I. Introduction
Attenuation is a quantitative representation of the degree to which electromagnetic waves attenuate as they propagate through a transmission line. For electromagnetic measurements, coaxial or waveguide attenuators are widely used as built-in or separate external devices. For instance, built-in step attenuators operate automatically when the front button of a spectrum analyzer or vector network analyzer (VNA) is pressed to change the level of the radio frequency (RF) input signal. The attenuators can be divided into fixed and variable types. Variable attenuators can be further subdivided into step and continuous types. Attenuation of the attenuators used at measurement sites can be conveniently measured using spectrum analyzers and signal generators, VNAs, power sensors and power meters, among other methods. The nonlinearity of these instruments, which is one of their fundamental performance indicators, can be evaluated using a reference attenuator that is traceable to the national measurement standard [1].
In response to the demand for accurate measurement, attenuation measurement standards have been established by the Korea Research Institute of Standards and Science (KRISS). First, a 90-dB attenuation standard was developed in the frequency range of 10 MHz to 18 GHz, with an expanded uncertainty (coverage factor k = 2, level of confidence of approximately 95%) of 0.003 dB to 0.013 dB [2]. Next, an 80 dB attenuation standard was developed in the K- and Ka-bands, with an expanded uncertainty of 0.004 dB to 0.02 dB [3]. These attenuation standards were designed and constructed by applying the RF substitution method, which does not require the use of a mixer. Over time, the attenuation measurement range has been extended up to 100 dB in subsequent studies.
However, since the test frequency of conducted emissions from electrical and electronic equipment ranges from 9 kHz to 30 MHz [4, 5], it is crucial to extend the lower frequency of the current attenuation measurement standard. Therefore, in this paper, an attenuation measurement system for the frequency range of 9 kHz to 10 MHz is developed. To devise a measurement system that satisfies this frequency and attenuation measurement range, the feasibility, uncertainty, and cost of implementation of various methods are compared, considering the intermediate frequency (IF) substitution method as the measurement method. Notably, the RF substitution method, which is used in attenuation measurement systems above 10 MHz [2], requires thermistor mounts with good linearity. However, since thermistor mounts covering the frequency range from 9 kHz to 10 MHz are not available, we employed the IF substitution method in this study.
We selected and secured the necessary parts for an attenuation measuring instrument, designed and fabricated it, and also developed a related control program. Furthermore, we constructed an attenuation measurement system comprising a local oscillator (LO), an in-house attenuation measuring instrument, and a receiver to measure the attenuation of a device under test (DUT). Moreover, the measurement uncertainty of the measured attenuation was evaluated by investigating the uncertainty sources, such as mixer linearity, performance of the receiver, electromagnetic wave leakage, and others. Based on the evaluated uncertainty, the calibration and measurement capability (CMC) of the developed standard was submitted to the International Bureau of Weights and Measures (BIPM), where the listing process is currently underway.
II. Attenuation Measurement System
The proposed low-frequency attenuation measurement system operating in the frequency range of 9 kHz to 10 MHz is presented in Fig. 1. The dotted line in Fig. 1 encloses the proposed attenuation measuring instrument, which integrates a mixer, two RF switches, an RF switch controller, and a power supply. The measurement program, which runs on the “Mini PC” inside the attenuation measuring instrument, is written in LabWindows using C language. The RF signal of the attenuator under test passes from the “RF in” port of the attenuation measuring instrument through a 30-dB attenuator only when the attenuator is in its initial state, i.e., 0 dB setting, and in its final state of less than 38 dB. Otherwise, the RF signal passes directly through the RF switch to the RF port of the mixer. The 30-dB attenuator is employed in the setup to reduce the RF signal level so that the signal level at the RF port of the mixer is within its linear region. A 1-kHz signal corresponding to the frequency difference between the RF and the LO is considered the IF output of the mixer. The mixer used in this study is a double-balanced mixer, ZLW-6+, with its mini-circuits operating at frequencies of 3 kHz to 100 MHz. The LO and the spectrum analyzer are controlled by the measurement program through a general purpose interface bus (GPIB). Furthermore, an Ethernet-based control module is employed to control the signal path. Fig. 2 displays a photograph of the proposed attenuation measuring instrument, and Fig. 3 shows an example of the measurement program in operation.
III. Attenuation Measurement
Fig. 4 presents a diagram demonstrating the instrument connection for measuring the attenuation of a DUT. Here, the DUT is a variable attenuator with 100 dB attenuation. The attenuation measuring instrument denoted in Fig. 4 is the same as the one illustrated by the dotted section in Fig. 1.
1. Measurement Experiment
The measurement procedure is as follows:
(a) Set the frequency of the signal generator to the frequency at which the attenuation is to be measured.
(b) Run the measurement program shown in Fig. 3 and adjust “Freq.” on the execution screen to the frequency of the signal generator. Set the variable attenuator to 0 dB, which is referred to as the initial state. Set the signal generator power level to ensure that the input power to the mixer ranges from −14 dBm to −15 dBm. Wait for the “Tuned RF Level” value to stabilize and then click “Set Ref.” The “Tuned RF Level” value should be set to 0 dB.
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(c) Increase the attenuation until the “Tuned RF Level” value in the initial state reaches the amount of attenuation to be measured in the range of 10 dB to 30 dB by slowly turning the adjustment knob on the variable attenuator or pressing the button. Read the value displayed in “Tuned RF Level” and then record it as a measurement value. This represents the insertion loss LI. The state of the variable attenuator at this point is called the final state.
If the “Tuned RF Level” reaches more than about 38 dB, the program will display “Now calibrating Cal factor2… Wait.” “Cal factor2” indicates the insertion loss of the 30-dB attenuator depicted in Fig. 1. During this process, the program automatically measures “Cal factor2” and displays it on the screen. Once the “Cal factor2” is determined, the value is used to measure attenuations of 40 dB to 100 dB. At the same time, the “Tuned RF Level” corresponding to the attenuation setting of the variable attenuator is automatically displayed. (d) Measure the scattering coefficients of the final state of the DUT—S11f, S21f, S12f, and S22f—as well as the reflection coefficients ΓG and ΓL using a VNA. Here, ΓG and ΓL are the reflection coefficients looking into the signal generator and the attenuation measuring instrument, respectively, both of which are independent of the attenuation setting of the DUT.
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(e) Mismatch loss of the DUT can be obtained from [6] using the following equation:
where Siji, Sijf (i,j = 1,2) are the scattering parameters of the DUT, with subscripts i and f denoting the initial and final states of the DUT, respectively. For an attenuation of 10 dB, the magnitude of the numeric value of S12fS21f is usually less than 0.1. In this case, the term S12fS21fΓGΓL becomes insignificantly small compared to the other term of the numerator of the logarithmic factor in Eq. (1). This phenomenon becomes more plausible when the attenuation is greater than 10 dB, since S12fS21f will then be smaller. Therefore, the measurement of S21f and S12f can be omitted in the case of an attenuation greater than 10 dB. For the denominator of the logarithmic factor in Eq. (1), the measured scattering parameters of the initial state of the DUT, Siji, are inserted into Eq. (1), since usually S21i ≈ 1 and S12i ≈ 1. -
(f) Calculate the attenuation A by substituting the insertion loss LI and the mismatch loss ɛM into the following equation:
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(g) Measure attenuations by repeating steps (a)–(f), starting with a nominal attenuation value of 10 dB of the DUT and increasing by 10 dB in each step until 100 dB is reached. For every nominal attenuation value, e.g., 10 dB, 20 dB, …, 100 dB, the initial state should be measured again to compensate for the source drift.
To investigate the consistency of the measurement paths with and without the 30-dB attenuator, a nominal 40 dB attenuation of the variable step attenuator was measured using the direct path and the 30-dB attenuator path. As described earlier, the 30-dB attenuator represents the measurement path in the range of the final state of the step attenuator under test, which is less than 38 dB. Notably, since the attenuation of the step attenuator was 10 dB, consistency was checked at 40 dB, which is the value closest to the boundary value of 38 dB. The measured results, averaged five times, agree within 0.002 dB, thus validating the proposed method.
2. Measurement Uncertainty
We evaluated the measurement uncertainty of the attenuation measurements. In this paper, measurement uncertainty refers to expanded uncertainty (coverage factor k = 2, level of confidence of approximately 95%). Each uncertainty source and its contribution are briefly described below.
A 10-dB variable attenuator was used to examine the linearity of the mixer up to 70 dB at 9 kHz, 10 kHz, 100 kHz, 1 MHz, and 10 MHz. When measuring the attenuation in the 0 dB to 38 dB range, the output of the DUT passed through the 38 dB attenuator, as shown in Fig. 1, to reduce its magnitude before reaching the mixer RF input. In contrast, when measuring the attenuation in the 38 dB to 100 dB range, the signal directly reached the mixer RF input without passing through the 30-dB attenuator. Therefore, even if the linearity of the selected mixer is limited to 70 dB, the measurement range of the attenuation measurement system can be extended to 100 dB.
The spectrum analyzer, which is used as the receiver, was calibrated in terms of attenuation at 1 kHz using an inductive voltage divider (IVD), as shown in Fig. 5. The IVD, also called the decade transformer, employed in this study is model DT72A from Electro-Scientific Industries. It is traceable to the electrical measurement standard at 1 kHz.
When measuring an attenuation of less than 38 dB, the 30-dB attenuator located inside the attenuation measuring instrument presented in Fig. 1 had no influence on the attenuation measurement of the DUT, since the DUT’s signal output is directly used as the input to the mixer. Meanwhile, when measuring attenuation from 38 dB to 100 dB, the 30-dB attenuator had a 0.0025 dB effect.
Fluctuations in the output power of the signal generator were measured over a period of 10 minutes to evaluate the uncertainty arising from source drift.
Since the IF receiver had a resolution of 0.001 dB, the received IF signals were read considering the reference and measurement settings of the DUT. The standard uncertainty due to the resolution was 0.0006 dB.
Considering AS as the attenuation through the signal path in decibels and AL as the attenuation through the leakage path that shunts the DUT in decibels, the upper and lower limits of the leakage error [6] can be given by:
The value of AL was approximately 150 dB, as estimated from the shielding effectiveness of the two interconnecting cables, i.e., 75 dB + 75 dB = 150 dB. The leakage path resulting from the DUT and the measurement system was assumed to be negligible. This was verified by measuring the system noise floor using an airline as the DUT in Fig. 4. By substituting the values of AS and AL in Eq. (3), we identified the limit of the leakage error.
For measurements above 80 dB, the uncertainty due to leakage was observed to be very large compared to other uncertainties. This indicates that proper care should be taken to shield the cables and connectors. In particular, in the tens of the kHz band, ferrite cores or isolation transformers should be used to reduce the effect of common-mode leakage currents.
Since the mismatch loss in the measured frequency band is typically small, the mismatch loss of Eq. (1) was assumed to be 0 dB, and only the magnitudes of the reflection coefficients were measured to calculate the mismatch uncertainty according to the method in [7].
In Eq. (4), the scattering parameters with subscripts i or f were measured when the DUT was initially set to 0 dB and also when it was finally set to the measured attenuation level.
The attenuation values at each attenuation level and at each frequency were repeatedly measured 10 times. Subsequently, the standard uncertainty was obtained by Type A evaluation; the standard deviation of the measured values was divided by
n
To further verify the proposed attenuation measurement system, uncertainty sources that could affect the measurement results were also analyzed. The measurement uncertainty was obtained by accounting for the uncertainty contributions from each uncertainty source. Table 1 lists the uncertainty budget obtained at 10, 30, 60, 80, and 100 dB at a frequency of 10 MHz, i.e., the highest frequency from 9 kHz to 10 MHz.
Fig. 6 highlights the difference between Ameas, which refers to the measured attenuation, and Anorm, indicating the nominal attenuation from 10 dB to 100 dB with expanded uncertainty, at 10 MHz. It is evident that the attenuation measurements made with both systems show good agreement in the expanded uncertainty.
Fig. 7 presents a comparison of the expanded uncertainties in the attenuation measurement of the variable attenuator at 10 MHz, which is a frequency common to the proposed attenuation measurement system in the 9 kHz to 10 MHz range and the existing system measuring in the 10 MHz to 40 GHz range [2].
It is observed that the uncertainty of the low-frequency attenuation measurement system is larger than that of the existing attenuation measurement system, since the uncertainty contributions made by the source drift and leakage become larger when measuring attenuations above 80 dB at 10 MHz, as shown in Table 1. Fig. 7 shows that the uncertainty of the proposed low-frequency attenuation measurement system is comparable to that of the National Metrology Institute of Japan (NMIJ) at 10 dB attenuation. However, at 100 dB attenuation, the proposed system exhibits a larger uncertainty than the NMIJ measurement system. The NMIJ attenuation measurement system is regarded as one of the best systems. However, it can conduct measurements only for frequencies at which an IVD can be calibrated, because it uses the audio frequency (AF) substitution method. Nonetheless, the NMIJ measurement system consists of very complex dual subsystems compared to the KRISS system.
The IF substitution method, established long ago, is mostly traceable to the 30-MHz waveguide below cutoff (WBCO) attenuator [6]. In contrast, the proposed system is traceable to the 1-kHz IVD, meaning that it can achieve lower uncertainty in the low-frequency range.
Table 2 presents a brief comparison of the CMC entries for low-frequency attenuation by some of the national metrology institutes listed in [8]. The measurement uncertainty of the National Institute of Metrology (NIM), China, is 0.003 dB and 0.12 dB at 10 dB and 100 dB of attenuation at frequencies of 10 kHz and 100 kHz, respectively. Meanwhile, as also shown in Table 1, expanded uncertainties of 0.005 dB to 0.058 dB at attenuations of 10 dB to 100 dB in the frequency range of 9 kHz to 10 MHz are achieved by KRISS. This indicates that NMIJ, which reported values of 0.003 dB at 10 dB and 0.016 dB at 100 dB, achieved smaller uncertainty values than KRISS at frequencies above 100 kHz. However, while the NMIJ system starts at 100 kHz, the present KRISS system starts at 9 kHz. Meanwhile, the National Physical Laboratory (NPL), United Kingdom, registered an attenuation measurement range of 140 dB at 10 kHz, 50 kHz, 500 kHz, and above in 2021.
One of the most capable methods for improving measurement uncertainty is to apply the AF substitution method using an IVD calibrated up to 100 dB at the measurement frequencies as a reference attenuator. This can eliminate mixer linearity uncertainty as well as the uncertainty caused by the 30-dB attenuator shown in Fig. 1. Using a dual-system null detection method [9] can further improve uncertainty.
IV. Conclusion
An attenuation measurement standard was established in the frequency range of 9 kHz to 10 MHz. The proposed attenuation measurement system consists of an LO, an attenuation measuring instrument, and a receiver. In this paper, the core device, i.e., the attenuation measuring instrument, was designed and fabricated by applying the IF substitution method. The instrument generated an IF signal of 1 kHz from an input RF signal ranging from 9 kHz to 10 MHz using a built-in mixer. Subsequently, the IF output level was measured using a spectrum analyzer as the receiver, characterized by an IVD traceable to the electrical measurement standard. The measurement uncertainty was evaluated by investigating uncertainty sources, such as receiver performance, mismatch, and mixer linearity, among others. The resulting expanded uncertainty was 0.005 dB to 0.058 dB (k = 2) in the attenuation range of 10 dB to 100 dB.
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