necessary to either increase the loop gain K ₀ or to reduce the time constant T ₄. Since the loop gain should in practice be between 100 s ^-1 and 1000 s ^-1 , the possibilities for better noise suppression at higher frequencies depend on the extent to which T ₄ can be reduced. Did you want z. B. raise the basic frequency f _n = 1/2 π T _n to 10 kHz, then from the formula s ²2 T ₄ / K ₀ = 1 with s ² = w ² = (2 π f _n ) ² and K ₀ = 300 s ^{-1 determine} a value for T ₄ of 3.75 × 10 ^-8 s. To ensure the stability of the control loop, the amplifier used in the filter must not cause a negative phase at the corresponding frequency 1/2 π T ₄ = 4.25 MHz; it must therefore have a sufficiently high upper cut-off frequency f _og .

Since this is not possible with conventional amplifiers, the cut-off frequency f _n cannot be increased to the 10 kHz just assumed. Accordingly, noise frequencies above 5 kHz cannot be sufficiently attenuated in practice.

With the use of another filter according to the invention, the basic frequency f _n can be increased with the same functioning of the vibration generator, so that the noise suppression with respect to the higher-frequency noise components is improved. The following considerations common in filter technology are used to determine the time constants and other constants for the filter in the vibration generator according to the invention:

One starts, for example, from the first of the filter transfer functions specified in claim 2 (with F ₀ = 1) and then first obtains a fifth order frequency response for A ₁ (s) with equation b:

where M ₁ to M ₅ are abbreviations for coefficients and T ₄, T ₇, T ₉ filter time constant and ϑ ₇ is the degree of filter damping.

If you wanted the amount of this function in the soil diagram construct, the function could also be written as follows:

In this equation, the time constants can be used immediately if one records the desired course of the amount of A ₁ (s) on a logarithmic scale approximately over the frequency by asymtotes (bottom diagram). The corner frequencies then correspond to the values in such a floor diagram

An example of such a bottom diagram is given in FIG. 6, the reference frequency F _{r being} 1 MHz. Noise suppression is to take place according to the drawn-in desired curve V below the frequency 1/2 π T ₃≈1 / 2 π √ of approximately 100 kHz.

In order to obtain the desired mode of operation, the filter circuit is dimensioned so that the time constant T ₄ can be selected as before and the required noise suppression is nevertheless achieved.

T ₄ is thus determined so that the frequency 1/2 π T ₄ is sufficiently far below the upper cut-off frequency f _{og of} the amplifier in the filter that it does not cause a negative phase which could impair the stability of the control loop.

The filter time constants T ₄, T ₇, T ₉ are thus already defined.

K ₀ is determined by the individual gain factors of the components contained in the control loop including the factor F ₀ in the transfer function F (s) , where F ₀ is expediently set to 1. The damping constant ϑ ₇ of the filter and the damping constants ϑ ₁ and ϑ ₂ of A ₁ (s) are preferably experimentally known in a range of values from 0.5 to 10 corresponding to the desired course of A ₁ (s) in the vicinity of the corner frequencies fixed, e.g. B. ϑ ₁ = 1, ϑ ₂ = 0.8, ϑ ₇ = 1. The stipulations influence the stability of the control loop. Therefore, redefinitions may be necessary later if the stability check leads to unsatisfactory results.

After inserting the numerical values for T ₁, T ₂, T ₃, ϑ ₁, ϑ ₂ resulting from the desired course V in equation 2, by comparing the two functions given above for A ₁ (s) (Eq. 1 and Eq 2) Calculate numerical values for the coefficients M ₁ to M ₅.

After Einehmen these values, the coefficient M ₁ and M ₅ (and after the time constant of T ₁, T ₂, T ₃, T ₇ and t ₉ already determined T ₄ and out of the Bode diagram of FIG. 6 and the damping constant θ ₁, θ ₂, ϑ ₇ are provisionally determined) it is now still necessary to determine the remaining time constants T ₀, T ₆ and the damping constants ϑ ₀ and ϑ ₆ for the transfer function F (s) of the filter.

This can be done by comparing those expressions for which the coefficients M ₁ to M ₅ are abbreviations with the determined values for M ₁ to M ₅. This results in equations of determination for the unknowns ϑ ₀, ϑ ₆, T ₀ and T ₆.

This may result in matches occurring; you go z. B. from the filter function F (s) mentioned first in claim 2, it results after insertion in A ₁ (s) = s / (s + K ₀ F (s)) and shaping into a form according to equation 1: M ₅ = T ₄ T ₇² T ₉ / K ₀, while comparing Equation 1 with Equation 2 gives: M ₅ = T ₁² T ₂² T ₃. So it applies

T ₁² T ₂² T ₃ = T ₄ T ² T ₉ / K ₀, (Eq. 3)

which means that not every desired course V ( FIG. 6) can be realized, but that the corner frequencies have to be set in such a way that equation 3 is fulfilled. If the choice of the variables contained in equation 3 is corrected accordingly, the unknowns ϑ ₀, ϑ ₆, T ₀ and T ₆ can be determined using the determination equations.

After the properties of the filter have been determined, the stability of the control loop must be checked. The function A ₀ (s) must therefore be determined, its amount and phase plotted in a soil diagram and the stability reserve (gain and phase reserve) determined. This is shown in FIG. 7 for the example according to FIG. 6. It turns out that at the zero crossing of the amount of A ₀ (s) / dB there is still a phase reserve of approximately 50 °, while a zero crossing of phase ϕ , where the gain reserve could be determined, is missing.

If the check of the stability reserve shows that with the desired course V of the amount of A ₁ (s) chosen according to FIG. 6, a sufficient stability reserve cannot be achieved, then the damping constants ϑ ₁, ϑ ₂, ϑ ₇ and / or a new desired course for the amount of A ₁ (s) determined and the same procedure as described are carried out until there is a sufficient stability reserve. A computer can expediently be used for this procedure.

Fig. 5 shows a realized example of the filter.

The equation for the transmission frequency response F (s) of this fourth-order filter is like the first function specified in claim 2.

Analysis of the circuit of Fig. 5 provides the equation

The coefficient comparison between the two notations given above for A ₁ (s) (Eq. 1 and Eq. 2) shows for the time constants:
T ₀² = C ₂ R ₂ C ₁ R ₁ 2 ϑ ₀ T ₀ = R ₁ C ₂ + R ₁ C ₁ + R ₂ C ₂ T ₄ = C ₂ (R ₄ + R ₅) T ₆² = C ₄ R ₆ C ₅ R ₇ 2 ϑ ₆ T ₆ = C ₄ R ₆ + R ₇ C ₅ T ₇² = C ₄ R ₆ R ₇ C ₅ 2 j ₇ T ₇ = C ₄ R ₆ + R ₇ C ₅ + R ₈ C ₄

For the circuit according to FIG. 5, the following conditions for the relevant time constants result from the desired course V :

T ₁ » T ₂ where T ₂≈ T ₃
T ₇ < T ₃
T ₉ < T ₇
T ₁ < T ₉

An example is a vibrator with a reference frequency F _r of 1 MHz.

With the following numerical values for

T ₁ = 1 s ϑ ₁ = 2 T ₂ = 1.5 · 10 ^-6 s ϑ ₂ = 0.5 T ₃ = 1.5 · 10 ^-6 s T ₄ = 0.003 s T ₆ = 5 · 10 ^-6 s j ₆ = 0.5 T ₇ = 3.9 · 10 ^-6 s ϑ ₇ = 1 T ₉ = 0.0159 s T ₀ = 0.2 s ϑ ₀ = 1 K ₀ = 300 s ^-1

results for the interference frequency response | A ₁ (s) | the practical course, as shown in Fig. 6. Noise reduction up to approximately 100 kHz is achieved there. The time constant T ₄ = 0.003 s with a loop gain K ₀ = 300 s ^-1 , so that the frequency f ₄ = 1 / T ₄2 π = 53 Hz, so that conventional amplifiers can be used, the phase of which is already at 1 kHz can drop sharply even if the cutoff frequency is 10 MHz.
The amount associated with this example | A ₀ (s) | and the phase of the open loop reinforcement is shown in FIG. 7, the phase profile running throughout in the positive region and assuming a value of ϕ ≈50 ° as a minimum. This ensures good stability of the control loop.

In summary, the procedure is as follows to dimension the electrical vibration generator in accordance with claim 1:
It is initially assumed that there is a (e.g. known) filter type (e.g. FIG. 5) with a filter function F (s) (e.g. according to one of the formulas from claim 2). By inserting the filter function F (s) in equation b, it is checked whether an expression according to equation 1 results. For a desired course of the interference frequency response A ₁ (s) , which is below the course s ² · 2 T ₄ / K ₀ in Fig. 4, numerical values for T ₁, T ₂, T ₃, T ₇, T from the corner frequencies ₉ determined and the damping constants ϑ ₁, ϑ ₂ and ϑ ₇ provisionally determined. These values are inserted into the denominator of equation 2, and the comparison with the denominator of equation 1 gives numerical values for M to M ₅. The comparison of these numerical values with the expressions for which M ₁ to M ₅ are abbreviations gives (with simultaneous use of T ₄, T ₇, T ₉ and K ₀) values for T ₀, ϑ ₀, T ₆ and ϑ ₆ (whereby any matches that may occur must be corrected beforehand by correcting the corner frequencies and / or damping constants. Subsequently, the T ₁... T ₉, ϑ ₁... ϑ ₇, K ₀ are used to check A ₀ (s) If the stability is inadequate, the procedure is repeated with changed corner frequencies, damping constants and / or a changed desired curve until the stability is sufficient. The components of the filter circuit are then calculated using the time constants and damping constants that are ultimately obtained.

Since the first steps of this procedure only serve to check the suitability of a filter type, they can be omitted if the filter shown in FIG. 5 is used, the suitability of which for suppressing phase noise has already been proven.

Claims (3)

1. Electrical vibration generator with an oscillator, the frequency of which can be controlled electrically via a control input, and a control circuit with a phase comparator, which is used to compare the phase of the oscillator oscillation or an oscillation derived therefrom with the phase of a reference oscillation, and with an active low pass filter , provided with an amplifier in the control loop, which is connected upstream of the control input with a transfer function F (s) for damping phase noise, the amplifier having an upper cut-off frequency f _og and the control loop an open loop gain A ₀ (s) = K ₀ F ( s) / s , where s is the complex angular frequency at the control input of the oscillator and K ₀ is the total loop gain, and the zeros and poles of the filter are selected such that for the interference frequency response A ₁ (s) = s / (s + K ₀ F (s) of the vibration generator:

• a1) it has a first increase in amount in the lowest frequency range,
• a2) there is at least one pole below the actual oscillator frequency, which causes the magnitude of the oscillator interference frequency response to set to a constant value in this high frequency range after a second rise at frequencies below it,

characterized in that the filter is of at least second order and is designed in such a way

• b) that the following applies to the interference frequency response of the vibration generator:
  • b1) between the frequencies in the lowest and those in the high frequency range there is at least one pole and then at least one zero with increasing frequency in such a way that the amount of the oscillator interference frequency response in a medium frequency range in the vicinity of the zero remains significantly below the values, which are reached in this middle frequency range by the first increase extrapolated into this middle frequency range,
  • b2) the complex frequencies of the poles and the complex frequency of the zero point can have a real part,
• c) that the loop gain A ₀ (s) = K ₀ F (s) / s meets the conditions for asymptotic stability of the control loop.

2. Vibration generator according to claim 1, characterized in

• a) that the transfer function of the filter has the form or where T ₀, T ₄, T ₆, T ₇ and T ₉ are time constants and ϑ ₀, ϑ ₆, ϑ ₇ constants, and T ₆ and / or T ₇ could be zero,
• b) that with a time constant T ₄ »1/2 π f _og the loop gain K ₀ is selected so that √ / 2 π is more than a power of ten smaller than the lowest permissible operating frequency of the controlled oscillator during operation,
• c) that in the bottom diagram for the oscillator interference frequency response A ₁ (s) = s / (s + K ₀ F (s)) the highest basic frequency f _{n is placed} just below the lowest permissible operating frequency of the controlled oscillator during operation, but greater than √ / 2 π is selected,
• d) that A ₁ (s) for f < f _n at most s ²2 T ₄ / K ₀, but in frequency ranges with particularly high phase noise of the oscillator is at least a power of ten less than s ²2 T ₄ / K ₀.