Magnitude of steady state transfer
function
6 × 10
−3
5 × 10
−3
4 × 10
−3
3 ×10
−3
2 × 10
−3
1 × 10
−3
ε = 0 cm
ε = 30 cm
10 1
10
2
10
3
10
4
10
5
10
6
45
Coupling of Electromagnetic Fields into Biological Systems
ω = 2πf
FigurE 1.20 Magnitudes of steady state transfer functions for muscle materials at different
depths as a function of frequency. (From Lin, J. C. 1975. Interaction of electromagnetic transient
radiation with biological materials. IEEE Trans Electromagn Compat 17:93–7. With permission.)
It follows that for ω → 0, T → 0.00125. Therefore, a negligible amount of the incident wave
is transmitted into the muscle. This means that the incident wave experiences almost
total reflection. In the high-frequency range, that is, ω >> ω s
T ~ 0.00447/(1 − j5.88 ω s /ω)
(1.56)
Again, the transmitted wave has small, constant amplitude and is independent of position. The magnitude of the steady state transfer function given by Equation 1.54 at different depths is shown in Figure 1.20 as a function of frequency for muscle material
(Lin 1975). Note that the curve starts as a constant as the frequency is increased from
zero. The upper limit of the low-frequency range is around 10 Hz. The constant value
of 0.00125 is equal to that predicted by the asymptotic analysis given by Equation 1.52.
The high-frequency range begins at 10 kHz. The magnitude of H(z,ω) in this case is
0.00447 as obtained earlier in the limit of ω s /ω → 0. In addition, within the distances
considered, H(z,ω) is independent of location inside the muscle layer. This evidently is a
consequence of the assumed complex dielectric permittivity.
For a Gaussian EMP (Figure 1.21), the incident electric field is
e 0 (t) = e 0 (0) exp [−t 2 /(2τ 2 )]
(1.57)
where τ is the pulse width and exp is the exponential function. The Fourier transform of
Equation 1.57 is (see Figure 1.22 for representative spectral distributions of the incident
Gaussian electric pulses).
E 0 (z,ω) = (2π) 1/2 τe 0 (0) exp (−ω 2 τ 2 /2) exp (−jωz/c)
(1.58)