Determining the impact of electrical loss in coaxial cable

Determining the impact of electrical loss in coaxial cable Here's a discussion on cable attenuation based on the differences in dielectric loss of low density polyethylene resins and quantify the consequent increase in electrical power loss. By Anny L. Flory Senior Engineer Electrical & Telecommunications Unit The Dow Chemical Company and Chester J. Kmiec Development Leader Electrical & Telecommunications Unit The Dow Chemical Company Coaxial / radio frequency (RF) cables made of highly foamed polyethylene are widely used as antenna feeders, cabling of antenna arrays, equipment interconnections, mobile telecommunication systems, microwave transmission systems, broadcast transmission systems and other communication systems. Since the 1980s the operating frequency of cellular phones has continuously increased. In fact, many domestic and overseas telecommunication carriers are currently using a frequency of.5-.6 GHz (4G). To meet the transmission requirements at high frequencies, RF cables require the use of highly foamed dielectric made with polymer resins which are as pure as possible, therefore with minimum polar groups attached to the polymer and minimum polar additives. In this paper, we compare rheology and dielectric loss properties of various Low Density Polyethylene (LDPE) gas injection compounds. Reduction of the attenuation of the coax cable is important since it can lead to increase in energy efficiency or reduction in cable weight, two desirable characteristics for cellular communication carriers. In this paper we model cable attenuation based on the differences in dielectric loss of LDPE resins and quantify the consequent increase in electrical power loss. Typically, a high frequency cable is made by an inner conductor surrounded by a foamed insulation. In early attempts, the foaming step was implemented by compounding the polymer resin with a specific chemical foaming agent capable of blowing closed cells of desired size in the polymer. The issue with this approach is that the polymeric dielectric material traps residue of the foaming agent that deteriorate the dissipation factor (Df), also called tan δ and consequently the attenuation of the cable especially at the upper end of the frequency range. To overcome this, a physically foamed dielectric approach was developed based on injecting an inert gas (such as nitrogen, carbon dioxide) to blow the gas filled expanded cell 1. Adding a nucleating agent is a frequently used and effective technique to reduce cell size, enhance cell density and uniform cell distribution. Characteristics of the base polymer used to make the insulating material include good dissipation factor, Df (low Df), good extrudability and foaming capability and flexibility. Candidate materials are fluorocarbon polymer, polypropylene and polyethylene. Fluorocarbon polymers are expansive and polypropylene is stiff and difficult to foam. On other hand, polyethylene is cheap, has good electrical properties and is flexible. Therefore, it is a material of choice for insulation of coax cable. Generally, a blend of HDPE and LDPE resins is used. HDPE which has no or very little Long Chain Branching (LCB) provides good physical properties to the foam (stiffness, tensile strength, high EE Times-India eetindia.com Copyright 011 emedia Asia Ltd. Page 1 of 8

temperature resistance) 3. LDPE is selected because of its strain hardening and melt strength behaviors due to the presence of LCB and entanglement (as the deformation rate increases) 4. These properties are crucial for foaming in order to prevent the melt from rupture and stabilize the bubble. A small dissipation factor (for low signal loss) presupposes polyethylenes which are as pure as possible, i.e. with minimum polar groups 5. Dissipation factor of polyethylene increases with decreasing density. This is because LDPE has side chains inducing dipole polarization 6. HDPE has a few side chains resulting in dissipation factor values that are in general at least three times lower than LDPE. This is the reason why improvement of dissipation factor of LDPE component is crucial for low cable attenuation. The paper provides quantification of attenuation loss in coaxial / RF cable due to dissipation factor differences of available commercial grades of LDPE. Rheology in foaming To understand the importance of rheology in foaming, a simple bubble growth model from Newtonian fluid is useful. The model shows that the change in bubble radius R is proportional to the pressure difference inside (P D) and outside (P c) the bubble and inversely proportional to the melt viscosity of the polymer (η) 7 : dr R = PD PC dt 4η γ R (1) Here γ is the surface tension of the polymer. The process of bubble growth is dictated by the magnitude of the viscosity. In fact, a balance between viscosity and elasticity dictates the bubble structure. It is desirable that the viscosity is low during the nucleation early stage of bubble growth (low η), increases gradually as the bubble grows further and becomes very high in the late stage of foaming (due to strain hardening behavior, melt strength, for example) to stabilize the foam structure. Higher degree of long-chain branching generally facilitates strain hardening behavior. Elasticity behavior (high recovery compliance) is desirable since it can prevent bubble collapse (due to viscous flow) at the exit of the die. Generally, narrow molecular weight distribution (MWD) polymers have a viscous dominating behavior. Influence of LDPE dissipation factor Definition of cable loss. Cable signal loss depends on several geometric factors and both dielectric constant and dissipation factor of the polymer 8 : Figure 1: Schematic of a coaxial cable. The cable is coated with highly foamed polyethylene to reduce attenuation. EE Times-India eetindia.com Copyright 011 emedia Asia Ltd. Page of 8

db / 100 ft = k1 F + k F () with k 0.4343 D + F (3) Z 0 D d ks 1 = bd k 1 is due to the skin effect, the property of electromagnetic waves to travel near the surface of the conductor. and k.78 tanδ = (4) V p k contain the contribution of the dissipation factor where: F: frequency in MHz Z 0: nominal impedance Z 0 = 60 D D ln d c k s (5) D: dielectric diameter (id of outer conductor) d: center conductor diameter k s: 1 for solid center conductor F bd: braid factor (1 for solid tube) tan δ: dielectric loss V p: velocity of propagation V p 1 = (6) D c D c: dielectric constant db : Decibel Definition of electrical power loss. The db is simply 10 times the log of the ratio of power input to the cable at one end to the power output at the other end: Power out = 10 log (7) Power in db 10 Results and discussion Six different grades of LDPE gas injection compounds are studied (A to F). Rheology. The key dynamic oscillatory shear, creep recovery and melt strength as well as density and melt index data are shown in Table 1. Also included in Table 1 is the level of long chain branching that is determined by the terminal zone behavior of the linear viscoelastic function G 4 ' G = A G ω EE Times-India eetindia.com Copyright 011 emedia Asia Ltd. Page 3 of 8

Here A G is a constant that depends on the molecular structure. More precisely, in typical experimental time scale, the terminal slope (LCBf) of log G versus Log ω is precisely equal to 1 for linear polymers and it deviates from this value (LCBf < 1) when branching are present in the polymer chain. SAMPLE SAMPLE Density (g/cm3) MI (g/min) Conv TDGPC Mw/Mn A 0.90.0 6.0 B 0.919 7.0 11.0 C 0.9 7 10.0 D 0.93 10 9.0 E 0.9 6 10.0 F 0.91 11.0 Eta0 (kpa.s) Ea (kcal/mole) LCBf Recovery compliance (1E-5/Pa) Melt Strength (cn) A 11 13.1 0.68 49 8.8 B. 10.9 0.85 190 6.5 C.9 11.4 0.85 163 7.0 D 1.3 11.8 0.99 90 3.6 E.7 11.6 0.85 180 7.0 F 4.3 1.1 0.79 177 6. Table 1: Rheological properties of LDPEs. The following observations can be made: All samples have broad MWD (9-11) except for sample A which has narrow MWD (6). A broad MWD facilitates processing. Samples A has higher zero shear rate viscosity, Eta0. This parameter is important for bubble growth and initiation. A low Eta0 is preferred. The activation energy is slightly higher for sample A which indicates more sensitivity to temperature. This is a slight disadvantage because, in this case, the melt temperature is more difficult to control which makes the material more unstable to process. Other samples are in that regards more stable during processing. The higher activation energy grades have more LCB (lower LCBf values) which is typical. The grades with more LCB have higher melt strength except for sample F probably because of its broader MWD. This is illustrated in figure. Good melt strength is an advantage to stabilize the bubbles. 10 Melt strength (cn) 8 6 4 0 0.6 0.7 0.8 0.9 1 LCB Figure : Dependence of melt strength on LCB. EE Times-India eetindia.com Copyright 011 emedia Asia Ltd. Page 4 of 8

Sample A has lower recovery compliance, therefore less of an elastic response. This is a disavantage since it does not prevent bubble collapse upon pressure release at the exit from the die of the extruder. This low creep compliance value is due to a narrow MWD though the LCB value is high. Based on the above rheological study, ranking of the various LDPE samples for dielectric foam application is summarized in table. SAMPLE Processi ng (MWD) Bubble initiation (Eta0) Bubble Growth (Eta0) Bubble size control (Melt strength) Bubble stability (Elasticity) A - - + + + B + + - 0 - C + + - 0 - D + + - - 0 E + + - 0 - F + 0 0 0 - Table : Comparison of processing and rheological attributes of LDPEs. Dissipation factor. Figure 3 shows dissipation factor values for the different grades..5e-04 Dissipation factor @.47GHz.0E-04 1.5E-04 1.0E-04 5.0E-05 0.0E+00 A B C D E F Figure 3: Dissipation factor @.47 GHz. The larger difference in dissipation factor is between sample A and sample C (Delta DF = 0.5 x 10-4 ). The dielectric constant is plotted in figure 4. Dielectric constant @.47GHz.85.80.75.70.65.60.55.50.45 A B C D E F Figure 4: Dielectric constant @.47 GHz. EE Times-India eetindia.com Copyright 011 emedia Asia Ltd. Page 5 of 8

If a coaxial cable A was made with resin A and coaxial cable C was made with resin C then according to Equation, the difference in attenuation between cable A and cable C due to the difference in dissipation factor between resin A and resin C is: ( k ) F ( db /100 ft) = ( k1 ) F + ( k) F = (8) Here the assumption is made that k 1 = 0 because dielectric constant is similar for resin A and resin C and cable A and cable C have the same size (figure 4): db ft k F.78 ( /100 ) = ( = ) V p Using (4) in (9), we obtain: ( Df ) F (9) ( db /100 ft) =.78.7 4 3 (.1 1.6) 10.47 10 = 0. 5 The main coaxial cable of cell tower is about 170ft (50 meters). So the 170ft cable A has an excess of 0.88db compared to the 170ft cable C. ( db /170 ft) = 0.88 Difference in electrical power loss Using Equation 6: Power in Power out = 0.88 10 10 = 80% So 0% more of energy is dissipated in cable A compared to cable C due to the difference in Df of LDPE resins. However, in general, dielectric insulations are made with a blend of HDPE and LDPE. The table below gives the attribute of cable C over cable A for various blend ratios. The assumption is made is that contribution of Df for the HDPE component is the same for both cables. HDPE / LDPE 0/100 50/50 70/30 decibels saving 0.88 0.44 0.6 Energy saving (%) 0 10 6 Table 3: Disadvantages of cable A compared to cable C as a function of resin blending ratio. In general, a cell tower comprises of more than one antenna and therefore more than one coaxial cable. As a result, the impact in terms of energy saving is much greater for a cell tower than listed in table 3. Difference in electrical power loss. As we increase the frequency F, ΔdB increases (Equation 8). The resulting electrical power loss is plotted in figure 5 for a HDPE/LDPE ratio of 50/50. EE Times-India eetindia.com Copyright 011 emedia Asia Ltd. Page 6 of 8

% Electrical power loss 40 35 30 5 0 15 10 5 0 HDPE/LDPE = 50/50 0 3 6 9 1 15 Frequency (GHz) Figure 5: Electrical power loss when using coaxial cable A instead of coaxial cable C. The above plot fundamentally assumes that Df is frequency independent. Note that this is not the case and dielectric relaxation processes (γ, β and α c transitions in polyethylene) are function of frequency. A frequency sweep of Df for resins A and C will therefore give a better estimate of the advantages of cable C versus cable A. Conclusions We have shown that the molecular structure of LDPE can be tune to provide a balance between viscous and elastic behavior and therefore improve bubble structure. Based on the differences in Df between the grade with the higher Df and the grade with the lower Df, we have predicted the cable loss for a HDPE/LDPE blend ratio of 50/50. The difference is 0.44dB for a 170 ft main coax tower cable. The 0.44dB represents an electrical power loss of 10% more for cable A. Since cell towers have more than one coaxial cable, the impact in terms of energy loss is much greater than 10%. References: 1 K.A. Arora et al., Macromolecules, 31, p4614, 1998 E reverchon and S.J Cardea, Journal of supercritical Fluids, 40, p144, 007 3 R. Watanabe et al., Fujikura Technical Review, 008 4 J.D. Ferry, Viscoelasticity of polymers, Wiley, 3rd Ed. 5 R.F Eaton and C. J. Kmiec, Proceedings of the 57th IWCS 6 F. Kremer, Broadband dielectric spectroscopy, Springer 7 R. Liao et al., Polymer, 51, p568, 010 8 The American Radio Relay League Handbook 001, C. Hutchinson Ed. Newington CT, 001 EE Times-India eetindia.com Copyright 011 emedia Asia Ltd. Page 7 of 8

About the authors Anny L Flory is a senior engineer in Dow s Wire and Cable group. She has a B.S. in Physics from Universitee Paul Sabatier in Toulouse France and a Ph.D. in Chemical Engineering from Texas Tech University. Her present research areas include gas injection polyolefin compounds and flame retardant technologies for wire and cable applications. Chester J. Kmiec is a Development Leader for Wire and Cable Compounds group at the Dow Chemical Company. Chet has 36 years of experience in Polymer Applications Research an Development, the last 1 years at The Dow Chemical Company. He hold a B.S in Plastics Technology from Lowell Technological Institute and a M.B.A from the State University of New York at Buffalo. EE Times-India eetindia.com Copyright 011 emedia Asia Ltd. Page 8 of 8