Category: Electromagnetic Compatibility

Inductance of Loops

These equations are from Inductance: Loop and Partial — Clayton R Paul.

Note that the inductance is fairly similar for either square or circular loops for a given length of wire (circumference/perimeter).

Inductance of a circular loop:

\(L_{circular} = \mu_0a(\ln{\frac{8a}{r_w}}-2)\)

with:
a = radius of loop
r_w = radius of wire
(assumed a >> r_w)

For a 22 AWG wire:
1 cm = 45 nH (wire length 6.3 cm)
10 cm = 740 nH (wire length 63 cm)
100 cm = 10 uH (wire length 630 cm)

Inductance of a square loop:

\(L_{square} = 2\frac{\mu_0}{\pi}l(\ln{\frac{l}{r_w}}-0.774)\)

with:
l = length of side
r_w = radius of wire
(assumed l >> r_w)

For a 22 AWG wire:
1 cm = 22 nH (wire length 4 cm)
10 cm = 400 nH (wire length 40 cm)
100 cm = 6 uH (wire length 400 cm)

Inductance of a rectangular loop:

\(L_{rectangle} = \frac{\mu_0}{\pi}[-l\ln(1+\sqrt{1+(\frac{w}{l})^2})
-w\ln(1+\sqrt{1+(\frac{l}{w})^2})
+l\ln\frac{2w}{r_w}+w\ln\frac{2l}{2w}
+2\sqrt{l^2+w^2} -2w -2l]\)

Parasitic Elements

All conductors always have resistance, inductance and capacitance. As a circuit designer it is important to know how large these so-called parasitics are and when they are significant.

In general parasitics become more important with increasing frequency.
All parasitics end up being proportional to length therefore as a general rule conductors should be kept as short as possible. This typically means that wires and cables are the first to show parasitics.

Continue reading “Parasitic Elements”

Radiation

Radiation refers to the transmission of electromagnetic energy through propagating waves in free space.

There are two components to an EM wave – electric and magnetic.
A radiation source will inevitably be dominant in either electric or magnetic fields.

Magnetic Sources

A magnetic field is generated by current, and loop geometries emphasize magnetic fields.
A coil geometry strengthens magnetic fields by the square of the number of turns.
These structures are associated with inductance and low impedance.

Example magnetic sources:
-multi-turn coils
-loops
-apertures (openings) in metal structure

Electric Sources

Electric field is generated by voltage between conductive elements. This is the most common antenna type.

Larger surface areas tend to increase electric field.
These structures are associated with capacitance and high impedance.

Example electric sources:
-monopoles and dipoles
-parallel plates
-horn antennas
-wire antennas

Interference Model

A general model for electrical interference is quite simple and very powerful.
Any interference problem is composed of 3 elements:
1) Source
2) Coupling path
3) Victim

If any of the 3 components are removed or hardened then the interference problem is resolved.

Sources

Sources are what generate the electrical noise that causes the interference.
Often noise is a high frequency phenomenon but not necessarily.
In actuality it is the rate of change, or fast, large edges that create the most problems.
A pulse of 1 V amplitude and 1 ns rise time has theoretically the same coupled amplitude as 100 V with 100 ns rise time.
Low frequency noise is also possible with certain coupling paths.

Coupling Paths

A coupling path is what allows the energy from the source get to the victim.
This includes electric field, magnetic field, EM waves, and common impedance.

Common impedance is when two different circuits share a conductor, coupling energy through its non-zero impedance (V = IZ). This is the only mechanism that can couple DC energy betwren circuits.

Victims

A victim is a circuit, typically a sensitive one, that cannot function correctly in the presence of the electrical interference.
Often this means analog systems such as audio or RF communication, but even digital systems are susceptible to strong interference.