One way analysis of variance for parameter S of isolator and regression analysis to the correlation between parameter S and ACPR

Abstract

In the design of the single board of mobile communication, isolator is often used in between the amplifier stage and the drive stage to enhance the interaction between circuits and to improve the adjacent channel power ratio (ACPR) of power amplifier channel and other wireless performance indexes. In this paper, the one way analysis of variance (ANOVA) was used to study whether there is indicator difference in single board when using different isolatorfirstly. Then, the regression analysis method was employed to verify the correlation between $y$ (ACPR of the single board of radio frequency power amplifier) and $x$ (parameters S11 or S12 of isolator). Finally, it concluded that the ACPR values may be affected by different types of isolators, and there is no significant univariate linear fitting relationship between the parameters S11/S12 of isolators and the ACPR of single boards.

Keywords

Isolator ACPR parameter S one way analysis of variance regression analysis

1. Introduction

The vender provided 6 groups of isolators, TYPE1 $\sim$ TYPE6 (which was sampled randomly in the same batch), with 5 samples in each group. After welding them onto the single board of radio frequency power amplifier in the production line, we tested the ACPR [1, 2] (adjacent channel power ratio) indexes of the single board under each isolator (the single board of radio frequency power amplifier used in outdoor units of TD [3, 4, 5]) by using automatic testing software.

2. Objective

1)
Apply the one way analysis of variance (ANOVA) to study whether there is index difference among the TLPB single boards with different isolators;
2)
Use the regression analysis method to verify whether there is certain relationship between the parameters S11 and S12 of isolators [6] and the ACPR of the single board of radio frequency power amplifier (i.e., to study the correlation between $y$ (ACPR) and $x$ (S11 or S12) [7]).
3)
One way ANOVA [8, 9] is a statistical method to compare the mean difference between two groups or above.
4)
Regression analysis [10, 11, 12] is a method which, based on a group of data, determines the functional relation among variables and tests statistically the credibility of the relational expression. It has been widely employed for empirical formulas and determining the best production conditions.

3. Steps

3.1 Hypothesis test

1)
Propose the null hypothesis $H_{0}$ and alternative hypothesis $H_{1}$ , and specify the significance level;
2)
Stability analysis to the measured data;
3)
Normality analysis to the measured data;
4)
Equal variance analysis to the measured data;
5)
Make 1 way ANOVA analysis;
6)
Make statistical decision.

3.2 Regression analysis

1)
Make data analysis of residual and relativity;
2)
Obtain the conclusions.

Figure 1.
Testing chart of the tested object.

4. Experimental data acquisition and analysis

4.1 Testing chart of ACPR indexes of single board

Testing chart of the tested object is shown in Fig. 1. Brief explanation: operations on production line are to control the spectrum analyzer and signal sources through background computer software, and test automatically the ACPR indexes of the single board of radio frequency power amplifier, thus data acquisition has nothing to do with human factors.

4.2 Data acquisition

There are 6 types of isolators: TYPE1 $\sim$ TYPE6, 5 for each type, tested on 1# $\sim$ 5# single boards respectively, for each of which there are three frequency points to be tested: 2010 MHz, 2017 MHz, 2025 MHz.

For simplification, we only analyzed the ACLR (Adjacent Channel Leakage Ratio) of frequency point 2017 MHz.

Figure 2.

Data stability test.

4.3 Data analysis

4.3.1 Propose the hypothesis testing proposition

Firstly, it can confirm that all data have been acquired under exactly the same testing conditions (including environment and testing method) based on testing at production line, which is to say, the MSA (Measurement System Analysis) [4] meets the requirement. Therefore, we assumed that:

Null hypothesis $H_{0}$ [13]: the ACPR values of 6 types of TLPB single boards using different types of isolators are not distinctly different, namely: $\mu_{1}=\mu_{2}=\mu_{3}=\mu_{4}=\mu_{5}=\mu_{6}$ ;

Alternative hypothesis $H_{1}$ : the ACPR values of 6 types of TLPB single boards using different types of isolators are distinctly different, namely: among $\mu_{1},\mu_{2},\mu_{3},\mu_{4},\mu_{5}$ and $\mu_{6}$ , at least one group is different from others.

We set significance level $*=$ 0.05.

For simplification, we have only drawn the figure of TYPE1 in terms of stability and normality by Minitab [14, 15, 16], because it is similar to those of TYPE2 $\sim$ TYPE6.

Table 1
P_value of TYPE1–6

	TYPE1	TYPE2	TYPE3	TYPE4	TYPE5	TYPE6
P_value	0.508	0.247	0.355	0.188	0.532	0.477

Figure 3.

Data normality test.

Figure 4.

Data variance consistency test.

4.3.2 Stability analysis

Data stability test is shown in Fig. 2.

Conclusion: Based on the same principle, it can be seen from Fig. 2 that the testing data of TYPE1 $\sim$ TYPE6 show no abnormity and the process is stable and controllable.

4.3.3 Normality analysis

Normality test is shown in Fig. 3 and Table 1.

Conclusion: From Fig. 3 and Table 1, $P$ is greater than 0.05, therefore, although the quantity of the 6 groups of data is relatively small, it can be regarded approximately as normal distribution.

4.3.4 Variance consistency test

Data variance consistency test is shown in Fig. 4.

Conclusion: Fig. 4, integrated with P_value $=$ 0.979 $>$ 0.05, shows that the variation is the same.

Figure 5.

One way variance test to the testing data.

4.3.5 One way ANOVA

4.3.5.1 Residual analysis in ANOVA

Set the confidence level as 95%; One way variance test to the testing data is shown in Fig. 5.

One-way ANOVA: TLPB versus NO

S $=$ 2.087, R-Sq $=$ 9.27%, R-Sq (adj) $=$ 0.00%.
Source	DF	SS	MS	F	P
NO	5	10.69	2.14	0.49	0.780
Error	24	104.58	4.36
Total	29	115.27

Individual 95% CIs for mean based on pooled StDev
Pooled StDev $=$ 2.087, $P$ is greater than 0.05 and $F$ is approximately 1.
Level	$N$	Mean	StDev	—–+———+———+———+—-
1	5	52.240	2.060	(———–*————)
2	5	52.438	1.821	(———–*————)
3	5	52.412	1.632	(———–*————)
4	5	53.470	2.266	(———–*————)
5	5	53.246	2.203	(———–*————)
6	5	53.802	2.436	(———–*————)
				—–+———+———+———+—-
				51.0 52.5 54.0 55.5

Figure 6.

Main effect graph in one way.

Figure 7.

Inter-group effect graph in one way.

Conclusion: Since $P=$ 0.780 $>$ 0.05, and F-Test $=$ 0.49 which is approximately 1.00, this shows that the null hypothesis is not denied, i.e., the mean values in ACPR data of the 6 groups of TLPB single boards with different isolators show no differences.

4.3.5.2 Main effect graph and inter-group analysis in ANOVA

The main effect graph in one way ANOVA is shown in Fig. 6, and the inter-group effect graph in one way ANOVA is shown in Fig. 7.

Conclusion: It can be seen from the Figs 6 and 7 that, different types of isolators may affect the ACPR values.

4.3.5.3 Multiple comparisons in ANOVA

Using Fisher’s method to compare can easily find out the difference among mean values, although there is high risk of wrong confirmation.

Fisher 95% Individual Confidence Intervals

All Pair wise Comparisons among Levels of NO

Simultaneous confidence level $=$ 66.17%

It shows the similarity degree of the 6 groups of data in Fisher comparison.

NO $=$ 1 subtracted from:

NO	Lower	Center	Upper	——+———+———+———+—
2	$-$ 2.527	0.198	2.923	(———-*———-)
3	$-$ 2.553	0.172	2.897	(———-*———-)
4	$-$ 1.495	1.230	3.955	(———-*———-)
5	$-$ 1.719	1.006	3.731	(———-*———-)
6	$-$ 1.163	1.562	4.287	(———-*———-)
				——+———+———+———+—
				$-$ 2.5 0.0 2.5 5.0

NO $=$ 2 subtracted from:

NO	Lower	Center	Upper	——+———+———+———+—
3	$-$ 2.751	$-$ 0.026	2.699	(———-*———-)
4	$-$ 1.693	1.032	3.757	(———-*———-)
5	$-$ 1.917	0.808	3.533	(———-*———-)
6	$-$ 1.361	1.364	4.089	(———*———-)
				——+———+———+———+—
				$-$ 2.5 0.0 2.5 5.0

NO $=$ 3 subtracted from:

NO	Lower	Center	Upper	——+———+———+———+—
4	$-$ 1.667	1.058	3.783	(———-*———-)
5	$-$ 1.891	0.834	3.559	(———-*———-)
6	$-$ 1.335	1.390	4.115	(———-*———-)
				——+———+———+———+—
				$-$ 2.5 0.0 2.5 5.0

NO $=$ 4 subtracted from:

NO	Lower	Center	Upper	——+———+———+———+—
5	$-$ 2.949	$-$ 0.224	2.501	(———-*———-)
6	$-$ 2.393	0.332	3.057	(———-*———-)
				——+———+———+———+—
				$-$ 2.5 0.0 2.5 5.0

NO $=$ 5 subtracted from:

NO	Lower	Center	Upper	——+———+———+———+—
6	$-$ 2.169	0.556	3.281	(———-*———-)
				——+———+———+———+—
				$-$ 2.5 0.0 2.5 5.0

Conclusion: The above matrix shows the comparison among mean values. As in the 95% of confidence intervals (CI) above, the CIs of all the 6 groups of data include zero, so we believe that there is no distinct difference among mean values.

4.3.6 Relativity and regression analysis

4.3.6.1 Scatter diagram between S11 and ACPR

Scatter diagram between S11 and ACPR is shown in Fig. 8.

Figure 8.

Scatter diagram between S11 and ACPR (with fitting curve).

Conclusion: It can be seen from Fig. 8 that S11 and ACPR values seem to show a linear correlation.

4.3.6.2 Correlation coefficient between S11 and ACPR

Correlations: TLPB, newS11

Pearson correlation of TLPB and new S11 $=$ 0.094

P-Value $=$ 0.620

Conclusion: In accordance with the correlative coefficient table, sample size $=$ 5, d.f. $=$ 3, and significance level $=$ 0.8783.

While $P=$ 0.620 $<$ 0.8783, which means the correlation is not distinct statistically.

Figure 9.

Regression analyses to S11 and ACPR values.

4.3.6.3 Regression relationship between S11 and ACPR

Regression analyses to S11 and ACPR values is shown in Fig. 9.

Regression analysis: TLPB versus newS11

The regression equation is

TLPB $=$ 51.6 $+$ 0.054 newS11

S $=$ 2.01990, R-Sq $=$ 0.9%, R-Sq (adj) $=$ 0.0%.
Predictor	Coef	SE	Coef	T	P
Constant	51.576	2.731	18.88	0.000
newS11	0.0538	0.1072	0.50	0.620

Analysis of variance

Source	DF	SS	MS	F	P
Regression	1	1.028	1.028	0.25	0.620
Residual Error	28	114.240	4.080
Total	29	115.269

Unusual observations

R denotes an observation with a large standardized residual.
Obs	newS11	TLPB	Fit	SE	Fit	Residual	St	Resid
18	25.5	56.920	52.948	0.370	3.972	2.00	R

Analysis: The result $P=$ 0.620 $>$ 0.05 indicates non-significance. Correlative coefficient R-Sq $=$ 0.9% and R-Sq (adj) $=$ 0.0% are quite different. Besides, there is an abnormal point (Obs 18), of which the ACPR is too great. According to the actual situation of the single board of radio frequency, this is due to its small output power and gain. As for the specific reason, it is related to other parts of the single board.

Conclusion: The data show that there is no significantly simple linear fitting relation between the S11/S12 of isolators and the ACPR of single boards.

Footnotes

Acknowledgments

Project: the Science and Technology Program of the Education Department of Shaanxi Province Government (number: 16JK1158).

References

Futatsumori

Hikage

Nojima

et al., A novel filter construction utilizing HTS reaction-type filter to improve adjacent channel leakage power ratio of mobile communication systems, IEICE Transactions on Electronics E92-C(3) (2009), 307–314.

Takano

Maniwa

Oishi

et al., Influence of frequency characteristics of RF circuits in digital predistortion type linearizer system on adjacent channel leakage ratio for W-CDMA power amplifier, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E87A(2) (2004), 324–329.

Zhou

Y.F.

B.Z.

and Sun

X.Y.

, Research and application for load control of TD-SCDMA system, Application Research of Computers 28(11) (2011), 4274–4277.

Shuai

C.J.

, The measurement system analysis method on TD network insertion loss, Modern Manufacturing Engineering (4) (2013), 108–113.

Peng

M.-G.

and Wang

W.B.

, A framework for investigating radio resource management algorithms in TD-SCDMA systems, IEEE Communication Magazine 43(6) (2005), 12–18.

S.M.

, Application of circulator/isolator in microwave communication, Journal of Magnetic Materials and Devices 34(1) (2003), 25–29.

L.L.

Chen

H.B.

et al., S-parameter characteristics in THz folded waveguide slow wave structures, High Power Laser and Particle Beams 25(4) (2013), 968–972.

Vijayvargiya

, One-way analysis of variance, Journal of Validation Technology 15(1) (2009), 62–63.

Cano

J.A.

Carazo

and Salmerón

, Bayesian model selection approach to the one way analysis of variance under homoscedasticity, Computational Statistics 28(3) (2013), 919–931.

10.

Viroli

, On matrix-variate regression analysis, Journal of Multivariate Analysis (111) (2012), 296–309.

11.

Ahmad Taher

, Assessment of haemodialysis adequacy: A novel regression analysis formula, International Journal of Biomedical Engineering and Technology 9(2) (2012), 122–132.

12.

Danh Cong

and Farhad

, Early detection of cancer by regression analysis and computer simulation of gene regulatory rules, Journal of Medical Imaging and Health Informatics 2(3) (2012), 336–342.

13.

Jia

J.P.

, Statistics , China Renmin University Press Co. Ltd, Beijing, 2012.

14.

Shuai

C.J.

, DOE to solve problem of low noise on RF board, Coal Technology (8) (2011), 45–47.

15.

R.M.

, The company’s stock price of forecast with ARIMA, Shandong Youth 470(3) (2013), 137–139+141.

16.

R.M.

and Zhang

J.S.

, The professional technicians performance appraisal of coal mine, Coal Technology (7) (2011), 249–251.

17.

Shuai

C.J.

Teng

K.M.

and Jia

H.E.

, On the error estimates of a new operator splitting scheme for the navier-stokes equations with coriolis force, Mathematical Problems in Engineering (12) (2012). Article ID 105735, 23 pages.

18.

Shuai

C.-J.

Nie

and He

, Influence of electromagnetic irradiation on grow and evelop of tea caterpillars based on principal component analysis method, Journal of Shaanxi University of Technology (Natural Science Edition) 30(3) (2014), 63–67.

19.

Shuai

C.J.

and Qian

, Finite-difference method analysis on the dissymmetrical double-ridge waveguide, Journal of Shaanxi University of Technology (Natural Science Edition) 29(6) (2013), 11–15.

20.

R.-M.

, Design of intelligent travel itinerary based on the improved teaching-learning algorithm, Journal of Shaanxi University of Technology (Natural Science Edition) 31(1) (2015), 68–71+78.

One way analysis of variance for parameter S of isolator and regression analysis to the correlation between parameter S and ACPR

Abstract

Keywords

1. Introduction

2. Objective

3.1 Hypothesis test

1) Make data analysis of residual and relativity; 2) Obtain the conclusions. OPEN IN VIEWERFigure 1.Testing chart of the tested object. 4. Experimental data acquisition and analysis

4.1 Testing chart of ACPR indexes of single board

4.2 Data acquisition

4.3.1 Propose the hypothesis testing proposition

Table 1 P_value of TYPE1–6

4.3.3 Normality analysis

4.3.4 Variance consistency test

4.3.5.1 Residual analysis in ANOVA

4.3.5.2 Main effect graph and inter-group analysis in ANOVA

4.3.5.3 Multiple comparisons in ANOVA

4.3.6.1 Scatter diagram between S11 and ACPR

4.3.6.2 Correlation coefficient between S11 and ACPR

4.3.6.3 Regression relationship between S11 and ACPR

Footnotes

Acknowledgments

References

1)
Make data analysis of residual and relativity;
2)
Obtain the conclusions.

Figure 1.
Testing chart of the tested object.

4. Experimental data acquisition and analysis

Table 1
P_value of TYPE1–6