Question

A low-loss dielectric is one with a small loss tangent, that is, (o/we) <1. We can reduce (6.52) for this special case by applying a binomial series expansion to the value within the 6.3.1 Low-Loss Dielectrics interior square root portion of the equations. The expansion is n(n-1);- + (1 + x)" = 1 + nx + 2! and for x< 1 this can be approximated as (1 + x)" = 1+ nx So we have + 1+ (6.53) 08 Inserting this approximation into (6.52) we find ae 2 V8 βαω με o (6.54) As before, o can be replaced with eff to account for complex permittivity in these equations. Low-loss materials have a small but definite attenuation. Otherwise, they have the same phase constant and same intrinsic impedance as lossless materials. Drill 6.6 Use (6.54) to determine a and B for glass at (a) 100. Hz and (b) 1.00 MHz. Assume Hr - 1.0 and use the parameters for glass listed in Table 6.1. Compare your results with a and B calculated from (6.52). (Answer: (a) a = 3.4 x 10-Np/m, ß = 6.6 x 10-6 radians/m; (b) a = 3.3% 10-SN Np/m, B = 0.066 radians/m) TABLE 6.1 Parameters Used for MATLAB 6.2 and Figure 6.4 (S/m) Copper Seawater Glass 58 x 10 5 10-12 72 10 0 12 0.010

Answer 1

Q.1 f = 1MHz ; G = 72 (for seawater) (Table E2) loss tongent WE = 2 af XE, X60 aafxGx | X10-9 36* - 5 X 36 XT f 1 X 106X 72 X10-9 Tom S, MHz = 1250 ► loss tonyent at from table = 0.9, which is incorrect. tom &= T ante t decreased by turns increases.