Calibration system and calibration method of directional coupler

Abstract

The invention discloses a calibration system and a calibration method of a directional coupler. The system comprises an input end assembly, a front-end monitoring assembly and a rear-end measuring assembly which are connected in sequence, the front-end monitoring assembly comprises a first directional coupler, a first power meter and a first matching load; the bandwidth of the first directional coupler comprises the frequency of a microwave signal source to be calibrated and the frequency of a corresponding first harmonic, and the frequency of a second harmonic corresponding to the frequency is outside the bandwidth of the first directional coupler; the rear-end measurement assembly comprises a second directional coupler, a second power meter, a second matching load and a high-power matching load, wherein the second directional coupler is provided with a reference directional coupler and a calibration directional coupler which are used for replacement; the bandwidth of the reference directional coupler is the same as that of the first directional coupler; the bandwidth of the directional coupler for calibration comprises the frequency of the microwave signal source to be calibrated but does not comprise the frequency of the first harmonic corresponding to the frequency, and a calibration factor is determined based on the reading of the power meter.

Description

Technical Field

[0001] The present invention relates to the technical field of microwave communications, and in particular to a calibration system and a calibration method for a directional coupler. Background Art

[0002] In the technical fields of wireless communication and radar communication, directional couplers can be used in wireless communication systems based on microwaves and millimeter waves. They are an important device in communication systems and are used for signal isolation, separation and mixing, such as power monitoring, source output power stabilization, signal source isolation, transmission and reflection frequency sweep testing, etc. The four-port coupler is often called a directional coupler because its coupled energy is directional. The four ports of the directional coupler are named input, isolation, through and coupling. The commonly used directional couplers are based on the quarter-wavelength impedance transformation theory. Since the length of the directional coupler is fixed, the directional coupler can only work in a certain frequency band. Some power calibration systems will include directional couplers. Active devices and nonlinear devices in the system will generate harmonics, which will be transmitted in the calibration system, resulting in deviations in the power measurement results. Since directional couplers of different bandwidths have different responses to harmonics, the deviation amplitude of power measurement is also different, so the measurement results need to be calibrated.

[0003] Current research mainly focuses on the suppression and control of harmonics. Reference 1 (H. Liu, M. Guan, X. Li and Z. Wang, "Coupled Line Forward Directional Coupler with Inherent Harmonics Suppression at 2f0," 2020 Cross Strait Radio Science & Wireless Technology Conference (CSRSWTC), Fuzhou, China, 2020, pp. 1-3) designed a compact coupler with harmonic suppression function, which achieves harmonic suppression by inserting open-circuit branches. Reference 2 (RN Simons and EG Wintucky, "Waveguide multimode directional coupler for harvesting harmonic power from the output of traveling-wave tube amplifiers," 2017 IEEE MTT-S International Microwave Symposium (IMS), Honololu, HI, USA, 2017, pp. 380-383.) introduces a new design method of waveguide multimode directional coupler (MDC), which uses a multimode directional coupler to separate harmonics from the fundamental wave, and can amplify the harmonics and use them as a signal source for millimeter wave propagation research. Regarding power calibration, Reference 3 (Yu Meng, Lan Yanmei. RF high-power calibration system with high harmonic suppression performance [J]. Foreign Electronic Measurement Technology, 2019, 38 (01): 116-121. DOI: 10.19652 / j.cnki.femt.1801107.) introduces a RF high-power calibration system with high harmonic suppression performance based on high power transfer standards and using high power filters.

[0004] The load can absorb microwave power in the entire frequency band, but the directional coupler can only work in a certain frequency band, so the traditional directional coupler power calibration system cannot accurately perform power calibration in the entire frequency band. Summary of the invention

[0005] In view of this, the present invention provides a calibration system for a directional coupler, the system comprising an input terminal component, a front-end monitoring component, and a back-end measurement component connected in sequence; wherein,

[0006] The input component is the microwave signal source to be calibrated;

[0007] The front-end monitoring component includes: a first directional coupler, a first power meter, and a first matching load; wherein the input end of the first directional coupler is connected to the output end of the input end component, the first power meter is connected to the coupling end of the first directional coupler; the first matching load is connected to the isolation end of the first directional coupler;

[0008] The bandwidth range of the first directional coupler includes the frequency of the microwave signal source to be calibrated and the frequency of the first harmonic corresponding to the frequency, and the frequency of the second harmonic corresponding to the frequency is outside the bandwidth of the first directional coupler;

[0009] The back-end measurement component includes: a second directional coupler, a second power meter, a second matching load, and a high-power matching load; wherein the input end of the second directional coupler is connected to the through end of the first directional coupler, the second power meter is connected to the coupling end of the second directional coupler, the second matching load is connected to the isolation end of the second directional coupler, and the high-power matching load is connected to the through end of the second directional coupler;

[0010] The second directional coupler includes a reference directional coupler for replacement and a calibration directional coupler; wherein the bandwidth range of the reference directional coupler is the same as the bandwidth range of the first directional coupler; the bandwidth range of the calibration directional coupler includes the frequency of the microwave signal source to be calibrated but does not include the frequency of the first harmonic corresponding to the frequency.

[0011] Furthermore, at least one first attenuator is added between the first directional coupler and the first power meter to match the measurement range of the first power meter with the signal power output by the input-end component.

[0012] Furthermore, at least one second attenuator is added between the second directional coupler and the second power meter to match the measurement range of the second power meter with the power output by the first directional coupler.

[0013] Further, a calibration factor is determined based on the reading of the first power meter and the reading of the second power meter.

[0014] Furthermore, a vector network analyzer is used to measure S parameters of the first directional coupler and the second directional coupler.

[0015] Furthermore, a calibration factor is determined based on a reading of the first power meter, a reading of the second power meter, and measured S parameters of the first directional coupler and the second directional coupler.

[0016] The present invention also provides a method for calibrating a directional coupler, comprising the following steps:

[0017] Step 1, determining the frequency point m of the microwave signal source to be calibrated and the frequency corresponding to the frequency point m; m = 1, 2, ... M, M is the total number of frequency points to be measured;

[0018] Step 2, based on the frequencies corresponding to the determined M frequency points, determine M first directional couplers and a group of second directional couplers corresponding to the bandwidth of each first directional coupler; wherein,

[0019] The bandwidth of the mth first directional coupler includes the frequency corresponding to the frequency point m and the first harmonic corresponding to the frequency, and the second harmonic corresponding to the frequency is outside the bandwidth of the mth first directional coupler;

[0020] The m-th group of second directional couplers at least includes: an m-th reference directional coupler and an m-th calibration directional coupler; wherein the bandwidth range of the m-th reference directional coupler is the same as that of the m-th first directional coupler; the bandwidth of the m-th calibration directional coupler includes the frequency corresponding to the frequency point m but does not include the frequency of the first harmonic corresponding to the frequency;

[0021] Step 3, let m=1, that is, select the first first directional coupler and the first group of second directional couplers;

[0022] Step 4, using the mth first directional coupler and the mth reference directional coupler to build the calibration system as described above;

[0023] Step 5, input the microwave signal of the frequency point m to be calibrated, read the power reading P1m of the microwave signal in the first power meter and the power reading P2m1 of the microwave signal in the second power meter and record them;

[0024] Step 6, keeping the mth first directional coupler unchanged, replacing the mth reference directional coupler with the mth calibration directional coupler, adjusting the power of the input microwave signal so that the power reading P1m in the first power meter remains unchanged, and reading and recording the power reading P2m2 in the second power meter;

[0025] Step 7, let m=m+1, that is, select the m+1th first directional coupler and the m+1th group of second directional couplers, and repeat steps 4, 5, and 6 until the measurement of M first directional couplers is completed;

[0026] Step 8, determining a calibration factor based on the power reading P1m in the first power meter, the power reading P2m2 in the second power meter, and the power reading P2m2.

[0027] Furthermore, step 8 is specifically as follows:

[0028] Step 81, using a vector network analyzer to measure the S parameters of all directional couplers;

[0029] Step 82, based on the power readings in the first power meter and the power readings in the second power meter read each time, calculate the net feed power of the directional coupler taking the mismatch factor into account by the following formula:

[0030]

[0031] Among them, Γ s is the reflection coefficient of the connecting component, Γ L is the reflection coefficient of the through-end load of the directional coupler, S21 is the transmission loss between the input end and the through-end, S31 is the attenuation coefficient between the input end and the coupled end, S23 is the loss from the coupled end to the through-end, S33 is the return loss of the coupled end, S22 is the return loss of the through-end, and S32 is the transmission loss from the through-end to the coupled end; P sm is the power reading of the second power meter;

[0032] Step 83, using the calculated net feed-in power P netm Calculate the calibration factor at frequency m:

[0033]

[0034] Among them, P netm1 With P netm2 are the reference net feed-in power and calibration net feed-in power corresponding to frequency m, respectively. netm1 Substituting P2m1 into the above formula, we can calculate P netm2 It is calculated by substituting P2m2 into the above formula.

[0035] The directional coupler calibration system and calibration method constructed by the present invention use directional couplers with different bandwidths to quantitatively measure the specific values ​​of harmonics on power measurement, and provide calibration factors of directional couplers at different frequencies, thereby reducing the influence of harmonics on measurement results and making the measurement results more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a structural schematic diagram of a calibration system for a directional coupler of the present invention.

[0037] Figure 2 It is a flowchart of the calibration method of the present invention. DETAILED DESCRIPTION

[0038] The calibration system of the directional coupler of the present invention is used to calibrate the influence of harmonics on the measurement in the power measurement system including the directional coupler. The calibration system includes a plurality of coaxial directional couplers with different bandwidths, two power meters, two matching loads and a large power capacity matching load. The total input power is controlled to be constant, and the calibration factor is obtained by calculating the difference between two power meter readings.

[0039] like Figure 1 As shown, the calibration system of the directional coupler of the present invention includes three parts connected in sequence: an input end component, a front-end monitoring component and a back-end measurement component.

[0040] The input component is a microwave signal source to be calibrated. In one embodiment of the present invention, a standard microwave signal source and a radio frequency power amplifier connected in sequence are included to simulate the microwave signal source to be calibrated. The power amplifier should operate in a linear region to avoid nonlinear distortion.

[0041] The front-end monitoring component includes: a directional coupler 1, a power meter 1, an attenuator 1 and a matching load. The input end of the directional coupler 1 is connected to the output end of the input end component, the power meter 1 is connected to the coupling end of the directional coupler 1, the measurement range of the power meter 1 should match the signal power output of the input end component, in order to prevent the measured power from exceeding the measurement range of the power meter 1, an attenuator 1 is added between the directional coupler 1 and the power meter 1; the matching load 1 is connected to the isolation end of the directional coupler 1.

[0042] The bandwidth range of the directional coupler 1 includes the frequency of the microwave signal source to be calibrated and the frequency of the first harmonic corresponding to the frequency, and the frequency of the second harmonic corresponding to the frequency is outside the bandwidth of the directional coupler 1. Preferably, the higher the out-of-band suppression of the second harmonic of the point frequency by the directional coupler 1 is, the better.

[0043] The back-end measurement components include: a directional coupler 2, a power meter 2, a matching load 2, and a high-power matching load. The input end of the directional coupler 2 is connected to the through end of the directional coupler 1, the power meter 2 is connected to the coupling end of the directional coupler 2, the measurement range of the power meter 2 should match the power output of the directional coupler 1, in order to prevent the measured power from exceeding the measurement range of the power meter 2, an attenuator 2 is added between the directional coupler 2 and the power meter 2, the matching load 2 is connected to the isolation end of the directional coupler 2, and the high-power matching load is connected to the through end of the directional coupler 2.

[0044] The directional coupler 2 includes a reference directional coupler 21 for replacement and a calibration directional coupler 22; wherein the bandwidth range of the reference directional coupler 21 is the same as the bandwidth range of the directional coupler 1; the bandwidth range of the calibration directional coupler 22 includes the frequency of the microwave signal source to be calibrated but does not include the frequency of the first harmonic corresponding to the frequency. Preferably, the calibration directional coupler 22 suppresses the first harmonic out-of-band of the frequency as high as possible. When calibrating, first use the reference directional coupler 21 to build a Figure 1 The calibration system shown in FIG. 1 reads the readings of power meter 1 and power meter 2; then replaces the reference directional coupler 21 with the calibration directional coupler 22 to build a calibration system as shown in FIG. Figure 1Calibration system shown, taking readings from Power Meter 1 and Power Meter 2.

[0045] Based on the calibration system of the directional coupler of the present invention, the calibration method of the directional coupler of the present invention comprises the following steps:

[0046] Step 1, determine the frequency point m of the microwave signal source to be calibrated and the frequency corresponding to the frequency point m; m = 1, 2, ... M, M is the total number of frequency points to be measured.

[0047] Step 2: based on the determined frequencies corresponding to the M frequency points to be calibrated, select M directional couplers 1 and a group of directional couplers 2 corresponding to the bandwidth of each directional coupler 1 .

[0048] The bandwidth of the mth directional coupler 1 should include the frequency corresponding to the frequency point m and the first harmonic corresponding to the frequency, and the second harmonic corresponding to the frequency should be outside the bandwidth of the mth directional coupler 1. Preferably, the mth directional coupler 1 has the higher out-of-band suppression of the second harmonic of the frequency point, the better.

[0049] The m-th group of directional couplers 2 at least includes: a reference directional coupler 21m and a calibration directional coupler 22m. The reference directional coupler 21m has the same bandwidth range as the m-th directional coupler 1, and serves as a calibration reference; the bandwidth of the calibration directional coupler 22m includes the frequency corresponding to the frequency point m but does not include the frequency of the first harmonic corresponding to the frequency point. Preferably, the calibration directional coupler 22m has the higher out-of-band suppression of the first harmonic of the frequency point, the better.

[0050] Step 3, let m=1, that is, select the first directional coupler 1 and the first group of directional couplers 2;

[0051] Step 4, follow Figure 1 The m-th directional coupler 1 and the m-th reference directional coupler 21m are connected in the manner shown;

[0052] Step 5: input the microwave signal of the frequency point m to be calibrated, read the power readings P1m and P2m1 of the microwave signal in the power meter 1 and the power meter 2, and record them.

[0053] Step 6, keep the mth directional coupler 1 unchanged, replace the reference directional coupler 21m with the calibration directional coupler 22m, adjust the power of the input microwave signal so that the power reading P1m of the power meter 1 remains unchanged, and read and record the power reading P2m2 of the power meter 2.

[0054] Step 7, let m=m+1, that is, select the m+1th directional coupler 1 and the m+1th group of directional couplers 2, and repeat steps 4, 5, and 6 until the measurement of M directional couplers 1 is completed.

[0055] Step 8: Determine the calibration factor at frequency point m based on the power reading P1m of power meter 1 and the power readings P2m1 and P2m2 of power meter 2.

[0056] In one embodiment of the present invention, the calibration factor at the frequency point m is determined directly using the power reading P1m of the power meter 1 and the power readings P2m1 and P2m2 of the power meter 2.

[0057] In another embodiment of the present invention, the calibration method of the present invention further includes measuring the S parameters of the directional coupler to eliminate the loss generated when the signal is transmitted through different directional couplers. The S parameters of all directional couplers (including directional coupler 1 and directional coupler 2) can be measured using a vector network analyzer.

[0058] Based on each measurement result, the net feed power of the directional coupler considering the mismatch factor is calculated by the following formula (Lin Haoyu, Huang Pan, Xie Jing, et al. A net feed power measurement method based on a single directional coupler [J]. Metrology Science and Technology, 2024, 68(05): 11-16+76):

[0059]

[0060] Where P s is the power reading of power meter 1 or power meter 2. The S parameter can be measured by a network analyzer. s is the reflection coefficient of the connecting component, Γ L is the reflection coefficient of the through-end load of the directional coupler, S21 is the transmission loss between the input end and the through-end, S31 is the attenuation coefficient between the input end and the coupled end, S23 is the loss from the coupled end to the through-end, S33 is the return loss of the coupled end, S22 is the return loss of the through-end, and S32 is the transmission loss from the through-end to the coupled end.

[0061] When calculating the net input power at the access point of directional coupler 2, P s is the power reading of power meter 1. When calculating the net feed-in power at the high power matching load access point, P s is the power reading of power meter 2.

[0062] Based on the calculated net injected power, calculate the calibration factor at frequency m:

[0063]

[0064] Among them, P netm1 With P netm2 are the reference net feed-in power and calibration net feed-in power corresponding to frequency m, respectively. netm1 Substituting P2m1 into the above formula, we can calculate P netm2It is calculated by substituting P2m2 into the above formula.

[0065] The calibration system of the directional coupler constructed by the present invention quantitatively measures the specific value of harmonics on power measurement by using directional couplers of different bandwidths. Combined with the net input power formula, the calibration factor of the directional coupler at different frequencies is given. The influence of harmonics on the measurement results is reduced, making the measurement results more accurate.

[0066] The present invention is described in more detail below by means of an embodiment.

[0067] Example

[0068] The calibration factors of each frequency point are determined by measuring the frequencies of 2GHz, 1GHz and 500MHz. The maximum output power of the RF power amplifier is 250w. Under normal circumstances, the output power of the RF power amplifier is kept at about 100W. The coupling coefficient of directional coupler 1 and directional coupler 2 is -30dB, the attenuation coefficient of attenuator 1 and attenuator 2 is -20dB and -10dB respectively, and the two matching loads are 50 ohms.

[0069] The coupling coefficients of directional couplers 1 and 2 used in the first group of experiments were both -30dB. After connecting the instruments, the input signal power was adjusted so that the reading of power meter 2 was 0dBm. At this time, the reading of power meter 1 was 10.70dBm. The back-end directional coupler 0690 (2GHz-4GHz) was replaced with 0531 (1GHz-2GHz), and the input signal power was adjusted again so that the reading of power meter 1 became 10.70dBm again. The reading of power meter 2 was recorded at this time.

[0070] The coupling coefficients of directional couplers 1 and 2 used in the second group of experiments were both -20 dB. To prevent the power meter from exceeding the range, an additional -10 dB attenuator was added at the connection between the power meter and directional couplers 1 and 2.

[0071] Table 1 shows the measurement results of the directional coupler when the input signal frequency is 2 GHz.

[0072] Table 1 2GHz directional coupler measurement results

[0073]

[0074]

[0075] Table 2 shows the measurement results of the directional coupler when the input signal frequency is 1 GHz.

[0076] Table 2 1GHz directional coupler measurement results

[0077]

[0078] Table 3 shows the measurement results of the directional coupler when the input signal frequency is 500MHz.

[0079] Table 3 500MHz directional coupler measurement results

[0080]

[0081] Table 4 shows the calculated calibration factors for 2 GHz, 1 GHz, and 500 MHz.

[0082] Table 4 Calibration factors

[0083] <![CDATA[P netm1 (-30dB)]]> <![CDATA[P netm2 (-30dB)]]> <![CDATA[P netm1 (-20dB)]]> <![CDATA[P netm2 (-20dB)]]> η 2GHz 98.401W 97.202W 99.341W 97.612W 98.804 1GHz 99.23W 97.732W 98.574W 97.129W 98.524 500MHz 97.499W 96.085W 97.647W 96.035W 98.45

[0084] In summary, the present invention constructs a calibration system for directional couplers, and quantitatively measures the specific values ​​of harmonic power measurement using directional couplers of different bandwidths. Combined with the net input power formula, the calibration factors of the directional couplers at different frequencies of the device are given.

[0085] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments can still be modified, or some or all of the technical features can be replaced by equivalents, and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A calibration system for a directional coupler, characterized in that: The system includes an input terminal component, a front-end monitoring component, and a back-end measurement component connected in sequence; wherein, The input component is the microwave signal source to be calibrated; The front-end monitoring component includes: a first directional coupler, a first power meter, and a first matching load; wherein the input end of the first directional coupler is connected to the output end of the input end component, the first power meter is connected to the coupling end of the first directional coupler; the first matching load is connected to the isolation end of the first directional coupler; The bandwidth range of the first directional coupler includes the frequency of the microwave signal source to be calibrated and the frequency of the first harmonic corresponding to the frequency, and the frequency of the second harmonic corresponding to the frequency is outside the bandwidth of the first directional coupler; The back-end measurement component includes: a second directional coupler, a second power meter, a second matching load, and a high-power matching load; wherein the input end of the second directional coupler is connected to the through end of the first directional coupler, the second power meter is connected to the coupling end of the second directional coupler, the second matching load is connected to the isolation end of the second directional coupler, and the high-power matching load is connected to the through end of the second directional coupler; The second directional coupler includes a reference directional coupler for replacement and a calibration directional coupler; wherein the bandwidth range of the reference directional coupler is the same as the bandwidth range of the first directional coupler; the bandwidth range of the calibration directional coupler includes the frequency of the microwave signal source to be calibrated but does not include the frequency of the first harmonic corresponding to the frequency.

2. The calibration system according to claim 1, characterized in that At least one first attenuator is added between the first directional coupler and the first power meter to match the measurement range of the first power meter with the signal power output by the input-end component.

3. The calibration system according to claim 1, characterized in that At least one second attenuator is added between the second directional coupler and the second power meter to match the measurement range of the second power meter with the power output by the first directional coupler.

4. The calibration system according to claim 1, characterized in that A calibration factor is determined based on the reading of the first power meter and the reading of the second power meter.

5. The calibration system according to claim 1, characterized in that The S parameters of the first directional coupler and the second directional coupler are measured using a vector network analyzer.

6. The calibration system according to claim 5, characterized in that A calibration factor is determined based on the reading of the first power meter and the reading of the second power meter and the measured S parameters of the first directional coupler and the second directional coupler.

7. A method for calibrating a directional coupler, characterized in that: The method comprises the following steps: Step 1, determining the frequency point m of the microwave signal source to be calibrated and the frequency corresponding to the frequency point m; m = 1, 2, ... M, M is the total number of frequency points to be measured; Step 2, based on the frequencies corresponding to the determined M frequency points, determine M first directional couplers and a group of second directional couplers corresponding to the bandwidth of each first directional coupler; wherein, The bandwidth of the mth first directional coupler includes the frequency corresponding to the frequency point m and the first harmonic corresponding to the frequency, and the second harmonic corresponding to the frequency is outside the bandwidth of the mth first directional coupler; The m-th group of second directional couplers at least includes: an m-th reference directional coupler and an m-th calibration directional coupler; wherein the bandwidth range of the m-th reference directional coupler is the same as that of the m-th first directional coupler; the bandwidth of the m-th calibration directional coupler includes the frequency corresponding to the frequency point m but does not include the frequency of the first harmonic corresponding to the frequency; Step 3, let m=1, that is, select the first first directional coupler and the first group of second directional couplers; Step 4, using the mth first directional coupler and the mth reference directional coupler to build the calibration system as claimed in any one of claims 1 to 6; Step 5, input the microwave signal of the frequency point m to be calibrated, read the power reading P1m of the microwave signal in the first power meter and the power reading P2m1 of the microwave signal in the second power meter and record them; Step 6, keeping the mth first directional coupler unchanged, replacing the mth reference directional coupler with the mth calibration directional coupler, adjusting the power of the input microwave signal so that the power reading P1m in the first power meter remains unchanged, and reading and recording the power reading P2m2 in the second power meter; Step 7, let m=m+1, that is, select the m+1th first directional coupler and the m+1th group of second directional couplers, and repeat steps 4, 5, and 6 until the measurement of M first directional couplers is completed; Step 8: Determine a calibration factor based on the power reading P1m of the first power meter, the power readings P2m1 and P2m2 of the second power meter.

8. The calibration method according to claim 7, characterized in that: Step 8 is as follows: Step 81, using a vector network analyzer to measure the S parameters of all directional couplers; Step 82, based on the power readings in the first power meter and the power readings in the second power meter read each time, calculate the net feed power of the directional coupler taking the mismatch factor into account by the following formula: Among them, Γ s is the reflection coefficient of the connecting component, Γ L is the reflection coefficient of the through-end load of the directional coupler, S21 is the transmission loss between the input end and the through-end, S31 is the attenuation coefficient between the input end and the coupled end, S23 is the loss from the coupled end to the through-end, S33 is the return loss of the coupled end, S22 is the return loss of the through-end, and S32 is the transmission loss from the through-end to the coupled end; P sm is the power reading P2m1 or P2m2 of the second power meter; Step 83, using the calculated net feed-in power P netm Calculate the calibration factor at frequency m: Among them, P netm1 With P netm2 are the reference net feed-in power and calibration net feed-in power corresponding to frequency m respectively; P netm1 Substituting P2m1 into the above formula, we can calculate P netm2 It is calculated by substituting P2m2 into the above formula.

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