Characterization and optimization of correction factor determination in waveguide microcalorimeters

Contents lists available at ScienceDirect Measurement journal homepage: www.elsevier.com/locate/measurement Characterization and optimization of correction factor determination in waveguide microcalorimetersI Windi Kurnia Perangin-Angina,b,c,∗, Jürgen Rühaak a, Karsten Kuhlmann a aHigh Frequency and Electromagnetic Fields, Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, Braunschweig, 38116, Germany bFaculty of Electrical Engineering, Information Technology, Physics, Technische Universität Braunschweig, Hans-Sommer-Straße 66, Braunschweig, 38106, Germany cNational Research and Innovation Agency, Jl. M.H. Thamrin No. 8, Jakarta, 10340, Indonesia A R T I C L E I N F O Keywords: Correction factor Microcalorimeter Radio frequency power measurement Waveguide Power sensor Effective efficiency Measurement uncertainty A B S T R A C T Accurate measurement of radio frequency and millimeter-wave power is essential for establishing traceability in high frequency metrology, particularly in wireless communication and radar systems. Waveguide microcalorimeters serve as primary standards by enabling precise radio frequency power measurements. A critical parameter in these systems is the correction factor, which compensates for radio frequency losses of the microcalorimeter and significantly influences measurement uncertainty. This paper presents a comparative study of correction factor determination in waveguide microcalorimeters across multiple frequency bands, ranging from 8.2 to 220 GHz. Three established techniques, namely the offset short method, the foil short method, and the vector network analyzer method were investigated using a R-500 waveguide microcalorimeter. Experimental evaluations demonstrate good agreement among the correction factors obtained from all three methods. An optimized implementation of the foil short method is proposed to enhance measurement efficiency. The comparative results highlight the strengths and limitations of each approach, offering National Metrology Institutes a practical basis for selecting appropriate techniques for the characterization of microcalorimeters. 1. Introduction Accurate and precise measurement of radio frequency (RF) and millimeter-wave power is indispensable across a wide range of scientific and industrial fields, including wireless communication systems, radar technologies, and next-generation standards such as sixth-generation (6G) technology. As a fundamental quantity in high frequency metrology, RF power requires reliable traceability to primary standards to ensure the comparability and consistency of measurements across laboratories and applications. National Metrology Institutes (NMIs), including the Physikalisch-Technische Bundesanstalt (PTB), have addressed this need by developing waveguide microcalorimeters as primary standards for RF power, enabling the calibration of power sensors with high accuracy [1]. Microcalorimeters operate on the principle of RF/direct current (DC) substitution, where the absorbed RF power is inferred from the equivalent heating effect produced by a known DC power [2]. However, a fraction of the heat from the applied RF power may dissipate outside the sensing element of an RF power sensor, particularly within the IThis article is part of a Special issue entitled: ‘MEASUR_XXIV IMEKO World Congress’ published in Measurement. ∗Corresponding author at: High Frequency and Electromagnetic Fields, Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, Braunschweig, 38116, Germany. E-mail address: [email protected] (W.K. Perangin-Angin). transmission line of the microcalorimeter. Commercial transmission lines usually exhibit poor heat insulation. Therefore, thermal isolation sections (TIS) are often custom-made and used in combination with commercial transmission lines to form the complete feeding line for a microcalorimeter. The thermal isolation section is used to minimize the fraction of heat contributing to the temperature difference between the feeding line and the reference line [3,4]. A correction factor is introduced to account for the fraction of heat that contributes to the temperature difference measured at the reference plane. It originates from RF losses in the microcalorimeter transmission line, the sensor feeding line, and, to a small degree, other RF effects (such as the skin effect and radiation). Determining this correction factor is crucial for microcalorimeter development and is a key parameter in the effective efficiency measurement of a power sensor [5]. The most significant source of uncertainty in effective efficiency measurements often comes from the correction factor. Much of the correction factor accounts for imperfections in the thermal isolation section of the microcalorimeter. This quantifies the difference between https://doi.org/10.1016/j.measurement.2025.118865 Received 28 May 2025; Received in revised form 27 August 2025; Accepted 28 August 2025 Measurement 257 (2026) 118865 Available online 3 September 2025 0263-2241/© 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC license ( http://creativecommons.org/licenses/bync/4.0/ ). W.K. Perangin-Angin et al. an ideal heat measurement, in which no heat is lost, and the actual measurement, in which a portion of the heat is lost [6]. Various techniques are available for determining the correction factor in microcalorimeters. These include the offset short method, the foil short method, and a newer method involving a vector network analyzer (VNA) [7–10]. NMIs determine the correction factors for their microcalorimeters using one of these methods. This paper describes the evaluation of the correction factor for waveguide microcalorimeters over a broad frequency range from 8.2 to 220 GHz. An optimization to the foil short method has been applied. A comparison of the three methods is also performed using a rectangular waveguide R-500 microcalorimeter. NMIs can choose the most suitable measurement technique by considering the specific benefits and constraints of each method. 2. Overview of the microcalorimeter A microcalorimeter is basically a heat-measuring instrument designed to detect temperature changes resulting from the absorption of RF power. It measures RF power by evaluating the heat generated inside a suitable RF power sensor, which serves as a transfer standard. When RF power is applied to the transfer standard, it is absorbed and converted into heat, leading to a measurable change in the sensor’s temperature. Ideally, the temperature rise caused by RF power should match that produced by an equivalent DC power input. However, in practice, discrepancies exist between the temperature changes caused by RF and DC power, and these must be corrected during the microcalorimeter measurement [1,3]. The DC substituted power 𝑃DC is calculated using Eq. (1), 𝑃𝐷𝐶 = 𝑉2 1−𝑉2 2 𝑅0 (1) where 𝑉1 is the DC voltage across the sensing element of the transfer standard without RF power, 𝑉2 is the voltage with applied RF power, and 𝑅0 is the operating resistance of the transfer standard. The microcalorimeter determines a measurement quantity of the transfer standard known as effective efficiency [11]. The transfer standard is typically a bolometric sensor, such as a thermistor mount. However, thermoelectric sensors have also been used in microcalorimetric measurements in recent years [12,13]. The effective efficiency 𝜂𝑒 is defined as the ratio of the DC substituted power to the absorbed RF power 𝑃𝑅𝐹𝑎𝑏𝑠 in the transfer standard, as shown in Eq. (2). For ideal measurements, the 𝜂𝑒 equals 1 or 100% when the applied RF power is fully absorbed and the transfer standard exhibits identical thermal behavior under both RF and DC power [14]. 𝜂𝑒=𝑃𝐷𝐶 𝑃𝑅𝐹𝑎𝑏𝑠 (2) Fig. 1 shows a schematic diagram of the waveguide microcalorimeter measurement system used to calibrate a thermistor mount as the transfer standard. The waveguide microcalorimeter is based on a twinline structure with the transfer standard and a dummy load symmetrically placed. The transfer standard is connected to the feeding line, while the dummy load, which serves as the temperature reference, is connected to the reference line. Using identical power sensors for both the transfer standard and the dummy load ensures that symmetry and thermal balance requirements are met. A microcalorimeter thermopile measures the temperature difference between the two sensors. An isolator is employed to prevent reflected signals from reaching the RF source, especially when using a foil short or offset short, both of which reflect RF signals. At higher frequencies, a multiplier is used to increase the frequency to the desired band, as the signal generator is limited to a maximum output of 67 GHz. A directional coupler is used for power leveling control, ensuring that the output power from the signal generator remains stable through a power leveling system. The entire microcalorimeter system is covered with thermal jackets to maintain a stable ambient temperature. The transfer standard is controlled by a self-balancing bridge, which maintains the operating resistance 𝑅0 constant when RF power is applied. As the transfer standard absorbs RF power, its resistance changes due to temperature rise. To balance the bridge, the DC power is reduced, and this reduction is proportional to the applied RF power. Microcalorimeters tend to have long time constants. Therefore, microcalorimeter calibrations often require measurement times of weeks or even months [1]. Four parameters of the transfer standard are determined at each frequency: the DC voltage 𝑉1 and microcalorimeter thermopile output voltage 𝑒1 without RF power, and the DC voltage 𝑉2 and microcalorimeter thermopile output voltage 𝑒2 with RF power applied. Additionally, the correction factor of the microcalorimeter 𝑔 is determined through a separate measurement process and included in Eq. (3) to get the effective efficiency. 𝜂𝑒=𝑔 1 − (𝑉2 𝑉1)2 𝑒2 𝑒1 −(𝑉2 𝑉1)2(3) When a waveguide thermoelectric sensor is used as the transfer standard, the RF/DC substitution technique is applied indirectly. This is because thermoelectric sensors contain two absorbers: an RF termination (the first heater) for RF power absorption and a DC resistive heater (the second heater) for DC power absorption [15]. RF and DC power measurements using thermoelectric sensors are performed separately, as these sensors cannot be used with a self-balancing bridge in the same way. Consequently, Fig. 1 should be modified to include additional components such as a DC power source and a nanovoltmeter, as shown in Fig. 2. Within the thermoelectric sensor, a sensor thermopile is embedded, resulting in the use of two thermopiles during thermoelectric sensor measurements. RF power measurements are performed first, with the DC heater left unbiased and the DC source circuit disconnected from the system. After the RF source is turned off, DC measurements are carried out by adjusting the DC source until the output voltage of the sensor thermopile during the DC measurement closely matches that recorded during the RF measurement. The substituted DC power is calculated using the output voltage from the DC heater and the resistance of the DC resistive heater [13]. Fig. 3 depicts a graphical flowchart that outlines the complete calibration procedure of the transfer standard. 3. Correction factor measurement methods Fig. 4 exemplarily shows the measurement setup used to determine the correction factor of a R-1.8k microcalorimeter. An ideal microcalorimeter is described by Eq. (3), where the correction factor 𝑔 is equal to 1. This correction factor can be calculated using the following techniques. 3.1. Offset short method The offset short method determines the correction factor by combining measurements from offset short standards of varying lengths, followed by a measurement of an RF power sensor. It relies on a series of custom-fabricated offset short devices with incrementally varied electrical lengths but consistent thermal and mechanical properties. These devices replicate the thermal response of RF power sensors and allow for the isolation and analysis of power losses within the microcalorimeter. In this study, six custom offset shorts developed for R-500 waveguide microcalorimeters were used, with offset lengths 𝑙𝑠 of 0 mm, 2.5 mm, 3 mm, 3.5 mm, 4 mm, and 4.5 mm, as illustrated in Fig. 5. The main waveguide sections of the offset shorts are made of brass and aluminum, with a DC heater located on the back side. In this method, each offset short is sequentially inserted into the microcalorimeter in place of the transfer standard shown in Fig. 1, Measurement 257 (2026) 118865 2 W.K. Perangin-Angin et al. Fig. 1. Schematic diagram of the microcalorimeter measurement system using a thermistor mount as the transfer standard. followed by the RF power sensor. The output voltage of the microcalorimeter thermopile is recorded for each offset length, and the resulting set of measurements is used to develop a model of waveguide loss and thermopile nonlinearity. Once the system behavior is characterized, the correction factor for an RF power sensor measurement in the microcalorimeter can be determined by incorporating the reflection coefficient of the power sensor 𝛤S, which is usually measured using a VNA. The correction factor 𝑔 is then calculated by accounting for waveguide line losses 𝑝 and thermopile nonlinearity 𝑞, which reflects the temperature dependence of the heating constant, as presented in Eq. (4), 𝑔=[1 + 𝑝𝑐𝑜𝑟 1 + |𝛤S|2 1 − |𝛤S|2]. 𝑞 (4) where 𝑝𝑐𝑜𝑟 is a waveguide line loss-related parameter independent of the power sensor. The parameter 𝑝𝑐𝑜𝑟 can be derived from measurements of the averaged waveguide losses 𝑃𝑊 𝐺,𝑎𝑣𝑔 in front of the reference plane for the offset-short configurations, and the incident power at the reference plane 𝑃𝑖𝑛𝑐 , as shown in Eq. (5) and described in [7]. The value of 𝑞 is determined by evaluating the linearity of the thermopile. 𝑝𝑐𝑜𝑟 = 𝑃𝑊 𝐺,𝑎𝑣𝑔 2𝑃𝑖𝑛𝑐 (5) Measuring multiple offset shorts provides a more accurate estimation of losses in the feeding waveguide. The correction factor 𝑔 only needs to be determined once for calibrating all RF power sensors of the same type by deriving the parameter 𝑝𝑐𝑜𝑟. The same type refers to sensors with identical model, internal construction, and thermal behavior, as well as comparable reflection coefficients. For example, in this measurement, a thermistor mount of model Hughes 45773H was used. Therefore, the correction factor can also be applied to other thermistor mounts of the same model (Hughes 45773H) with different serial numbers. However, this method is time-consuming, as it involves seven Measurement 257 (2026) 118865 3 W.K. Perangin-Angin et al. Fig. 2. Schematic diagram of the microcalorimeter measurement system using a thermoelectric sensor as the transfer standard. separate measurement steps. Additionally, multiple offset shorts must be custom-fabricated, as they are usually not commercially available. One strength of the offset short method is that it eliminates the need to measure the RF power incident to the reference plane. However, a drawback is that it is time-consuming and relies on several custom-fabricated offset shorts, which are not commercially available. 3.2. Foil short method The foil short method offers an efficient measurement approach by introducing a thin reflective element (short foil) at the reference plane (between the thermal isolation section and the RF power sensor). This reflective foil, typically made of copper or aluminum with minimal thermal mass, creates a well-defined reflection at a location that is both thermally and geometrically close to the sensor under test. Fig. 6 shows the custom-fabricated short foil made of copper, used in this study for both the foil short method and the VNA method. This technique involves two measurement steps: first, a microcalorimeter measurement of the foil short with the power sensor, and second, a measurement of the power sensor alone under identical conditions. In each case, the foil short and power sensor assembly, or the power sensor alone, replaces the transfer standard shown in Fig. 1. The difference in microcalorimeter thermopile output voltages between these two configurations forms the basis for calculating the amount of power dissipated outside the sensing element of the power sensor. The correction factor is then determined using Eq. (6), 𝑔= 1 + 1 + |𝛤S|2 1 − |𝛤S|2 ⋅(𝛥𝑒FS 𝑘FS𝑃iFS (1 + |𝛤FS|2)− 1 − |𝛤FS|2 1 + |𝛤FS|2)(6) where 𝑃iFS is the incident power at the short, 𝛥𝑒FS is the thermopile voltage change due to RF power reflection from the foil, 𝑘FS is a proportionality constant related to thermopile sensitivity, 𝛤FS and 𝛤S are the reflection coefficients of the foil short and the RF power sensor, respectively [16]. Measurement 257 (2026) 118865 4 W.K. Perangin-Angin et al. Fig. 3. Flowchart of the complete calibration procedure of the transfer standard. The value of 𝑃iFS is obtained using a directional coupler experiment, which involves measuring the incident power at the reference plane for a standard power sensor, as well as the side-arm power when both the standard sensor and short foil are connected to the microcalorimeter, as described in [5,17]. The constant 𝑘FS is determined by evaluating the linearity of the thermopile. The foil short measurement method uses a thin shorting foil, thus nearly not changing the thermal properties of the power sensor, which is an advantage of this method. The drawback is, that it requires an additional measurement to determine the incident power. In conventional approaches, the foil short measurement must be repeated for each individual power sensor calibration [6]. However, the correction factor can be determined only once, as demonstrated in this work, by calculating the intrinsic correction factor 𝑔𝑐, which is independent of the power sensor. This approach enhances efficiency in the measurement process. The value of 𝑔𝑐 can be derived using Eq. (7) which corresponds to the parenthesized term on the right-hand side of Eq. (6). The intrinsic correction factor 𝑔𝑐 characterizes the power dissipation in the thermal isolation section independently of the sensor used. This assumes that the sensor’s thermal and electromagnetic interaction with the feeding waveguide remains consistent. However, if the sensor type differs significantly in thermal behavior or reflection coefficient, the correction factor 𝑔 may vary between different types of sensors. 𝑔𝑐=𝛥𝑒FS 𝑘FS𝑃iFS (1 + |𝛤FS|2)− 1 − |𝛤FS|2 1 + |𝛤FS|2(7) 3.3. VNA method The VNA method establishes an instrument-integrated approach to correction factor determination, as shown in Fig. 7. This setup allows the VNA to replace several discrete components, including the RF source, directional coupler, and monitoring system [18]. The VNA is used to measure wave parameters and incident power. A foil short is also employed to isolate reflection-related losses near the thermal isolation section. The intrinsic correction factor 𝑔𝑐 is determined based on the power dissipated in the thermal isolation section and the power incident on the foil short. The parameter 𝑔𝑐 is calculated using Eq. (8), as outlined in [9], 𝑔𝑐=𝑃FS 𝑃inc (1 + |𝛤FS|2)− 1 − |𝛤FS|2 1 + |𝛤FS|2(8) where 𝛤FS represents the reflection coefficient of the foil short, 𝑃inc is the incident power to the foil short, and 𝑃FS denotes the RF power dissipated in the foil and thermal isolation region. The first term in Eq. (8) corresponds to the power absorbed within the thermal isolation section, while the second term accounts for the loss associated with the foil short. The value of 𝑃FS is derived from the change in thermopile voltage, while 𝑃inc is computed using the 𝑏-wave parameter obtained from the VNA. The correction factor 𝑔 for the microcalorimeter is determined using Eq. (9), incorporating the reflection coefficient of the power sensor 𝛤S. 𝑔= 1 + 𝑔𝑐⋅ 1 + |𝛤S|2 1 − |𝛤S|2(9) The VNA method offers the advantage of reduced measurement time and simplified instrumentation in the determination of the correction factor. However, it also has the disadvantage of requiring an external RF source, coupler, and monitoring unit for effective efficiency measurements of a power sensor. While both the foil short and VNA methods utilize a reflective foil, they differ in several important aspects. One key difference lies in the determination of the incident power. In the foil short method, the incident power is determined using a directional coupler experiment and requires a separate measurement. In contrast, the VNA method determines the incident power directly by measuring the b-wave parameter within the VNA system. Another distinction concerns the output power level. The RF power output of a VNA is generally limited to around 0 dBm, and at higher frequencies, it may be lower. This limitation can restrict the measurement dynamic range, especially for sensors with low sensitivity. On the other hand, the foil short method typically employs a signal generator capable of delivering higher RF power levels (above 0 dBm), which is advantageous when characterizing sensors that require stronger excitation. 4. Results and discussion The correction factor of a R-500 waveguide microcalorimeter was experimentally determined using the offset short, foil short, and VNA methods across the frequency range of 40 to 60 GHz. Additionally, correction factor measurements were performed for ten waveguide microcalorimeters, ranging from R-500 to R-1.8k, covering a broad frequency range from 8.2 to 220 GHz. Each microcalorimeter’s correction factor was evaluated using at least one of the three methods. The offset short method is commonly used at PTB. However, the newly developed WR-5 microcalorimeter was evaluated using the foil short method. Measurement 257 (2026) 118865 5 W.K. Perangin-Angin et al. Fig. 4. Measurement setup for determining the correction factor of a microcalorimeter. Fig. 5. Offset short for R-500 waveguide microcalorimeter [6]. 4.1. Comparative analysis of correction factor determination methods Prior to the correction factor measurements (e.g., using the R-500 microcalorimeter), the RF power at the reference plane was set to 1 mW (0 dBm) by adjusting the output level of the signal generator. This power level was chosen to ensure a sufficient signal-to-noise ratio (SNR) for accurate thermopile voltage measurements, while also avoiding nonlinear thermal effects in the power sensors. Fig. 8 presents a comparison of the intrinsic correction factors (i.e., correction factors independent of the power sensor) obtained using all three methods for the R-500 microcalorimeter. The results demonstrate consistent agreement between the methods, with deviations not exceeding 0.006. The close alignment of the correction factors confirms the validity of each method when properly applied. The VNA and foil short methods, both utilizing the foil short, exhibited nearly identical correction factor trends, with discrepancies of less than 0.3% across most of the frequency range. A comparison of the correction factor 𝑔 obtained using the three methods is provided in [6]. The small variations observed in the VNA and foil short methods are primarily attributed to uncertainties in the measured reflection coefficients of the foil short. Ideally, a foil short reflects nearly all incident RF power (|𝛤FS| = 1). However, due to finite conductivity and interface imperfections, some power is either absorbed or lost. A comprehensive uncertainty analysis was conducted in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM) [19]. The expanded uncertainties (with a coverage factor of 𝑘 = 2, representing a 95% confidence level) of the intrinsic correction factor for each method are shown in Fig. 9. The offset short method demonstrated the lowest overall uncertainty, although the differences among the methods were not substantial. For the offset short technique, the dominant uncertainty source was the reflection coefficient of the offset short standards. In the foil short and VNA methods, the largest contribution originated from uncertainties in the reflection coefficient of the foil short. Other contributing factors include thermopile voltage measurements, bias voltage fluctuations, connector repeatability, and VNA measurement errors. The uncertainty associated with the intrinsic correction factor is found to be comparable to that of the overall correction factor. Table 1 presents the uncertainty budget for the intrinsic correction factor at 60 GHz, determined using the foil short method, and Table 2 shows the uncertainty budget for the offset short method. Measurement 257 (2026) 118865 6 W.K. Perangin-Angin et al. Table 1 Uncertainty budget for the intrinsic correction factor at 60 GHz, determined using the foil short method. Quantity Probability Type Uncertainty distribution contribution Repeatability Normal A 0.001239 Reflection coefficient Normal B 0.002795 of the foil short Thermopile voltage Normal B 0.000012 Bias voltage Normal B 0.000591 VNA noise Normal B 0.000598 VNA drift Normal B 0.000180 Combined standard 0.003175 uncertainty Expanded uncertainty, 0.0064 (k = 2) Table 2 Uncertainty budget for the intrinsic correction factor at 60 GHz, determined using the offset short method. Quantity Probability Type Uncertainty distribution contribution Repeatability Normal A 0.000476 Reflection coefficient Normal B 0.002651 of the offset short Thermopile voltage Normal B 0.000013 Bias voltage Normal B 0.000018 VNA noise Normal B 0.000011 VNA drift Normal B 0.000028 Combined standard 0.002694 uncertainty Expanded uncertainty, 0.0054 (k = 2) Fig. 6. Foil short for R-500 waveguide microcalorimeter [6]. 4.2. Correction factor behavior across waveguide bands (r-100 to R-1.8k) To extend the applicability of the correction factor determination methods beyond a single waveguide system, measurements were performed across ten waveguide microcalorimeters, covering a broad frequency range from 8.2 to 220 GHz. Over the years, PTB has developed a series of microcalorimeters as RF power standards, including R-100 (WR-90), R-140 (WR-62), R-220 (WR-42), R-320 (WR-28), R-400 (WR22), R-500 (WR-19), R-620 (WR-15), R-900 (WR-10), R-1.4k (WR-7), and R-1.8k (WR-5), each corresponding to distinct segments of the microwave and millimeter-wave spectrum. This comprehensive dataset supports the investigation of frequency-dependent behaviors and facilitates the evaluation of performance across a range of geometrically diverse microcalorimeter configurations. Table 3 shows a comparative analysis of the correction factor values for ten waveguide microcalorimeters developed at PTB. The results highlight the increasing challenges associated with RF losses at higher frequencies by showing how correction factors vary across different waveguide configurations. A gradual increase in correction factor values is observed as the operating frequency range increases. Each waveguide microcalorimeter used in this study is specifically designed for a particular frequency range, based on its waveguide dimensions, flange type, and thermal design. Therefore, differences in geometry, thermal response, and RF loss characteristics across the bands result in different correction factors. This trend reflects the growing impact of power losses in microcalorimeter components such as waveguide walls, connectors, and transitions at higher frequencies, which the correction factor is designed to compensate for. At higher frequency waveguide bands, the correction factor exhibits greater sensitivity to frequency variations. The R-1.8k band demonstrates the highest correction factor range, indicating the increased complexity and sensitivity involved in achieving accurate measurements in the sub-terahertz range. This currently represents one of the highest measurement frequency ranges for millimeter-wave power available among NMIs [20]. Furthermore, as the operating frequency increases, the heat distribution generated by RF dissipation within the waveguide becomes less uniform. This variability in thermal distribution amplifies nonlinearities in the thermopile response, which in turn affects the correction factor. Therefore, precise measurement techniques for determining the correction factor are essential for the accurate characterization of a microcalorimeter. 4.3. Effective efficiency determination The effective efficiency of a Hughes 45773H thermistor mount was calculated to assess the practical impact of the correction factor on power sensor calibration. Fig. 10 shows the measurement results of the Measurement 257 (2026) 118865 7 W.K. Perangin-Angin et al. Fig. 7. Schematic diagram of the microcalorimeter correction factor measurement using the VNA method. Table 3 Correction factor values for waveguide microcalorimeters developed at PTB. Microcaloriemeter Frequency range Intrinsic Correction factor correction factor R-100 8.2–12.4 GHz 0.00107–0.00191 1.0011–1.0020 R-140 12.4–18 GHz 0.00114–0.00210 1.0012–1.0022 R-220 18–26.5 GHz 0.00144–0.00354 1.0015–1.0037 R-320 26.5–40 GHz 0.00153–0.00421 1.0016–1.0044 R-400 33–50 GHz 0.00182–0.00554 1.0019–1.0058 R-500 40–60 GHz 0.00827–0.01209 1.0083–1.013 R-620 50–75 GHz 0.01191–0.01592 1.012–1.016 R-900 75–110 GHz 0.01487–0.02569 1.015–1.026 R-1.4k 110–170 GHz 0.01888–0.03821 1.020–1.040 R-1.8k 140–220 GHz 0.03872–0.05711 1.041–1.062 thermistor mount’s effective efficiency, derived from correction factors measured using the offset short method. Ideally, effective efficiency should approach unity and remain stable across frequencies. A perfectly absorbing sensor would yield 100% efficiency. In practice, however, efficiency varies with frequency and reflects the ability of the power sensor to absorb RF power. These variations are influenced by the sensor’s characteristics, as depicted in Fig. 10, where a gradual decline is observed at higher frequencies. Fig. 11 illustrates the difference in effective efficiency between the offset short method and the other two methods. The offset short method shows slightly higher values, while the foil short and VNA methods closely agree across most of the frequency range. The resulting effective Measurement 257 (2026) 118865 8 W.K. Perangin-Angin et al. Fig. 8. Comparison of intrinsic correction factors for the R-500 microcalorimeter. Fig. 9. Expanded uncertainty of the intrinsic correction factor of the R-500 microcalorimeter (coverage factor 𝑘 = 2, representing a 95% confidence level). efficiencies follow one another with differences remaining under 0.006, reflecting the variation in correction factors among the three methods. This alignment indicates the significant role of accurate correction factor measurement in achieving reliable power sensor calibration results. 5. Conclusion A comprehensive evaluation of correction factor determination for waveguide microcalorimeters operating across a broad frequency range from 8.2 to 220 GHz has been presented. The correction factor is a critical microcalorimeter parameter for accurately determining the effective efficiency in power sensor calibration, as it compensates for imperfections in the equivalence of the RF-DC substitution. Three established techniques, namely the offset short method, the foil short method, and the VNA method were investigated with experimental verification carried out using a R-500 rectangular waveguide microcalorimeter. The comparison demonstrates agreement among the methods. An improved implementation of the foil short method was proposed, offering a more efficient characterization process. The comparative analysis highlights Measurement 257 (2026) 118865 9