Question E4E07:
Which of the following can cause shielded cables to radiate or receive interference?  

Choices:  
A: Low inductance ground connections at both ends of the shield  
B: Common-mode currents on the shield and conductors  
C: Use of braided shielding material  
D: Tying all ground connections to a common point resulting in differential-mode currents in the shield    

Correct Answer is  B: Common-mode currents on the shield and conductors  

Correct answer: B — Common-mode currents on the shield and conductors

1) Why B is correct
- Common-mode (CM) current flows in the same direction on all conductors, including the outside of the shield. That turns the cable into part of the antenna, so it can both radiate and receive RF noise.
- In contrast, differential-mode (DM) currents are equal and opposite inside the shield, so fields cancel and the cable does not radiate.
- CM current on the shield produces radiated power approximately proportional to current squared:
  $$P_{\text{rad}} \propto I_{\text{CM}}^2$$
- CM current magnitude is set by the CM source voltage and the CM path impedance:
  $$I_{\text{CM}} = \frac{V_{\text{CM}}}{Z_{\text{CM}}}$$
  Raising the CM impedance (chokes, bonding) reduces radiation.

2) Why the other choices are incorrect
- A: Low inductance ground connections at both ends of the shield
  - Low-inductance bonds reduce CM impedance and help drain CM current safely, reducing radiation. It’s floating or high-inductance terminations that aggravate CM radiation.
- C: Use of braided shielding material
  - Braided shields have finite transfer impedance and less than 100% coverage, but they do not cause radiation by themselves. Radiation occurs when CM current flows on the outside of the shield.
- D: Tying all ground connections to a common point resulting in differential-mode currents in the shield
  - Single-point grounding is generally good practice to control noise. DM currents flow between the signal conductors and largely cancel outside the shield; they do not cause the shield to radiate. It’s CM currents that do.

3) Useful formulas and rules of thumb
- Common-mode control:
  - Add a choke so that:
    $$Z_{\text{choke}} \gtrsim 1\ \text{k}\Omega \quad \Rightarrow \quad I_{\text{CM}} \approx \frac{V_{\text{CM}}}{Z_{\text{env}} + Z_{\text{choke}}} \ \text{is small}$$
- Short “pigtail” leads on shields increase RF impedance; keep them very short:
  $$X_L = 2\pi f L$$
  Example: a 25 nH lead has $X_L \approx 4.7\ \Omega$ at 30 MHz and $23.6\ \Omega$ at 150 MHz.
- Avoid resonant shield lengths; a cable segment near $l \approx \lambda/4$ can support larger CM currents.
- Radiation resistance of unintended short radiators (order of magnitude):
  - Short dipole: $$R_{\text{rad}} \approx 80\pi^2\left(\frac{l}{\lambda}\right)^2 \ \Omega$$
  - Short monopole: $$R_{\text{rad}} \approx 40\pi^2\left(\frac{l}{\lambda}\right)^2 \ \Omega$$
  CM current flowing on the outside of the shield into such a radiator increases $P_{\text{rad}} \approx I_{\text{CM}}^2 R_{\text{rad}}$.