Bento, J

Caspers, Friedhelm

Mostacci, A

Caspers, F

CERN Document Server

Coupling Impedance Measurements with the Coaxial Wire Method on the CPS RF Bypass

 EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH ORGANISATION EUROPEENNE POUR LA RECHERCHE NUCLEAIRE  CERN - PS DIVISION      PS/RF/ Note 2002-217   Coupling Impedance Measurements with the Coaxial Wire Method on the CPS RF Bypass J. Bento, F. Caspers, A. Mostacci               Geneva, Switzerland December 2002  1. Abstract The CPS contents a large number of isolated flanges which are required to avoid induced currents in the ring due to the time dependent magnetic deflection field. Without additional measures, these gaps present a large coupling impedance, which would cause serious problems for the beam. Thus in order to minimize the gap related beam-coupling impedance a so-called RF bypass is installed at each gap. It consists essentially of several chip capacitors and a series resistance. The values of these lumped elements were originally carefully determined in order to minimize resonances and also avoiding the dB / dt related eddy currents mentioned. However no detailed measurements of the beam coupling impedance of this bypass were found to be available. Here we present several bench measurements for impedance evaluation of the isolated gap equipped with one or more bypass units in several configurations and discuss the results.     2. Introduction  In the course of the continuing CPS impedance monitoring campaign it was decided to carefully analyze the impedance properties of an isolated gap with its bypass. The basic strategy of these measurements was, first to evaluate the impedance of the bypass chip alone and subsequently considering the impedance of a single gap with and without different bypass elements including DC short-circuits. As the test instrument, a Vector Network Analyzer (VNA) type HP 8753D with a frequency range from 10 kHz to 6 GHz and time domain option was adopted. This instrument can operate both in reflection (S11) and transmission (S21) mode. In this context the terms S11 represents a "scattering parameter" defined as a complex ratio of reflected to incident wave at a port of the device under test (DUT) and S21 stands for the complex ratio of the transmitted wave versus incident wave through two different ports of the DUT. The S parameters as raw data permit subsequent transformation into complex impedance numbers via suitable conversion formulae [1].    3. Reflection Measurements  3.1 Measurements on individual bypass chips  As a first step it was decided to report the input impedance of a single bypass chip as it is in use in the CPS since many years. In order to get a properly defined reference plane, a SMA connector has been soldered to the bypass chip (Fig. 1b).   1  Fig. 1a – bypass units as used in CPS   Fig. 1b – RF bypass with SMA connector for measurement purposes   Fig. 1c – Electrical elements of a single bypass  The S11 has been measured in different frequency ranges and converted to impedance Z using the formula for reflection measurement (which is already programmed into the VNA) 111111SSZZ c −+⋅=   where Zc = 50 Ω. From the equivalent circuit we would expect in our frequency range a real part of the bypass impedance around 1 Ω, and an imaginary part as given by 1 / jωC with C = 415 nF.    2Re(Z) [Ω ]0.900.951.001.051.101.151.201.0E+05 2.6E+06 5.1E+06 7.5E+06 1.0E+07Frequency [Hz]Im(Z) [Ω ]-4-3-2-10121.0E+05 2.6E+06 5.1E+06 7.5E+06 1.0E+07Frequency [Hz] Fig. 2 – Low frequency complex bypass impedance (1st series res. at 1.64 MHz)  Already in Fig. 2 we recognize the real part is fairly constant up to 10 MHz between 1 and 1.15 Ω, but the imaginary part is changing sign at 1.64 MHz (series resonance). This means the capacitor has the first resonance close to 1 MHz and the bypass no longer behaves as a capacitor but rather as an inductance. Going to higher frequencies (Fig. 3) we can identify a parallel resonance at 185 MHz. Note that for a series resonance the real part of Y has a maximum while for the parallel resonance we obtain a maximum in the real part of Z.   Re(Z) [Ω ]0204060801001201.2E+06 2.5E+08 5.0E+08 7.5E+08 1.0E+09Frequency [Hz]Im(Z) [Ω ]-60-40-200204060801001.2E+06 2.5E+08 5.0E+08 7.5E+08 1.0E+09Frequency [Hz] | Z | = √  [Re(Z)2+Im(Z)2] [Ω ]0204060801001201.2E+06 2.5E+08 5.0E+08 7.5E+08 1.0E+09Frequency [Hz] Fig. 3 - Complex impedance of an individual bypass (1st parallel res. at 185 MHz)  In Fig. 3 and 4 the complex impedance (Z) and admittance (Y) of this individual bypass is shown between roughly 1 and 1000 MHz as well as the complex reflection coefficient (S11) normalized to 50 Ω, in the Smith-Chart.   3Re(Y) [1/Ω ]0.00.10.20.30.40.50.60.70.80.91.01.2E+06 2.5E+08 5.0E+08 7.5E+08 1.0E+09Frequency [Hz]         Im (Y)  [1/Ω ]-0.5-0.4-0.3-0.2-0.10.00.10.21.2E+06 2.5E+08 5.0E+08 7.5E+08 1.0E+09Frequency [Hz] |Y| = √  [Re(Y)2+Im(Y)2]  [1/Ω ]0.00.10.20.30.40.50.60.70.80.91.01.2E+06 2.5E+08 5.0E+08 7.5E+08 1.0E+09Frequency [Hz]     -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 Fig. 4 – Complex admittance and S11 in the Smith-Chart (2nd series res. at 275 MHz)   3.2 Measurements on a 1 m long test vacuum chamber  So far we have been looking only at the actual bypass unit as a small lumped element (see Fig. 1), now we are considering a 1 m long vacuum chamber with an isolated flange (Fig. 5 and 6). We start S11 measurements without any bypass or short circuit and also without the matching resistors of 290 Ω on the inner wire. This is done in order to obtain proper results for an interrupted external conductor of a coaxial structure for frequencies below 1 MHz.     Fig. 5 – 1 m long test vacuum chamber with isolated flange in the center as used for bench measurements  4 Fig.6 - One port measurement on the coaxial wire bench setup  Re(Z) [Ω]0.00.20.40.60.81.01.21.41.0E+06 2.8E+06 4.6E+06 6.4E+06 8.2E+06 1.0E+07Frequency [Hz]Im(Z) [Ω]-150-100-500501001.0E+06 2.8E+06 4.6E+06 6.4E+06 8.2E+06 1.0E+07Frequency [Hz]Re(Y) [Ω ]-1.5-1.0-0.50.00.51.01.51.0E+06 2.8E+06 4.6E+06 6.4E+06 8.2E+06 1.0E+07Frequency [Hz]Im(Y) [Ω ]-1.5-1.0-0.50.00.51.01.51.0E+06 2.8E+06 4.6E+06 6.4E+06 8.2E+06 1.0E+07Frequency [Hz]  Fig. 7 – S11 measurements on a 1m long test vacuum chamber without bypass   Measured resonant frequency: 4.419 MHz  Vacuum chamber with inner conductor: - Inner diameter (d) of the outer conductor: 145 mm - Outer diameter (D) of the inner conductor: 0.5 mm - Length: 1000 mm  At 100 kHz (not shown in Fig. 7) we measured an imaginary part of Z = -1402 Ω on this shorted vacuum chamber. From this value we can deduce a quasi-static capacity as:  5jXC ⋅= ω1   This returns a value of 1.13 nF for the gap capacity. With a measured resonance frequency (ωr / 2π) of 4.419 MHz, we can deduce the corresponding inductance L as:  HCLrµω 148.112 =⋅=   This inductive part is assumed to be essentially due to the thin inner wire in the beam pipe section as we are going to show below.   The characteristic impedance Zc of our vacuum chamber with coaxial wire is given as: Ω=⋅= 340ln60dDZc   The input impedance Zi of a shorted lossless coaxial line with a length l is given by:  LlZZ ci ωλπ = ⋅⋅=02tan   with λ0 being the free-space wavelength of the corresponding frequency ω. We obtain a numerical value of the wire inductance L at 4.419 MHz as 1.15 µH, which is very close to the 1.148 µH calculated from the resonance frequency and static capacity of the gap.  ∆f = 0.1114 MHz for the 3 dB points which correspond to change by 50% on the real part of the admittance (Fig. 7).    68.39=∆= ffQ r   Also from Fig. 7 we can read the value for R1 = 1/ Yr = 0.789 Ω to be used in the series equivalent circuit shown below    This value for R1 corresponds roughly to the RF resistance at 4.419 MHz in the 1 m long inner coaxial copper wire of our DUT.    6These results should not be confounded with the parallel equivalent circuit shown in ref. [2], since there the equivalent circuit takes the external ground loop of an in situ bypass into account.  Re(Z) [Ω ]1.01.21.41.61.82.02.22.42.62.83.01.0E+05 5.1E+06 1.0E+07Frequency [Hz]Im(Z) [Ω ]-10010203040506070801.0E+05 5.1E+06 1.0E+07Frequency [Hz]  Fig. 8 - S11 Measurements (converted into impedance) on a 1m long test vacuum chamber with one bypass. The resonance frequency is the frequency at which the Im(Z)=0.  As shown in Fig. 8, adding the bypass has two distinct effects on the input impedance of the 1 m long test chamber, namely lowering the series resonance frequency by about a factor 20 and slightly increasing the real part. This behaviour has been described already in ref. [2] and is essentially the aim of the bypass. A comparison of the numerical values gives consistent results (changing the capacity for a factor of 400 leads to a change in resonant frequency by a factor of 20). We also observe a slight increase of the real part due to the 1 Ω resistor of the bypass. Note that the slope of the imaginary part above 1 MHz is entirely due to the inductance (≈ 1µH) of the inner coaxial wire in our S11 test setup. This may be put in comparison with the 10 µH grounding loop inductance quoted in ref. [2].  4. Transmission Measurements  4.1 Transmission Measurements on a 1 m long test chamber   Fig. 9 – Transmission measurements set up (coaxial wire method)  7 For impedance evaluation above roughly 10 MHz we use the classical coaxial wire method for bench measurements as shown in Fig. 9. For practical reasons, we used flat end plates and resistive matching of the coaxial wire on either side with a 290 Ω carbon resistor. This value is calculated taking into account the characteristic impedance of the wire in the pipe which amounts to 340 Ω  (= ZcWire) and using the following relation for the matching resistor (RM)  50−= cWIREM ZR   The coaxial wire method should not be used at low frequencies (i.e. below several MHz) because the image currents, which normally flow in the inner surface of the outer conductor, would find their way onto the outer surface of the outer conductor via the open gap.  In order to get a suitable reference measurement we have installed three short circuits evenly distributed over the circumference of the isolating gap. Then we compare to the DUT measurement by removing these three short circuits and replacing by one or more bypass units. This technique does not correspond exactly to the classical coaxial wire method since there, as a reference, a smooth beam pipe with homogenous cross-section should be used. However in our case such a reference tube with required length, diameter and flanges was not available.  |S21| [dB]-25.0-20.0-15.0-10.0-5.00.01.0E+06 2.5E+08 5.0E+08 7.5E+08 1.0E+09Frequency [Hz]arg(S21) [deg]-200.0-150.0-100.0-50.00.050.0100.0150.0200.01.0E+06 2.5E+08 5.0E+08 7.5E+08 1.0E+09Frequency [Hz]  Fig. 10 – Reference measurement in transmission raw data (S21)  In Fig. 10 the raw data of the transmission reference measurement are shown. The dependence of the phase versus frequency in fig. 10 is due to the finite length of the cables connecting the DUT to the VNA. We also recognize an attenuation of approximately 16 to 17 dB which is mainly due to the losses in the matching resistors: the slope is due to the frequency dependent cable losses while the ripple (increasing with frequency) is due to the frequency dependent characteristics of the matching resistors.  In the following we compare measurement of the S12 with one or two or three bypass units to the reference  case (three short circuits). The measurement looks very similar both in amplitude and phase. The amplitude and phase of the complex quotient between DUT and reference measurement are shown in fig. 11.   8| S21 / Ref | [dB]0.960.970.980.991.001.011.021.031.041.0E+06 2.5E+08 5.0E+08 7.5E+08 1.0E+09Frequency [Hz]arg [S21 / Ref] [deg]-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.01.0E+06 2.5E+08 5.0E+08 7.5E+08 1.0E+09Frequency [Hz]  Fig. 11 – Amplitude and phase (S21) of one bypass / reference measurement  The result seems to be surprising at the first glance. We notice a positive peak at 143 MHz and a negative one near 40 MHz. The negative peak which has an amplitude of about 0.25 dB is the effect of a single bypass seen by the beam and may be converted into an impedance by using the relation  Ω=−⋅= 4.1012 ~21~21SSZZ c  with REFDUTSS2121~21 =S  and  Ω= 340zZ The positive peak at 143 MHz is of course not an impedance with a negative real part, but simply it is due to the fact that even with 3 short circuits the capacitive bypass still has a resonance (143 MHz). As a test for this hypothesis we have compared two and one short circuits respectively with our three short circuits reference. The results are shown in Fig. 12. One can clearly recognize that the “positive” resonance frequency with two and one short circuits is shifting down, but the 143 MHz peak is unchanged.   | S 21  / Ref | [dB]          2 Short Circuits -0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 1.0E+06 2.5E+08 5.0E+08 7.5E+08 1.0E+09Frequency [Hz] Corrupted data !  Sweep time too fast ? | S21 / Ref | [dB]          1 Short Circuit-0.30-0.20-0.100.000.100.200.301.0E+06 2.5E+08 5.0E+08 7.5E+08 1.0E+09Frequency [Hz]  Fig. 12 – Measurement ratio for two and one short circuits in comparison with 3 short circuit reference    9| S21 / Ref | [dB]          No Short Circuits (open)-3.00-2.50-2.00-1.50-1.00-0.500.001.0E+06 6.0E+06 1.1E+07 1.6E+07 2.1E+07Frequency [Hz]| S21 / Ref | [dB]          No Short Circuits (open)-3.00-2.50-2.00-1.50-1.00-0.500.000.501.0E+06 2.5E+08 5.0E+08 7.5E+08 1.0E+09Frequency [Hz]  Fig. 13 - Measurement ratio for open gap in comparison with 3 short circuit reference  In Fig. 13 the results for open gap in transmission measurement are shown. In the left picture we can see the resonance of the three short circuits as a positive peak at 143 MHz and towards very low frequencies a single negative data point. This is depicted in an expanded view on the right hand side. From the lowest frequency data point (which is at 1 MHz) one might conclude that the impedance is very small at this frequency; however here we see the previously discussed, inherent error of the transmission measurement at very low frequencies. The image current passes through the gap onto the outer surface of the outer conductor of the coaxial cable and the loop is closed via the front panel of the network analyzer. However this minimum is close to the frequency (1.5MHz) found in ref. [2], which means that the external inductance of our measurement loop is comparable to the inductance of the ground loop in the CPS machine.   4.2 Transmission Measurements in “pick up” mode  ≈0 ΩBypass with SMAConnectorVacuum ChamberIsolatedFlange≈0 ΩVectorNetworkAnalyzerHP8753DRG214 / 50Ω CableRG214 / 50Ω Cable50 Ω Fig. 14 – Transmission measurements set up in “pick-up” mode  10As an additional check, we have used the setup as described in section 4.1, terminating the downstream end of the test chamber with a 50 Ω load, and replacing the normal bypass with one with an SMA connector similar to that one shown in Fig. 1b. In other words, we are considering the gap with a bypass as a pick-up and measure transfer impedance (sensitivity) using the coaxial wire method. The results are shown in Fig. 15.  |S 21 | [dB] -90 -80 -70 -60 -50 -40 -30 -20 1.E+05 1.E+07 2.E+07 3.E+07 4.E+07 5.E+07 6.E+07 7.E+07 8.E+07 9.E+07 1.E+08 Frequency [Hz]0 [Ohm] series resistance 1 [Ohm] series resistance  Fig. 15 – Transfer impedance measurement (S21) on a connectorized bypass  From the data in Fig. 15, we recognize two resonances for the case where R1 equal 0 (Fig. 1c), namely at 2 MHz and 46 MHz and for the normal case with the 1 Ω series resistance, a maximum sensitivity around 41 MHz. It may be useful to insert such bypass with output connector in the CPS machine and carry out a similar pick-up sensitivity measurement in situ.   5. Conclusion  The bench measurements described in this paper confirm the results obtained in ref. [2] and [3] below 10 MHz. However they show the presence of higher order resonances, which are relevant to the beam coupling impedance at higher frequencies (40 MHz c.f. Fig. 11). The impedance seen by the beam at these frequencies is moderate (around 10 Ω per isolated flange) and likely to be staggered in frequency by the influence of the ground loop inductance. Thus it does not pose an immediate danger for the presently used beams in the CPS. But such resonance may lead to an unexpected voltage excursion on the bypass capacitors and to subsequent damage. The series of S11 measurements done during the 2001/2002 shutdown on these bypass units in the CPS from outside the vacuum chamber has shown typical maxima in the real part of the input impedance around 50 MHz with a strong frequency scatter. This observation [4] confirms indirectly the bench measurement results, which were obtained without the grounding loop.   6. Acknowledgement  The authors would like to thank R. Cappi and J.-P. Terrier for providing very helpful information as well as F. Pedersen and R. Garoby for their support.     11 12http://psrfll.home.cern.ch/psrfll/PS_Flanges/2002/index.htm7. References  [1] A. W. Chao "Handbook of Accelerator Physics and Engineering", World Scientific Chapter 7.5.1 [2] R. Cappi "RF ByPass on the Proton Synchrotron Vacuum Chamber Flanges", PAC 89 Chicago, CERN/PS 89-22 (PA); [3] M. Bole-Feysot et. al. "Minutes of a Meeting on 17.1.1995 on Grounding of the PS Vacuum Chamber and RF By-passing",  PS-RF-Note 95/4 (Min.) [4]   

Coupling impedance measurements with the coaxial wire method on the CPS RF bypass

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