# Theoretical and Experimental Results of Substrate Effects on Microstrip Power Divider Designs

Authors: Suhair Mansoor Mahmood; Asaad M. Jassim Al-Hindawi
Journal: International Journal of Microwave Science and Technology
 (2011)

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## Abstract

The effects of substrate materials on the design of microstrip power divider are investigated theoretically and experimentally. Three dielectric substrate materials, Duroid 3003, G10/FR4 epoxy Glass, and Duroid 3010, are chosen to be studied. A three-way two-stage power divider is designed at S-band frequency of  2.25 GHz and etched on each studied substrate separately. The substrate effects on the characteristics and performance of the microsrip circuits are studied taking into consideration the large difference in dielectric constant and the dissipation factor. The circuit designs presented  here are analyzed using the Genesys CAD program and implemented and tested experimentally. The simulated and measured results are compared and discussed, and they indicate that significant changes in the characteristics of the microstrip power divider are observed.


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## Body

## 1. Introduction

The power divider technology has undergone a substantial change over the past decade, due to smaller size, lighter weight, potentially lower cost, high reliability, broad bandwidth capability, and function reproducibility [1, 2]. When selecting a suitable substrate material, factors to be considered in the designs of the microstrip power dividers are cost, availability, ease of machining, and etching. There are a whole range of mechanical, electrical, thermal, and chemical criteria to be taken into account [3, 4]. Most of these criteria are mechanical stability with high and low storage temperature, thermal expansion similar to that of metals, good electrical properties (homogeneity of εr and high electric insulation strength), chemical resistance and easy workablity with low cost [3]. There is no substrate material that simultaneously fulfils all the above requirements. The best compromise must be found for all applications [5]. The materials commonly used for microwave substrate have dielectric constants typically range from 2.0 to 10.0. Microstrip circuits designed to be fabricated on such dielectric materials will be most compact or pressed because of the wave-slowing action of the electric signal. Usually, this is an advantage, but such small size makes it difficult to fit any conventional discrete parts into microstrip layout. There are Teflon/ceramic mixture with lower dielectric constants, such as 6.0, which produce physical layer microstrip layout; this helps to alleviate the components mounting problem [6].The present study investigates the effects of the dielectric substrate materials on the design of microstrip power dividers on which they are etched. Duroid 3003, G10/FR4 epoxy glass, and Duroid 3010 substrates are chosen to be studied. The effects of the differences in the dielectric constants and the dissipation factors on circuit design are included.


## 2. Microstrip Power Divider Designs

A schematic diagram of the two-stage Wilkinson N-way divider is shown in Figure1.Figure 1
Schematic representation of two-stage power divider.The common port is designated the number 0 and is assumed to be terminated inZc. The divider ports are designated the number 1 through N, and each is terminated in Zd. The characteristic impedance of each quarter-wave line is Z0,1 and Z0,2 while the isolation resistors are designatedR1 and R2. The justification for the coupling among all transmission lines beyond the first stage of the divider is that such lines would be reasonably separated from one another [7]. Also the junction effects will be neglected. It will be assumed that port 0 (input port) is perfectly matched at the center frequency. Thus, for two-stage hybrid(1)Z0,1=Z0,2(NZcZd)1/2,
where Zc and Zd are the input and output impedances of the power divider, respectively. For a maximally flat input-output frequency response, the following impedances are(2)Z0,1=(NZc)3/4(Zd)1/4,(3)Z0,2=(NZc)1/4(Zd)3/4.The addition of input and output transformers to improve the frequency response is allowed provided that (1) is satisfied with Zc and Zd referred to terminals of the dividers [7]. Table 1 represents the optimum resistor of two-stage N-way power divider [7].Table 1
Optimum resistors of two-stage N-way power divider [7].
N[R1Zd/Z0,2]opt(Zd/R2)opt21.287190.1782830.750000.2500040.500000.2500050.399910.3360960.366760.3628570.396520.3500080.524930.30118100.524820.30121120.524830.30120The characteristic impedance of the microstrip lineZ0L may be expressed in terms of line width w and substrate thickness h, and effective dielectric constant εe as [4](4)Z0L={60εeln⁡⁡(8hw+w4h)forwh≤1[120π][εe(wh+1.393+0.677×ln⁡⁡(wh+1.44))]-1forwh>1},
where
(5)εe=εr+12+εr-12(1+12hw)-1/2
and εr represents relative dielectric constant of the substrate. The dielectric loss αd is given by [4](6)αd=πλ0qtanδ,Np/m,
where   q=(εr(εe-1)/εe(εr-1)) and tanδ represents dissipation factor.Table2 illustrates the specifications of the studied substrate materials with the dimensions of 50 ohms line for each one.Table 2
Specifications of the studied substrates with the dimensions of quarter wavelength line (50 ohms) for each.
Duroid 3003Epoxy glassDuroid 3010Dielectric constantεr34.410.2Dielectric thicknessh1.52 mm1.6 mm1.25 mmDissipation factor0.00130.0130.0035Width of  quarter wavelength line3.84 mm2.47 mm1.10 mmLength of quarter wavelength line21.91 mm18.42 mm12.71 mm


### 2.1. Power Divider with Duroid 3003 and Epoxy Glass Substrates

A 50 ohms,λg/4 line at midband frequency of 2.25 GHz is 3.84 mm wide, 21,91 mm long for the Duroid 3003 substrate and 2.47 mm wide, 18.42 mm long for epoxy glass substrate. The main difference between these two substrates is the dissipation factor (tanδ).  They are near in the dielectric constants and the thickness of the substrate, therefore the layout design is changed in the range of a few millimeters. The dissipation factor does not affect the dimensions of the power divider design, its effect will be clear in the simulated and practical response curves.Using (2), the impedance design values are Z0,1=113.975Ω,Z0,2=65.803Ω,R1=64.954Ω, and R2=200Ω, with the input and the output impedances set at  Z1n=Zout=Zd=Zc=50Ω.Figure2 shows the schematic diagram  of power divider designed on Duroid 3003 or epoxy glass substrate noticing that only the slight differences in the dimensions of the microstrip lines related to the change in dielectric constant  and thickness of the used board.Figure 2
Schematic diagram of 3-way 2-stage power divider designed on Duroid 3003.Figures3 and 4 illustrate the photograph of the designed power dividers etched on Duroid 3003 and epoxy glass substrates, respectively.Figure 3
Picture of 3-way 2-stage power divider etched on Duroid 3003 board (Dim.100mm×55mm).Figure 4
Picture of 3-way 2-stage power divider etched on epoxy glass board (Dim.93mm×49mm).


### 2.2. Power Divider with Duroid 3010

The main difference between this substrate and the other is the high dielectric constant. The comparison is with the Duroid 3003 because it has approximately the same dissipation factor. A 50 ohms,λg/4  line at midband frequency of 2.25 GHz is 1.10 mm wide and 12.71 mm long. Following the same design procedure of power divider, the microstrip lines needed in the design are such thin that it is difficult to be fabricated; therefore the values of Z0,1 and Z0,2 are selected to give large dimensions Zin=25Ω,Zout=19Ω,Z0,1=53Ω,Z0,2=26Ω,R1=22Ω,R2=76Ω.An additional transformation matching line{B} is inserted in the design to transform the impedance  {A}=25Ω  to  50Ω  line {C} for matching purposes. Also an additional  30Ω  stub is inserted to transform  19Ω  output to the 50Ω  line as shown in Figure 5. Figure 6 illustrates the  photograph  of the power divider etched on  Duroid 3010 substrate.Figure 5
Schematic diagram of 3-way 2-stage power divider designed on Duroid 3010.Figure 6
Picture of 3-way 2-stage power divider etched on Duroid 3010 board (Dim.110mm×90mm).


## 2.1. Power Divider with Duroid 3003 and Epoxy Glass Substrates

A 50 ohms,λg/4 line at midband frequency of 2.25 GHz is 3.84 mm wide, 21,91 mm long for the Duroid 3003 substrate and 2.47 mm wide, 18.42 mm long for epoxy glass substrate. The main difference between these two substrates is the dissipation factor (tanδ).  They are near in the dielectric constants and the thickness of the substrate, therefore the layout design is changed in the range of a few millimeters. The dissipation factor does not affect the dimensions of the power divider design, its effect will be clear in the simulated and practical response curves.Using (2), the impedance design values are Z0,1=113.975Ω,Z0,2=65.803Ω,R1=64.954Ω, and R2=200Ω, with the input and the output impedances set at  Z1n=Zout=Zd=Zc=50Ω.Figure2 shows the schematic diagram  of power divider designed on Duroid 3003 or epoxy glass substrate noticing that only the slight differences in the dimensions of the microstrip lines related to the change in dielectric constant  and thickness of the used board.Figure 2
Schematic diagram of 3-way 2-stage power divider designed on Duroid 3003.Figures3 and 4 illustrate the photograph of the designed power dividers etched on Duroid 3003 and epoxy glass substrates, respectively.Figure 3
Picture of 3-way 2-stage power divider etched on Duroid 3003 board (Dim.100mm×55mm).Figure 4
Picture of 3-way 2-stage power divider etched on epoxy glass board (Dim.93mm×49mm).


## 2.2. Power Divider with Duroid 3010

The main difference between this substrate and the other is the high dielectric constant. The comparison is with the Duroid 3003 because it has approximately the same dissipation factor. A 50 ohms,λg/4  line at midband frequency of 2.25 GHz is 1.10 mm wide and 12.71 mm long. Following the same design procedure of power divider, the microstrip lines needed in the design are such thin that it is difficult to be fabricated; therefore the values of Z0,1 and Z0,2 are selected to give large dimensions Zin=25Ω,Zout=19Ω,Z0,1=53Ω,Z0,2=26Ω,R1=22Ω,R2=76Ω.An additional transformation matching line{B} is inserted in the design to transform the impedance  {A}=25Ω  to  50Ω  line {C} for matching purposes. Also an additional  30Ω  stub is inserted to transform  19Ω  output to the 50Ω  line as shown in Figure 5. Figure 6 illustrates the  photograph  of the power divider etched on  Duroid 3010 substrate.Figure 5
Schematic diagram of 3-way 2-stage power divider designed on Duroid 3010.Figure 6
Picture of 3-way 2-stage power divider etched on Duroid 3010 board (Dim.110mm×90mm).


## 3. Experimental Setup

The implemented designs of the studied microstrip power dividers are tested, and their characteristics are found by using the network analyzer 8510 HP. The network analyzer has two ports (1 and 2) that are connected, respectively, to the input and one of the outputs of the tested power divider, while the remaining outputs of the power divider are connected to50Ω load for each. Voltage standing ratio VSWR, the coupling  and  the  isolation between  the   power  divider input and each output are  measured by connecting the power divider input (representing port 1 of a device under test DUT as  shown in Figure 7) to port 1 of the network analyzer (a1 and b1), while the each power divider output representing port 2 of  DUT is connected to port 2 of the network analyzer (a2 and b2).a1 and b1 represent the incident and reflected or received voltage signals, respectively, at port 1 while a2 and b2 are the incident and reflected or received voltage signals, respectively, at port 2 of the network analyzer. Based on this setup, the following parameters are measured and the results are displayed directly on the analyzer [4].(a)
S11 represents the forward reflection coefficient and S11=b1/a1, a2=0.(b)
Input VSWR represents the input match andVSWR=(1+|S11|)/(1-|S11|).(c)
S22 represents  the  reverse reflection coefficient and S22=b2/a2, a1=0.(d)
Output VSWR represents the output match andVSWR=(1+|S22|)/(1-|S22|).(e)
S21 is the forward transmission coefficient that represents the coupling between the input and output ports and S21=b2/a1 when a2=0.(f)
S12 is the reverse transmission coefficient that represents the coupling between  the input and output ports and S12=b1/a2 when a1=0.Figure 7
Block diagram of the experimental setup.The above procedure is repeated for each tested output of the studied power divider taking into consideration that the calibration of the network analyzer ports should be made before the test beginning, regarding that the reference planes are taken at the power divider ports.


## 4. Results and Discussion

By the aid of Genesys software package, the previous three designs of microstrip  power dividers etched on the studied substrates are simulated and implemented. The characteristics of  the implemented  designs are determined using the experimental setup discussed in Section3. Figure 8 shows the simulated and the measured VSWR on Duriod 3003.Response curves of 3-way 2-stage power divider printed on Duroid 3003 substrate. (a) Simulated input and output VSWR, (b) and (c) measured input and output VSWR, respectively.
(a)(b)(c)The input VSWR is varying and less than 2 : 1 for frequency range 1.3–2.95 GHz, while  the  output  VSWR  is  between 1 and 1.5 for  the studied frequency  range 1.5–3.5 GHz.Figure9  illustrates  the coupling of the power divider printed on Duroid 3003.Response curves of 3-way 2-stage power divider printed on Duroid 3003 substrate. (a) Simulated coupling and (b) measured coupling.
(a)(b)The isolation parameter of power divider is shown in Figure10. Agreement is found between the simulated and measured results, in term of the shape of the curves on Duriod 3003.Response curves of 3-way 2-stage power divider printed on Duroid 3003 substrate. (a) Simulated isolation and (b) measured isolation.
(a)(b)The corresponding figures to those of the first prototype are shown in Figures11, 12, and 13 for the power divider printed on epoxy glass substrate.Response curves of 3-way 2-stage power divider printed on epoxy glass substrate. (a) Simulated input and output VSWR, (b) and (c) measured input and output VSWR, respectively.
(a)(b)(c)Response curves of 3-way 2-stage power divider printed on epoxy glass substrate. (a) Simulated coupling and (b) measured coupling.
(a)(b)Response curves of 3-way 2-stage power divider printed on epoxy glass substrate. (a) Simulated isolation and (b) measured isolation.
(a)(b)It can be seen that the increase in the split ratio indicates that there is more power lost compared to the first one and is related to higher dissipation factor in the second substrate. Figures14, 15, and 16 represent the simulated and measured VSWR, coupling and isolation of the third prototype etched on Duroid 3010, respectively.Response curves of 3-way 2-stage power divider printed on Duroid 3010 substrate. (a) Measured input VSWR and (b) measured output VSWR.
(a)(b)Figure 15
Measured coupling curve of 3-way 2-stage power divider printed on Duroid 3010 substrate.Figure 16
Measured isolation curve of 3-way 2-stage power divider printed on Duroid 3010 substrate.It is clear that the measured coupling curves agree with the computed curve, and the coupling remains less than −5.3 dB for different ports over the major part of the studied frequencies. The measured results are satisfactory.It is seen that the most measured results presented in this study have a small shift in the center frequency, this is related to the etching that does not give the exact dimension of the lines. Table3 compares the obtained results of the main parameters of the studied substrate materials.Table 3
Comparison of the studied substrates at 2.25 GHz.
Duroid 3003Epoxy glassDuroid 3010Input VSWR1.41.31.14Output VSWR1.191.181.12Coupling (dB)−5.3−5.4−5.38Isolation (dB)−34−23.9−30


## 5. Conclusion

The present study has introduced and discussed the effects of three substrate materials: Duroid 3003, epoxy glass, and Duroid 3010 on the characteristics of  three-way two-stage microstrip power dividers. The obtained results have indicated that the used Duroid 3010 has seemed better input and output VSWR than the others except the isolation in addition to that the used Duroid 3003 has indicated better characteristics than epoxy glass as observed in Table3. The availability of the substrate material, its price, the size required, the number of divider needed, and generally the cost are the main parameters to fulfill the design requirements.



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*Source: 980982-2011-09-12.xml*