Understanding EMC Basics Part 1: 1of 7 EM Field Theory and Three Types of EM Analysis Keith Armstrong
Understanding EMC Basics series Webinar #1 of 3, February 27, 2013 Webinar Sponsored by: EM field theory, and 3 types of EM analysis
AR provides EMC solutions with our high power RF/Microwave Amplifiers to complete systems. EurIng Keith Armstrong CEng, FIET, Senior MIEEE, ACGI Learn more at www.arworld.us
Presenter Contact Info Email: [email protected] Website: www.cherryclough.com
Contents of Webinar #1
1. Electromagnetic fields, waves, and the importance Understanding EMC Basics of the return current path 2. Field theory, permittivity, permeability, wave impedance and velocity 3. Near-field and Far-field 4. Three types of EMC analysis (includes Skin Effect) 1 Electromagnetic fields and waves, and the importance of the return current path Send
Return
Electromagnetic (EM) fields Of course, a wave has different amplitudes along its path Every non-DC voltage/current is a wave of When a conductor is long enough propagating EM energy... – it cannot experience the same voltage or current, – guided by send and return current paths at the same time, over its whole length… ● and the insulators (dielectrics) that surround them (e.g. air) ● which is why high frequencies seem to behave so weirdly! EM waves spread out and create EM fields, (like ripples spreading out and making a pattern on a pool)... The ratio between wavelength () and conductor
● and we measure fields in terms of field strength dimension is very important – we can usually ignore “wave effects” when the Design for EMC is mostly about controlling fields dimension we are concerned with is < 1/100th of the – so that they are high where we want power or signals ● e.g. at 1GHz: – and low where we don’t want emissions or susceptibility < 3mm in air ( = 300mm); < 1.5mm in FR4 ( = 150mm) Understanding EMC Basics Part 1: 2of 7 EM Field Theory and Three Types of EM Analysis Keith Armstrong
Importance of the return current path Understanding EMC Basics
Electric and magnetic fields are the true nature of electrical and electronic power and signals – and they both depend on the physical routes taken by 2 the send and return currents Field theory , permittivity , A great deal of EMC design depends on permeability, wave impedance controlling the paths of the return currents and velocity All currents always flow in complete loops… – taking the path of least impedance – the path with the least area – i.e. the return current flows as close to its send path as it is allowed to
We don’t need field theory Permeability (µ) and permittivity () – just a few concepts All media or materials have conductivity/resistivity
Fluctuating voltages create Electric fields (E) (i.e. loss of EM energy, turned into heat), µ and ... -7 – which are measured in Volts/metre (V/m) – in vacuum (and air): µ0 = 410 Henries/metre… ● i.e. the vacuum can contain magnetic field energy Fluctuating currents create Magnetic fields (H) – And: = (1/36)10-9 Farads/metre – which are measured in Amps/metre (A/m) 0 ● i.e. the vacuum can also contain electric field energy EM waves have power (P) Other media and materials are characterised by – measured in Watts/square metre (W/m2) their relative permeability (µR) and permittivity (R) (i.e. the rate ate which energy passes through an area) – so their absolute permeability is: µ0µR and their absolute permittivity is: 0R
Permeability (µ) and permittivity () µ and govern an EM wave’s impedance, continued... and it’s propagation velocity (e.g. wires, PCB traces) In conductors : µ and are what For the wave’s ‘far field’ impedance … causes them to have inductance (L) and capacitance (C)… Z = E/H = V/m A/m = (0R/0R) – so whenever there is a fluctuating voltage (V) there is Z = 377in air or vacuum always an associated current (I), and vice-versa Z = 377 (R/R) in a medium or material
In insulators (e.g. PVC, FR4, air): µ and cause effects For the velocity of the wave’s propagation … similar to inductance and capacitance… v =1/ (0R0R) metres/second – so whenever there is a fluctuating electric field (E) 8 there is always an associated magnetic field (H), v = 3.10 m/s in air or vacuum (i.e. the speed of light) and vice-versa 8 v = 3.10 /(RR) m/s in a medium or material Understanding EMC Basics Part 1: 3of 7 EM Field Theory and Three Types of EM Analysis Keith Armstrong
And the velocity of wave propagation (v) links frequency () to wavelength () Understanding EMC Basics v = In vacuum or air: v = c = 300 million metres/second 3 – 1/ ( ), equivalent to 3ns/metre, 3ps/millimetre 0 0 Near Field and Far Field But in media or materials with R and/or R >1.0, v is slower than c
– so the wavelength () is shorter (for a given f )
● e.g. for a printed-circuit board trace, v is approx. 50% of c ….so a is approx. 50% of what it would be in air
NearNear--fieldfield and Far-Far-fieldfield An example of a nearnear--fieldfield field distribution
Near fluctuating voltages or currents, E and H fields This shows the fields in one 3 plane at 5.32GHz, but the have complex patterns: field strengths vary as 1/r , simulator calculates all of the 2 frequencies in all of the three 1/r and 1/r dimensions ● where r is the radial distance from the source – because of stray capacitance and stray mutual inductance effects (i.e. E and H field coupling)
But, far enough away, the fields become EM waves (E and H fields in the ratio of the wave impedance: Z)… This simulation is of a heatsink in free space – proximity to enclosure – and have simple ‘plane wave’ spherical distributions will have an effect with field strengths that vary as 1/r
NearNear--fieldfield and farfar--fieldfield when the source’s largest dimension is << (for illustration only) NearNear--fieldfield and FarFar--fieldfield continued… Wave impedance 10,000 For sources with longest dimensions <<, Near (induction) field Far (radiation) field 5,000 the boundary between the near and far field regions (fields vary as 1/r3, 1/r2 and 1/r) EM fields 2,000 is: (also called plane waves, r = /2 1,000 which vary as 1/r) 500 377 But for sources with dimensions >, 200 The final value of the the near/far field boundary is: 100 wave impedance depends on the medium it is 50 propagating through r = 2D2/ 20 (e.g. 377 in vacuum / air) – where D is the largest dimension of the source 10 0.1 0.2 0.3 0.5 1 23 5 Radial distance (r) from source in units of /2 Understanding EMC Basics Part 1: 4of 7 EM Field Theory and Three Types of EM Analysis Keith Armstrong
Understanding EMC Basics 4 Poll Questions Three types of EMC analysis (includes Skin Effect)
EMC uses three types of analysis Resonances
For conductor dimensions < /6 we can use All circuits have RF resonant modes ‘lumped circuit analysis’ methods (based on R, L, C) – where their currents or voltages experience resonant When conductor dimension is > /6 along one axis gain, called their ‘Q factor’... (i)(e.g. a wire) we must‘t use ‘transmission line ’li’ analysis – Qs of 100 or more are common (i.e. gains of 40dB or more)
But when conductors are > /6 in two or three As the voltage peaks, the current nulls, and vice-versa dimensions we must use ‘full-wave analysis’ (to maintain a constant energy as the wave propagates) – based on Maxwell’s Equations High levels of emissions (and poor immunity) ● only practical for very simple situations, tend to occur at resonances… or when using computers to do the analysis – so we often need to control them to achieve EMC
Lumped analysis… Lumped analysis: everything has resistance (R), Resistance and Skin Effect
inductance (L), and capacitance (C) DC currents travel through the whole cross- sectional area of a conductor – including all components, wires, cables, PCB tracks, connectors,,,, silicon metallisation, bond wires, etc – but AC currents are forced to flow close to the surface – also including their ‘stray’ or ‘parasitic’ Rs, Ls, and Cs This is known as the “skin effect” ● which can be intrinsic (e.g. the self-inductance of a wire lead)
● or extrinsic (e.g. stray C or L coupling due to proximity to So, high-frequency currents only penetrate weakly other objects) into the depth (thickness) of a conductor
Resistance increases with f due to Skin Effect – increasing the resistance in their path Understanding EMC Basics Part 1: 5of 7 EM Field Theory and Three Types of EM Analysis Keith Armstrong
Examples of crosscross--sectionalsectional current density in a copper sheet Resistance and Skin effect continued...
One skin depth () is the depth into the conductor Vdc by which the current density has reduced to 1/e 1 = metres (f µ0 µR ) Example at d.c Uniform current density ● where = conductivity V ac For copper conductors: = 66/f ( f in Hz gives in millimetres) – e.g. at 160MHz = 0.005mm, so 0.05mm below the surface (10 skin depths) the current density is negligible Example of surface currents at 1MHz ( = 0.07mm)
Graph of skin depth () Lumped analysis: Stray Inductance for copper, aluminium, and mild steel Skin depth (in mm) E.g. a thin wire has self-inductance of about 1µH 100 per metre (1nH per mm)
● this assumes its return current path is very far away 10 ● a close return path reduces the overall inductance experienced by the send/return current 1 Close proximity to ferromagnetic materials (e.g. steel) 0.1 with µr > 1 will increase its self-inductance 50Hz 0.01 But close proximity to conductors (e.g. cables, 0.00001 metalwork, etc.) will decrease self-inductance 0.0001 0.001 0.01 0.1 1MHz 10 100
Lumped analysis: Stray Capacitance Lumped Analysis: Resonances
L and C store energy in their E and H fields E.g. a thin wire on its own in free space has about 40pF per metre length (approx. 0.04pF per mm).... – this is true for intentional Ls and Cs (e.g. components) and ‘stray’ or ‘parasitic’ Ls and Cs – this is its ‘space charge’ capacitance....
– close proximity to dielectrics (r > 1) will add more stray All types of circuits have L and C (even if they are only space charge capacitance strays) and these cause resonances, at:
Proximity of conductors adds stray capacitance... fRES = 1/( 2LC )
– (8.8/d) nF/square metre in air (d is the spacing in mm) These resonances are ‘damped’ by the resistances
– (8.8 r/d) nF/sq. m., when d is the spacing through insulation in the circuit Understanding EMC Basics Part 1: 6of 7 EM Field Theory and Three Types of EM Analysis Keith Armstrong Transmission line analysis… all send/return conductors have The effects of keeping Z0 constant
characteristic impedance (called Z0 ) If Z is kept constant from source to load, almost The L and C associated with a small length governs 0 the velocity (v) with which EM waves travel through 100% of the wave (= signal) is communicated that length... v = 1/ (()LC) – which means that there must be low emissions from the wanted signal (because there is very little energy lost) And the ratio of the L to the C governs the characteristic impedance (Z0) of that length... This is called matched transmission line design Z0 = (L/C) – and a matched transmission line is a very inefficient antenna Note: the L and C values used in the above expressions are ‘per unit length’ (e.g. 1µH/metre, 100pF/metre) where the unit ● which is why all general purpose RF test equipment lengths used are shorter than /6 has 50 inputs and outputs, connected with ‘50 cable’
Changes in Z0 TransmissionTransmission--lineline analysis: Resonances over dimensions greater than /6 When a conductor has the same type of Z0 discontinuity at each end (whether the source and load These cause propagating EM waves to be reflected impedances are both too high, or too low)… (whether they are signals or power) – resonances occur when conductor length is a whole
number of half-wavelengths... fres = 150 l/L (()air dielectric) – like the r ipp les sprea ding in a poo l o f wa ter re flec ting where l is an integer (1, 2, 3, etc.), L is conductor length
from a floating stick (metres) and fres is in MHz E field H field l = 3 shown The technique called “EMC filtering” relies upon here creating changes in characteristic impedance 0 drive 0 – to reflect unwanted noise away from a protected circuit load Z0
TransmissionTransmission--lineline analysis: Resonances 22--dimensionaldimensional structural resonances: continued... ‘standing waves’ caused by reflections at the edges of a metal plate When a conductor has opposing types of Z0 discontinuity at its ends… Resonances can only occur at integer multiples of – resonances occur when conductor length is an odd number half-wavelengths, at: 2 2 (in MHz) of quarter-wavelengths… fres = 75 l/L (air dielectric) fres = 150 {(l/L) + (m/W) } where l is an odd-numbered integer (1, 3, 5, etc.), L is ● where: l and m are integers (0 , 1 , 2 , 3 , etc . ) conductor length (metres) and fres is in MHz and L and W are the plate’s length and width (in metres) E field H field l = 5 shown here H fields 0 drive load Z0 l = 3, m = 0 l = 1, m = 0 Understanding EMC Basics Part 1: 7of 7 EM Field Theory and Three Types of EM Analysis Keith Armstrong
‘Standing waves’ caused by reflections 33--dimensionaldimensional structural resonances: at the edges of a metal plate ‘standing waves’ caused by reflections continued... at the walls inside a metal box Magnetic field standing waves must have minima at Resonances can only occur at integer multiples of the edges of the metal plate half-wavelengths, at: (air has much higher impedance than metal)... 2 2 2 fres = 150 {(l/L) + (m/W) + (n/H) } (in MHz) – whilst electric fields must be a maximum at the edges ● where: lmnl, m, n are integers (0, 1, 2, 3, etc. ) and L, W, H are the box’s length, width, height (in metres)
E fields
l = 3, m = 0 l = 1, m = 0 l = 3, m = 0, n = 0 l = 1, m = 0, n = 0
A FLO/EMC simulation of the electric field distribution inside a shielded box The simulator calculates all frequencies, in three dimensions. This figure shows a ‘slice’ through a box at one of its resonant frequencies – probably the (3,0,0) mode
Poll Questions
Notice the field ‘leaking’ out through an aperture
Understanding EMC Basics series Webinar #1 of 3, February 27, 2013 EM field theory, and 3 types of EM analysis the end
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Presenter Contact Info Email: [email protected] Website: www.cherryclough.com