Power plane resonances in printed circuit boards

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Power plane resonances

in printed circuit boards

Viggo Brøndegaard Nielsen, DELTA

November 2002

SPM's sekretariat DELTA Dansk Elektronik, Lys & Akustik

Venlighedsvej 4 DK-2970 Hørsholm Telefon: 72 19 40 00 Fax: 72 19 40 01 www.delta.dk/spm

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SPM

Society for Reliability and Environmental Testing

SPM is an independent organisation consisting of about 100 company members in Scandinavia.

SPM initiates and finances unprejudiced investigations of common interest for its members – mainly in the field of reliability and testing of electronic components and materials.

NOTE: The report must not be reproduced without the written approval of the Society for Re-liability and Environmental Testing (SPM).

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Scope

In the last five years, the electronic engineers have increased the interest in matters of electromagnetic design of printed circuit boards, PCB's. This fact is caused by increased demand on EMC specifications and increased working frequencies of modern electro-nics.

Power plane resonances normally occur as an electromagnetic field between the refer-ence plane and the power plane in a PCB. Normally the resonance frequencies are pre-sent above 300 MHz. In PCB's with only one plane, these resonances are abpre-sent. Digital electronics often generate high frequency currents in the supply leads and it has been common practice to use decoupling capacitors and the supply plane to carry these currents by low impedance. However power plane resonances cause higher impedance of the supply at the resonance frequencies. If the electronics produce supply currents of these frequencies then the PCB is likely to cause unacceptable radiation of radio fre-quency electromagnetic fields. In some cases the high ripple voltage or significant cou-pling to signals cause malfunction of the electronics itself. The signal tracks penetrating the planes by vias cause the noise from the planes to couple into the signal.

This report gives a brief theoretical analysis of the power plane problem in section 3 and in section 4 the basis and formulas for numerical simulation by ordinary circuit analysis software are presented. A study and measurement on some decoupling capacitors and RC- components are given in section 5. Different methods for coping with this resonance problem have been investigated through several printed circuit boards. Measured results are revealed in section 6.

The University of Missouri-Rolla, EMC laboratory has been active in the research of these matters in several years and many papers have been published from them. A few other universities have been involved in such studies. However, measurement reports from real product digital circuit boards with focus on this matter have still not been pub-lished.

A list of literature references are given in section 9. Novak [1] has made a significant study of dissipative edge termination. The Morris patent [9] on edge termination shall be noted. Tarvainen [2] has studied the coupling effect from planes to penetrating signals by vias.

This report is financed by Society for Reliability and Environmental Testing, SPM and the project has been carried out by DELTA, Danish Electronics, Light & Acoustics. A previous study on printed circuit board design was made in the years 1999-2000 and this report continues the investigations regarding power plane resonances.

A student from the Danish University of Technology, Torben Rasmussen participated as part of his study in the project and has been helpful in the work of measurements, pre-sentation and analysis.

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2.

Conclusion

An analytical approach to power plane resonances is given in section 3. A large number of decoupling capacitors connecting the reference plane and power plane can be treated mathematically as an evenly distributed inductance between the planes. The simple solu-tion for the power plane resonance frequencies is interesting:

ωmn = ω_p2 +ω'_mn2

ωp is the first parallel power plane resonance frequency caused by the parallel

connec-tion of the capacitance of the two planes and the inductance of all the decoupling capaci-tors. ω'mn is the resonance frequencies of the same PCB with no decoupling capacitors.

This formula explains how all the resonance frequencies are increased by an increase in the parallel plane resonance frequency for instance by increasing the number of decoup-ling capacitors.

Low inductance is an important feature of decoupling capacitors and damping RC-components. The measurement results in section 5 reveals that very low inductance can be achieved by SMD components with four internal capacitors. The use of single capaci-tors with only two vias connecting the planes on each capacitor gives an unacceptable high inductance. Components from the manufacturers, AVX and Murata have been in-vestigated. The AVX array types W3A (4xC) and Z3A (4xRC) have excellent perfor-mance when used for reducing problems of power plane resonances.

Different PCB's of the same size are made to measure the damping effect on the reso-nances:

• PCB with 10 decoupling capacitors are made as a reference board with significant power plane resonance frequencies.

• PCB with 10 decoupling capacitors and 10 RC-links along the edge to terminate the two dimensional transmission line formed by the power planes. This approach seems to be the best technical solution in order to achieve low coupling to signal tracks, low radiation, and low impedance of the power supply at high frequencies. A possible problem is, that the RC-links may still be manufactured in small numbers.

• PCB with two reference planes encapsulating the power plane. The reduced plane impedance requires lower inductance of all the decoupling capacitors in order to keep the resonance frequencies high. The encapsulated plane gives low radiation. • PCB with the power plane split in two different sized triangles and the reference

pla-ne is of cause still a full plapla-ne. The triangular form did not reduce the presence and significance of the power plane resonances.

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• PCB with two triangles as above, but the two power planes are connected across the slid by eight parallel resistors of 10 ohm. A significant damping of the resonances is achieved, but the coupling to a signal track is still significant.

• PCB with 10 decoupling capacitors as the first board, but a large number of vias are placed on the board to perforate the power planes. The perforation causes the reso-nance frequencies to be slightly reduced, but no change of damping is observed. • PCB with no power plane, but you have a reference plane, power tracks, ferrite beats

and decoupling capacitors. No resonances are present due to the missing power plane. The performance of this approach seems good, but the impedance of the sup-ply to an integrated circuit is higher than achieved by the RC-decoupling solution. A network analyser is used to measure all PCB’s at different board positions. Further-more a semi-anechoic chamber is used to measure the radiated field at a distance of 3 meters.

A Numerical model with a grid of transmission lines has been used to simulate some of the boards and the used circuit analysis program is LTSpice from Linear Technology. It is a PSpice version. The model performs well and is able to produce results near the measurement results at frequencies below 2 GHz.

A simple design guide for the design of a power plane is given in section 8.

It is recommended, that the subject of power plane resonances is addressed in the design of PCB's with high speed digital circuits and microwave circuits. By simple damping measures, a reduction of the coupling and radiation of about 20 dB seems achievable in the frequency range 0,1 - 2 GHz.

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3.

Analytical 2D-models of PCB with power planes

3.1 The simple 2D wave model

A printed circuit board (PCB) with one reference plane (typically named gnd.) and one power plane (typically named +5V or pwr.). are used to supply the electronics on the board. No decoupling between the planes is considered yet. In several papers the analyti-cal mathematianalyti-cal 2D-model for such a rectangular printed circuit board has been given. Actually, it is almost the same problem, as has been solved previously as other physical problems, such as vibrations of a membrane or a metallic plate. When a simple boundary condition is in place, such as a rectangle or a circle, then using the mathematical separa-tion method can solve the 2D wave problem.

The basis for the physical equations is a lumped circuit for a little part (dxdy) of the pla-nes. (x,y) is considered as coordinates for a point on the PCB.

The inductance in the x-direction for this circuit is Ldx/dy and a similar inductance is gi-ven for the y direction. L is the inductance from one side to the opposite side of a square of the power plane and the formula is:

L = µ0µrh

µr is the relative magnetic permeability of the material, and h is the height between the

planes. In this case we consider that µr=1, because no magnetic material is present.

C is the specific capacitance per square meter of the planes, and it is given by:

C = ε0εr/h εr is the relative permittivity of the material between the planes.

After some circuit calculations for the x and y direction on this system you find the fol-lowing differential equation for the power plane voltage V(x,y,t):

2 2 2 2 2 2 t V CL y V x V ∂ ∂ = ∂ ∂ + ∂ ∂

Fig. 3.1 - Diagram of small area, dxdy of power and reference plane

Cdxdy Ldx/dy

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In case of no connection between the planes at the edge, then no current can flow across the edge of the power plane, and this statement forms the boundary conditions.

For a rectangular PCB with the length, l and the width, w, the differential equation can be solved using the separation method. For (x,y) = (0,0) on a corner on the PCB with x in the length direction and y in the width direction, the voltage can be expressed by:

V(x,y,t)= ( cos( ) sin( ))cos( )cos( )

0 0 y w n x l m t d t c_mn _mn _mn _mn m n π π ω ω +

Σ

∞₌ ∞₌ ωmn = 2 2       +       w n l m LC

π

and m,n = 0,1,2…

If we recalculate the LC part you find the phase velocity, vp:

vp = r r c h h LC

µ

ε

0 0 0 / 1 1 =

= c0 is the free space light velocity

and then the resonance frequencies becomes:

ωmn = 2 2 0 _      +       w n l m c r

ε

π

and m,n = 0,1,2…

A sketch of different modes of V(x,y) is given in figure 3.3. When n≠0 and m≠0 com-bined standing waves in both directions are formed. For m=1 and n=1 the voltage forms a "twisted butterfly" on the planes. For m=0 and n≠0 then standing waves are present in only the width direction.

In a separate case, the two planes may be well connected along the edge for instance in the cases of two reference planes. Then a cavity is formed in this "box" of metal. The same resonant frequencies can be found in this case except that m,n cannot be 0. The voltage has to be zero on this boundary and then V(x,y,t) is changed accordingly. It is also possible to define the specific plane impedance, Z0:

Z0 = h h h h C L r r r

ε

π

ε

µ

₌ Ω ₌ Ω = 120 377 / 0 0

This impedance has the dimension [Ωm], and it has to be divided by the wave width in order to find the "real" impedance.

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In case of n=0 and m≠0 the problem is equal to the one-dimensional problem for a sim-ple transmission line with standing waves. In the length direction you then have the solu-tions:

V(x,t)= ( cos( ) sin( ))cos( )

1 x l m t d t c_m _m _m _m m

π

ω

+

Σ

∞ = ωm = LC l m

π

and m = 1,2… Z0 = w h r

ε

Ω 377

The similar formulas can be found for the width direction of the waves for m=0.

0 0, 15 _0,3 0, 45 _0,6 0, 75 _0,9 0 0,45 0,9 -3 -2 -1 0 1 2 3 0 0, 15 0, 3 0, 45 0, 6 0, 75 0, 9 0 1 -3 -2 -1 0 1 2 3 0 0, 15 0, 3 0, 45 0, 6 0, 75 0, 9 0 0,25 0,5 0,75 1 -3 -2 -1 0 1 2 3 m=1, n=0 _{m=2, n=0} _{m=1, n=1}

Figure 3.2 - Sketch of the plane voltage, V(x,y) for different modes

0 0,2 0,4 _0,6 0,8 1 0 0,25 0,5 0,75 1 -3 -2 -1 0 1 2 3 0 0,25 0,5 0,75 _{1 0} 0,25 0,5 0,75 1 -3 -2 -1 0 1 2 3 m=0, n=3 m=2, n=1

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3.2 The 2D model with decoupling capacitors

When decoupling capacitors are placed between the planes the model has to be changed accordingly. If we consider a case with "many" decoupling capacitors well distributed on the board you can adopt a model of evenly distributed decoupling of the planes. For the frequencies of interest, it is only the inductive part of the decoupling capacitors, which is significant to describe these components impedance or admittance. The lumped circuit diagram is given in figure 3.3.

Lp is a constant describing the inductance of the decoupling capacitors distributed on the

board. The susceptance, dxdy/ωLp is evenly distributed and proportional to the area of

interest. If you solve the circuit equations for this circuit, the following differential equa-tion for the voltage, V(x,y,t) is:

V L L t V CL y V x V p + ∂ ∂ = ∂ ∂ + ∂ ∂ 2 2 2 2 2 2

This equation is slightly different from the previous equation without decoupling "induc-tance". If Lp is increased, the impedance of the decoupling will increase, and the

decoup-ling becomes insignificant - and then the two equations becomes the same.

This new equation can also be solved by the separation method and the solution is simi-lar:

V(x,y,t)= ( cos( ) sin( ))cos( )cos( )

0 0 y w n x l m t d t c_mn _mn _mn _mn m n

π

ω

+

Σ

∞₌ ∞₌ ωmn = 2 2 2       +       + w n l m L L LC π p π and m,n = 0,1,2…

It is possible to interpret this result further by:

r c LC

ε

0 1 = and ωp = C L_p 1 Cdxdy Ldx/dy Lp/dxdy Ldy/dx

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ωp is the parallel plane resonance frequency, which is the normal first power plane

reso-nance frequency. Now ωmn can be expressed as:

ωmn = _             +       + 2 2 2 0 2 2 w n l m c r p

ε

π

ω

= ω_p2 +ω'_mn2

ω'mn is the resonance frequencies of the PCB without the decoupling capacitors.

This equation is significant, because it explains how all the "standing wave" resonance frequencies are increased up and above the parallel plane resonance frequency. If the number of decoupling capacitors is increased, Lp is reduced, ωp is increased, and

there-fore all the standing wave resonance frequencies are increased too.

Another important thing to realize is, that this decoupling increases the sine wave phase velocity on the planes, and this velocity can be increased above the velocity of light. This velocity is:

vp = 2 0 1 _      − ω ω ε p r c for ω > ωp

The specific impedance of the planes, Z0 is:

Z0 = 2 0 2 ₁ ' 1       − = −

ω

p p Z L C L

Z0' is the impedance of the planes without the decoupling "inductances". For frequencies

above ωp then when you increase the number of decoupling capacitors, Lp is reduced, ωp

is increased, and therefore Z0 is increased. It seems like a contradiction, that this

imped-ance should increase in this case, but you actually increase the parallel plane resonimped-ance frequency, so ωp get closer to the frequency of interest, and therefore the impedance

in-creases. The impedance at a point on the plane is of cause also dependent of the wave re-flections from the edges of the plane.

The special one-dimensional special cases with m=0 or n=0 is just the same in this case as explained in the previous section with no decoupling components.

Later on in section 6.1 the results of this model shall be compared with measurement re-sults on real test PCB's.

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4.

Numerical models of power planes in a PCB

4.1 The 2D grid model

A model of the planes has been proposed by Lee and Barber [4] and consists of a grid of one dimensional transmission lines. This grid is then defined for an electrical circuit analysis program, and an AC-analysis is performed. In this way it is possible to simulate different placed decoupling capacitors and power plane RC-termination along the edges of the planes.

Consider a cell with the length, dx and the width dy on the plane. In order to replace this cell with one dimensional transmission lines, then look at the diagram below.

The inductances of this cell in the x-direction, y-direction, and the cell capacitance are:

Lx = dy hdx 0

µ

Ly = dx hdy 0

µ

C = h dxdy r

ε

₀

The capacitance has to be evenly distributed to the two transmission line axes. For one-dimensional transmission lines the inductance and capacitance pr. length is specified, and it becomes: L'x = dy h 0

µ

L'y = dx h 0

µ

C'x = h dy r 2 0

ε

C'y = h dx r 2 0

ε

Then we get: Zx = dy h dy dy h C L r r x x

ε

µ

377 2 2 ' ' 0 2 0 ₌ Ω = and Zy = dx h r

ε

2 377Ω dx dy Zy,Tdy Zx,Tdx Zy,Tdy Zx,Tdx

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The phase velocity in x-direction is:

vpx = r r x c dxdy hdx dyhdx dx C dx L

µ

ε

0 0 0 2 ₂ 2 2 1 = =

The phase velocity is the same in the y direction and they are modified to be 2 times the speed of a normal transmission line for this relative permittivity. The time delays in each of the transmission lines are then:

Tdx = 0 2c dx v dx r p

ε

= , Tdy = 0 2c dy v dy r p

ε

=

When such a number of cells are placed in a grid to model a PCB, then the edges has to be somewhat different. You have to shorten the edge transmission line in half by using the half time delay, but still the impedance is the same. Some circuit analysis program has problems when a transmission line has no connection, so a "dummy" connection to large resistor can solve the problem.

The cell can also be placed in other ways with reference to the grid as seen in figure 4.2.

In this case you find the same impedances in the grid, but at the PCB edge you have to double the impedance of the transmission lines along the edge.

The author has not seen mathematical proof, that a grid properly can model the PCB planes. It might seem wrong, those inductances of neighbour cells have no mutual induc-tance in this model, but it may be modelled correctly anyway due to the galvanic connec-tions.

It is also possible to work with simpler one-dimensional models for the PCB planes. Then the resonance of waves in only one direction can be simulated.

dx dy Zy,Tdy Zx,Tdx Zy,Tdy Zx,Tdx

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4.2 Difficulties of correct inductance of decoupling capacitors

When a PCB is modelled by a grid network as explained in the previous section, then it becomes possible to connect decoupling capacitors to the joints in the grid. The decoup-ling capacitors will normally have a dominating inductive part at frequencies of interest in regard to power plane resonances. The inductance is formed by the magnetic field around the decoupling capacitor and its connections from the surface of the board down to the reference plane and the power plane. Some of this field is actually also simulated by the inductance of the transmission lines in the grid. This part of the inductance gives a circular magnetic field around the connection to the lowest plane and between the two planes.

Let us think of an example with the decoupling connected to the centre of a square cell, and we want to know the inductance from the cell edge to the centre due to the circuit diagram. If the cell is small, it is only the reactance, X of the grid elements witch be-comes important - see figure 4.3:

The reactance from the cell edge to the cell centre with a decoupling capacitor is X/8. If we reduce the cell size to one third of the size above with 9 times the number of cells then the inductance of the grid element remains the same (see the inductance formulas in the previous section). The diagram of the 9 cells is given in figure 4.4.

X

X X

X

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Now the reactance from the edge of the previous sized cell to the centre can be calcu-lated: X3 = 8 5 13 40 13 2 2 1 2 4 1 X X X X X X = =            + +

This reactance is 2,6 times the reactance calculated before. So if we attempt to make our model better by increasing the number of cells, then we also have to readjust the reac-tance (inducreac-tance) of the components connected to the grid. It can be explained by the fact, that the grid element starts to model a larger part of the components inductance, and therefore you have to reduce the inductance of the component in the model.

It is possible to make a simple calculation of the inductance for a via and the planes in a special case. Consider two circular metallic planes with an isolating material between them and the two planes are connected along the edge. In the centre a via connects the two planes in series with a current generator:

According to Amperes Law the field, H at the distance, r from the centre can be deter-mined: H = I = r I_g

π

2 B = µ0 H = r I_g

π

µ

2 0 Ig r1 r2 r I H h V

Figure 4.5 - Model with two small circular metallic planes connected on edge

X X X X X X X X X X X X X X X X X X X X X X X X X

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The magnetic flux, Φ in the area from r1 to r2 is

Φ =

∫

2 1 r r hBdr = _     1 2 0 ln 2 r r hI_g

π

µ

And the inductance becomes:

L = dt dI V g/ = dt dI dt d g/ / Φ = _      1 2 0 _ln 2 r r h

π

µ

The formula equals the formula for the inductance of a coaxial cable.

When an integrated circuit or a noise generator injects current into the power plane through the supply via, the first part of the current path causes an inductive voltage drop due to the inductance of the via. At some distance, r2, it must be assumed that the

capaci-tance between the planes becomes more significant and supplies the current. This model of inductance alone is useful only when the dimensions are small compared to the wave-length of the actual frequency. At higher frequencies this geometry forms a cavity, and this kind of problems are treated differently (see reference [2]).

Let us make an example:

The plane distance, h = 0,71mm, cell size 10x10 mm, and it is reduced to 3,33x3,33 mm. Then the inductance from the cell edge to the centre is:

L= µ0h/8 = 112 pH and then for the reduced cells: L = 291 pH

The difference in inductance is 179 pH. Therefore it is important also to publish the used measurement set-up, when you publish the measured inductance of a decoupling capaci-tor for decoupling of a power plane.

It is not possible to reduce the cell size around the decoupling component indefinitely, because at some point you will reach the size of the connecting vias to the component, and then you have to connect the component to more nodes of the grid in order to make a proper model. In this case, the inductance does not increase any more.

It is possible to make a similar example of the via inductance similar to 3,33x3,33 mm (r1 ≈ 1,83mm) and to the edge of 10x10 mm (r2≈ 5,5mm), and it is:

L = h r r       1 2 0 _ln 2π µ = 156 pH

This inductance is 12,5% below the cell model value of 179 pH, and it may be consid-ered a small difference with the approximations made.

The inductance of a single via, with a radius of 0,27 mm and a return pass of the planes in a distance of 20 mm becomes 613 pH.

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5.

Equivalent diagrams of decoupling SMD components

In order to make predictions of the resonance frequencies in power planes by using the formulas or models in the previous section, then you have to know the decoupling com-ponents in more detail and especially the inductance. Low inductance of the decoupling capacitors increases the power plane resonance frequencies or fewer capacitors are needed on the board. A number of capacitors and RC-components have been measured. The impedance of decoupling depends of the SMD component itself, the printed circuit board connections to the planes, and how the measurement connections are placed. The printed circuit board used for the measurements are a standard four-layer type with the specifications given in figure 5.1 and they are partly measured. It is possible to use more expensive PCBs using micro-via technology, which may increase the decoupling performance further.

Material type: FR4

No. of cobber layers: 4

Relative permittivity < 100 MHz: about 4,7 Relative permittivity > 100 MHz: about 4,3

Plated via hole diameter: 0,4 mm

Plane hole diameter at nc. via: 1,1 mm

Layout design firm: GH-design

Manufacturer: ELCON

Layer Thickness [µm]

Mask 25

Cu layer 1 37

Prepreg 370

Cu layer 2 35 (Ref. plane)

Core 710

Cu layer 3 35 (Power plane)

Prepreg 370

Cu layer 4 37

Mask 25

All together 1644

Figure 5.1 - PCB specifications for experiments

Network analyser 47 Ω 47 Ω Component impedance PCB _Capacitance Cp PCB

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The diagram for measurement of the impedance of different components are given in figure 5.2. An example of the PCB-layout for one component with SMA connectors are given in figure 5.3. A network analyser is used to measure the frequency response from the two SMA connectors of the circuit. The power plane (layer 3) is separted and the component to be measured connects to a small power plane of 10x10 mm, or 6x6 mm for the 0603 sized SMD components. The remaining part of the power plane is connected to the reference plane (layer 2) along the edge of the PCBs and at several other places. The layouts use several vias on each component in order to reduce

inductance. Photos of the PCBs for measurement on the SMD components are given in figure 5.4.

Figure 5.3 - PCB layout for 0603 components. This power plane area is 6x6 mm.

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Each component configuration is measured in the frequency range 1 MHz to 3 GHz using 1600 measurements points distributed evenly with the logarithm of frequency, and a plot from measurement of one component is given in figure 5.5.

The measurement results are compared to the calculated results using a equivalent circuit, and the component values are estimated by use of curve fitting. The diagram used for estimation of the capacitors and RC-components are a simple series connection of capacitance, inductance and resistor - see figure 5.6. The capacitance of the parallel PCB power plane capacitance, Cp and some loss, Rp are also estimated. An example of

an estimated and measured frequency responce are given in figure 5.5. The nature of Rp

is not investigated – how much is caused by the PCB material, skin effect, or the component itself.

Z12 measurement for 0805 X7R decoupling capacitor using 8 vias and comparison with component model. -80 -70 -60 -50 -40 -30 -20 -10 0 1 10 100 1000 10000 Frequency [MHz] dB

Estimated result Measured values

Figure 5.5 - Comparison of measured component and estimated component model

Figure 5.6 - Equivalent circuit diagram for estimation of capacitors and AVX RC components

47 Ω (measured) Vg 50 Ω V 50 Ω R L C Cp 47 Ω (measured) Rp

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Estimated component values Component

type identification Component PCB layout

L [pH] R [Ω] C [nF] Cp [pF] Rp [Ω] 100 nF X7R Size 0805 2 terminals PCB 8 vias Not known 683 0,028 91,4 8,7 44 22nF X7R Size 0603 2 terminals PCB 4 vias AVX 06035C223KAT2A 787 0,067 18,0 3,3 42 100 nF Size 0805 4 terminals PCB 7 vias AVX KNH21104 315 0.016 86,8 7,8 37 100 nF Size 0805 4 terminals PCB 11 vias AVX KNH21104 308 0.016 86,8 8,4 37 4 x 100 pF Size 1206 8 terminals PCB 12 vias AVX W3A45A101KAT 245 0,084 0,420 11,5 Hardly (14,8) valid 100 nF Size 1206 8 terminals PCB 12 vias AVX W3L16C104MAT 210 0,036 86,8 9,5 37 22pF 10Ω Size 0603 2 terminals PCB 4 vias AVX Z1D13Y220M100K hardly (380) valid 9,5 0,025 2 no estim. 4x33pF,100Ω Size 1206 8 terminals PCB 12 vias AVX

Z3A43Y330M101K no estim. 25 0,132 9,4 estim. no

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The table in figure 5.7 gives the results for the tested capacitors and AVX

RC-components. The AVX W3A has 4 internal capacitors, which are connected in parallel, and the estimation is performed on the parallel connection only. The AVX W3L16 is a very low inductance decoupling capacitor and the distributor indicates an expensive component. The W3A-type has almost the same low inductance for much lower prices. One capacitor type, AVX KNH21104 100nF is a 4 terminal feed through type connected with two terminals to the reference plane and two terminals to the power plane in order to reduce inductance.

The Murata RC-components are somewhat different, because it is a kind of T low pass filter with the capacitance distributed along the resistor part. They are supplied in a 4 terminal 0805 package with one filter or in a 10 terminal 1206 package with 4 filters. Figure 5.8 to 5.10 gives the different kinds of connection diagrams of these filters for the measurement of decoupling. The equivalent diagram is given in figure 5.11 and it

contains two RC-links in order to simulate the distributed capacitance. A plot of the measured and estimated calculated result is given in figure 5.12.

Figure 5.8 - Plane connection diagram for Murata, NFR21GD1014702L, 100pF 47Ω

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The results of the estimated component values for the Murata components are given in the table figure 5.13. Generally the values of R1 is much smaller than R2, and this fact

actually disqualify the Murata components to be used for damping of power planes, because C1 then prevents energy to be absorbed in R2 at higher frequencies above the

resonance frequency formed by L and C1. Much of the component capacitance is

pressent on the terminal ends of the component - see photo figure 5.14.

In this project the fact about the Murata component was not realized before the PCB layout was made for damping of power planes with RC-components, so they were made for the Murata components.

Vg 50 Ω V 50 Ω R1 L C1 47 Ω (measured) Cp 47 Ω (measured) C2 R2

Figure 5.11 - Model used for Murata components with distributed capacitance Figure 5.10 - Plane connection diagram B for Murata, NFA31GD470101D array 47pF 100Ω

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RC-links made of discrete capacitors and resistors are possible and an example is re-ported in [10]. The difficulties of this solution are the increased inductance due to the se-ries connection of two components and the extra required occupied PCB area.

Coupling of Murata NFM21P compared w ith estimated diagram calcutaltion

-45 -40 -35 -30 -25 -20 -15 -10 -5 0 1 10 100 1000 10000 Fre que nc y [ M H z] dB Estimated Measured

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Estimated component values Component

type identification Component PCB layout

L [pH] R1 [Ω] C1 [pF] R2 [Ω] C2 [pF] Cp [pF] 100pF 47Ω Size 0805 4 terminals PCB 11 vias (fig. 5.8) muRata NFR21GD1014702L 291 0,110 44,8 6,93 62,1 6,4 Array 4 x 47pF, 100Ω Size 1206 10 terminals PCB 10 vias (fig. 5.9) muRata NFA31GD470101D 331 0,82 111 14,0 46,9 6,1 Array 4 x 47pF, 100Ω Size 1206 8 terminals PCB 12 vias (fig. 5.10) muRata NFA31GD470101D 189 1,12 22,1 20,1 15,7 17,6

Figure 5.13 - Estimation results of Murata RC decoupling components

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6.

Measurements and simulations on some PCBs

Some simple PCB's is produced to investigate the power plane resonances and to evalu-ate the mathematical models. Some other PCB's are produced to investigevalu-ate the effect of many vias and triangle formed power planes.

The PCB material was equal to the boards used for impedance measurements and the PCB data is given i figure 5.1. The capacitance of the power plane to reference plane for the three boards named, "Plane Resonance 10C", "Plane Resonance 6C 6RC Low Z" and "Plane Resonance 10 C perf." was measured at a frequency of 100 kHz using a LCR me-ter (EC 23642, HP 4274A):

• Plane Resonance 10C: 943 pF

• Plane Resonance 6C 6RC Low Z: 2770 pF • Plane Resonance 10 C perf: 1057 pF

Furthermore the thickness of the boards is measured, and they indicate that the distance between the layers is within 3% of the specified values. The low frequency permittivity, εr was calculated to be 4,7. At higher frequencies (>100 MHz) a value of εr = 4,3 was

chosen for use in simulation of the boards. The calculated capacity of Plane Resonance 10 C is:

C = ε0εr

h A

= 8,85 pF/m x 4,7 x 0,1m x 0,16m / 0,00071m = 937 pF

All boards have the dimensions 160 x 100 mm and they do all have several SMA con-nectors on board to measure on the power plane. Each SMA connector centre pin is at-tached to an on board 47 ohm resistor which connects to the power plane. In this way a network analyser was used to measure the coupling between different positions on the board. The measurement results are compared to calculated results.

Furthermore a battery powered noise generator can be attached to a SMA connector and the radiated emission is measured in a semi-anechoic chamber with reflecting ground floor. The noise generator gives a significant signal at harmonic frequencies of 5 MHz. These measurements are made using an antenna distance of 3 m and antenna heights of 1 m, 1,4 m and 1,8 m. The PCB with generator was turned in three different orientations. For each PCB and for some of the SMA connectors 9 frequency sweeps are received and the maximum field value at each frequency is presented in the frequency range 0,1-2 GHz. Photos of the test set-up is given on figure 6.3.

The noise floor of the receiver is given in figure 6.1. However leakage of the signal is provided by the noise signal track on the top of the boards, which connects to a resistor to the power plane. This track provides a mutual inductive coupling around the shield of the coaxial connection between the board and the noise generator. The generator and test board can be seen as two dipole antenna elements, which are utilized via this coupling. A

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test was made on a board with the short signal track connected to a resistor to the refer-ence plane, and the result of this measurement is given in figure 6.2. This curve can be interpreted as the "real noise floor" due to this leakage, which are present at most of the field measurements.

DELTA Electronics Testing. EMC section

EUT: Ambient noise Manufacturer:

Operating Condition: Max of Antenna in 1 m, 1,4 m, and 1,8 m horizontal Test Site: EMC-5 - 3 m distance

Operator: TR - K221808 Test Specification: no Comment: Sheet 1 0 10 20 30 40 50 60 70 80 Level [dBµV/m] 100M 200M 300M 400M 600M 800M 1G 2G Frequency [Hz] MES field_0001_pre PK

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DELTA Electronics Testing. EMC Section.

EUT: Plane Resonance low Z Manufacturer: DELTA

Operating Condition: X1 with resistor connected to ground Test Site: EMC-5

Operator:

Test Specification: 3 m distance antenna hights 1, 1,4 1,8 m Comment: Sheet 20 0 10 20 30 40 50 60 70 80 Level [dBµV/m] 100M 200M 300M 400M 600M 800M 1G 2G Frequency [Hz] MES field_0001_pre PK

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6.1 PCB named Plane Resonance 10C

A photo of the PCB, Plane Resonance 10 C is given in figure 6.1.1, and it has 10 de-coupling capacitors each with eight via-connections to the planes and the specifications and layout given in the first row of figure 5.7. A window from the simulation model in LTSpice is given in figure 6.1.2. Measurements from the network analyser on the con-nectors, X1 and X6 of opposite corners are given in figure 6.1.3 as well as the simulated results from a model without PCB losses. The model gives good results at frequencies below 500 MHz, above 500 MHz the power plane resonance frequencies are seen, and the model predicts almost the same resonance frequencies, but the coupling or Q-value at the resonance frequencies is not correct. The calculation time for a 1,6 GHz Pentium PC is about 10 seconds.

A coupling of -20 dB equals a plane coupling impedance of 12 Ω, and the impedance ac-tually exceeds this impedance at several frequencies above 500 MHz as seen in figure 6.1.3.

The first parallel plane resonance frequency is measured to be 560,6 MHz. The LTSpice model predicts this frequency to be 561 MHz, and it is indeed very close. From the ana-lytical model in section 3.1, the first parallel plane resonance frequency is calculated from the distributed inductance (see figure 5.7) and the plane capacity. They are:

C = 8,85 pF/m x 4,3 / 0,00071m = 53,6 nF/m2

Figure 6.1.1 - Photo of the board, Plane Resonance 10C

X6

X1

X3

X4

X5

X2

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Lp = 683 pH/10 x 0,1m x 0,16 m = 1,093 pHm2

The frequency, f is:

f = C L_p

π

2 1 = 657,5 MHz.

This frequency is much higher than the measured value, and the reason is an error in the calculation of Lp. The correct Lp has to be compensated for the inductance of the planes

to reach out for all the capacitance on the planes from each decoupling device. The in-crease needed in inductance is hard to predict, and it makes the analytical model harder to use. In this case it is possible to estimate the correct value from the measurements:

Lp = 1/(C x (2πfp)2) = 1,504 pHm2

This value equals an increase in inductance for each capacitor of 257 pH from 683 pH to 940 pH. Especially the capacitors near the edge have a higher inductance in the planes. When this value of Lp is used a comparison of the first predicted resonance frequencies

from the analytical and numerical model and the measured values can be compared, and they are given in figure 6.1.4. The frequencies from numerical model and measurements are close. The results from the analytical model seem in order for the first 5 frequencies, but at higher frequencies significant deviations appear.

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Resonance

mode m,n Analythical frequency [MHz] Frequency at maximum from numerical model [MHz] Frequency at measured maximum [MHz] 0,0 561 561 561 1,0 720 720 713 0,1 915 902 (two frq. collaps) 1,1 1021 968 (two frq. collaps) 2,0 1064 1042 1047

2,1 1158 not seen not seen

3,0 1356 1259 1259

0,2 1447 1442 (three frq. collaps)

Figure 6.1.4 - Resonance frequencies from measurements and models. Plane resonance 10C X1 to X6 and simulation without PCB loss

-120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 1 10 100 1000 10000 Fre que nc y [ MHz] dB

Measured coupling X1 to X6 Simulated coupling

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In order to improve the numerical model regarding the losses each transmission line is supplied with a two parallel resistors of 1,6 kΩ, and the results are given in figure 6.1.5. A total of 440 resistors are added in this way, so the total parallel resistance is 3,6 Ω. The simulated losses seem to be severe at low frequencies and too small at higher frequen-cies. The linear losses produced by a parallel resistor do not have the correct dependency of the frequency. The tan δ losses and skin effect losses become more severe by in-creased frequency.

Coupling factor for Plane Resonance 10C from X1 to X6 and simulated results with PCB losses -70 -60 -50 -40 -30 -20 -10 0 100 1000 10000 Frequency [MHz] dB

Measured Simulation with PCB loss

Figure 6.1.5 - Comparison of measured and simulated results with PCB losses.

Measured coupling on different connectors of Plane Resonance 10C

-80 -70 -60 -50 -40 -30 -20 -10 0 100 1000 10000 Fre que nc y [ MHz] dB X1 to X2 X1 to X3 X1 to X4 X3 to X4 X1 to X6

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Figure 6.1.6 gives measurement results between different connectors on the board. The resonance frequencies are more or less present on all the connectors.

Figure 6.1.7 gives measurement results regarding radiated emission from the board. The first three resonance frequencies are well presented in the emission.

One 50 Ω stripline is placed on layer four on the board from X5 to the opposite corner, where the stripline is terminated by a 47 Ω resistor to the reference plane. The noise gen-erator was connected to this stripline, and the radiated emission is given in figure 6.1.8. Again it is the power plane resonance frequencies which are to be seen in the radiated field.

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EUT: Plane Resonance 10C Manufacturer:

Operating Condition: Photo 16.15-23 3 orientations, 9 sweeps in all Test Site: EMC-5

Operator: HEN - K

Test Specification: Distance 3 m, Antenna hights 1m, 1,4m and 1,8m Comment: Sheet 6 0 10 20 30 40 50 60 70 80 Level [dBµV/m] 100M 200M 300M 400M 600M 800M 1G 2G Frequency [Hz] MES field_0001_pre PK

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DELTA Electronics Testing. EMC Section.

EUT: Plane Resonance 10C Manufacturer:

Operating Condition: Corn. X5 track 3 orientatiosn, 9 sweeps in all Test Site: EMC-5

Operator: HEN - K

Test Specification: Distance 3 m, Ant. hight 1m, 1,4m and 1,8m Comment: Sheet 15 0 10 20 30 40 50 60 70 80 Level [dBµV/m] 100M 200M 300M 400M 600M 800M 1G 2G Frequency [Hz] MES field_0001_pre PK

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6.2 PCB named Plane Resonance 10C perf

The board Plane Resonance 10C perf is almost the same as Plane Resonance 10C, but it is filled with vias of no connection, so the reference plane and power plane has a lot of holes in them. The holes are placed in a mesh of 2x2 mm and each hole has a diameter of 1,1 mm. A photo of the board and coupling measurements are given in figure .6.2.1

M e a su r e d c o u p l i n g o n P l a n e R e so n a n c e 10 C P e r f -80 -70 -60 -50 -40 -30 -20 -10 0 100 1000 10000 F re q u e n c y [ M H z ]

dB

X 1 t o X 2 X 1 t o X 4 X 2 t o X 4

X1

X2

X3

X4

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The resonance frequencies of this board have fallen about 9 % compared to the previous board with no perforation. The increase in plane capacitance was 12 % (see section 6), so it accounts for a decrease in resonance frequency of 6 %. The reason for the remain-ing difference should be an increase in plane inductance of about 6 %. The radiated emission is almost the same, so these results are not repeated here. Generally the perfora-tion causes only small changes in the planes behaviour.

6.3 PCB named Plane Resonance 10C 10RC

The Plane Resonance 10C 10RC board is the same as Plane Resonance 10C, but 10 Mu-rata RC components are placed along the edge on the board in order to make edge termi-nation of the planes. Edge termitermi-nation is proposed by reference [1] and [9]. A photo of the board is given in figure 6.3.1. At least one RC-link should be placed in each corner because all resonance modes have a significant voltage at this position. The-RC-links are of the NFR21G type and the layout and characteristics are given in the first row of figure 5.13.

The measured coupling results are given in figure 6.3.2. The coupling impedance reso-nance peaks are reduced significantly compared to the results without the RC compo-nents given in figure 6.1.6. However the first resonance frequency has been reduced to about 400 MHz due to the extra direct undamped capacitance, C1 of the decoupling

components. Figure 5.12 gives the impedance of an RC-link, and it is capacitive at fre-quencies below its series resonance frequency at about 1300 MHz. Therefore the RC-links cause the resonance frequencies to decrease.

Figure 6.3.1 - Photo of Plane Resonance 10C 10RC

X6

X1

X3

X4

X5

X2

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At figure 6.3.3 the radiated emission is given, and the noise generator is connected to X1. A significant emission is present at the new lower resonance frequency at about 400 MHz. The coupling factors at 300 MHz are also higher, and it seems that the system of board and noise generator provides a good antenna at this frequency. At frequencies above 700 MHz the RC-links provide good damping, and the field equals the field given in figure 6.2 in section 6.

Measured coupling on Plane Resonance 10C 10RC different connectors

-80 -70 -60 -50 -40 -30 -20 -10 0 100 1000 10000 Fre que nc y [ MHz] dB X1 to X2 X1 to X3 X1 to X6 X3 to X4

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EUT: Plane Resonance 10C 10RC Manufacturer:

Operating Condition: Photo 16.25-40 3 positions, 9 sweeps in all Test Site: EMC-5

Operator: HEN - K

Test Specification: Distance 3 m, Max of 3 sweeps ant. hight 1m, 1,4m and 1,8m Comment: Sheet 7 0 10 20 30 40 50 60 70 80 Level [dBµV/m] 100M 200M 300M 400M 600M 800M 1G 2G Frequency [Hz] MES field_0001_pre PK

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6.4 PCBs named Double Triangle 6C and Double Triangle 6C 6R

The Double Triangle PCB’s has the power plane divided into two different sized gles. It is the purpose to investigate the possible different resonance pattern of the trian-gle and try partitioning of a power plane. The reference plane is still a full sized plane on the boards. The 6C-type has two separated power planes and each one has 3 decoupling capacitors connected to the reference plane. The 6C 6R-type has the same layout and de-coupling capacitors, but here the two power planes are connected along the slid by 8 re-sistors of 10 ohm in order to cause damping. The different size to the two triangles cause different resonance frequencies in the two power planes.

A photo of Double Triangle 6C 6R is given in figure 6.4.1. The slid of the plane can be noticed by the diagonal row of resistors above the slid. The connection layout of the de-coupling capacitors is the same as for the other PCB’s. The SMA connectors connect to each corner of each triangle and one terminated stripline on layer four is also connected to a SMA connector.

Measurements of coupling between the connectors for the 6C-type are given in figure 6.4.2. The different resonance frequencies of the triangles can be studied and the differ-ent shape of the power plane does not prevdiffer-ent resonances. However, the coupling level at the resonances seems about 5-10 dB lower than the coupling in Plane Resonance 10C. The coupling between the two separated planes are more than 20 dB below the direct coupling, but the resonance frequencies of both planes is seen in this coupling.

Figure 6.4.1 - Photo of Double Triangle 6C 6R

X1

X2

X3

X4

X5

X6

X7

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When the two planes are connected by resistors, it is expected that losses for the reso-nances of both planes are introduced, and it seems to be correct. Fig. 6.4.2 gives the re-sult and the coupling of this configuration is about 20 dB below the levels of Plane Re-sonance 10C up to 1,7 GHz.

Figure 6.4.2 - Network analyser results from Double Triangle 6C

M e as u r e d co u p lin g o n Do u b le T r ian g le 6C -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 1 10 100 1000 10000 Fr e q u e n cy [M Hz ] dB

X1 to X3 Coupling betw een triangles X1 to X6 Large triangle X3 to X7 Small triangle

M e as u r e d co u p lin g o n Do u b le T r ian g le 6C 6R -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 1 10 100 1000 10000 Fr e q u e n cy [M Hz ] dB

X1 to X3 Coupling betw een triangles X1 to X6 Large triangle X3 to X7 Small triangle

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The power planes normally acts as a mirror for the signal tracks, and provides a return path of signal current along the signal track. When a slid in a plane is introduced, then this return path is disconnected, and coupling between the planes and the signal is in-creased. Therefore the power plane separation method can be questioned if the integrity of signals passing the slid is important. However, to pass a power plane with a signal via is the same offence as passing a slid. In both cases the return path is normally not present and coupling to the power plane is introduced. One signal track is placed on layer four of the present two boards and on some previous boards with no slid. The coupling to the signal track for the different boards is given in figure 6.4.4.

The radiated emission from the two triangle boards is given on figure 6.4.5 and 6.4.6. The coupling to the external field is still significant on both boards and at the emission from the undamped triangle board is at the same level as the emission from Plane Reso-nance 10C. The radiated emission from the damped triangle board is however better and about 10 dB lower than the other two boards.

Measured coupling from pow er plane to signal track on different boards

-120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 1 10 100 1000 10000 F r eq uency [ M Hz ] dB

Plane Resonance 10C X5-X6 Double Triangle 6C X1-X4 Double Triangle 6C 6R X1-X4 Plane Resonance 10C 10RC X5-X6

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Figure 6.4.5 - Radiated emission from Double Triangle 6C with generator on X1 DELTA Electronics Testing. EMC Section.

EUT: Double Triangle 6C Manufacturer:

Operating Condition: 60 dg. Corn. Large Triangle 3 positions, 9 sweeps in all Test Site: EMC-5

Operator: HEN - K

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DELTA Electronics Testing. EMC Section.

EUT: Double Triangle 6C 6R Manufacturer:

Operating Condition: 60 dg. Corn. Large Triangle 3 positions, 9 sweeps in all Test Site: EMC-5

Operator: HEN - K

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6.5 PCB named Plane Resonance 6C Low Z

The board, Plane Resonance 6C Low Z has an extra reference plane on layer 4, so the power plane on layer 3 is placed between the two reference layers. The two reference layers are well connected by vias along the edge and at ground connections for several components. A photo of the board is given on figure 6.5.1.

The distance between layer 3 and 4 is 370 µm and the expected characteristic plane im-pedance are reduced with a factor 3. The board uses six low inductance decoupling ca-pacitor type AVX W3L16, and it is prepared for six RC-links type AVX Z3A4, but AVX has got some delivery problems regarding the appropriate component values. But significant information can be seen without the RC-links. In order to limit the leakage field emission, the signal track to the power plane connected to X1 has been shielded by copper tape soldered to the connector and reference planes.

Figure 6.5.2 gives the coupling results between some of the connectors. The coupling seems 5 dB lower than the similar measurements on Plane Resonance 10C. The first pa-rallel plane resonance frequency is 400 MHz. The high capacitance of the power plane requires lower inductance or a higher number of decoupling components in order to keep or increase the power plane resonance frequencies.

Figure 6.5.1 - Photo of Plane Resonance 6C Low Z

X1

X2

X3

X4

X5

X6

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The radiated emission from the board is given in figure 6.5.3. The measured field is low, but it is possible to see the first two or three resonance frequencies of the board. For a real digital PCB a large number of tracks on top of the board are connected to the power plane, and about 50% of all digital signals are kept at power plane potential by the driver circuit. Therefore the shielding of the power plane is expected to be less effective in real use.

Measured coupling on Plane Resonance 6C Low Z

- 100 - 90 - 80 - 70 - 60 - 50 - 40 - 30 - 20 - 10 0 1 10 100 1000 10000 Fre que nc y [MHz] dB X1 to X2 X1 to X3 X1 to X6 X3 to X4

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EUT: Plane Resonance low Z Manufacturer: DELTA

Operating Condition: X1 with extra shield on track Test Site: EMC-5

Operator:

Test Specification: 3 m distance antenna hights 1, 1,4 1,8 m Comment: Sheet 21 0 10 20 30 40 50 60 70 80 Level [dBµV/m] 100M 200M 300M 400M 600M 800M 1G 2G Frequency [Hz] MES field_0001_pre PK

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6.6 PCB named Power Tracks

Maybe a power plane is not needed and with no power plane the resonances disappear. Reference [7] Janssen suggests, to remove the power plane and to use local decoupling of power to the digital circuits and ferrite beads for connection to power tracks. This PCB named Power Tracks has no power plane, but a small system of power tracks and decoupling capacitors. A photo of the board is given in figure 6.6.1.

Ten 0805 sized X7R 100 nF decoupling capacitors connects to ten ferrite beats, which connects to a common power track. The Ferrite type is a Murata BLM21PG600SN1 and according to the datasheet, the impedance at 100 MHz is 330 Ω. Each decoupling ca-pacitors connects to the reference plane by 4 vias in order to achieve low inductance and the power track passes the connection pad to the capacitor. The power track itself is de-coupled by one capacitor near the SMA connector X2b. The SMA connectors are placed to simulate noise from a possible digital circuit, and to measure the impedance of the power and coupling to other parts of the power system.

The coupling between the connectors is given in figure 6.6.2. The coupling between two power "consumers" from X1a to X1b is very low. The impedance of the supply to the "consumer" is indicated by the coupling from X1a to X2a and is higher than the expected impedance for a power plane. The coupling from a "consumer" to the power distribution is also quite low.

Figure 6.6.1 - Photo of Power Tracks

X1a

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The measured radiated emission is given in figure 6.6.3 and it seems higher than the ex-pected leakage by the inductive coupling to the SMA connector. However a coupling like this may be hard to avoid on this kind of board with power tracks, because each de-coupling capacitor has to carry the high frequency part of the current to their consumer (alone) causing a high local magnetic field.

Measured coupling on PCB with Power Tracks

-120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 1 10 100 1000 10000 Frequency dB

X1a to X2a X1a to X1b X1a to X2b X1b to X2b

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EUT: Power tracks Manufacturer:

Operating Condition: Photo 15.28-46 3 positions, 9 sweeps in all Test Site: EMC-5

Operator: HEN - K

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7.

Numerical simulation experiments

In section 6.1 a numerical model was used to simulate the behaviour of the Plane Reso-nance 10C with good results. Consider it possible to change the ESR resistance of the decoupling capacitors - how does it affect the coupling? The answer is given in figure 7.1. The black curve is the current ESR resistance of 0,028Ω of the X7R decoupling re-sistor. If the ESR resistance is increased, better performance is achieved at the high reso-nance frequencies, but the coupling increases at lower frequencies below 300 MHz. A better compromise seems to be an ESR-value at 0,4Ω.

If we replace the capacitors with a low inductance-type like the AVX W3A4 type with four capacitors in each package of 22 nF. The effect of such a change and the effect of using only 2 vias to the decoupling capacitor is given in figure 7.2. The impedance of the plane is improved by about 15 dB in the frequency range 25-700 MHz by the W3A4 type.

Capacitor ESR value: 0,028Ω black, 0,1Ω blue, 0,4Ω red, and 1,2Ω green Figure 7.1 - Simulated coupling X1 to X6 on Plane Resonance 10C

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The Plane Resonance 10C 10RC can be improved by using better RC-links like the AVX Z3A4 with 4 RC-links. First the best R-value is selected with C= 4 x 100pF - see figure 7.3. The best choice of R is 4 x 22Ω (red curve). Now the capacitance is changed - see figure 7.4. The best choice seems to be 4 x 22pF.

This optimization provides the values for the RC-link to be 4 x 22Ω and 4 x 22 pF. In this case the maximum calculated coupling is better than -41 dB below 1,9 GHz and -30 dB below 2,8 GHz. This performance is excellent. For these values the coupling from X3 to X4 is calculated, and it is better than -33 dB up to 2 GHz - see figure 7.5. The impedance of the power plane according to section 3:

Z0 = 377Ω x 0,00071 m / 4,3 = 0,129Ωm.

Each RC component shall cover about 52 mm of an edge so the matching resistor value should be: 0,129/0,052Ω = 2,5Ω. The chosen R value is 22Ω/4 = 5,5Ω. So it seems that the preferred termination resistance is two times the matching impedance of the plane. The total capacitance of the RC-links is 880 pF, and it is about the same as the capaci-tance of the plane.

Capacitor inductance value: black 2100 pH, 0805 2 vias blue 683pH, 0805 8 vias

red 245pH, 1206 12 vias 4 cap. Figure 7.2 - Simulated coupling X1 to X6 on Plane Resonance 10C

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RC: C=100 pF, R= 10Ω (black), 15Ω (blue), 22Ω (red), and 33Ω (green) Figure 7.3 - Simulated coupling X1-X6 for Plane Resonance 10C 10 RC

RC: R=22Ω, C=10pF(black), 15pF(blue), 22pF(red), 47pF(green), 100pF(violet) Figure 7.4 - Simulated coupling X1-X6 for Plane Resonance 10C 10 RC

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8.

Simple design guide for edge termination of power plane

This section sums up a simple design guide for decoupling of a power plane in multi-layer printed circuit boards using RC-links.

The reference plane shall be placed in layer 2 of multilayer boards to provide a good mirror plane for the signal tracks on layer 1 for connections to the components. More reference planes are included for 8-layer boards or boards with more layers. An extra reference plane may also be placed on a 6-layer board.

The impedance of the power plane is calculated:

Z0 = h r

ε

Ω 377 [Ωm]

If more reference planes are used then the impedance of each plane to plane relation shall be connected in parallel and the resulting impedance shall be used.

The capacitance of the power plane is calculated:

Cp = h A r o

ε

The plane area is given by A. If more reference planes are used then the capacitance of each plane to plane relation shall be added.

The number, Nc of decoupling capacitors should be in the range 4-20. A capacitor type

with a footprint of connections to the planes is selected and the inductance, Lc of such an

decoupling is predicted from this report or other sources. The parallel plane resonance frequency is calculated by:

fp = c c pL N C / 2 1 π

This frequency should be at least 300 MHz. The number, Nc, the inductance, Lc and the

capacitance, Cp may be altered to achieve an acceptable high minimum resonance

fre-quency, fp. It is preferred, that the capacitors are evenly distributed all over the board. It

is normally not necessary to place the capacitors near integrated circuits and the space may be well needed for signal vias at this point. The capacitors should not be placed closer than 3 mm from the edges.

An RC-link of some type is selected. The numbers, NRC used could for instance be 6-24

pieces of the AVX Z1D-type or 4-12 pieces of the AVX Z3A-type. For array type com-ponents, it is the resulting component capacitance, CRC and resistance, RRC which is used

in calculations. The total capacitance of all the RC-links should be near the capacitance of the power plane:

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NRCCRC≈ Cp

The total length, le of all the power plane edges shall be calculated. The resistance, RRC

of each RC-links are calculated by:

RRC≈ e RC l Z N ₀ 2

It is preferred, that at least one RC-link is placed in each corner of the power plane, but not closer than 3 mm from the edges. All resonance modes have maximum voltage at the corners – see figure 3.2. The remaining RC-links should be placed so they are almost evenly distributed along the edge of the power plane.

An example is the PCB analysed in section 7:

The board properties are: h= 0,71 mm, A= 0,016 m2, εr= 4,3, le= 0,52 m.

Selected values are: Lc= 683 pH + 250 pH, Cc= 100 nF, Nc= 10, NRC= 10

The formulas give: Cp= 858 pF, Z0= 0,129 Ωm, fp= 563 MHz, CRC= 86 pF, RRC= 5,0Ω

Lc is selected from the measured value, 683 pH and an “assumption” of extra inductance,

250 pH, caused by the plane in the present configuration. In this case Lc is used for

cal-culation of fp only.

A verification of the performance of the designed power plane performance can be cal-culated by use of a numerical model as demonstrated in section 4 and section 6. This model can be used for further optimisations of the design.

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9.

References

[1] Istvan Novak, SUN Microsystems Inc.: Reducing Simultaneous Switching Noise and EMI on Ground/Power Planes by Dissipative Edge Termination, IEEE Tr. CPMT, Vol.22, No.3, August 1999, pp.274-283.

[2] Timo Tarvainen: Studies on via coupling on multilayer printed circuit boards. Department of Electrical Engineering, University of Oulu and Esju Oy, Oulu, FIN-90570, 1999, Finland, ISBN 951-42-5189-X (URL:

http://herkules.oulu.fi/isbn951425189X/), ISBN 951-42-5188-1, ISSN 0355-3213 (URL: http://herkules.oulu.fi/issn03553213/)

[3] Timo Tarvainen, Simplified Modeling of Parallel Plate Resonances on Multilayer Printed Circuit Boards, IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 42, NO. 3, AUGUST 2000 pp. 284

[4] Keunmyung Lee and Alan Barber: Modeling and Analysis of Multichip Module Power Supply Planes, IEEE Transactions on Components, Packaging, and Manu-facturing Technology - Part B, Vol. 18. No. 4, November 1995.

[5] Hao Shi, Fei Sha, James L. Drewniak, Thomas P. Van Doren, and Todd H. Hub-ing: An Experimental Procedure for Characterizing Interconnects to the DC Power Bus on a Multilayer Printed Circuit Board, IEEE Transactions on Electro-magnetic Compatibility, Vol. 39, No. 4, November 1997.

[6] Wei Cui, Jun Fan, Hao Shi, and James L. Drewniak: DC Power Bus Noise Isola-tion with Power Islands (EMC Laboratory University of Missouri-Rolla).

[7] L. P. Janssen: Reducing the emission of multi-layer PCBs by removing the supply plane, EMC 1999, Zürich.

[8] Y. Imanaka et al.: Decoupling Capacitor with Low Inductance for High-Frequency Digital Applications, FUJITSU Sci. Tech. J., 38,1,(June 2002) [9] T. Morris, “AC coupled termination of a printed circuit board power plane in its

characteristic impedance,” US Patent 5,708,400, Jan.13, 1998

[10] V. B. Nielsen: EMC-rigtigt Printkortdesign, SPM-152, March 2000, Sammen-slutningen for Pålideligheds- og Miljøteknik.

Power plane resonances in printed circuit boards