Schelkunoff’s Theory of Shielding Revisited
Schelknuoff in his book Electromagnetic Waves presented the presently accepted Shielding Effectiveness Equations. He illustrated the use of the equations with an example where the shield material (copper tube 0.2mm thick) was 1.0 centimeter from the source of the radiated wave. The frequency he used in his example was 1.0MHZ.
Al Broaddus presented a paper at the 1992 IEEE International Symposium on EMC in Anaheim and George Kunkel presented a demonstration at the 1999 IEEE International Symposium on EMC in Seattle. Both the paper and demonstration illustrated test data over the frequency range of 100kHZ to 1.0MHZ. The test sample in both cases was an aluminized mylar space blanket having an impedance of about 2 ohms. In both cases the test sample was in the near field of the radiating sources where both the E and H fields were measured for shielding effectiveness.
The arguments and results of Schelkunoff’s example are compared with the test data obtained by Broaddus and Kunkel. A thorough evaluation of the “Shielding Effectiveness Equations” is presented.
The example used by Schelkunoff to illustrate the use of the “Shielding Effectiveness Equations” consisted of a pair of “closely spaced current filaments” centered inside a 2 centimeter copper tube 0.2 millimeters thick as shown in figure 1.
Figure 1: Two Parallel current filaments and a cylindrical shield.
The impedance of the wave radiating from the “closely space current filaments” is consistent with the impedance of a wave 1 centimeter from a magnetic dipole antenna. The wave according to Schelkunoff is reflected at the incident side of the shield and again inside the barrier at the exit side. There is also an attenuation factor inside the barrier due to skin effect. A level of shielding efficiency was given where it is implied that the shielding level is to power.
The test performed and reported in the paper by Broaddus had the shield material (1.4 ohm space blanket) attached to the wall of a shielded enclosure with a 24 by 24 inch opening. The radiating sources were both an electric and a magnetic dipole antenna (see Figure 2 for typical setup.)
The shielding effectiveness to both the E and H fields were measured and recorded for both of the sources of the wave. There was no detectable shielding of the H field using either of the sources of radiated field strengths.
The demonstration performed by Kunkel at the 1999 IEEE, EMC Symposium used a 10 by 12 by 4 inch thick shielded box with a 2.4 ohm space blanket attached to the front of the box and an electric dipole antenna inside the box as the source of radiated field strength (see photograph in Figure 3.)
The observed shielding effectiveness test data was for both the E and H fields generated by the electric dipole antenna over the frequency range of 100kHZ to 1.0MHZ. There was no appreciable shielding to the H field observed during the demonstration.
Schelkunoff’s Theory of Shielding
Schelkunoff documented the presently accepted shielding effectiveness equations, i.e.,
A correction factor for assumptions made in the reflective co-efficient “R” is included (see arguments below in “Shielding Effectiveness Equations.”)
In Schelkunoff’s example, the variables used were (1) the distances from the radiating filaments to the shield was 1 centimeter; (2) the thickness of the shield was 0.2mm; (3) the frequency was 1.0 MHZ ; and (4) the impedance of the wave generated by the current in the filaments was consistent with that radiating from a magnetic dipole antenna.
The results for the values of R and A were:
R = 35 dB
A = 26 dB
S = 51 dB
where the value of “R” (the reflective coefficient) is a combination of a reflection loss at the incident side of the shield and at the exit side (inside the shield) i.e., “the wave is partially reflected at the outer surface of the shield and then partially re-reflected at the inner surface. The level of the re-reflected wave is lowered by a t nepers.”
This implies that the power in the wave is equally reflected at the incident side of the barrier and at the exit (or transmitted) side. Subsequent authors (Ott, White, etc) stipulate that the E field in the wave is reflected at the incident side and the H field at the transmitted side where the impedance of the wave leaving the shield is the impedance of free space (377 Ohms).
Broaddus Test Results
In the shielding effectiveness Testing performed and reported by Al Broaddus the 1.4 ohm space blanket material was attached to a 24 by 24 inch hole in a shielded enclosure wall. The testing consisted of using both an electric and magnetic dipole antenna as the source of the radiated field strength over the frequency range of 100 kHZ to 10 MHZ.
The shielding test results were for both the E and H fields generated by the two sources of radiated energy. Figures 4 and 5 illustrate the level of shielding that was recorded for the E field from both sources of radiated energy. The shielding to the H field for both sources of energy was zero (0).
In 1999 Kunkel presented a shielding effectiveness demonstration using a 2.4 ohm space blanket material. The source of the radiated field strength was an electric dipole antenna mounted inside a box as illustrated in figure 3. Shielding data was observed and recorded for both the E and H fields generated by the dipole antenna over the frequency range of 100 kHZ to 1.0 MHZ. The results of the E field shielding is illustrated on figure 6.
There was no apparent shielding effectiveness to the H field.
Table 1 illustrates that the value of the E field emanating from the space blanket was closely estimated by multiplying the value of the received H field with the 2.4 Ohm space blanket.
Shielding Effectiveness Equations
The shielding equations documented by Schelkunoff is identical to the universally accepted equations by the EMC community which are:
The value “R” is derived from “Wave Theory” as obtained using transmission lines. The wave theory assumptions are that the source and load impedances are the same as the characteristic impedance of the transmission line. When the load impedance varies from that of the characteristic impedance of the line there is a reflection coefficient “R”.
With regard to Shielding theory using radiated waves, the assumption is that the barrier impedance Zbarrier is the same as the wave impedance Zw at the incident side of the barrier. When the impedance of the barrier varies from that of the incident wave there is a reflection coefficient as illustrated above.
When using the shielding equation the barrier impedance Zb is assumed to be consistent with an infinitely thick barrier, i.e.:
Attenuation Factor “A” (Absorption Loss)
The impedance of the wave Zw equals the following:
At the barrier surface of the incident side of the barrier the values of E and H field are:
E = JS Zb (V/m)
Ht = JS (A/m)
where JS = Current Density at the incident surface of the barrier.
The relationship between E, H and J values remain constant as the wave penetrates the barrier. Therefore, at any barrier thickness “t” the values of E and H are:
Et = Jt Zb
HJ = Jt
Since the value of Jt equals Js = e-t/d
The attenuation equals:
20 log e-t/d = 20 log e-at = 8.686at
Reflection Coefficient Correction Factor (Re-reflection Coefficient)
Is defined as a re-reflection coefficient by many of the authors of books and papers dealing with “Shielding Theory” and is tied to power loss due to the wave “bouncing back and forth inside a barrier”.
The value is always negative (reduces the attenuation of a wave) when the thickness of a barrier is thin and/or when the wave impedance Zw is less than the barrier impedance Zb.
In Schelkunoff’s Shielding Equation
Barrier Thickness Factor equal to the reflection loss “R” when the wave impedance Zw is less then the barrier impedance Zb. As an example using Broaddus’s test data for the shielding effectiveness at 100 kHz using the magnetic dipole antenna as the source of the wave.
R = 6.67 dB
A = 0 dB
B = -6.67dB
SE “ 0
The shielding effectiveness to the E field of the test data obtained by Broaddus and Kunkel is closely related to that which is obtained using Schelkunoff’s “Shielding Efficiency” equations. However, Schelkunoff’s statement that the wave is reflected at the incident side and inside the barrier implies that the equations refer to the attention of both the E and H fields equally. This was not detected by the test data. Additionally, Schelkunoff implies that the reflection loss in his example is the same for the reflection at the incident side of the barrier and inside the barrier at the exit side. Definitions associated with his theory cannot support this hypothesis, i.e.:
k incident = Zw/Zb = .0790/,0004 = 214
and R incident = 17.3 dB @ incident side
k inside barrier = Zb/Z0 = .0004/377 = 9.77x10-7
R inside barrier = 54.1 dB
Schulkenoff gave them equal values.
2 (17.3) = 34.6 dB
Using the wave theory definitions which the “reflection loss” equations are based on yields the following:
R Total = 17.3 + 54.1 = 71.4 dB
It is interesting to note that when using his equations with an incident wave of .0004 Ohms impinged on a shielding barrier of 377 Ohms yields a shielding effectiveness of zero dB. This is consistent with the data documented by Broaddus and leads to a conclusion that there is not a reflection inside the barrier.
The EMC Community attributes the presently accepted “shielding effectiveness” equation and the interpretations of these equations to Schelkunoff. This interpretation has led the EMC community to the belief that there is a reflection factor for a wave inside the barrier and that the E and H fields are attenuated equally. The data obtained by Broaddus and Kunkel does not support t his interpretation.
The use of the equations do, however, yield results closely related to the E field data obtained by Broaddus and Kunkel. This lead to the conclusion that the author of the shielding effectiveness equations intended for the equations to predict the shielding of the E field.
The EMP design engineering community taught us that in order to calculate the values of the current and voltage levels induced into equipment signal and power lines we need to know the values of the E and H fields impinged on the wires. To be able to use the information, we need a “Shielding Theory” that can provide us with that information.
Broaddus, Al & Kunkel, George, “Shielding Effectiveness Testing of Aluminized Mylar,” IEEE International Symposium on EMC, Anaheim, CA, 1992.
Frederick Research Corporation, “Handbook of Radio Frequency Interference, Vol. 3,” Frederick Research Corp., Wheaton MD, 1962.
Hallen, Erik, “Electromagnetic Theory,” John Wiley & Sons, New York, NY 1962.
Kunkel, George, Demonstration: “Penetration of an Electromagnetic Field into and Through A Conductive Metal Barrier,”IEEE International Symposium on EMC, Seattle, WA 1999.
OH, Henry W., “Noise Reduction Techniques in Electronic Systems,” John Wiley & Sons, New York, 1976.
Schelkunoff, S.A., “Electromagnetic Waves,” D. Van Nostrand Co., New York, 1943.
White, Donald R.J., “Electromagnetic Shielding Materials and Performance,” Don White Consultants, Inc., 1975.