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# Things You May Not Have Heard About Shielding

What determines how effective a cable shield is going to be? And how does the decision to ground or not ground a shield impact its effectiveness? Fortunately, there is a well-developed theory of shielding, which will be discussed as a way to get a general understanding of what can be expected of shield performance. But there’s more to it. The manner in which the shield is terminated can significantly affect its effectiveness, as we shall see.

## The Theory of Shielding

### A model of the physical environment

The theory of shielding starts with a model of the physical environment of the shield. The model assumes that the cable is jacketed, so that a shield is not in contact with a ground plane anywhere except possibly at the ends. That being the case, a transmission line is formed by whatever ground plane exists and the outside of the shield. Likewise the inside of the shield and the conductors enclosed also form a transmission line. Thus what we have is two transmission lines coupled by the leakage through the shield (see Figure 1).

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Figure 1: The basic model of the physical environment

The coupling of the inner and outer transmission lines is characterized by a mechanism called surface transfer impedance, Zt. In most installations, the shield, and hence the outer transmission line, is shorted to ground either at both ends or one end, shown schematically in Figure 2, by the switch SW being closed or open respectively.

Figure 2: The model of the physical environment including terminations

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The inner conductors are terminated at each end in some impedance, which when measurements are done, is generally an open, short or matched load.

### A model of the electrical environment

If the shield is terminated at both ends, current can flow along the outside of the shield. This current can be due either to ground loops caused by the grounds at the ends of the cable being at different potentials (Vd), or it can be due to induction from external fields, or both. In either case the external shield current is coupled into the inner circuits via the surface transfer impedance, Zt.

If the shield is terminated at only one end, the ground loop is broken. Current is limited to that which is induced to flow through the distributed capacitance between the outside of the shield and the ground plane (see Figure 3).

Figure 3: Model of a cable terminated at only one end

The induced current may be small, in which case the important quantity is the voltage distribution along the cable. The voltage is zero where the cable is terminated but can be high at the open end for frequencies where the cable exceeds one-tenth of a wavelength, because, at that point, it becomes a very efficient antenna.

At the open end, there is capacitive coupling between the shield and the conductors of the cable due to the fringing capacitance Cf (see Figure 4). As the voltage across this capacitance can be high, a significant current can be coupled into the conductors of the cable through the fringing capacitance.

Figure 4: The basic schematic for coupling when one end of the shield is open-circuited

So far we have considered a model of the physical and electrical environment of a shield. Now we need to consider the characteristics of a shield’s construction, and how that impacts shield performance.

### Surface transfer impedance

To begin with, let’s consider a cable grounded at both ends. To see how a cable grounded in that way works, we need to discuss surface transfer impedance. Simply stated, surface transfer impedance relates the voltage developed across circuits inside a shielded cable to currents flowing on the outside of the cable. Thus in Figure 2 with the switch closed, the current Ishield on the outside of the shield gives rise to V1 and V2 on the conductors inside the shield, via Zt.

So how do we determine what Zt is? Well, we can measure it, or we can calculate it. The measurement route has been described in [3], and an example will be shown later. The calculation route is worth discussing because it provides an insight to the physics involved.

We said earlier that the cable shield and the ground plane form a transmission line. We cannot say much about the general case of this, so for simplicity, we’ll consider a coax with a ground plane wrapped around it, as shown in Figure 5.

Figure 5: Basic configuration for calculating Zt

In this case, the shield and the ground plane form a coax (so we have a coax within a coax, often called a triax). This configuration can be achieved in practice for a jacketed shielded cable by pulling a braid over the jacket; which is often done for measuring Zt, as explained in [4].

Now let’s suppose a current is flowing along the outside of the shield. From Maxwell’s equations, this current will generate a travelling wave which has electric and magnetic fields, as illustrated in Figure 6. If the conductors have no resistance, the E-field (Er) is radial, and the H-field (HΘ) is circumferential (the TEM mode that some of you may be familiar with). However, since the shield has some resistance, the product of the current flowing on the shield and the shield resistance will generate an E-field EZ in the Z direction, so that the resultant E-field is no longer radial but “tipped” as shown in Figure 7.

Figure 6: Shows the fields of the travelling wave

Figure 7: Orientation of the fields for calculating Zt

Because the shield has a finite resistance, the EZ field does not vanish in the shield, but has a strongly decaying value as a function of the penetration depth (related to the concept of “skin depth”), shown schematically in Figure 8. The EZ wave reaches some (greatly attenuated value) EZ(a) on the inside of the shield.

Figure 8: A wave with an EZ(b) component travelling on the outside of a shield, having a decaying component in the shield, reaching EZ(a) inside the shield

From circuit theory, EZ(a) is related to EZ(b) by the relations:

EZ(a) = ZaaIa + ZtIb

EZ(b) = ZtIa + ZbbIb

Where Ia is the current on the inside of the shield, Ib is the current on the outside of the shield, Zaa is the surface impedance of the shield inside, and Zbb is the surface impedance of the shield outside. Zaa, Zbb and Zt can be calculated from the physical properties of the case, e.g. Schelkunoff [1].

Rearranging the equations on the previous slide, the EZ(a) field at the inside of the shield can be expressed in terms of the current Ib and voltage EZ(b) at the outside of the shield as:

Ignoring the terms that are small

EZ(a) = ZtIb

### The calculation route for Zt: Solid shields

A formula for calculating Zt was given by Shelkunoff as

where RDC is the dc resistance of the shield, t is the thickness of the shield in centimeters, µr is the permeability of the shield relative to air, σr is the conductivity of the shield relative to copper, and f is the frequency in megahertz. Notice that Zt depends on frequency.

Inside the shield, EZ(a) drives a, basically, TEM wave (if the conductor resistance is small) that propagates along the conductors. The current Ia caused by the wave that travels inside the shield gives rise to voltages V1 and V2 across the terminations of the cable (see Figure 2). The amplitude of the current [and hence V1 and V2] depends on EZ(a) and Zt.

To see whether Shelkunoff’s formula actually works, we made a measurement on RG402, a solid-shield coax [3]. The results are shown in Figure 9, where the terms short-short and short-matched refer to two different methods of measuring surface transfer impedance. Figure 9 shows that Shelkunoff’s formula is a good predictor of surface transfer impedance [and hence shielding effectiveness]. It also shows that, for a solid shield, shielding effectiveness keeps getting better as frequency increases.

Figure 9: Example of Zt for a solid shield

### The measurement route for Zt: Cables with braided (wrapped) shields

Braided shields behave differently from solid ones, due to the holes in the shield created during the braiding process. The situation is similar for wrapped shields, which look like slot antennas. The holes or slot couple the fields outside the shield to the fields inside the shield by mutual inductance and capacitance. Surface transfer impedance can be calculated for this case, e.g. see [2]. But it’s messy, in particular, because it is hard to determine what the mutual capacitance and inductance are.

Generally what is done is to produce a sample of the braided or wrapped cable, and then measure its Zt as a function of frequency (as a measure of shielding effectiveness). As an example, using a method developed to do this [3], we measured the Zt of RG-58U, a widely used coaxial cable. The result is shown in Figure 10. Notice that, in contrast to solid shields, Zt for a braided shield increases with frequency, and eventually becomes oscillatory. Wrapped shields, in general, show the same behavior as braided ones.

An important point, as explained in [5], is that Zt increases to a first peak value as frequency is increased, and this peak is never exceeded as frequency is further increased. The frequency at which the first peak occurs depends on the length of the cable, and moves to lower frequencies as cable length increases. Indeed Zt can be plotted against the product of frequency and cable length. For example, a plot like the one in Figure 11 can be generated by fitting a curve to the peak values of the data plotted in Figure 10.

Figure 10: Example of Zt for a braided shield

Why this happens is explored further in [5] and [4], where the oscillatory behavior as a function of the length of the cable and frequency is discussed; and also why Zt reaches a peak value at some frequency, and then decreases as frequency is further increased.

## Effect of a Shield on Waveshape

Regardless of how the braided or wrapped cable shield is terminated, it basically acts like a high-pass filter. The result is that a surge travelling on the inner conductors of a shielded cable will have a steeper rise-time than the inducing surge on the outside of the shield. As an illustration, the effect of a shield grounded at both ends on the frequency spectrum of a lightning surge is shown in Figure 12. Here the frequency spectrum of a 4.5×77 negative first lightning surge has been multiplied by the Zt spectrum shown in Figure 11, assuming a 10 m long cable. Figure 12 shows that the low-frequency components of the surge are suppressed. The result is that the surge appearing on the inner conductors of the cable will have a steeper rise time than the surge on the outside of the shield. Note that a similar effect would occur if the shield were grounded at only one end, since the resulting capacitive coupling also suppresses the low-frequency components of the surge.

Figure 11: Zt from Figure 10 plotted as the product of frequency and cable length

Figure 12: The effect of a 10 m RG-58 coax shield grounded at both ends on a
4.5×77 negative first lightning surge

## The Effect of Shield Termination

Having looked at shielding theory, there is the practical matter of how to terminate the shield. This decision depends on the environment in which the cable is installed.

If a shield is terminated at only one end, a relatively high voltage may exist at the open end of the shield. Because a capacitance exists between the end of the shield and the cable conductors, electrical interference can be injected directly into the cable loads. The magnitude of this capacitance depends a lot on the installation, so it cannot really be calculated. The capacitive coupling is greatest at high frequencies, where the capacitive reactance is the lowest.

The argument has been made [6] that bonding a shield at only one end destroys its effectiveness, and there is some truth to it, especially at high frequencies, as shown in Figure 13 based on data in [7]. The implication of that remark is that a shield should never be bonded at one end only. But the remark was made in the context of saying that a properly designed system does not have ground loops – a condition that may not be achievable in practice.

Figure 13: The effect of terminating a shield at only one end

As a note, the difference between the “no shield” and the “360° at one side” plots in Figure 13 is 18 dB at 1 mHz. Extrapolating this plot to 100 Hz [a pretty risky thing to do] leads to an estimated difference between the two curves of 63 dB. So a shield grounded at only one end may have reasonable performance at audio frequencies, but not at broadcast radio frequencies and higher.

Grounding a shield at both ends eliminates the capacitive coupling problem and is most effective when the potential difference between the two shield terminations is low. In this case, the ground loop currents will be small, and the shield will have its maximum effectiveness, provided it is terminated properly. As pointed out in [6], proper termination is for the shield to be bonded at each end with a 360° termination. Figure 14 shows two examples.

Figure 14: Two examples of 360° shield termination

If that is not done, much of the benefit of terminating a shield at both ends may be diminished or lost; for example, as shown in Figure 15 from data in [7]. Note the loss of shielding effectiveness when pigtails are used (see also [8]).

Figure 15: Loss of shielding effectiveness due to terminating the shield with pigtails

## Conclusions

Back to the original questions: What determines how effective a cable shield is going to be? And how does the decision to ground or not ground a shield impact its effectiveness?

The theory of shielding gives a general understanding of what can be expected of shield performance, but the manner in which the shield is terminated also has a significant impact on the effectiveness of the shield.

An important factor to consider is whether or not the grounds at opposite ends of the cable are at close to the same potential. If they are, ground-loop currents will be minimal. In this case, grounding both ends of the shield is likely to give the best shielding performance. If the grounds are at substantially different potentials, ground-loop currents could be a problem, and in this case, leaving one end of the shield unterminated may give the best overall shielding performance, providing that shielding against high frequencies is not an issue.

The decision to terminate or not terminate depends on the application. Unfortunately, there is no rule that applies to all situations, and an experiment is often required to determine the best way to terminate the shield.

#### References

1. Shelkunoff, S.A. “The Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields.” Bell Syst. Tech. J. 13 (October 1934): 532-579.
2. Merewether, D.E. and T.F. Ezell. “The Effect of Mutual Inductance and Mutual Capacitance on the Transient Response of Braided-Shield Coaxial Cables.” IEEE Trans. on EMC, EMC-18 (February 1976): 15-20.
3. Martin, A.R. and M. D. Mendenhall. “A Fast, Accurate and Sensitive Method for Measuring Surface Transfer Impedance,” IEEE Trans. on EMC, EMC-26 (1984): 66-70.
4. Martin, A.R., and S.E. Emert. “Shielding Effectiveness of Long Cables.” IEEE International Symposium on EMC, San Diego (1979): 13-18.
5. Martin, A.R., “The Shielding Effectiveness of Long Cables, III: Maximum Leakage,” 5th Symposium and Technical Exhibition on EMC, Zurich, Edited by T. Dvorak. (1983): 379-84.
6. Waldron, Tony and Keith Armstrong. “Bonding Cable Shields at Both Endsto Reduce Noise.”www.compliance-club.com/archive/old_archive/020514.htm.
7. Üstüner, F., N. Tarim, and E. Baran. “Experimental Investigation of the Shield Termination Effect on the Field-to-Cable Coupling Level.” Progress in Electromagnetics Research Symposium Proceedings, KL, Malaysia, (2012): 19-22.
8. Paul, C.R. Introduction to Electromagnetic Compatibility, 2nd ed. New Jersey: Wiley Interscience, 2006.

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