Power plane resonances in printed circuit boards

Transcription

1 Sammenslutningen for Pålideligheds- og Miljøteknik SPM-166 Power plane resonances in printed circuit boards Viggo Brøndegaard Nielsen, DELTA November SPM's sekretariat DELTA Dansk Elektronik, Lys & Akustik Venlighedsvej 4 DK-97 Hørsholm Telefon: Fax:

2 SPM Society for Reliability and Environmental Testing SPM is an independent organisation consisting of about 1 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 Reliability and Environmental Testing (SPM).

3 3 Table of contents Page 1. Scope Conclusion Analytical D-models of PCB with power planes The simple D wave model The D model with decoupling capacitors Numerical models of power planes in a PCB The D grid model Difficulties of correct inductance of decoupling capacitors Equivalent diagrams of decoupling SMD components Measurements and simulations on some PCBs PCB named Plane Resonance 1C PCB named Plane Resonance 1C perf PCB named Plane Resonance 1C 1RC PCBs named Double Triangle 6C and Double Triangle 6C 6R PCB named Plane Resonance 6C Low Z PCB named Power Tracks Numerical simulation experiments Simple design guide for edge termination of power plane References...57

4 4 1. 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 electronics. Power plane resonances normally occur as an electromagnetic field between the reference plane and the power plane in a PCB. Normally the resonance frequencies are present above 3 MHz. In PCB's with only one plane, these resonances are absent. 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 frequency electromagnetic fields. In some cases the high ripple voltage or significant coupling 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 published. 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 [] 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 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, presentation and analysis.

5 5. 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 solution for the power plane resonance frequencies is interesting: ω mn = p ω' mn ω + ω p is the first parallel power plane resonance frequency caused by the parallel connection of the capacitance of the two planes and the inductance of all the decoupling capacitors. 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 decoupling capacitors. Low inductance is an important feature of decoupling capacitors and damping RCcomponents. 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 capacitors with only two vias connecting the planes on each capacitor gives an unacceptable high inductance. Components from the manufacturers, AVX and Murata have been investigated. The AVX array types W3A (4xC) and Z3A (4xRC) have excellent performance 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 resonances: PCB with 1 decoupling capacitors are made as a reference board with significant power plane resonance frequencies. PCB with 1 decoupling capacitors and 1 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 plane is of cause still a full plane. The triangular form did not reduce the presence and significance of the power plane resonances.

6 6 PCB with two triangles as above, but the two power planes are connected across the slid by eight parallel resistors of 1 ohm. A significant damping of the resonances is achieved, but the coupling to a signal track is still significant. PCB with 1 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 resonance 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 supply 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. Furthermore 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 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 db seems achievable in the frequency range,1 - GHz.

7 7 3. Analytical D-models of PCB with power planes 3.1 The simple D 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 analytical mathematical D-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 separation method can solve the D wave problem. Ldy/dx Ldx/dy Cdxdy Fig Diagram of small area, dxdy of power and reference plane The basis for the physical equations is a lumped circuit for a little part (dxdy) of the planes. (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 given 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 = µ µ r h µ r is the relative magnetic permeability of the material, and h is the height between the planes. In this case we consider that µ r =1, because no magnetic material is present. C is the specific capacitance per square meter of the planes, and it is given by: C = ε ε r /h ε r 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 following differential equation for the power plane voltage V(x,y,t): V x V + y V = CL t

8 8 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) = (,) on a corner on the PCB with x in the length direction and y in the width direction, the voltage can be expressed by: mπ nπ V(x,y,t)= Σ ( cmn cos( ω mnt) + d mn sin( ω mnt))cos( x)cos( y) l w Σ n= m = ω mn = π LC m l + n w and m,n =,1, If we recalculate the LC part you find the phase velocity, v p : v p = 1 LC 1 c = = c is the free space light velocity µ h ε hε ε r / r and then the resonance frequencies becomes: ω mn = πc ε r m l + n w and m,n =,1, A sketch of different modes of V(x,y) is given in figure 3.3. When n and m combined standing waves in both directions are formed. For m=1 and n=1 the voltage forms a "twisted butterfly" on the planes. For m= and n 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. 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, Z : Z = L C = µ h 1πΩh 377Ω = = h ε ε / h ε ε r r r This impedance has the dimension [Ωm], and it has to be divided by the wave width in order to find the "real" impedance.

9 ,15,3,45,6,75 m=1, n=,9,45, ,15,3,45,6,75, ,15,3,45,6,75,9 m=, n= m=1, n=1 1,75,5,5,5,5,75 1,5,5,75 1 m=, n= ,,4,6,8 m=, n=1 1,5,5 1,75 Figure 3. - Sketch of the plane voltage, V(x,y) for different modes In case of n= and m the problem is equal to the one-dimensional problem for a simple transmission line with standing waves. In the length direction you then have the solutions: mπ V(x,t)= ( cm cos( ω mt) + d m sin( ω mt))cos( x) l Σ m= 1 ω m = Z = πm l LC 377Ωh ε r w and m = 1, The similar formulas can be found for the width direction of the waves for m=.

10 1 3. The D 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. Ldy/dx Ldx/dy Cdxdy L p /dxdy Figure Lumped diagram for planes with distributed parallel inductance L p is a constant describing the inductance of the decoupling capacitors distributed on the board. The susceptance, dxdy/ωl p is evenly distributed and proportional to the area of interest. If you solve the circuit equations for this circuit, the following differential equation for the voltage, V(x,y,t) is: V x V + y V = CL t + L L p V This equation is slightly different from the previous equation without decoupling "inductance". If L p is increased, the impedance of the decoupling will increase, and the decoupling 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 similar: mπ nπ V(x,y,t)= Σ ( cmn cos( ω mnt) + d mn sin( ω mnt))cos( x)cos( y) l w Σ n= m = ω mn = π LC L m n + + π L l w p and m,n =,1, It is possible to interpret this result further by: 1 c 1 = and ω p = LC ε L p C r

11 11 ω p is the parallel plane resonance frequency, which is the normal first power plane resonance frequency. Now ω mn can be expressed as: ω mn = π c m n ω + p + = ε r l w p ω' mn ω + 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, L p is reduced, ω p is increased, and therefore 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: v p = ε r c ω p 1 ω for ω > ω p The specific impedance of the planes, Z is: Z = L = 1 C L ω p 1 Z ' ω p ω Z ' is the impedance of the planes without the decoupling "inductances". For frequencies above ω p then when you increase the number of decoupling capacitors, L p is reduced, ω p is increased, and therefore Z is increased. It seems like a contradiction, that this impedance should increase in this case, but you actually increase the parallel plane resonance frequency, so ω p get closer to the frequency of interest, and therefore the impedance increases. The impedance at a point on the plane is of cause also dependent of the wave reflections from the edges of the plane. The special one-dimensional special cases with m= or n= 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 results on real test PCB's.

12 1 4. Numerical models of power planes in a PCB 4.1 The D 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. dx Z y,td y dy Z x,td x Z x,td x Z y,td y Figure Cell of power plane simulated by transmission lines The inductances of this cell in the x-direction, y-direction, and the cell capacitance are: L x = µ hdx dy L y = µ hdy dx ε C = ε r dxdy h The capacitance has to be evenly distributed to the two transmission line axes. For onedimensional transmission lines the inductance and capacitance pr. length is specified, and it becomes: L' x = µ h dy L' y = µ h dx C' x = ε ε rdy h C' y = ε ε rdx h Then we get: Z x = L' C' x x µ h 377Ω h = = and Z y = dyε ε dy ε dy r r 377Ω h ε r dx

13 13 The phase velocity in x-direction is: v px = 1 Lx C dx dx = dyhdx µ hdxε ε dxdy r = c ε r The phase velocity is the same in the y direction and they are modified to be times the speed of a normal transmission line for this relative permittivity. The time delays in each of the transmission lines are then: Td x = dx v p ε r dx =, Td y = c dy v p = ε dy r c 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.. dx Z y,td y Z x,td x Z y,td y dy Z x,td x Figure 4. - Cell of power plane simulated by transmission lines on cell edge 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 inductance in this model, but it may be modelled correctly anyway due to the galvanic connections. 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.

14 14 4. 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 decoupling 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 becomes important - see figure 4.3: X X X Figure Reactance to centre of small cell X 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.

15 15 X X X X X X X X X X X X X X X X X X X X X X X Figure Circuit of 9 smaller cells Now the reactance from the edge of the previous sized cell to the centre can be calculated: X 3 = 1 X 1 X X X + X + = X = This reactance is,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 reactance (inductance) 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: h r 1 I g V r r H Figure Model with two small circular metallic planes connected on edge I According to Amperes Law the field, H at the distance, r from the centre can be determined: H = I = I g πr B = µ H = µ I g πr

16 16 The magnetic flux, Φ in the area from r 1 to r is r Φ = hbdr = r 1 µ hi g r ln π r1 And the inductance becomes: L = V di / = g dt d / dt di Φg / dt µ h r = ln π r1 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, r, it must be assumed that the capacitance 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 wavelength of the actual frequency. At higher frequencies this geometry forms a cavity, and this kind of problems are treated differently (see reference []). Let us make an example: The plane distance, h =,71mm, cell size 1x1 mm, and it is reduced to 3,33x3,33 mm. Then the inductance from the cell edge to the centre is: L = µ h/8 = 11 ph and then for the reduced cells: L = 91 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 capacitor 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 (r 1 1,83mm) and to the edge of 1x1 mm (r 5,5mm), and it is: µ L = r ln h r = 156 ph π 1 This inductance is 1,5% below the cell model value of 179 ph, and it may be considered a small difference with the approximations made. The inductance of a single via, with a radius of,7 mm and a return pass of the planes in a distance of mm becomes 613 ph.

17 17 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 components 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 < 1 MHz: about 4,7 Relative permittivity > 1 MHz: about 4,3 Plated via hole diameter:,4 mm Plane hole diameter at nc. via: 1,1 mm Layout design firm: GH-design Manufacturer: ELCON Layer Thickness [µm] Mask 5 Cu layer 1 37 Prepreg 37 Cu layer 35 (Ref. plane) Core 71 Cu layer 3 35 (Power plane) Prepreg 37 Cu layer 4 37 Mask 5 All together 1644 Figure PCB specifications for experiments Network analyser 47 Ω 47 Ω Component impedance PCB Capacitance C p PCB Figure 5. - Diagram for measurement of component impedance

18 18 The diagram for measurement of the impedance of different components are given in figure 5.. 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 1x1 mm, or 6x6 mm for the 63 sized SMD components. The remaining part of the power plane is connected to the reference plane (layer ) 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 PCB layout for 63 components. This power plane area is 6x6 mm. Figure Photos of PCBs used for component impedance measurements

19 19 Each component configuration is measured in the frequency range 1 MHz to 3 GHz using 16 measurements points distributed evenly with the logarithm of frequency, and a plot from measurement of one component is given in figure 5.5. Z1 measurement for 85 X7R decoupling capacitor using 8 vias and comparison with component model. Estimated result Measured values db Frequency [MHz] Figure Comparison of measured component and estimated component model 47 Ω (measured) 47 Ω (measured) R 5 Ω V g C L C p R p 5 Ω V Figure Equivalent circuit diagram for estimation of capacitors and AVX RC components 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, C p and some loss, R p are also estimated. An example of an estimated and measured frequency responce are given in figure 5.5. The nature of R p is not investigated how much is caused by the PCB material, skin effect, or the component itself.

20 Component type Component identification PCB layout Estimated component values L [ph] R [Ω] C [nf] C p [pf] R p [Ω] 1 nf X7R Size 85 terminals PCB 8 vias Not known 683,8 91,4 8,7 44 nf X7R Size 63 terminals PCB 4 vias AVX 635C3KATA 787,67 18, 3,3 4 1 nf Size 85 4 terminals PCB 7 vias AVX KNH ,8 7, nf Size 85 4 terminals PCB 11 vias AVX KNH ,8 8, x 1 pf Size 16 8 terminals PCB 1 vias AVX W3A45A11KAT 45,84,4 11,5 (14,8) Hardly valid 1 nf Size 16 8 terminals PCB 1 vias AVX W3L16C14MAT 1,36 86,8 9,5 37 pf 1Ω Size 63 terminals PCB 4 vias AVX Z1D13YM1K (38) hardly valid 9,5,5 no estim. 4x33pF,1Ω Size 16 8 terminals PCB 1 vias AVX Z3A43Y33M11K no estim. 5,13 9,4 no estim. Figure Estimation results of decoupling components

21 1 The table in figure 5.7 gives the results for the tested capacitors and AVX RCcomponents. 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 KNH114 1nF 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 85 package with one filter or in a 1 terminal 16 package with 4 filters. Figure 5.8 to 5.1 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 5.1. Figure Plane connection diagram for Murata, NFR1GD1147L, 1pF 47Ω Figure Plane connection diagram A for Murata, NFA31GD4711D array 47pF 1Ω

22 Figure Plane connection diagram B for Murata, NFA31GD4711D array 47pF 1Ω 47 Ω (measured) 47 Ω (measured) 5 Ω L R 1 R C p V g C 1 C 5 Ω V Figure Model used for Murata components with distributed capacitance The results of the estimated component values for the Murata components are given in the table figure Generally the values of R 1 is much smaller than R, and this fact actually disqualify the Murata components to be used for damping of power planes, because C 1 then prevents energy to be absorbed in R at higher frequencies above the resonance frequency formed by L and C 1. Much of the component capacitance is pressent on the terminal ends of the component - see photo figure 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.

23 3 RC-links made of discrete capacitors and resistors are possible and an example is reported in [1]. The difficulties of this solution are the increased inductance due to the series connection of two components and the extra required occupied PCB area. Coupling of Murata NFM1P compared with estimated diagram calcutaltion Estimated Measured db Frequency [MHz] Figure 5.1 Measured coupling and estimated curve from model Murata components

24 4 Component type Component identification PCB layout Estimated component values L [ph] R 1 [Ω] C 1 [pf] R [Ω] C [pf] C p [pf] 1pF 47Ω Size 85 4 terminals PCB 11 vias (fig. 5.8) murata NFR1GD1147L 91,11 44,8 6,93 6,1 6,4 Array 4 x 47pF, 1Ω Size 16 1 terminals PCB 1 vias (fig. 5.9) murata NFA31GD4711D 331, , 46,9 6,1 Array 4 x 47pF, 1Ω Size 16 8 terminals PCB 1 vias (fig. 5.1) murata NFA31GD4711D 189 1,1,1,1 15,7 17,6 Figure Estimation results of Murata RC decoupling components Figure Microscope photo of the Murata NFR1GD1147L

25 5 6. Measurements and simulations on some PCBs Some simple PCB's is produced to investigate the power plane resonances and to evaluate the mathematical models. Some other PCB's are produced to investigate 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 1C", "Plane Resonance 6C 6RC Low Z" and "Plane Resonance 1 C perf." was measured at a frequency of 1 khz using a LCR meter (EC 364, HP 474A): Plane Resonance 1C: 943 pf Plane Resonance 6C 6RC Low Z: 77 pf Plane Resonance 1 C perf: 157 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, ε r was calculated to be 4,7. At higher frequencies (>1 MHz) a value of ε r = 4,3 was chosen for use in simulation of the boards. The calculated capacity of Plane Resonance 1 C is: C = ε ε r h A = 8,85 pf/m x 4,7 x,1m x,16m /,71m = 937 pf All boards have the dimensions 16 x 1 mm and they do all have several SMA connectors on board to measure on the power plane. Each SMA connector centre pin is attached 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,1- 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

26 6 test was made on a board with the short signal track connected to a resistor to the reference plane, and the result of this measurement is given in figure 6.. 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 - K188 Test Specification: no Comment: Sheet 1 8 Level [dbµv/m] M M 3M 4M 6M 8M 1G G Frequency [Hz] MES field_1_pre PK Figure Noise floor for the receiver of electromagnetic field

27 7 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 8 Level [dbµv/m] M M 3M 4M 6M 8M 1G G Frequency [Hz] MES field_1_pre PK Figure 6. - "Real noise floor" do to leakage of noise coupled from track on board

28 8 Figure Test set-up for measurement of radiated electromagnetic field

29 9 6.1 PCB named Plane Resonance 1C A photo of the PCB, Plane Resonance 1 C is given in figure 6.1.1, and it has 1 decoupling 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 Measurements from the network analyser on the connectors, X1 and X6 of opposite corners are given in figure as well as the simulated results from a model without PCB losses. The model gives good results at frequencies below 5 MHz, above 5 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 1 seconds. X X6 X4 X3 X1 X5 Figure Photo of the board, Plane Resonance 1C A coupling of - db equals a plane coupling impedance of 1 Ω, and the impedance actually exceeds this impedance at several frequencies above 5 MHz as seen in figure The first parallel plane resonance frequency is measured to be 56,6 MHz. The LTSpice model predicts this frequency to be 561 MHz, and it is indeed very close. From the analytical 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 /,71m = 53,6 nf/m

30 3 L p = 683 ph/1 x,1m x,16 m = 1,93 phm The frequency, f is: f = π 1 L p C = 657,5 MHz. This frequency is much higher than the measured value, and the reason is an error in the calculation of L p. The correct L p 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 increase 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: L p = 1/(C x (πf p ) ) = 1,54 phm This value equals an increase in inductance for each capacitor of 57 ph from 683 ph to 94 ph. Especially the capacitors near the edge have a higher inductance in the planes. When this value of L p 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 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. Figure Simulation diagram with grid of transmission lines and 1 decoupling capacitors

31 31 Plane resonance 1C X1 to X6 and simulation without PCB loss Measured coupling X1 to X6 Simulated coupling db Frequency [MHz] Figure Measurement and simulation of coupling X1 to X6 (opposite corners) Resonance mode m,n Analythical frequency [MHz] Frequency at maximum from numerical model [MHz] Frequency at measured maximum [MHz], , , (two frq. collaps) 1, (two frq. collaps), , not seen not seen 3, , (three frq. collaps) 1, (three frq. collaps) 3, (three frq. collaps) Figure Resonance frequencies from measurements and models.

32 3 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 A total of 44 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 frequencies. 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 increased frequency. Coupling factor for Plane Resonance 1C from X1 to X6 and simulated results with PCB losses Measured Simulation with PCB loss db Frequency [MHz] Figure Comparison of measured and simulated results with PCB losses. Measured coupling on different connectors of Plane Resonance 1C X1 to X X1 to X3 X1 to X4 X3 to X4 X1 to X db Frequency [MHz] Figure Network analyser results for Plane Resonance 1C

33 33 Figure gives measurement results between different connectors on the board. The resonance frequencies are more or less present on all the connectors. Figure gives measurement results regarding radiated emission from the board. The first three resonance frequencies are well presented in the emission. One 5 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 generator was connected to this stripline, and the radiated emission is given in figure Again it is the power plane resonance frequencies which are to be seen in the radiated field.

34 34 DELTA Electronics Testing. EMC Section. EUT: Plane Resonance 1C Manufacturer: Operating Condition: Photo 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 8 Level [dbµv/m] M M 3M 4M 6M 8M 1G G Frequency [Hz] MES field_1_pre PK Figure Measured field strength in 3 m distance with noise on power plane corner

35 35 DELTA Electronics Testing. EMC Section. EUT: Plane Resonance 1C 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 8 Level [dbµv/m] M M 3M 4M 6M 8M 1G G Frequency [Hz] MES field_1_pre PK Figure Measured field strength in 3 m distance with noise signal track

36 36 6. PCB named Plane Resonance 1C perf The board Plane Resonance 1C perf is almost the same as Plane Resonance 1C, 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 x mm and each hole has a diameter of 1,1 mm. A photo of the board and coupling measurements are given in figure.6..1 X X4 X1 X3 Measured coupling on Plane Resonance 1C Perf X1 to X X1 to X4 X to X db Frequency [MHz] Figure Photo of Plane Resonance 1C perf and coupling measurements

37 37 The resonance frequencies of this board have fallen about 9 % compared to the previous board with no perforation. The increase in plane capacitance was 1 % (see section 6), so it accounts for a decrease in resonance frequency of 6 %. The reason for the remaining 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 perforation causes only small changes in the planes behaviour. 6.3 PCB named Plane Resonance 1C 1RC The Plane Resonance 1C 1RC board is the same as Plane Resonance 1C, but 1 Murata RC components are placed along the edge on the board in order to make edge termination of the planes. Edge termination is proposed by reference [1] and [9]. A photo of the board is given in figure 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 NFR1G type and the layout and characteristics are given in the first row of figure X X6 X4 X3 X1 X5 Figure Photo of Plane Resonance 1C 1RC The measured coupling results are given in figure The coupling impedance resonance peaks are reduced significantly compared to the results without the RC components given in figure However the first resonance frequency has been reduced to about 4 MHz due to the extra direct undamped capacitance, C 1 of the decoupling components. Figure 5.1 gives the impedance of an RC-link, and it is capacitive at frequencies below its series resonance frequency at about 13 MHz. Therefore the RClinks cause the resonance frequencies to decrease.

38 38 Measured coupling on Plane Resonance 1C 1RC different connectors X1 to X X1 to X3 X1 to X6 X3 to X db Frequency [MHz] Figure Network analyser results from Plane Resonance 1C 1RC At figure 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 4 MHz. The coupling factors at 3 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 7 MHz the RC-links provide good damping, and the field equals the field given in figure 6. in section 6.

39 39 DELTA Electronics Testing. EMC Section. EUT: Plane Resonance 1C 1RC Manufacturer: Operating Condition: Photo 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 8 Level [dbµv/m] M M 3M 4M 6M 8M 1G G Frequency [Hz] MES field_1_pre PK Figure Radiated emission from Plane Resonance 1C 1RC

40 4 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 triangles. It is the purpose to investigate the possible different resonance pattern of the triangle 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 decoupling capacitors, but here the two power planes are connected along the slid by 8 resistors of 1 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 The slid of the plane can be noticed by the diagonal row of resistors above the slid. The connection layout of the decoupling 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. X X6 X7 X1 X3 X4 X5 Figure Photo of Double Triangle 6C 6R Measurements of coupling between the connectors for the 6C-type are given in figure The different resonance frequencies of the triangles can be studied and the different shape of the power plane does not prevent resonances. However, the coupling level at the resonances seems about 5-1 db lower than the coupling in Plane Resonance 1C. The coupling between the two separated planes are more than db below the direct coupling, but the resonance frequencies of both planes is seen in this coupling.

41 41 Measured coupling on Double Triangle 6C X1 to X3 Coupling betw een triangles X1 to X6 Large triangle X3 to X7 Small triangle db Frequency [MHz] Figure Network analyser results from Double Triangle 6C Measured coupling on Double Triangle 6C 6R X1 to X3 Coupling betw een triangles X1 to X6 Large triangle X3 to X7 Small triangle db Frequency [M Hz] Figure Network analyser results from Double Triangle 6C 6R When the two planes are connected by resistors, it is expected that losses for the resonances of both planes are introduced, and it seems to be correct. Fig gives the result and the coupling of this configuration is about db below the levels of Plane Resonance 1C up to 1,7 GHz.

42 4 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 increased. 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 Measured coupling from power plane to signal track on different boards Plane Resonance 1C X5-X6 Double Triangle 6C X1-X4 Double Triangle 6C 6R X1-X4 Plane Resonance 1C 1RC X5-X db F req uency [ M Hz] Figure Coupling to signal track in different boards The radiated emission from the two triangle boards is given on figure and 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 Resonance 1C. The radiated emission from the damped triangle board is however better and about 1 db lower than the other two boards.

43 43 DELTA Electronics Testing. EMC Section. EUT: Double Triangle 6C Manufacturer: Operating Condition: 6 dg. Corn. Large Triangle 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 8 8 Level [dbµv/m] M M 3M 4M 6M 8M 1G G Frequency [Hz] MES field_1_pre PK Figure Radiated emission from Double Triangle 6C with generator on X1

44 44 DELTA Electronics Testing. EMC Section. EUT: Double Triangle 6C 6R Manufacturer: Operating Condition: 6 dg. Corn. Large Triangle 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 9 8 Level [dbµv/m] M M 3M 4M 6M 8M 1G G Frequency [Hz] MES field_1_pre PK Figure Radiated emission from Double Triangle 6C 6R with generator on X1

45 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 X X6 X4 X1 X3 X5 Figure Photo of Plane Resonance 6C Low Z The distance between layer 3 and 4 is 37 µm and the expected characteristic plane impedance are reduced with a factor 3. The board uses six low inductance decoupling capacitor 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. gives the coupling results between some of the connectors. The coupling seems 5 db lower than the similar measurements on Plane Resonance 1C. The first parallel plane resonance frequency is 4 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.