Research on Accurate Measurement of Power Value in Radio Frequency

1. Introduction

With the rapid development of the communications and radio and television industries, the requirements for accurate measurement of RF power are getting higher and higher, especially for transmitter testing, which is basically required to be tested on site. The simplest method for RF power testing is to use a power meter method, but the measurement uncertainty can only reach 8%~10%, which sometimes cannot meet the requirements. For this reason, we use a combination of a high-power attenuator and a small power meter to complete the measurement of RF power, and the measurement uncertainty reaches 5%, which can meet the current requirements of most RF power measurements.

2. Solution Selection

We chose Weinschel Crop's high-power attenuator 40-40-43 and R/S's power meter NRVS to form this measurement system. The high-power attenuator 40-40-43 is a fixed attenuator with a 40dB, a maximum continuous wave input of 150W, and an operating frequency range of DC to 1.5GHz. The power meter NRVS has a measurement range of 10MHz to 18GHz and 1nW to 20mW. The measurement range of the entire device is designed to be frequency: 10MHz to 1GHz, power: <50W.

1. Measurement principle

The measurement principle of this method is shown in Figure 1.

In the figure:

PS is the net power absorbed by the small power seat;

PL is the net power absorbed at the input of the high-power attenuator;

PG0 is the output power of the measured signal source when it is connected to a non-reflective load;

ΓS is the reflection coefficient of the input end of the low-power socket;

ΓL is the reflection coefficient at the input of the attenuator;

ΓG is the reflection coefficient at the output end of the measured signal source.

Taking the attenuator as a two-port network, the non-reflective load output power PG0 of the measured signal can be expressed as follows:

Where S11, S12, S21, and S22 are the four scattering parameters of the attenuator.

According to the definition of attenuation:

In the above formula, the mismatch term is represented by M, that is,

Formula (4) can be rewritten as

Assume PbS is the DC (or audio) replacement power of the small power meter, K is the calibration factor of the small power socket. Then the net power PS can be expressed by the following formula:

It can be seen that if the attenuation A' of the attenuator and the calibration factor K of the low-power socket are known, the power PG0 can be obtained by replacing the power PbS.

2. Measurement plan

The calibration values ​​of the attenuator and power meter in this measurement system are shown in Table 1 and Table 2, where UA′M is the expanded uncertainty of the attenuator calibration value, and UK is the expanded uncertainty of the power seat calibration factor calibration value.

Considering that the attenuation of the attenuator will change with the input power, when calibrating it with the attenuation standard, the measurement is performed when a small power signal is input. In actual measurement, a high power signal is input, so the uncertainty it brings to the measurement result must be considered.

Weinschel Company has given the relationship between the power and the attenuation value when using the high-power attenuator 40-40-43, as shown in the following formula:

ΔA<0.0001A·P ( dB) ( 8)

Where ΔA is the attenuation change of the attenuator: A is the attenuation of the attenuator: P is the input power of the attenuator. According to the formula, when the attenuation is 40dB and 50W, the attenuation change is less than 0.2dB.

Considering that the attenuation change given by the manufacturer is relatively conservative, and the attenuation change increases with the increase of the passing power, we measured the attenuation of the attenuator at room temperature and after passing a 50W power signal for a long time.

Table 3 shows the attenuation value of the attenuator measured by a network analyzer at room temperature and after passing 50W power. UA′T in the table is the standard uncertainty of A′ caused by 50W input power, assuming that it obeys uniform distribution.

From the previous analysis, it can be obtained that the measurement uncertainty of PG0 is calculated using formula (7):

uP is the standard uncertainty of the PG0 measurement result; UA′M is the standard uncertainty of the high power attenuator calibration value; UA′T is the standard uncertainty of the attenuation change when the high power attenuator measures a high power signal; uS is the standard uncertainty of the PS measurement value; uM is the standard uncertainty of the system mismatch.

For the NRVS small power meter, the standard uncertainty of its PS measurement value is expressed by formula (10), and the specific values ​​are shown in Table 2.

Where: uPbs is the standard uncertainty of the DC replacement power of the small power seat, which is <0.3% for the NRVS small power meter; uK is the standard uncertainty of the calibration factor of the small power seat.

The standard uncertainty of the attenuator includes two parts. One part is the standard uncertainty of the attenuator at room temperature, as shown in Table 1. The other part is the uncertainty of the attenuation caused by the temperature rise after the attenuator inputs a high-power signal when performing high-power measurement. This part of the data is shown in Table 3.

The uncertainty caused by mismatch is calculated by equation (11):

In the formula: ΓG = 0.3 is the reflection coefficient of the measured signal; ΓS = 0.02 is the reflection coefficient of the input end of the low-power socket; S11<0. 0050 is the input reflection coefficient; S12 ≈0.01 is the reverse transmission coefficient; S21 ≈0.01 is the forward transmission coefficient; S22<0.005 is the output reflection coefficient.

According to formula (11), we can get: UM <0. 32% For UA′M, due to (k= 2), uA′M = UA′M/ 2. For detailed data, see Table 1. For US, due to (k= 2), uS = US / 2. For detailed data, see Table 2. For uA′T, see Table 3. For UM, due to (k= √2), uM = UM / 2.

According to formula (9), the standard uncertainty up of power measurement can be obtained as shown in Table 4. Taking k = 2 and the confidence level of 95%, the expanded uncertainty up is shown in Table 4.

Conclusion

After measurement and uncertainty analysis, the measurement uncertainty of the device is less than 5%. It is a better method to accurately measure the power value in radio frequency.