AU2019100351A4 - Cable filters for the feedback system of BEPC II - Google Patents

Abstract

Two types cable filters are used in the feedback system of Beijing Electron and Positron Collider (BEPC II) which always runs under the conditions with multi-bunch and high current. One is a band-pass filter and the other is a notch filter. Due to the influence of high-order model in high-frequency cavity or resistance of wall of the storage ring, the beam will be unstable. Thus, the collision luminosity will be decreased. In order to improve the beam current and luminosity, the feedback system is needed to suppress the beam instability. The band-pass filter used in front-end electronic system of the feedback system on BEPC II is composed of: a splitter which could divide a signal to several signals (three or more signals generally) with equal magnitude, several cables to transmit the signals and a combiner that could perform sum operation. Sometimes attenuators and delaylines are also needed. The notch filter is set in the signal-processing electronicsof the feedback system. Its components are consistent with band-pass filter except that the combiner performs subtract operation and there are only two cables to be used. Because the propagation time of electromagnetic signals in cables with different lengths is distinct, the band-pass filter and notch filter can be manufactured if we take advantage of the different characteristics of the response of cables with fixed length difference to different frequency signals. After filtered by band-pass filter and notch filter, the signals from the detector are processed and the information we are interested in is selected from them. Then the signal will excite kickers after being amplified. In this way, instability of beams in the storage ring of BEPC II could be suppressed.

Description

TITLE

Cable filters for the feedback system of BEPC II

FIELD OF THE INVENTION

The invention relates to cable filters, particularly, to cable filters having a special structure capable of filtering signals at certain frequencies, especially the 1.5GHz signal generated by electrons and positrons rotating in the storage ring.

BACKGROUND OF THE INVENTION

With the increasing demands to the higher energy of particles in the field of physics especially particle physics, the development of accelerator has been taking place in a speed we cannot imagine. To solve the problems related to it has already become the hotspot in engineering. Research on Beijing Electron Positron Collider (BEPC) is the best instance.

The high order mode in the radio-frequency cavity on the BEPC gives rise to the horizontal and vertical oscillating beam simultaneously, creating the unstable beam. The resistive wall cause excited wake fileds. Then with the effect of wake field, the subsequent bunches start oscillation. It could be said that wake field is the most important factor to horizontal instability. In addition, the unstable electron cloud in the positron ring and ion effect in the electron ring could also lead to oscillation of beam. Such oscillation affects luminosity of accelerator. Therefore, it is necessary to design a feedback system to reduce the effect of instability.

The feedback system magnifies the oscillation signal at the position of the beam to drive the kicker. Because of several reasons such as the closed orbit distortion and the gain of 4 channels in the pickup monitor is different, there is some direct current components in the oscillation signal. It wastes the power of a power amplifier and reduces the dynamic range of signal processing. One of the most important factors in the electronic circuit of feedback system is the cable filter, through which the DC in signals is reduced. Thus the efficiency of amplifier is increased.

In this invention, we made two filters, one notch filter and the other is band-pass filter. The filter is composed of a 0-degree splitter, a 180-degree combiner and two or three transmission lines. First, the splitter divides the energy of a signal equally. Then the two signals from the splitter propagate with different delay times, which are a revolution period of a particle beam in storage. Finally, the two delayed signals are subtracted using the 180-degree combiner. If the beam is stable, the amplitudes of the two signals are equal. While the beam is unstable, the amplitudes are not symmetrical and the output signal is in direct proportion to the difference between two signals in the lines. The time dominated combining signal could be used to drive the kicker, to damping the beam..

SUMMARY OF THE INVENTION

Nowadays the main three filters that are widely used are RC circuit filter, fiber optic filter and digital filter. Although they are widely used, there still have some drawbacks and deficiencies. A RC filter can be designed according to the required bandwidth and center frequency, but the circuit design is so complicated that it brings a lot of trouble to the productive process. For a fiber optic filter, instead of using cable transmission, it uses optical fiber transmission which reduces the demand for the amount of the cable. But still it costs a lot for producing optical fibers. Furthermore, because of the use of some master copies like photoelectric transducer, the structure of the filter becomes very complex. And for a digital filter, it filters the waves by digitalizing the analog signal and then filter it in a programmable device through software algorithm. As a result, inside a digital filter it contains different kinds of hardware like analog-digital convert (ADC) and field-programmable gate array (FPGA), which greatly increase the cost of a digital filter. In the lateral beam current feedback system of the storage phase of the Beijing Electron-Positron Collider Phase II, a cable filter (band-pass filter) is needed to select the frequency that we are interested in (250 MHz bandwidth around 1.5 GHz) and use a cable filter (notch filter) performs filtering of frequency signals (revolution frequency) that are not of interest. For the small storage ring of BEPC II, the cable filter has the advantages of simple structure, low cost, flexible adjustment of bandwidth and center frequency according to different requirements. There are some factors impacting the filtering effect. 1. Relationship between center frequency and the difference of the length of the cable

The center frequency is inversely related to the difference of the length of the cable. The greater the length difference is, the lower the center frequency is. The difference in length is related to the propagation velocity of the electromagnetic waves in the cable. Usually, the propagation velocity of the electromagnetic waves in the cable is 0.6c-0.8c. 2. Relationship between filter bandwidth and number of cables

The filter bandwidth is inversely related to the number of cables, and the larger the number of cables is, the narrower the filter bandwidth is. 3. The role of the hybrid on the signal

In this experiment, due to the structural characteristics of the hybrid, the hybrid is only applied to the notch filter. Hybrid can be used to perform a sum operation on two signals, and when the hybrid performs the sum operation, the hybrid is a 0-degree combiner and the two signals are directly added; when the hybrid performs the subtract operation, the hybrid is a 180-degree combiner, one of the signals is inverted and then added to the other.

The structure of notch filter is shown by Fig.l. There are two cables, a 0-degree splitter and a 180-degree combiner. The lengths of the two cables are different leading to a rotating period T of beams in the storage ring difference between the transmission times of signals in two cables. But the attenuation and phase characteristics of signals are required to be consistent. At first, signals are divided to two signals with equal amplitude by the splitter. After the transmission in the two cables, the subtract operation is achieved by the combiner. For our invention, the splitter and the combiner are both produced by company Tele-Tech and the model of them is HC22-27, the pass-band width is 10 KHz-250MHz.The Amplitude-frequency response and phase-frequency response are not symmetrical, at the same frequency, magnitude of attenuation and corresponding phases of the two signals in different cables are not the same. To make the two signals have the same magnitude of attenuation and their transmission time are a revolution period apart, the cables should be selected carefully. In the notch filter, for the long cables, we choice HJ5-50 produced by the company Andrew. The delay time of it is 3.639ns/m and the length of it is 245m. Thus, the total delay time is 891.555ns. The attenuation coefficient of the long cable is 1.21dB/100m at 100MHz. The short cable was made by RG223, with delay time 5.055ns/m. The length of the short cable is 17.7m. So the total delay time of it is 89.5ns. The attenuation coefficient of the short one is 14dB/100m at 100MHz. The difference between two transmission times of the two signals is a revolution period, approximately 802ns. The more accurate adjustment should be determined by notch depth of the filter.

The structure of band pass filter is shown by Fig.2. In the band pass filter, there are three or more than three cables, a 0-degree splitter and a 0-degree combiner. The model of them is RG316 and the models of splitter and combiner are both DS-4-4 produced by the company MACOM. The input signal is divided to four signals with equal amplitude by the splitter. The scope of application is 2-2000MHz. The transmission time difference between two signals transmitting in the two cables is the period of signals with the central frequency of the band pass filter.

In the experiment, we made cables with different length according to the requirement of horizontal feedback system in the BEPC II. Then we connected the cables in accordance with the schematic diagrams.

We tested how the response function of the two filters change when the length difference and the number of cables changes through our prototypes in the laboratory. 1. Influence of length difference between two cables to central frequency of the filters

As for notch filter, when the length difference increases 10cm, the notch frequencies of filter move from 341.462MHz, 689.720MHz, 1.03797GHz, 1.37934GHz to 310.429MHz, 620.758MHz ,927.639MHz, 1.24141GHz respectively. As for band pass filter, when length difference increases from 14.6cm to 50cm, the central frequency of filter with three cables moves from 1.37101GHz to 383.900MHz and the central frequency of the one with four cables moved from 1.44005GHz to 386.689MHz. 2. Influence of the number of cables to the pass band width of the filters

We tested filters with cable length difference 14.6cm. The filter with one cable cannot filter any signals. The pass band width of filter with two cables is 674.21MHz, the bandwidth of the one with three cables is 433.61MHz and the bandwidth of the one with four cables is 318.45MHz.

DESCRIPTION OF THE DRAWINGS

The appended drawings are only for the purpose of description and explanation bur not for limitation, wherein:

Fig.l illustrates the structure of the notch filter, wherein 1- cable, 2- 0 degreesplitter, 3-delay line, 4- attenuator, 5- 180-degree combiner;

Fig.2 illustrates the structure of the band-pass filter, wherein 1- cable, 2- 0-degree splitter, 3-delay line, 4- attenuator, 5- O-degree-combiner;

Fig.3 illustrates the amplitude-frequency response of splitter;

Fig.4 illustrates the phase-frequency response of splitter;

Fig.5 illustrates the response function of notch filter;

Fig.6 illustrates the response function of band-pass filter with three cables;

Fig.7 illustrates the response function of band-pass filter with four cables;

Fig.8 illustrates the effect of length difference of cables.

Fig.8(a)-Fig.8(b) illustrate the response functions of band-pass filter with three and four cables when the length difference is 14.6cm, the propagation velocity of signals is approximately O.7co ( co is the speed of light in vacuum). Fig.8(c)-Fig.8(d) is the response functions when the length difference is 50cm. Fig.8(e)-Fig.8(f) show the response functions of notch filter when the propagation velocity of signals is approximately O.7co ( co is the speed of light in vacuum), the length difference increases from 14.6cm to 24.6cm.

Fig.9 illustrates the effect of the number of cables. Fig.9(a)-Fig.9(d) show the response function of filters with different number of cables when the length difference is 14.6cm, the propagation velocity of signals is approximately O.7co ( co is the speed of light in vacuum)

Fig.10 illustrates the role of hybrid. Fig.10(a) shows the response function of filters when the hybrid performs the sum operation, Fig. 10(b) shows the response function when the hybrid performs subtract operation.

DESCRIPTION OF PREFERRED EMBODIMENT

Now the widely applied methods to design a filter include using RC circuits or optic fibers and designing a filter in digital mode. But to make a band-pass filter or a notch filter, these three methods are limited more or less. RC circuit is widely used in analog circuit and pulse digital circuit. If the RC parallel circuit is cascaded in the net, it could attenuate the signals components with low frequencies. While if the parallel RC circuit is connected in parallel, it could attenuate the components with low frequencies. However, for RC circuit, it is almost impossible to realize the function of comb filter at the present stage. Although band-pass filter with RC circuit can be realized in theory, in fact, to realize the selection of a certain frequency signal requires a rather complex circuit design, which brings great difficulties to the production of band-pass filter. Optical fiber filter is suitable for choosing and filtering low frequency signals when the length difference between two cables is large. Cables used in Band-pass filters are rather shorter, so it is virtually unnecessary to apply optical fibers in a band-pass filter. In the notch filter, the use of optical fiber can achieve good results, but due to the application the photoelectric conversion module in the circuit of filters, the cost of these notch filters is very high. For the application of Digital circuits, both band-pass filters and notch filters can be achieved, but the high price of Digital circuit hardware such as Analog-Digital Convert (ADC) and field-programmable Gate Array (FPGA) is the main factor that restricts the manufacture of filters. In addition, to a certain extent, the signal bandwidth of ADC is limited. For some signals with particular frequencies, such as the signal with desired central frequency on BEPCII (Beijing Electron Positron Collider Upgrade Project) 1.5GHz and a bandwidth about 250MHz, it is difficult for available ADC to select such signals.

Considering the above way of shortcomings, and considering the short storage ring of the Beijing electron-positron collider small, the actual situation, in this study we used the splitter and combiner (or hybrid) to design a new structure to make a band-pass filter and a notch filter, in order to realize the selection of signals with frequencies which we are interested in (about 1.5 GHz and 250 MHz bandwidth) and to filter signals we are not interested in (cyclotron frequency). The filter designed in our new way is simple to achieve and the cost of it is low. Furthermore, it is flexible to adjust the bandwidth and the center frequency according to different requirements, so as to achieve the purpose of filtering different signals. The filters have been applied in the feedback system of BEPC II and the effect of them was good.

In this experiment, a simple prototype was made in the laboratory. The vector network analyzer AV3656A (range: 100kHz-3GHz), the oscilloscope 760ΖΪ-Α and the spectrometer RSA51038 (range: lHz-3GHz) were used in the test of the prototype. The network analyzer is a kind of comprehensive microwave measuring instrument which is used to obtain the network parameters by scanning measurement in broad band. The full name of it is microwave network analyzer. The network analyzer can directly measure the complex scattering parameters of active or passive, reversible or irreversible dual-port and single-port networks. Automatic network analyzer can correct the error of measurement results point by point, and figure out dozens of other network parameters, such as input reflection coefficient, output reflection coefficient, voltage standing wave ratio, impedance (or admittance), attenuation (or gain), phase shift and group delay, the transmission parameters and parameters of isolation and orientation . An oscilloscope is used to convert invisible electrical signals into visible images, so that people can study the changing process of various electrical phenomena. Spectrum analyzer is an equipment for test and measurement, mainly used for analysis of radio frequency (RF) and microwave signal in the frequency domain, including the power, frequency, distortion products of the measured signals. In this experiment, network analyzer, oscilloscope and spectrum analyzer were used to measure the amplitude-frequency response of the filters to test the effect.

The filter is applied in the feedback system of BEPC II, and the beam oscillation information is detected by the Beam Position Monitor (BPM). Then the signal with a 1.5GHz central frequency and a 250MHz bandwidth is selected through the band-pass filter, and the high-frequency signal is converted down to the baseband frequency through the mixer. Then the signal with revolution frequency and its frequency multiplication is filtered by the notch filter. Afterwards, the oscillating signal is sent to the amplifier for amplification and then to the kicker. The amplified signal generates an electromagnetic field in the kicker and acts on the beam, thereby damping the beam oscillation.

The composition of the comb filter(also be called notch filter) is shown in Fig.l.

The filter consists of two transmission cables, a 0-degree power divider, the splitter and a 180 degree mixer, the combiner. The lengths of the two transmission lines are different, and the transmission times differs by one beam cyclotron period T, but the attenuation and phase characteristics are required to be consistent. First, the signal is divided into two signals with equal amplitude through 0-degree splitter, which are transmitted on two cables with different lengths, and then they are subtracted through 180-degree hybrid. Splitter and hybrid here are both HC22-27 from Tele-Tech with a bandwidth of 10kHz - 250MHz. The amplitude-frequency response and phase-frequency response of two circuits of the device are respectively shown in (a) and (b) in Fig.3 and (a) and (b) in Fig.4.

As shown in Fig.3 and Fig.4, the amplitude-frequency response and phase-frequency response of splitter are not symmetrical. At the same frequency, the attenuation amplitude and corresponding phase of the two channels are different. Identically, the two outputs of combiner are asymmetric. In order to meet the requirement that the attenuation amplitude of two cables are equal and the time difference is one beam rotation period, the cables need to be selected carefully. Generally, the delay time of short cables is required to be about 10% of that of long cables, and the attenuation coefficient per meter of short cables is greater than that of long cables. In the notch filter, the selected long cable is HJ5-50 from the company Andrew, with a delay time 3.639ns/m, and a length 245m. Its total delay time of 891.555ns and the attenuation coefficient of it is 1.21dB/ 100m at lOOMHz.The model of the short cable is RG223, and the delay time is 5.055ns/m, so the selected length is 17.7m, the total delay time is 89.5ns. Its attenuation coefficient is 14dB/ 100m at lOOMHz.The delay time difference between the two cables is about one beam rotation period, about 802ns.More accurate adjustment is required to be determined considering the oscilloscope and notch depth. The amplitude-frequency response and phase-frequency response of the two cables are also different. In order to obtain the consistent attenuation coefficient and phase shift of the two transmission lines, a delay line, SRC-SMJ-205P and a programmable attenuator, Weinschel 3209-1 are set at the end of the short cable. Thus, the attenuation coefficient and time delay of the cable can be adjusted conveniently to achieve the best effect of the notch filter.

The composition of the band-pass filter is shown in Fig.2.

There are three or more transmission cables, the cable type is RG316. A 0-degree splitter and a 0-degree combiner are also indispensable .The model of power divider ( or the splitter) and mixer (or the combiner) is DS-4-4, which are the products of the company MACOM. It is a four way power divider with frequency range from 2MHz to 2000MHz.The time difference between the propagation of the electromagnetic signal in the two cables is the period of the signal with central-frequency of the band-pass filter.

The design principle of the two kinds of cable filter is shown in the following text.

Here, τ represents the delay of splitters, shortest cable, other interconnections, etc. A represents the overall attenuation, including the splitters, filtering cables, other interconnections, etc. Δ77 is the delay time difference of two cables, when Δ/ represents the length difference and c is the propagation velocity of signals, ω represents the rotation frequency of beams in the storage ring. Thus, φ is the phase shift caused by delay in splitters, shortest cable, other interconnections, etc. While Δφ is the delay caused by length difference of two cables.

(1)

There are 2 cables with length difference ΔΙ, merged with phase difference π fn notch filter. The output signal of notch can be expressed as: (2)

Fourier transform of this formula is:

(3) Similarly, there are n cables with length difference ΔΙ, merged with no phase difference in band-pass filter. The output signal is:

(4)

Fourier transform of this formula is:

(5) (6)

Attenuation of different cables are balanced with additional attenuators or ignored if difference negligible

At notch frequency of notch filter, phase difference should be: (7) (8) (9)

At pass band center of notch filter, phase difference should be: ( 10) (11) ( 12)

At passband center of band-pass filter, phase difference should be: ( 13) (14) ( 15)

Pass-band width is an important parameter of a filter. The definition of it is the difference between the upper and lower frequencies in a continuous band of frequencies. In our invention, at the upper and lower frequencies, the signal strength attenuates 3dB compared with the signal

strength at central frequency.

In our calculation, H represents response function of filters.

The response function of notch filter could be expressed as:

( 16) //(co) is shown in Fig.5.

The response function at central frequency and two endpoints of the band are:

( Π) After simple calculation the endpoints of band could be expressed as: ( 18) ( 19)

The response function of band-pass filter is:

(20) H(o>) with different n are shown in Fig.6 and Fig.7.

The response function at central frequency and two endpoints of the band are in the same form:

(21 ) Do the same calculations as notch filter, we could get the endpoints of band: (22) (23)

Where x{n) should meet the following condition:

(24) x(n) can be numerically solved.

On the basis of the analysis above, we could see that the central frequency of band-pass filter and the notch frequency of the notch frequency are inversely related to the difference of the length of the cables. The greater the length difference is, the lower the center frequency and the notch frequency are. The pass-band width is inversely related to the number of cables, and the larger the number of cables is, the narrower the filter bandwidth is.

In our invention, we measured the effect of length difference and the number of cables and calculated the results. The calculated results of some parameters are shown in the following table:

The effect of length difference of cables is shown in Fig.8(a)-Fig.8(f). When the length difference is 14.6cm, the propagation velocity of signals is approximately O-7co ( co is the speed of light in vacuum), the calculated central frequency of band-pass filter is about 1437MHz, the

observed central frequencies of band-pass filter with three and four cables are 1371.01MHz and 1440.05MHz respectively. While the length difference is 50cm, the calculated central frequency of band-pass filter is about 395MHz, the observed central frequencies of band-pass filter with three and four cables are 383.900MHz and 386.689MHz respectively.

When the length difference is 14.6cm, the propagation velocity of signals is approximately O.7co ( co is the speed of light in vacuum), the observed notch frequencies of notch filter are about 341.462MHz, 689.720MHz, 1037.97MHz, 1379.34MHz. While the length difference increases by 10cm, the observed notch frequencies are 310.429MHz, 620.758MHz, 927.639MHz, 1241.41MHz.

The effect of the number of cables is shown in Fig.9(a)-Fig.9(d). When the length difference is 14.6cm, the propagation velocity of signals is approximately O.7co ( co is the speed of light in vacuum), the calculated bandwidth of 2-wire,3-wire and 4-wire filters are 685.37MHz, 425.76 MHz and 327.89 MHz respectively, the observed bandwidth of them are 674.21 MHz, 433.61 MHz and 318.45 MHz respectively.

The role of hybrid is shown in Fig.10. Fig.10(a) shows that the hybrid performs the sum operation, Fig. 10(b) shows that the hybrid performs subtract operation.

Claims (1)

1. Cable filters for the feedback system of BEPC II, the cable filters may suppress the beam instability of BEPC II, characterized in that: the processed signal may be sent to excite kicker to suppress the instability of beams in the storage ring of BEPC II; since the cable filters are simple to make, low-cost and easy to adjust to meet different requirements, they could be widely applied in various fields; each cable filter is equipped with a splitter, a combiner (performs sum or subtract operation) and several cables with different lengths; the response functions of the two filters could be adjusted by changing the length difference and the number of cables.