Millimeter-Wave Attenuation Measurement standard from 26.5 GHz to 40 GHz, EU microwave conf 2009

A Millimeter-Wave Attenuation Measurement Standard from 26.5 GHz to 40 GHz Thomas Y. Wu 1, S. W. Chua National Metrology Centre, A*STAR, 1 Science Park Dr, Singapore 118221, Republic of Singapore 1 thomas_wu@nmc.a-star.edu.sg Abstract— A millimeter-wave attenuation measurement standard using the audio frequency substitution method is described in this paper. Attenuation of up to 90 dB from 26.5 GHz to 40 GHz can be measured by this standard. An Inductive Voltage Divider is used as a reference voltage ratio standard at 5 kHz. A dual channel high-sensitivity receiver has been designed to make accurate measurement using a lock-in amplifier. The measurement uncertainty of the new standard is analyzed. The expanded measurement uncertainty of a 0.01 dB ~ 90 dB step attenuator at 40 GHz is estimated to be 0.0037 dB ~ 0.011 dB. I. INTRODUCTION Millimeter-wave technology is increasingly being used in many applications, such as broadband communication, high- resolution imaging, automotive radar, etc. Correspondingly there is a growing demand for precision measurement at millimeter-wave frequencies. Accurate attenuation measurement is critical for successful component design and system development. Attenuation measurement standards for frequencies from 26.5 GHz to 40 GHz have been developed by several national standard laboratories. A waveguide attenuation measurement system using the power ratio method was described in [1], which could measure attenuation values of up to 30 dB in this band. A coaxial attenuation standard from 26.5 GHz to 40 GHz using the power ratio transfer method was described in [2], and its dynamic range is 60 dB. The audio frequency (AF) substitution method has been used to measure attenuation of up to 80 dB from 26.5 GHz to 40 GHz [3 - 5]. In such systems, the millimeter-wave signal is converted to AF signal (1 kHz ~ 50 kHz) using a mixer, and the millimeter-wave attenuation is derived from the voltage ratio at AF. An Inductive Voltage Divider (IVD) is used as a traceable low frequency voltage ratio reference standard for the millimeter-wave attenuation measurement since it has very good accuracy in AF voltage ratio (about 0.1 ppm at 1 kHz). A broadband AF series substitution system for microwave attenuation measurement from 10 MHz to 26.5 GHz has been developed at the National Metrology Center of Singapore [6 - 7]. Attenuation of up to 110 dB can be measured by this system. To provide traceability for millimeter-wave attenuation measurement, a new attenuation standard has been developed in the frequency range from 26.5 GHz to 40 GHz. This paper will describe the design of the measurement system, discuss the sources of measurement error and evaluate the measurement uncertainties. The system has been designed to achieve good accuracy and a wide dynamic range of 90 dB. II. MILLIMETER-WAVE ATTENUATION MEASUREMENT SYSTEM Our millimeter-wave attenuation measurement standard is an IVD-based AF substitution system. A seven-decade programmable IVD is used as a ratio reference standard, and is connected in-series with the device under test (DUT). The block diagram of the system is shown in Fig 1. A mixer is used to convert the millimeter-wave signal in Ka-band (26.5 GHz to 40 GHz) to a 5.02 kHz AF signal. The AF signal first goes through a 10-section low-pass LC filter with a cut-off frequency of 100 kHz to suppress the harmonics signals. It then goes through a low-noise pre-amplifier, a band-pass filter and an IVD. The output of the IVD enters the input of a digital lock-in amplifier (LIA). The ratio of IVD can be adjusted to offset the attenuation change of the DUT and maintain the same AF signal level detected by the LIA. Thus the DUT attenuation can be derived from the change in IVD ratios. The DUT is usually a step attenuator and its incremental attenuation is measured. When a DUT is set to 0 dB range (datum position), the IVD ratio is set to a reference value D1 and the LIA detects a AF signal with a magnitude of V1. After the DUT is set to a particular attenuation range, the IVD ratio setting is adjusted automatically via a computer program until the LIA detects a signal with a magnitude of V2 ≈ V1 at an IVD ratio setting of D2 (V1 ≈ 1 mV, |V2 - V1| < 2 µV). The millimeter-wave attenuation of the DUT is then calculated as ( ) 12 21 10log20 DV DV A = (dB) (1) A digital LIA can be used as a highly sensitive weak signal detector which uses a frequency reference signal to extract a desired signal from noisy background. Precision measurement of the signal’s amplitude and phase is possible even at very low signal-to-noise ratio (SNR). The signal power of our signal source at 40 GHz is about 5 dB lower compared to the signal power at 18 GHz, and the transmission loss through the coaxial cables and various devices also increases significantly at 26.5 GHz ~ 40 GHz. The phase noise of the signal source and local oscillator (LO) increase dramatically compared to the band below 26.5 GHz. These factors all lead to reduced SNR and stability at receiver. If a function generator is used to provide a 5.02 kHz sinusoidal frequency reference signal to the LIA, large fluctuation of the voltage reading can be observed at the LIA, and such voltage fluctuation will lead to a 0.1 dB error in Fig. 1 Block diagram of the millimeter-wave attenuation measurement system from 26.5 GHz ~ 40 GHz. attenuation measurement. This is due to the mismatch in the frequency between the AF signal from mixer output and the reference signal. The frequency of the AF signal produced by the mixer fluctuates due to the phase noise of the millimeter- wave source and LO. Whereas the frequency of the reference signal provided by the function generator is very stable, therefore it is not a good reference for the LIA. To improve the receiver stability, a frequency reference channel is introduced to provide a good reference signal for the LIA. The signal from the source is split via a directional coupler and the coupled signal goes into a reference mixer which shares the same LO with the main mixer. The reference mixer thus provides a reference signal at 5.02 kHz with the same frequency fluctuation of the main AF signal. The bandwidth of the band-pass filter in the reference channel is set to be 20 Hz. This reference signal reduces the LIA voltage reading fluctuation significantly and the error in low attenuation measurement can be reduced to 0.001 dB. In order to reduce the mismatch uncertainty in attenuation measurement, two slide screw impedance tuners are used to provide good test port impedance matching. The tuner can be tuned to achieve a return loss of 45 dB. Two isolators are placed before and after the matching tuner to reduce the reflection from the source and the mixer RF input respectively. There is an internal leakage path going through the reference mixer (from RF to LO port), isolators, directional coupler and enters the signal mixer RF port (from LO to RF port). Six isolators (each with 14 dB reverse isolation) and a directional coupler are used in the leakage path between LO port of two mixers to reduce this leakage. A 70 dB attenuator is also inserted before the reference mixer RF input to further reduce the internal leakage. The estimated internal leakage path attenuation is about 235 dB. There is also an external leakage due to radiation from slide screw tuners and isolators. Some signals would radiate from the tuner connected before the DUT, propagate through the air and couple into the tuner connected after the DUT. The tuner and the isolator attached to it are put inside a shield box to reduce the radiation leakage. The two shield boxes used in the system could provide about 40 dB effective shielding at 40 GHz, thus the total external leakage attenuation through the two shield boxes is about 80 dB. Various millimeter-wave components in the measurement system are connected via coaxial cables and adaptors. There are leakage signals radiated from the cables and connectors. Such leakage is expected to be higher compared to lower frequency bands. The connectors are wrapped using aluminium foils to reduce the leakage. To minimize the interference between different millimeter-wave portions of the system, the main mixer and the reference channel (indicated by the dotted boxes in the Fig. 1) are placed inside two separate shield boxes. Although such arrangement increases the millimeter-wave signal loss and decreases the SNR in the receiver, it proves to be necessary in order to reduce the leakage error in attenuation measurement. Leakage is one of the major errors in high attenuation measurement, thus careful isolation of different millimeter-wave portions of the system helps to increase the dynamic range of attenuation measurement. IVD ratios from 1 to 0.01 are used in direct measurement of attenuation from 0 dB to 40 dB. This arrangement is made to ensure best linearity and voltage ratio accuracy. Calibration of an attenuator from 40 dB to 80 dB is done by comparing Tuner LP Filter Pre-Amp Ref LO RF Gauge Block Attenuator Tuner IVD Lock-in Amp Pre-Amp LP Filter Attenuator LO AF (5.02 kHz) RF DUT Computer GPIB GPIB 10 MHz Reference Isolators Isolator Isolator LO Source (26.5 GHz ~ 40 GHz) RF Source (26.5 GHz ~ 40 GHz) BP Filter Ref Mixer Main Mixer BP Filter AF (5.02 kHz) the DUT to a 40 dB gauge block attenuator and their attenuation difference A is derived from the IVD ratio changes. The DUT attenuation is then obtained from ADUT = A + AGB (2) where AGB is the gauge block attenuation. Similarly, calibration of an attenuator from 80 dB to 90 dB is done by comparing the DUT to an 80 dB gauge block attenuator. III. MEASUREMENT UNCERTAINTIES A. IVD Error A seven decade IVD is used as the voltage ratio reference standard. The accuracy of the IVD is 1 ppm for ratio setting from 0.1 to 0.01. The standard uncertainty due to the IVD error is estimated as { }]/)[(log205.0 1110 DDu γ+= (dB) (3) where γ is the IVD ratio error when D1 is set to 0.01 for measurement of attenuation up to 40 dB. This error is assumed to have a normal distribution, and the standard uncertainty is estimated to be 0.0004 dB for direct attenuation measurement from 0 dB to 40 dB and indirect measurement from 40 dB to 80 dB. For IVD ratio setting from 1 to 0.1, its accuracy is 10 ppm and the standard uncertainty is estimated to be 0.0004 dB for 80 dB ~ 90 dB attenuation measurement. B. Receiver Fluctuation The detected signal by the LIA has a root-mean-square magnitude around 1 mV and it has small fluctuations in its magnitude (about 0.2 ~ 0.8 µV) when measuring attenuation of up to 80 dB. Such fluctuations will lead to an uncertainty in the attenuation measurement. For a 90 dB attenuation measurement, receiver fluctuation increases to around 1.2 µV due to the thermal noise effect in the mixer, filter, pre- amplifier and the LIA. To reduce the uncertainty in measurement of attenuation above 60 dB, 15 readings taken within 15 seconds (one sample per second) are averaged to reduce the random fluctuation effect. The error due to fluctuation has a rectangular distribution. The standard uncertainty due to fluctuation is estimated to be 0.001 dB for 0 ~ 40 dB measurement, 0.0019 dB for 40 ~ 80 dB measurement and 0.003 dB for 80 ~ 90 dB measurement. C. Receiver Nonlinearity The mixer and pre-amplifier nonlinearity is an important uncertainty factor in the AF substitution attenuation measurement. The signal level at the mixer RF input should be at least 30 dB below the LO level to achieve the smallest nonlinearity error. For measurement of attenuation below 40 dB, a 20 dB attenuator is placed before the DUT to ensure the mixer is operating in its linear region. We have checked the system nonlinearity by repeatedly measuring a 10 dB attenuator at decreasing mixer RF input levels from -37 dBm to -87 dBm. A step attenuator was inserted before the mixer input and its attenuation was increased from 30 dB to 80 dB in 10 dB step. Table I gives the measurement data at 40 GHz. The signal level at mixer RF input given in the table indicates the level before the 10 dB attenuator is inserted. Six measurements were made at each signal level. A reference value of 9.887 dB was obtained from the mean value of measurements made at signal levels from -37 dBm to -77 dBm. The deviation of each measurement value from the reference value is taken as the nonlinearity error for the corresponding signal level. The maximum nonlinearity error is 0.002 dB. Assuming it has a rectangular distribution, the standard nonlinearity uncertainty is estimated to be 0.0011 dB. The deviation of 0.003 dB at signal level of -87 dBm is an indication of the leakage error. TABLE I RECEIVER NONLINEARITY CHECK AT 40 GHZ BY MEASURING A 10 DB ATTENUATOR AT DECREASING MIXER RF INPUT LEVELS (REFERENCE ATTENUATION VALUE IS 9.887 DB) Signal level at mixer RF input (dBm) Mean of measurement Repeatability Deviation from reference value -37 9.888 0.0021 0.001 -47 9.887 0.0022 0.000 -57 9.889 0.0018 0.002 -67 9.887 0.0010 0.000 -77 9.886 0.0017 -0.001 -87 9.890 0.0021 0.003 D. Leakage Millimeter-wave leakage is a dominating uncertainty component for measurement of high attenuation. The resultant signal amplitude at the receiver due to the paths through the DUT and the leakage path is given by: 2/122 10 )cos2(log20 ϕLALA YYYYY ++= (dB) (4) where YA and YL are the signals at the receiver via the DUT and the leakage paths respectively with a phase difference φ between them. The phase can take on any value, depending upon the path differences. In practice the phase of the leakage relative to the wanted signal is difficult to measure and probably changes randomly. To keep the error caused by leakage to be smaller than 0.001 dB, the leakage path signal YL has to be 80 dB below the wanted signal YA . We have checked the leakage error by repeatedly measure a 20 dB attenuator at decreasing signal level. Table II gives the measurement data at 40 GHz. The signal level at mixer RF input indicates the level before the 20 dB attenuator is inserted. Six measurements were made at each signal level. A reference value of 19.996 dB was obtained from the mean value of measurements made at signal levels from -37 dBm to -67 dBm. For the signal levels below -67 dBm, the deviation of the measurement value from the reference value is taken as the leakage error. It shows that the leakage error is -0.028 dB at -87 dBm, which means that leakage error would be -0.028 dB for indirect measurement of a 100 dB attenuator via comparing to an 80 dB gauge block attenuator. If a 90 dB attenuator is compared to 70 dB gauge block attenuator, the leakage error will be about -0.005 dB (corresponding to the mixer RF input level of -77 dBm in Table II). Table I shows a leakage error of 0.003 dB for 90 dB attenuation measurement when compared to 80 dB gauge block (corresponding to the mixer RF input level at -87 dBm in Table I). The leakage error is assumed to have rectangular distribution and the standard uncertainty for 90 dB measurement is estimated to be 0.0023 dB. We have measured the attenuation of a 70 dB and an 80 dB attenuator using a 40 dB attenuator as the gauge block. These values were compared to those obtained by a two-step indirect measurement: first measure a 60 dB attenuator using the 40 dB attenuator as the gauge block, then measure the 70 dB and 80 dB attenuator using the 60 dB attenuator as the gauge block. Table I & II have shown that there is no leakage error in the above two-step measurement (corresponding to the mixer RF input level at -47 dBm and -67 dBm). The differences in the attenuation values obtained by the two different approaches are less than 0.003 dB, which are due to the repeatability error. This experiment shows that there is no leakage error in the measurement of the 70 dB and 80 dB attenuator using the 40 dB attenuator as the gauge block. TABLE II LEAKAGE ERROR CHECK AT 40 GHZ BY MEASURING A 20 DB ATTENUATOR AT DECREASING MIXER RF INPUT LEVELS (REFERENCE ATTENUATION VALUE IS 19.996 DB) Signal level at mixer RF input (dBm) Mean of measurement Repeatability Deviation from reference value -37 19.996 0.0006 0.000 -47 19.995 0.0019 -0.001 -57 19.996 0.0015 0.000 -67 19.997 0.0011 0.001 -77 19.991 0.0023 -0.005 -87 19.967 0.0037 -0.028 E. Gauge Block Attenuator Calibration of an attenuator in the range 40 dB ~ 90 dB is derived by comparing the DUT to a 40 dB or 80 dB gauge block attenuator. The gauge block attenuators have been calibrated previously with their own measurement uncertainties. Thus the uncertainty for the indirect attenuation measurement must include the gauge block attenuator calibration uncertainty. F. Combined and Expanded Uncertainty Repeatability (type A uncertainty) and type B uncertainties including nonlinearity, receiver fluctuation, IVD error, leakage and gauge block attenuator uncertainty are combined using root-sum-of-the-squares (RSS) method to yield the standard system uncertainty us. Mismatch uncertainties are dependent upon scattering parameters of DUT, thus it is not included in the system uncertainty budget. The expanded system uncertainty is Us = k us, where k is the coverage factor and we have set k=2. Table III give the system uncertainty budget for attenuation measurement in the band from 26.5 GHz to 40 GHz. The repeatability is obtained from ten measurements of a coaxial step attenuator (0 ~ 90 dB) at 40 GHz. The uncertainties due to leakage and receiver fluctuation are estimated from measurements made at 40 GHz, which give the maximum uncertainties in the frequency range from 26.5 GHz to 40 GHz. The expanded measurement uncertainty (k=2) is estimated to be 0.0037 dB for a 40 dB attenuator and 0.011 dB for a 90 dB attenuator at 40 GHz. TABLE III ATTENUATION MEASUREMENT UNCERTAINTY BUDGET FROM 26.5 GHZ TO 40 GHZ 0 - 40 40 - 80 90 IVD error 0.0004 0.0004 0.0004 Nonlinearity 0.0011 0.0011 0.0011 Leakage 0.0000 0.0000 0.0023 Fluctuation 0.0010 0.0019 0.0030 Gauge block attenuator 0.0000 0.0018 0.0033 Repeatability 0.0010 0.0016 0.0020 Combined uncertainty 0.0018 0.0033 0.0055 Expanded uncertainty (k=2) 0.0037 0.0066 0.011 Attenuation(dB) Source of uncertainty IV. CONCLUSIONS We have developed a millimeter-wave attenuation measurement standard from 26.5 GHz to 40 GHz using the AF substitution method. The standard is traceable to an IVD standard at 5 kHz. A dual channel system has been designed carefully to suppress leakage and achieve high-sensitivity measurement. Attenuation of up to 90 dB can be measured with high accuracy. Measurement uncertainty analysis of the system has been given. The expanded measurement uncertainty (k=2) is estimated to be 0.0037 ~ 0.011 dB for a 0.01 ~ 90 dB attenuator at 40 GHz. REFERENCES [1] D. Stumpe, “Recent developments in the PTB RF standard attenuation measuring equipment”, IEEE Trans. Instrum. Meas., Vol. IM-40, pp. 652-654, Jun. 1991. [2] J. G. Lee, J. H. Kim, J. S. Kang and T.