Posts Tagged ‘PCB’
Field Solver Nuances: How to avoid GIGO
To avoid “garbage in, garbage out” (GIGO) with any field solver, first you need to understand the little nuances of PCB fabrication process and how to interpret manufacturers’ data sheets. But most importantly you need to understand the tool’s user interface and what it is asking for.
All 2D or 3D field solvers will give accurate impedance predictions. The differences are the type of solvers used under the hood and complexity of the user interface. Simple 2D field solvers, used in many of today’s stackup planners, simply give predicted characteristic impedance based on material properties and trace geometries. More complex, 2.5D or 3D field solvers, allow for additional material parameters and can predict insertion loss, phase delay and impedance over frequency. Some will even export RLGC and touchstone files for further signal integrity analysis.
Standard PCBs are fabricated using cores and prepreg material. Prepreg sheets are a mixture of fiberglass (glass) cloth and resin which is partially cured. Cores are simply cured prepreg sheets with copper bonded to one or both sides of the laminate. Copper is etched away on each side of the foil to leave the circuit pattern.
In a multilayer PCB, cores and prepreg sheets are alternately stacked symmetrically above and below the middle of the layup then pressed under heat and pressure. The prepreg layers gets thinner when pressed allowing the resin to fill the voids between the copper features that were etched away on the cores.
One important parameter for accurate impedance modeling is dielectric constant (Dk). The best source is from laminate suppliers’ data sheets. But all data sheets from laminate suppliers are not the same.
“Marketing” data sheets are data sheets easily found on laminate suppliers’ websites. They are meant for quick comparison of dielectric properties to narrow your search for the right laminate for your application. They include mostly thermal and mechanical properties, which are important for the physical structure of the material and how it will perform with other material properties in the stackup during processing [3].
Marketing data sheets usually only report a typical Dk value at fifty percent resin content at two or three frequency points. Depending on glass style, resin content and thickness, Dk and dissipation factor (Df), will be different for different cores and prepreg thicknesses for the same laminate chemistry. In the end, they are not representative of what is needed to design an actual stackup, or to do impedance and loss modeling. Using these numbers will almost always lead to inaccurate impedance and signal integrity (SI) results.
Instead, you need to use the same Dk/Df construction table data sheets PCB fabricators use for the stackup. Dk/Df construction tables provide the actual core and prepreg thicknesses, resin content, and Dk/Df for the different glass styles, over different frequencies. Depending on the stackup, a combination of thicknesses is often needed to meet impedance requirements and have different Dk values.
Many engineers assume Dk published is the intrinsic property of the material. But in fact, it is the effective Dk (Dkeff) measured by a specific industry standard test method. It does not guarantee the values directly correspond to design applications. When compared against measurements from a design application, there is often a discrepancy in Dkeff due to increased phase delay caused by surface roughness [1].
Dkeff is highly dependent on the test apparatus and conditions of how it is measured. One popular test method, IPCTM650 2.5.5.5C clamped stripline resonator test method, assures consistency of product during fabrication. Due to the nature of this test method, the materials under test are not physically bonded together, air is entrapped between the various layers. These small air gaps are caused by: roughness of the copper foil plates in the fixture; roughness profile imprint left on the surface from the foil that was removed from the test samples; copper removed on the resonant element pattern card. Air entrapment results in a lower Dkeff than what is measured because in a real PCB everything is bonded together, with no air entrapment [3].
All glass weave reinforced laminates are anisotropic, which means Efield orientation, relative to the glass weave, is different depending on test method. Efields produced from tests like IPCTM650 2.5.5.5C are transverse to the glass weave and Dkeff measured is outofplane.
Efields produced by TM6502.5.5.13 split post cavity resonators, are parallel to the fiberglass weave Dkeff measured this way is inplane. Dkeff is typically higher for inplane measurements, compared to outofplane, depending on the glass resin mixtures used in the stackup.
Another source of discrepancy is not accounting for increased Dkeff due to the pressed thickness of prepreg. Since prepreg sheets have a certain percentage of resin content for the thickness, after pressing the resin content is reduced and since Dk is a function of resin and glass mixture, there will be a higher percentage of glass after pressing and thus slightly higher Dkeff.
The most common PCB trace geometries are microstrip and stripline. A simple microstriip geometry is bare copper traces over a reference plane, separated by a dielectric height H, as shown in Figure 1. Depending on the stackup, there may be a core and prepreg layer between the outer layer and reference plane with the same or different Dk values for Dk1 and Dk2.
Simple stripline geometry has copper traces between two reference planes. For singleended (SE) signals, there is only one trace used in the field solver to calculate the SE impedance. For differential pairs, there are two traces separated by a space. Because resin fills the voids between copper features the Dk_{resin} will be lower than Dk1 or Dk2, shown in Figure 1.
The last thing to note is the wider side of the trace always faces the core material. This is a very important point to remember when using any field solver. If you get it reversed, it will lead to inaccurate results.
Figure 1 Generic microstrip and stripline geometries.
Thickness of copper traces is an important parameter for accurate impedance prediction. Copper thickness is usually specified in ounces per square foot. Most common thicknesses for inner layer traces are ½ oz. and 1 oz. foil. But field solvers expect an actual thickness dimension.
Most designers assume 0.7 mils (18um) thickness and 1.4 mils (36um) for ½ oz. and 1 oz. respectively. But because of the price of copper, the copper you get from foil manufacturers will likely be the minimum thickness allowed under IPC4562A. When you factor in the typical thickness after fabrication, the typical thickness can be 0.6 mils (15um) and 1.2 mils (30um). But the minimum thickness allowed under IPCA600G3.2.4 is 0.45 mils (11.4um) and 0.98 mils (24.9 um) for ½ oz. and 1 oz. respectively.
Due to the nature of the etching process, the traces will usually be trapezoidal in shape. This is known as the etch factor (EF), as defined by IPCA600G. It is the ratio of the thickness (t) to half the difference between W1 and W2.
Thus,
Some field solvers will define EF differently so it is important to understand how to specify it properly.
Once you’ve come up with a proposed stackup, the next step is to do some impedance modeling. Normally your fab shop comes up with this, but it is a good idea to validate their proposal, to ensure you are in sync with them.
The first thing to do, is identify the layers from which to model. Next, is to use your field solver, to model characteristic impedance. Since all field solvers are different, and user interfaces can be confusing, make sure you understand the little nuances of your tool.
The next thing is to identify the core layers in the stackup and input H1 and Dk1 for the dielectric. Then, input the pressed thickness for prepreg H2 and Dk2, not the thickness found in Dk/Df construction tables. You can usually trust the pressed thickness from your fab shop. But be careful how the field solver defines H2. Most field solvers define it as shown in Figure 1, but some solvers, like Polar Si9000e, define it as (H2+t), shown in Figure 2. Usually, you can trust the pressed thickness from your board shop stackup drawing.
Finally, if your field solver allows for it, fill in Dk_{resin} between two traces if you know it. It will be lower than Dk2. Since this number is generally hard to obtain, a rough estimate to use is the lowest Dk value from the highest resin content prepreg found in Dk/Df construction tables.
Once everything is set up, optimize the line width and space, until the desired characteristic impedance is reached. One last point to remember, is that all 2D field solvers only calculate lossless characteristic impedance. But when we measure an impedance test coupon with a time domain reflectometer (TDR), we are measuring the instantaneous impedance along the PCB trace.
More often than not, impedance is different than what was predicted. This is because a 2D field solver only calculates the lossless characteristic impedance of the crosssectional geometry; while a TDR measures the instantaneous impedance of a lossy transmission line at every point along its length.
A 2D field solver has no input for conductor resistivity, dielectric loss, or how long the conductor is. Resistive loss often results in a slow monotonic rise in the impedance profile. IPCTM650 specifies the measurement zone between 3070 % and most PCB fab shops, will measure an average impedance
In this example, shown in Figure 2, for a low loss dielectric, there is a 45 ohm difference depending on where the measurement is taken. When all input parameters are included correctly for a lossy transmission line model, you can see there is excellent correlation.
Figure 2 Lossless characteristic impedance from Polar SI9000 field solver (left) vs measured TDR plot from an impedance coupon and lossy transmission line model from Polar Si9000.
Although minor differences in individual parameters may have second order affects, collectively they could add up to give poor correlation to measurements. But if you consider all the nuances discussed in this article, you can get pretty good accuracy as shown in Figure 2.
[1] Bert Simonovich, “A Practical Method to Model Effective Permittivity and Phase Delay Due to Conductor Surface Roughness”, DesignCon 2017, Santa Clara, CA
[2] Bert Simonovich, “PCB Fabrication: What SI/PI Engineers Need to Know for First Time Modeling Success”, DesignCon 2021 Spring Break Webinar, April 12, 2021
[3] Bert Simonovich, A Tale of Two Data Sheets and How Foil Roughness Affects Dk, White paper
A Tale of Two Data Sheets: Part1
Originally published SI Journal April 26, 2022
When doing printed circuit board (PCB) stackup and signal integrity (SI) impedance modeling, we need to get the dielectric material properties from the right sources. One important parameter for accurate impedance modeling is relative permittivity (ε_{r}) of the dielectric material, otherwise known as dielectric constant (Dk). The best source is from laminate suppliers’ data sheets. Though there is an issue with these I like to think of as, “a tale of two data sheets.”
Marketing data sheets, like the example shown in Figure 1 [6], are easily found on laminate suppliers’ websites. They are meant for quick comparison of dielectric properties to narrow your search for the right laminate for your application. Dielectric properties on marketing data sheets include mostly thermal and mechanical properties, which are important for the physical structure of the material and how it will perform with other material properties in the stackup during processing.
But marketing data sheets are not representative of what is needed to design an actual stackup, or to do impedance and SI loss modeling. Depending on glass style, resin content, thickness, Dk, and dissipation factor (Df) will be different for different cores and prepreg thicknesses for the same laminate. Marketing data sheets usually only report a typical Dk/Df at fifty percent resin content and two or three frequency points. Thickness is not specified. Furthermore, Dk and Df are not constant over frequency. So, using numbers from these data sheets will lead to inaccurate impedance and phase delay results.
Figure 1. Example of a “Marketing” data sheet easily obtained from laminate supplier’s web site. Source Isola Group [6].
Instead, for transmission line modeling, one needs to use the same Dk/Df table data sheets PCB fabricators use to build the stackup. An example Dk/Df table is shown in Figure 2. Dk/Df tables provide the actual core and prepreg thicknesses, resin content, and Dk/Df for the different glass styles, over different frequencies. Depending on the stackup, a combination of thicknesses is often needed to meet impedance requirements. Each thickness will have a different Dk value.
In the example of Figure 2, Dk varies from 2.92 at 10 GHz for 1080 glass style to 3.19 at 10 GHz for 2116 glass style. This represents a Dk variation of 3.3% to 5.6% when compared to a Dk of 3.02 at 10 GHz specified in Figure 1.
Figure 2. Example of a typical “Engineering” data sheet showing Dk/Df table for different glass styles and resin content over frequency. Source Isola Group [6].
Many engineers assume Dk published is the intrinsic property of the material. But, in fact, it is the effective Dk (Dkeff) measured by a specific industry standard test method. When they are compared against real measurements from a design application, there is often a discrepancy in Dkeff due to increased phase delay caused by surface roughness [1].
Dkeff is highly dependent on the test apparatus and conditions of how it is measured. One method commonly used by many laminate suppliers is the clamped stripline resonator test method, as described by IPCTM650 2.5.5.5, Rev C, Test Methods Manual [10].
Since all glass reinforced laminates are anisotropic, any stripline based test method, like TM650 2.5.5.5, or Bereskin stripline test method [13], reports Dk values in which the Efields are transverse to signal propagation. That is, if the signal propagation is in the xy axis direction, then the Dk measured by this method is when Efields are in the zaxis direction.
For Isola’s Dk/Df table [6], shown in Figure 2, Dk values were measured by TM650 2.5.5.5 test method. From that data, the values for most of the constructions are calculated. Additional verification runs are performed to gather statistical data over time and validate that the calculations are reasonable and accurate.
The measurements are done under stripline conditions using a carefully designed resonant element pattern card. It is made with the same dielectric material to be tested. As shown in Figure 3, the card is sandwiched between two sheets of uncladded dielectric material under test. Then the whole structure is clamped between two large plates; each lined with copper foil and grounded. They act as reference planes for the stripline.
Figure 3. Illustration of clamped stripline resonator test method, as described by IPCTM650, 2.5.5.5, Rev C, Test Methods Manual [10].
This test method assures consistency of product when used in fabricated boards. It does not guarantee the values directly correspond to design applications.
Here is why:
Since the resonant element pattern card and material under test are not physically bonded together, air is entrapped between the various layers. These small air gaps are caused by the:

roughness of the copper foil plates in the fixture

roughness profile imprint left on the surface from the foil that was removed from the test samples

copper removed on the resonant element pattern card
Air entrapment, due to the TM650 test method, is the primary reason for effective Dk and phase delay discrepancies between simulation using laminate suppliers’ Dk/Df tables and real measurements from a design application. The small air gaps result in a lower effective Dk than what would be measured in a real PCB because everything is pressed together with no air entrapment, as shown in a crosssection view of Figure 4.
Figure 4. Example of foil bonded to core or prepreg dielectric. Rz_{1 }is rougher than Rz_{2} and H_{smooth} is the thickness of the dielectric as if the foil was removed.
When copper roughness is different on each side of the dielectric, like the example shown in Figure 4, Dkeff is determined heuristically by this simple correction factor:
Equation 1.
where:

H_{smooth} is dielectric core thickness from laminate suppliers’ Dk/Df table data sheet or pressed prepreg thickness from the PCB stackup drawing.

Rz_{1} and Rz_{2} are the conductor roughness of the foil for the respective side of the dielectric from foil suppliers’ data sheet. Typically, Rz is the 10point mean roughness as measured by a mechanical profilometer.

Dk is dielectric constant from laminate supplier’s Dk/Df table data sheet.
In Figure 4, Rz_{1} is the roughness of the top foil, and Rz_{2} is the roughness of the bottom foil. In this example, Rz_{1} is rougher than Rz_{2}. H_{smooth} is the core thickness of the dielectric, as specified in the Dk/Df table, or pressed thickness of the prepreg, often shown on a stackup drawing. It is the thickness of the dielectric as if the foil was removed.
When copper foil with the same Rz roughness is bonded to each side of the core or prepeg, Dkeff can be simplified as:
Equation 2
Figure 5 plots Dkeff over frequency derived from S21 phase or time delay (TD); Dkeff=(TDc_{0 }∕ length)^{2} from a Megtron6 stripline case study [3]. This method is different than IPCTM650 test method in that it determines Dkeff from unwrapped phase delay rather than calculating Dk/Df from resonant peaks over the frequency range defined in the spec.
The blue plot is a simulated case based on core and prepreg Dk values from published Dk/Df tables at 12 GHz. When Dk is corrected due to roughness, using Equation 2, and resimulated, Dkeff is shown in pink. Although the Dkeff has improved, it still does not agree with the measured Dkeff from the device under test (DUT), shown in red.
Figure 5. Comparisons of simulated Dkeff over frequency vs. measured. The red plot is actual measured Dkeff from the DUT. The middle pink plot is a simulation using Dkeff corrected due to roughness. The bottom blue plot is simulated using Dk at 12 GHz as published in Dk/Df tables and noncausal roughness model. The green dashed plot is a simulation using Dkeff due to roughness; a causal HurayBracken roughness model was used. Modeled with Simbeor [11] and simulated with Keysight ADS [12].
The discrepancy between the pink and red plots is because Dkeff from Equation 2 only corrects the phase delay due to self capacitance (C_{11}) per unit length of the transmission line. But roughness of the foil also increases the self inductance (L_{11}) per unit length of the transmission line, which adds additional phase or time delay [4].
This is counter intuitive and can be confusing since we usually relate Dkeff to capacitance only. By definition, Dkeff is the ratio of the actual structure’s capacitance to the capacitance when the dielectric is replaced by air. But this is only true for static electric fields. For timevariant electromagnetic fields, Dkeff becomes frequencydependent [14].
If the propagation delay (tpd) for a single transmission line, in seconds per unit length, is determined by:
Equation 3.
and c_{0} is the speed of light (~3.0E8 m/s) =1/sqrt(μ_{0} ε_{0} ); μ_{0} (4πE−7 H/m) and ε_{0 }(8.8542E−12 F/m) is permeability and permittivity of free space respectively, then:
Equation 4.
where: L_{11}; C_{11} are self inductance in Henries per unit length and self capacitance in Farads per unit length respectively.
Equation 4 clearly shows that with an increase in self inductance there will be a proportional increase in Dkeff. This means for PCB transmission lines, calculating Dkeff=(TDc_{0 }∕ length)^{2} cannot be trusted to be the same as relative permittivity (ε_{r}) of the dielectric material. The consequence for doing so leads to inaccurate impedance predictions and noncausal time domain simulations, resulting in poor correlation to measurements.
A causal model, when simulated, does not produce any change in its output signal before there is a change in its input signal. When field solvers properly correct the self inductance, by applying the roughness correction factor to the imaginary portion of the complex impedance of the metal [4][5], the model is then causal. When combined with the corrected Dkeff for cores and prepregs from Equation 2, there is excellent correlation, as shown by the dashed green plot in Figure 5. Unfortunately, not all field solvers have causal roughness models to correct the inductance in the simulation.
Since there is no simple way to backtrack from a phase measurement to establish the right Dkeff to use for your modeling, especially for lossy stripline constructions, heuristic methods are an alternative.
Using the right Dkeff for your modeling ensures a correct time domain reflectometer (TDR) impedance prediction, as shown in Figure 6. The red plot is measured differential TDR from [3]. When core and prepreg Dk from Dk/Df tables were used along with a noncausal roughness model in the simulation, the blue plot shows an overestimate for impedance. When Dkeff from Equation 2, and a noncausal roughness model was used in the simulation, the pink plot shows an underestimate in the impedance plot.
It is only when we apply a causal HurayBracken roughness model from [11], along with Dkeff from Equation 2, that we see the effect of the increased self inductance, shown by the green dashed line plot in Figure 6.
At first glance of Figure 6, one might interpret the pink plot as having better correlation to the measured red plot. But because the measured plot has an impedance ripple along its length, it is difficult to conclude which is the correct model from the TDR plots alone. It is only when we compare Dkeff derived from the green dashed phase delay plot from Figure 5 that we can conclude the green dashed line TDR plot is the correct impedance.
Figure 6. Simulated vs. measured differential TDR plots when different Dkeff was used in the model. The blue plot overestimates impedance when Dk from data sheets was used. The pink plot underestimates the impedance when Dkeff (Equation 2) and noncausal roughness model was used. The green dashed line plot is when Dkeff (Equation 2) and a causal HurayBracken roughness model were used. Modeled with Simbeor [11] and simulated with Keysight ADS [12].
Summary:
Dielectric constants from marketing data sheets cannot be trusted to properly design PCB stackups and model transmission lines for impedance and phase delay. Instead, laminate suppliers’ Dk/Df tables should be used.
Many laminate suppliers provide Dk/Df tables derived from a clamped stripline resonator test method [10] or similar Bereskin test method [13]. But the numbers do not factor the actual roughness of the foil. When a simple correction factor, based on the thickness of laminate and Rz foil roughness is considered, a more accurate value for Dkeff along with a causal roughness model can be used for impedance and transmission line modeling.
For PCB transmission lines, calculating Dkeff from phase or time delay measurement method cannot be trusted to be the relative permittivity of the dielectric material. Using this value will lead to inaccurate simulation results.
References:
1. L. Simonovich, “A Practical Method to Model Effective Permittivity and Phase Delay Due to Conductor Surface Roughness“, DesignCon 2017, Santa Clara, USA.
2. B. Simonovich, “Stackup Beware: Case Study of the Effects on Transmission Line Losses Due to Mixed Reference Plane Roughness”, Signal Integrity Journal article, August 10, 2021.
3. B. Simonovich, “PCB Fabrication: What SI/PI Engineers Need to Know for First Time Modeling Success”, DesignCon 2021 Spring Break Webinar Series, April 1216, 2021.
4. V. DmitrievZdorov, B. Simonovich, Igor Kochikov, “A Causal Conductor Roughness Model and its Effect on Transmission Line Characteristics“, DesignCon 2018, Santa Clara, USA.
5. J.E. Bracken, “A Causal Huray Model for Surface Roughness”, DesignCon 2012, Santa Clara, USA.
6. Isola Group, 6565 West Frye, Chandler, AZ 85226.
7. Circuit Foil, 6 Salzbaach, 9559 Wiltz, Grand Duchy of Luxembourg.
8. Rogers Corporation, 2225 W. Chandler Blvd., Chandler, AZ 85224.
9. J. Coonrod, “Managing PCB Materials: Dielectric Constant (Dk)”, Rogers Corporation, Blog Article, Sep 11, 2018
10. IPCTM650, 2.5.5.5, Rev C, Test Methods Manual
11. Simbeor THz [computer software].
12. Keysight ADS Keysight Advanced Design System (ADS) [computer software].
13. Bereskin, A. B. “Microwave Dielectric Property Measurements”, Microwave Journal, vol. 35, no.7, pp. 98 – 112
14. Wikipedia contributors. (2022, January 12). Relative permittivity. In Wikipedia, The Free Encyclopedia. Retrieved 18:14, January 14, 2022.
The Effects on Transmission Line Losses Due to Mixed Reference Plane Roughness Case Study
This article is an edited version of White Paper, “Heuristic Modeling of Transmission Lines due to Mixed Reference Plane Foil Roughness in Printed Circuit Board Stackups” [1].
Designing the right printed circuit board (PCB) stackup can make or break your product performance. If your product has circuitry that is transmission loss sensitive, then paying attention to conductor surface roughness is paramount.
Conductor surface roughness traditionally has been applied to copper foil to promote adhesion to the dielectric material. Early PCBs were only constructed with single or doublesided copper core laminates. The only important metric for copper was its purity and the roughness to improve peel strength. There was no such thing as a PCB stackup and nobody worried about impedance or transmission line losses.
But over the years PCBs have evolved into multilayer constructions with evermore attention being paid to impedance control and transmission line losses. Thus a PCB stackup definition became vital for consistent performance.
Like any construction project, you need a blueprint before you start building. Similarly for PCBs, you need a stackup drawing and detailed fabrication notes. Part of the stackup design process includes signal integrity (SI) modeling for characteristic impedance and transmission loss. If your design is running at 56Gig pulse amplitude modulation level 4 (PAM4), for example, you are probably looking at low loss dielectrics and low roughness copper for the signal traces.
But what is sometimes overlooked in the stackup, is the roughness of the reference planes. Often thin core laminate power and ground (GND) planes will specify reversetreated foils (RTF), which are rougher on the side that bonds to the prepreg. Sometimes one of these planes, usually GND, acts as a reference plane to an adjacent signal layer as shown in Figure 1. If that adjacent highspeed signal layer is using smoother copper than one or both reference planes, a higher insertion loss than expected for that layer will occur and possibly ruin your day.
A similar scenario could occur for high density interconnect (HDI) technology. This is a popular method to increase component density on modern PCBs. By the nature of their stackup construction, a rougher copper reference plane could sometimes also end up adjacent to a signal layer as well. Thus, if insertion loss is a concern, copper foil roughness of reference planes needs to be considered.
Figure 1 An example crosssection stripline geometry from a stackup showing thin core laminate (top) with RTF bonded to prepreg and adjacent to a highspeed differential pair with smooth foil.
So how do you know this before you design your stackup and build your first prototype? Since we do not have any empirical data to go by, we can rely on a heuristic, highlevel design (HLD) modeling method starting with published parameters found solely in manufacturer’s data sheets.
Heuristic HLD modeling is a practical technique that is not guaranteed to be perfect, but is still adequate in finding a satisfactory solution sooner, rather than later.
For dielectric parameters, we choose dielectric constant (Dk) / dissipation factor (Df) at or near the Nyquist frequency of the baud rate, then apply effective Dk (Dkeff) correction factor due to roughness, Equation 1 [5].
where:
H = thickness of core/prepreg; Rz is surface roughness of copper; Dk is as published in laminate supplier’s Dk/Df tables. Equation 1 assumes Rz of the foil on each side of the dielectric (core or prepreg) is the same.
For conductor loss, we use Rz roughness numbers from copper suppliers’ data sheets and oxide/oxide alternative Rz roughness numbers from your favorite fab shop, then apply the CannonballHuray roughness model [1][3].
CannonballHuray Model
The original Huray model is defined as:
Equation 2
The CannonballHuray model allows you to extract the right parameters using Rz roughness for core and prepreg sides of the foil [1]. Because the CannonballHuray model assumes the ratio of A_{matte}/A_{flat} = 1, and N_{i} = 14 spheres, the radius of a sphere (r) can be determined by:
and area of flat tile base (A_{flat}) by:
Equation 4
Wildriver Isola ITera® MT40 Custom Modeling Platform Case Study
To study the effect of reference plane roughness on transmission insertion loss, Wildriver Technology’s [7] custom modeling platform (CMP), shown in Figure 2, was used as a case study. This CMP was custom developed for Isola [6] to characterize their new ITera® MT40 very lowloss laminate material.
It combines 27 structures based on a consistent development of primitive structures; useful for performing a host of calibrations including automatic fixture removal, unknown THRU, WinCal XE™ calibration, and VNA gating and time transform analysis.
Figure 2 Wildriver Isola ITera® MT40 Custom Modeling Platform. Source: Wildriver Technology [7]
Stackup Validation
The PCB stackup is shown in Figure 3. Often PCB fab shop field application engineers (FAE) modify existing stackups and unintentionally make errors in transferring new parameters from data sheets into their software tools. Also, they may not necessarily know the design intent of the stackup. So the first step for any model correlation exercise is to sanitize the stackup, to ensure it meets the product design intent for signal integrity (SI) performance. In fact that is how the issue of different plane roughness was uncovered.
Since it is always a good practice to ensure the same roughness is specified for reference planes as the adjacent signal layers, I naively assumed it would be the case for any highspeed stackup. But that wasn’t the case here. Layers E1,E2 and E7, E8 specify 1oz RTF, while layers E3, E4 and E5, E6 specify 1oz VLP2 foil. Because the Isola ITera® MT40 CMP is intended to aid in modeling test structures, this is not a fatal flaw. On the contrary, it is a perfect platform to assess the effect of rougher reference planes.
Figure 3 Isola ITera® MT40 Custom Modeling Platform stackup. Source: Wildriver Technology [7]
Upon further review, it was discovered that the core laminates between E3,E4 and E5, E6 specified 1067/2×3313 glass styles, but this combination was not listed for 12 mil thickness. Instead, only 3×3313 core is offered. Because of that, the Dk shown is also wrong and will affect the impedance of the traces. The right Dk for 3×3313 is 3.53 instead if 3.33.
Foil Roughness
As mentioned earlier, the roughness of the foil affects the effective Dk, so we need to use the right number for our model validation. The standard VLP2 foil, used on ITera® MT40 core laminates is BFTZA foil. Optional RTF foil, used for layers E1, E2 and E7, E8, is TWLSB. Both are from Circuit Foil [8].
Relevant roughness parameters are shown in Figure 4. For the core side of the foil we are interested in the Rz parameters for the treated side listed in the table. But there are two Rz parameters, JIS B 601 and ISO 4287 specified. So which one do we use for modeling?
From IPCTM650 Section 1.2 [11] states, “The foil profile of foils shall be evaluated using the parameter Rz (DIN) or RTM, which is defined as the average maximum peak to valley height of five consecutive sampling lengths within the measurement length. This value is approximately equivalent to the values of profile determined from microsectioning techniques.”
and;
Section 1.3 states, “RZ (ISO) is a different parameter from Rz (DIN) and is not applicable to this method.”
Rz JIS represents the 10point mean value, which is the sum of the average of the 5 highest peaks and the 5 lowest valleys over the sample length. Rz DIN is similar; except it is defined as the average maximum peak to valley height of five consecutive sampling lengths within the measurement length. Thus we will use Rz JIS for modeling analysis.
Figure 4 Roughness parameters from Circuit Foil [8] data sheets. Top is VLP2 standard foil used on ITera® MT40, while bottom is RTF option used for relevant layers in the stackup
Determine Effective Dk Due to Roughness
The first step in HLD impedance modeling is to gather all the dielectric and foil data sheet parameters to determine the effective Dk.
Figure 5 summarizes thickness of core, prepreg and signal trace from the stackup geometry in Figure 3. Note that photos are for illustrative purposes only and are not actual crosssections from CMP PCB. Dk for core and prepreg were obtained from Isola ITera® MT40 Dk/Df tables [6].
Figure 5 Data sheet parameters for RTF/VLP2 foil roughness and dielectric properties for ITera® MT40 stackup geometry. Note: Photos are for illustrative purposes only and are not actual crosssections from CMP PCB. Surface roughness pictures source: Circuit Foil [8]
The top reference plane is TWLSB RTF foil with matte side 1 ≤ 7.5 JIS, obtained from Circuit Foil data sheet (Figure 4). The roughness surface profile is shown in the upper left. After OA smoothing, 1 ≤ 6.23 [1].
BFTZA foil is used for both sides of the core laminate. The top surface of the stripline trace, shown in the upper right picture, is the drum side of the foil, before OA treatment. After OA treatment, Rz2 ~ 1.9 μm [1].
The bottom surface profile of the stripline trace and the top surface of the bottom reference plane are the treated matte sides of the foil, shown in the bottom right and bottom left pictures respectively. They both share the same roughness (Rz3, Rz4 =2.5μm JIS) from the BFTZA data sheet (Figure 4).
The next step is to convert the imperial thickness units to metric, then use Equation 1 to determine Dkeff due to roughness for the prepreg and core.
Determine CannonballHuray Roughness Parameters
Several popular electronic design automation (EDA) tools include the CannonballHuray model directly as an option, so the respective Rz parameter is all that is needed.
Any of these tools can be used for HLD modeling, but my favorite is Polar SI9000 [9] because of its simplicity and sufficient accuracy for prefabrication modeling and analysis. Many fab shops use this tool for impedance prediction, so it is easy to stay in sync with them during the HLD stage of your project. Plus, it has the added benefit of modeling transmission loss and exporting Sparameters in touchstone format for further channel modeling in other tools.
Because Polar Si9000 assumes all the reference planes have the same roughness, it only allows Rz roughness parameters to be inputted for the matte and drum side of the signal trace. The best we can do, is take the average roughness of Rz1,Rz2 and Rz3,Rz4:
Simulation Correlation
When Dkeff due to roughness values were used instead of published Dk values, the new impedance prediction is 48.24 ohms, as shown in Figure 6.
Figure 6 Polar Si9000 impedance prediction with Dkeff due to roughness
Dkeff/Df for H1, H2 was then inputted into the causal dielectric model at 10GHz, as shown in Figure 7 (left), while Rz_{matte}, Rz_{drum} was inputted into the CannonballHuray model (right).
Figure 7 Causal Dkeff/Df dielectric and CannonballHuray roughness model input panels in Polar Si9000
After a 6inch transmission line was simulated, the Sparameters were exported in touchstone format. Keysight Pathwave ADS [10] was used for further processing and analysis.
Figure 6 compares simulated insertion loss vs deembedded reflectionless generalized modal (GM) Sparameter measurements, provided by Wildriver Technology [7]. As you can see there is excellent correlation without fitting to measured data!
Figure 8 HLD Insertion Loss simulation correlation for as designed stackup from data sheet and stackup parameters
Figure 9 plots simulated Dkeff vs measurements. At 10 GHz, simulated Dkeff is 0.105 (2.8%) lower than measured value. Without actual crosssection microscopic measurements, it is difficult to conclude if the published Dk is wrong, or if there is process variation with roughness parameters used in the model.
But it is also interesting to note that measured Dkeff is not a constant value over frequency, as shown in the ITera® MT40 Dk/Df tables. Instead Figure 9 reveals it varies over frequency, so the Dk/Df data sheet numbers are suspect.
Regardless, for the HLD modeling process, the simulation results are within acceptable tolerance.
Figure 9 HLD Dkeff simulation correlation for as designed stackup
Exploring the Effects of Alternate Foil Roughness
Now that we have good correlation to measurements, we can repeat the HLD modeling process to explore different foil roughness options. Figure 10 summarizes the thickness of core, prepreg and signal trace for VLP2/VLP2 foil (top) and VLP1/VLP1 foil (bottom). Note that photos are for illustrative purposes only and are not actual crosssections from CMP PCB.
Respective Dkeff, and CannonballHuray roughness parameters were recalculated with same steps as VLP2/RTF case above.
Figure 10 Alternate foil options simulated for whatif loss comparison. Top is VLP2/VLP2 foil parameters for all copper layers and bottom is VLP1/VLP1 foil parameters for all copper layers. Note: Photos are for illustrative purposes only and are not actual crosssection from CMP PCB. Surface roughness pictures source: Circuit Foil [8]
Figure 11 presents the simulation results of all three scenarios. As expected. when the reference plane foil roughness went from RTF/VLP2 to VLP2/VLP2 there was improvement. At 14 GHz it was 0.5 dB and at 28GHz it was 1 dB improvement.
When VLP1/VLP1 foil was used, it was further improved by 0.8 dB and 1.7 dB at 14 GHz and 28 GHz respectively. So if your design is loss sensitive, you might want to consider VLP1 foil option.
When we compare Dkeff plots, we see effective Dk approaches actual Dk/Df data sheet values in the tables when smoother copper is used, as expected [5].
Since Dkeff was derived by phase delay, propagation delay will be affected by rougher copper.
Figure 11 Whatif simulation comparison of VLP2/RTF, VLP2/VLP2, VLP1/VLP1 foil options and their effect on insertion loss and Dkeff
Conclusions
1. Roughness of reference planes make a significant difference in loss and phase delay, especially if one of the reference planes is RTF. If loss is important then all highspeed reference planes should have the same foil roughness specified
2. Heuristic HLD modeling method is a useful and accurate way to determine prefabrication impedance and loss predictions using data sheet parameters.
3. Published Dk from ITera® MT40 Dk/Df data sheet tables is not a flat constant over frequency.
4. Confirmed Rz JIS is the right parameter to use from Circuit Foil data sheet, instead of Rz ISO.
Acknowledgements
· Al Neves, CTO Wildriver Technology, for providing the custom modeling platform design details and measured data for the case study.
· Michael Gay, Director Business Development – Strategic Accounts at Isola Group, for providing foil supplier’s data sheets used on ITera® MT40 laminates.
References
[1] B. Simonovich, “Heuristic Modeling of Transmission Lines due to Mixed Reference Plane Foil Roughness in Printed Circuit Board Stackups”, White Paper, Lamsim Enterprises Inc.
[2] B. Simonovich, “Practical Method for Modeling Conductor Surface Roughness Using The Cannonball Stack Principle”, White Paper, Lamsim Enterprises Inc.
[3] L. Simonovich, “Practical method for modeling conductor roughness using cubic closepacking of equal spheres,” 2016 IEEE International Symposium on Electromagnetic Compatibility (EMC), 2016, pp. 917920, doi: 10.1109/ISEMC.2016.7571773.
[4] L. Simonovich, “PCB Interconnect Modeling Demystified”, DesignCon 2019, Proceedings, Santa Clara, CA, 2019
[5] B. Simonovich, “A Practical Method to Model Effective Permittivity and Phase Delay Due to Conductor Surface Roughness”. DesignCon 2017, Proceedings, Santa Clara, CA, 2017
[6] Isola Group S.a.r.l., 3100 West Ray Road, Suite 301, Chandler, AZ 85226, URL: http://www.isolagroup.com/
[7] Wild River Technology LLC 8311SW Charlotte Drive Beaverton, OR 97007, URL: https://wildrivertech.com/
[8] Circuit Foil 6 Salzbaach, 9559 Wiltz, Grand Duchy of Luxembourg URL: https://www.circuitfoil.com/portfolio/
[9] Polar Instruments Si9000e [computer software] Version 2018, URL: https://www.polarinstruments.com/index.html
[10] Keysight Pathwave Advanced Design System (ADS) [computer software], (Version 2021 update2). URL:http://www.keysight.com/en/pc1297113/advanceddesignsystemads?cc=US&lc=eng.
[11] IPCTM650 Test Methods Manual 2.2.17A, Surface Roughness and Profile of Metallic Foils (Contacting Stylus Technique), 2/2001 Rev. A
[12] IPCTM650, 2.5.5.5, Rev C, Test Methods Manual
The Poor Man’s PCB Via Modeling Methodology
You are a backplane designer and have been assigned to engineer a new highspeed, multigigabit serial link architecture from several line cards to multiple fabric switch cards across a backplane. These links must operate at 6GB/s day one and be 10GB/s (IEEE 802.3KR) ready for product evolution. The schedule is tight, and you need to come up with a backplane architecture to allow the rest of the program to progress on schedule.
You come up with a concept you think will work, but the backplane is thick with over 30 layers. There are some long traces over 30 inches and some short traces of less than 2 inches between card slots. There is strong pressure to reuse the same connector you used in your last design, but your gut tells you its design may not be good enough for this higher speed application.
Finally, you are worried about the size and design of the differential via footprint used for the backplane connectors because you know they can be devastating to the quality of the received signal. You want to maximize the routing channel through the connector field, which requires you to shrink the antipad dimensions, so the tracks will be covered by the reference planes, but you can’t easily quantify the consequences on the via of doing so.
You have done all you can think of, based on experience, to make the vias as transparent as possible without simulating. Removal of nonfunctional pads on the inner layers, and planning to backdrill the connector via stubs will help, but is it enough? You know in the back of your mind the best way to answer these questions, and to help you sleep at night, is to put in the numbers.
So you decide to model and simulate the channel. But to do so, you need accurate models of the vias to plug into your favorite circuit simulator. But how do you get these? You have heard it all before; “for highspeed, the best way to model a via is with a 3D electromagnetic field solver”. Although this might be true, what if you don’t have access to such a tool, because the cost is more than your company wants to spend, or because you don’t have the expertise nor the time to learn how to build a model you can trust to make a timely decision?
On top of that, 3D field solvers typically produce Sparameter behavioral models. Since they represent only one sample of a given construction, it is impossible to perform whatif, worst case, min/max analysis with a single behavioral model. Because of this, many iterations of the model are required; causing further delay in getting your answer.
A circuit model on the other hand, is a schematic representation of the actual device. For any physical structure, there can be more than one circuit model to describe it. All can give the same performance, up to some bandwidth. When run in a circuit simulator, it predicts a measurable performance of the structure. These models can be parameterized so that worst case analysis can be explored quickly.
The problem with a circuit model is that you often need a behavioral model to calibrate it, or need to use analytical equations to estimate the parameters. But, as my friend Eric Bogatin often says, “an OK answer NOW! is better than a great answer late”.
In the past, it was next to impossible to develop a circuit model of a differential via structure without a behavioral model to calibrate it. These behavioral models were developed through empirical formulas, measured data, or through the use of 3D EM field solvers.
Now, there is another way. I have nicknamed it, “The Poor Man’s PCB Via Modeling Methodology”. Here’s how it works.
Anatomy of a Differential Via Structure:
An example of a differential via structure, shown in Figure 1, is representative of vias used to connect surface mounted components or backplane connectors to internal layer traces.
The via barrel is a plated through hole extending the entire length of a PCB stackup. The outside diameter equals the drill diameter. The inside diameter is the finished hole size (FHS) after plating. Pads are used on layers to ensure there is sufficient copper for track attachment after drilling operation. When used in this fashion, they are referred to as functional pads. Antipads are the clearance holes in the plane layers allowing the via barrel to pass through them without shorting.
The via portion is the length of the barrel connecting one signal layer to another. It is often referred to as the through via since it is part of the signal net. The stub portion is the rest of the barrel extending to the outer layer of the PCB. In highspeed designs, a good rule of thumb to remember is that a via stub should be less than 300mils/BR in length; where BR is the bit rate in Gb/s.
Building a Simple Scalable Circuit Model:
On close examination of Figure 2, a differential via structure can be represented by a twinrod transmission line geometry with excess capacitance (shown in red) distributed over its entire length. The smaller the antipad diameter, the greater the excess capacitance. This ultimately results in lower via impedance, causing higher reflections.
In all highspeed serial link designs, it is common practice to remove all nonfunctional pads and to maximize the antipad clearance as much as practically possible. Oval antipads are often used in this regard to further mitigate excess via capacitance.
Figure 3 illustrates the equivalent circuit for a differential via that could be used in a channel topology simulation. Here it is modeled with Keysight ADS software using a coupled line transmission line model for each section. This equivalent circuit model can be scaled for any combination of layer transitions and integrated in any channel simulation scenario.
Since the crosssection of the via is constant throughout its length, the differential impedance of all sections of the via are the same. We only need to know the physical length of each segment and the effective dielectric constant (Dkeff) to get the time delay of each segment.
When driven differentially, the oddmode parameters of each via are of major importance. Since the evenmode parameters have no impact on differential performance, both odd and evenmode parameters are set to the same values in the model.
The challenge then is to calculate the odd mode impedance (Zodd), representing the individual via impedance (Zvia), of a differential via structure and the effective dielectric constant (Dkeff) based on its geometry. Simple equations are used to determine these parameters.
Developing the Equations:
Antipads can vary in size and shape. They can be anything from round, to oval around each via, or even a large oval surrounding both vias as illustrated in Figure 4. Square, or rectangular variations (not shown) are similar.
Referring back to Figure 2, we see the structure of each via looks a lot like two coaxial transmission lines with the inner layer reference planes acting like a shield. Electrostatically this is a good approximation, but because the shield is not continuous, the magnetic fields are not contained like they are in a coaxial structure. Instead they behave more like magnetic fields around a twinrod structure.
So here lies the secret in modeling a differential via. We take the best of both geometries to calculate the oddmode impedance representing Zvia.
For inductance, we will use the oddmode inductance formula from the twinrod transmission line geometry to calculate Lvia :
Referring to Figure 4, we then calculate the oddmode capacitance for Cvia derived from an approximate formula for an elliptic coaxial structure developed by M.A.R. Gunston in his book, “Microwave Transmission Line Impedance Data” . In the original formula, both shield (W’+b) and inner conductor (w+t) are elliptical in shape and are dimensioned as shown. When the antipads are circular, then ln[(W’+b) /(w+t)] reduces to just ln[b/t)]; which is the denominator in the Coax equation. If we use Gunston’s approximation to calculate Cvia, then the equation becomes:
Since conventional FR4 type laminates are fabricated with a weave of glass fiber yarns and resin, they are anisotropic in nature. Because of this, the dielectric constant value depends on the direction of the electric fields. In a multilayer PCB, there are effectively two directions of electric fields.
The one we are most familiar with has the electric fields perpendicular to the surface of the PCB; as is the case of stripline shown here in Figure 5. The dielectric constant, designated as Dkz in this case, is normally the bulk value of the dielectric specified by the laminate manufacturer’s data sheet.
The other case has the electric fields running parallel to the surface of the PCB, as is the case when a signal propagates through a differential via structure. In this situation, the dielectric constant, designated as Dkxy, can be1520% higher than Dkz .
Therefore, assuming a nominal 18% anisotropic factor, Dkxy = 1.18(Dkz)
Now that we have defined Lvia, Cvia and Dkavg, Zvia can be estimated using the following equation:
But we are not finished yet. We still need to determine the effective dielectric constant (Dkeff) in order to accurately model the delay through the via and stub portion. Without the correct value, the quarterwave resonant nulls in the insertion loss plot, due to the stub length, cannot be accurately predicted. The value for Dkeff is determined based on how much the via’s oddmode impedance is decreased due to the distributed capacitive loading of the antipads.
To help us with this task, we start with the twinrod formula. The oddmode impedance (Zodd) is half the differential impedance (Ztwin), and is expressed as:
By substituting Equation 1 for Zodd into the equation above, and solving for Dkeff we eventually come up with the following equation:
Validating the Model:
A simple 26 layer test vehicle was fabricated to compare the accuracy of the differential via circuit model to real vias. It consisted of two differential via pairs separated by 6 inches of 100 Ohm stripline differential pairs. Three sample via structures representing long, medium and short via stubs, as summarized in Figure 6, were measured using an Agilent N5230A VNA.
The differential vias had the following common parameters:
Via drill diameter; D = 28 mils
Center to center pitch; s = 59 mils
Oval antipads= 53 mils x 73 mils
Dk of the laminate = 3.65
Anisotropy in Dkxy = 18%
Zvia = Zstub = 31.7 Ohms (per Equation 1)
Dkeff = 6.8 (per Equation 2)
Agilent ADS software was used to model and facilitate simulation correlation of the measured data as captured in Figure 7. This simple model accounts for the discontinuity of the long through section and the long stub section. The top half is the measured channel using an Sparameter file. The bottom half is a circuit model of the channel. Since the probes were not calibrated out, they are part of the device under test. The balun transformers are used to facilitate the display of the Sparameter and TDR results.
The comparison between the measured and simulated results of the insertion loss and TDR response for the three via stub cases using this simple approximation methodology is summarized in Figure 8. The insertion loss plots, in the frequency domain, are shown on the left, while the TDR plots are shown on the right.
The resonant nulls in the SDD21 plots are due to the stub lengths. As you can see, the longer the stub, the lower the resonant frequency null. If this null happens at the Nyquist frequency of the bit rate, the eye will be totally closed. This is why we backdrill them out after the board has been fabricated.
The simulation correlation is excellent up to about 12 GHz. The TDR plots show excellent impedance matching and delay for all three cases, while the simulated stub resonant frequencies match the measured frequencies very well. As you can see, these simple approximations for Dkeff and Zvia are perfectly adequate in providing a quick and accurate circuit model for differential through hole vias typically used in backplane applications.
Summary:
As illustrated, a simple twinrod model (Figure 2) is used as the basis for a practical differential via circuit modeling methodology. By using Equation 1 and Equation 2, you can quickly determine the oddmode impedance and effective dielectric constant needed for the circuit model.
Of course, you should use this methodology first as a rough starting point to quickly estimate the performance of your differential via design. If your worst case topology simulations show the performance is marginal, then it is worth while to invest the time and money to develop a 3D full wave model to perform a more accurate analysis.
On the other hand, if you find this approximation shows the vias have little impact on the channel performance, it may be of greater value for you to invest your time and money in resolving other critical issues with your design.
Try it the next time you are losing sleep over your design challenges.
For more Information:
If you liked this design note and want to learn more, or get more details on this innovative via modeling methodology, you can visit my web site, LAMSIM Enterprises.com , and download a copy of the white paper I wrote along with Eric Bogatin and Yazi Cao titled, “Method of Modeling Differential Vias” .
While you are there, feel free to investigate my other white papers and publications.
If you would like more information on our signal integrity and backplane services, or how we can help you achieve your next highspeed design challenge, email us at: info@lamsimenterprises.com.
UPDATE: In collaboration with Saturn PCB, I am pleased to announce my differential via equations above have been incorporated in a new impedance calculator available now in Saturn PCB Tool Kit software suite.
PCB Crosssectional Geometries
PCB crosssectional geometries describe the details of the dielectric substrates, traces and reference planes within a PCB stackup. Their physical relationship with one another can then be used to predict the characteristic impedance of the respective traces. There are only three generic crosssectional geometries with variations within each. They are:

Coplanar

Microstripline

Stripline
Coplanar:
Coplanar geometry, or sometimes called coplanar waveguide (CPW), is a signal conductor sandwiched between two coplanar reference conductors or planes. These reference planes are usually ground. The characteristic impedance is controlled by the signal trace width and the gap between it and reference planes. This is a common transmission line structure for RF and microwave designs using singlesided printed circuit board technology. As a rule of thumb, the width of the reference plane on each side of the signal trace should be at least five times the distance between the left and right plane.
Microstrip line:
The microstrip line is the most popular transmission line geometry used in two or four layer printed circuit boards. The characteristic impedance is controlled by the signal trace width, on one side of the substrate, and the thickness of the substrate to the reference plane below it. The embedded microstrip line has the signal trace covered with prepreg or other dielectric material.
Cross section views below showing Microstrip line (left) and embedded microstrip line (right).
Stripline:
Cross section views below shows an example of single stripline (left) and dual stripline (right) geometries. These are geometries are typically found in multilayer PCBs of 6 layers or more. The characteristic impedance is controlled by the trace width, thickness and its proximity to the reference planes above and below.
Single stripline has one signal layer sandwiched between two reference planes. If the signal layer is exactly spaced between the two reference planes, the geometry is called a symmetrical stripline; as opposed to an asymmetrical stripline, where the signal trace is offset from the center of the crosssection.
Dual stripline geometries have two signal layers sandwiched between reference planes, and are mainly used to save layers; caveat is a trace on one layer is routed orthogonal to the trace on the other to mitigate crosstalk.
Differential Pair Geometry:
Differential signaling is when a signal and its complement are transmitted on two separate conductors. These conductors are called a differential pair. In a PCB, both traces are routed together with a constant space between them as edgecoupled or broadsidecoupled.
Edgecoupled routes the traces sidebyside on the same layer as microstrip or stripline. The advantage is that any noise on the reference plane(s) is common to both traces and thus cancelled at the receiver. Most differential pairs are routed this way.
Broadsidecoupled routes one trace exactly over the other on 2 separate layers as dual stripline. Since each trace is more tightly coupled to its adjacent reference plane than the opposite reference plane, any noise on the planes will not be common to both traces and thus, will not be cancelled at the receiver. Because of this, and the fact that it usually results in a thicker PCB, this geometry is rarely used.
OddMode Impedance:
Consider a pair of equal width microstrip line traces, labeled 1 and 2, with a constant spacing between them. Each individual trace, when driven in isolation, will have a characteristic impedance Zo, defined by the selfloop inductance and selfcapacitance of the trace with respect to the reference plane.
When a pair of traces are driven differentially, the mode of propagation is odd. If the spacing between the transmission lines is close, there will be electromagnetic coupling between the two traces. This coupling is defined by the mutual inductance and capacitance.
The proximity of the traces to a reference plane(s) influences the amount of electromagnetic coupling between traces. The closer the traces are to the reference plane(s), the lower the selfloop inductance and stronger selfcapacitance to the plane(s); resulting in a lower mutual inductance, and weaker mutual capacitance between traces. The result is a lower differential impedance.
A 2D field solver is usually used to extract the parameters for a given geometry. Once the RLGC parameters are extracted, an L C matrix can be set up as follows:
The selfloop inductance and selfcapacitance for trace 1 and 2 are L11, C11, L22, C22 respectively. The off diagonal terms in each matrix, L12, L21, C12, C21, are the mutual inductance and mutual capacitance. We use the LC matrix to determine the oddmode impedance.
The oddmode impedance is the impedance of one trace, of a differential pair, when driven differentially. It can be calculated by the following equation:
Where:
Zodd = odd mode impedance
Lo = selfloop inductance = L_{11} = L_{22}
Co = selfcapacitance = C_{11} = C_{22 }
Lm = mutual inductance = L_{12} = L_{21}
Cm = mutual capacitance = C_{12} =C_{21}
Even Mode Impedance:
When current flows down both traces, of the same polarity, the mode of propagation is even and the coupling is positive. The even mode impedance can be calculated using the following equation:
Differential Impedance:
The differential impedance is twice the oddmode impedance:
Average Impedance:
When current flows down two traces randomly, as if they were singleended, the mode of propagation is a combination of odd and even. The average impedance of each trace is affected by its proximity to the adjacent trace(s); calculated by the following equation:
Coupling Coefficient:
The coupling coefficient, Kcc, is a number that conveys the amount of electromagnetic coupling between two traces. Knowing the odd and even mode impedance, Kcc can be calculated by the following equation:
Backward Crosstalk Coefficient:
Two traces near one another will couple a portion of its own signal to the other. If we consider one trace as the aggressor, and the other as the victim, the amount of coupled noise travelling backwards on the victim’s trace, opposite to the aggressor’s direction, is called NearEnd crosstalk (NEXT) or backwards crosstalk. The amount of coupled noise, travelling in the same direction as the aggressor’s direction, is called FarEnd crosstalk (FEXT).
In stripline, there is little to no FEXT, but backwards crosstalk will saturate to a fraction of the amplitude of the aggressor’s voltage for the length of time the traces are coupled. This fraction of the aggressor’s voltage is called the backward crosstalk coupling coefficient Kb. It is equal to one half of the coupling coefficient Kcc :
Example:
A 898 mil differential pair; with 12mil core; 12 mil prepreg; Dk=4; stripline geometry; 1/2 oz copper; has the following R L G C matrix extracted from a 2D field solver:
If the two traces are driven differentially, then the differential impedance is 100 Ohms and there is 13% coupling of the two traces. On the other hand, if the traces are driven singleended then the characteristic impedance of each trace is 53 Ohms. With 9 mils of space between them, the backward crosstalk is 7%.
If you increase the spacing between traces until Zodd equals approximately Zeven, the coupling will reduce to near zero, and there will be little backward crosstalk. Depending on your design and your noise budget, you may be able to live with a certain amount of backwards crosstalk. The only way to know the spacing between traces to achieve the budget is to plug in the numbers.
Acknowledgment:
I would like to thank my old Nortel colleague, the late Dick Goulette, for sharing these equations many years ago. They have served me well over the years.
Via Stub Termination Brought to You by “The Stubinator”
Thick backplanes with long via stubs will cause unwanted resonances in the channel insertion loss compared to vias with little or no stub length as shown by the red and green traces in the plot of Figure 1. If these resonances occur at or near the Nyquist frequency of the bit rate, there will be little or no eyeopening left at the receiver.
Figure 1 Topology circuit model of 2 differential vias with 30 inches of PCB etch. Insertion loss plot of Long viano stub (green); short vialong stub (red); stub terminated (blue). Received eye diagrams after optimized FFE receive equalization at 10GB/s. Modeled and simulated using Agilent ADS.
In a typical backplane application, the signal entering the via structure from the top will travel along the through portion until it reaches the junction of the internal track and stub. At that point, the signal splits with some of the signal continuing along the trace, and the rest continuing along the stub. If the signal was Arnold Schwarzenegger, he would say, “I’ll be back!”. Having done this gig before, he knows that when he reaches the end of the stub it’s like hitting a brick wall; there’s no where to go but back up the stub. Like Arnold, when the signal reaches the end of the stub, it reflects back up the stub. When it arrives at the same junction, a portion combines with the original signal and the rest continues back toward the source. If the round trip delay is half a cycle, the two waves are completely 180 degrees out of phase and there is cancellation of the original signal. The frequency where maximum cancellation occurs is called the ¼ wave resonant frequency, fo. Resonance nulls due to stubs in an insertion loss plot, like the one shown in Figure 1, occurs at the fundamental frequency fo and at every odd harmonic.
If you know the length of the stub (in inches) and the effective dielectric constant Dkeff, the resonant frequency can be predicted with the following formula:
(1)
It is common practice to reduce stub lengths in highspeed backplane designs by backdrilling the stubs as close as possible to the active internal signal layer. This is a complex and costly process involving setting individual drill depths on a per board basis. Special design features must be designed into the artwork to set correct backdrill depth. Furthermore, it is difficult to verify ALL backdrilled holes were drilled correctly. I know of a case where a backplane came back and one via (that they knew of) had a significantly longer stub than was specified. The problem showed up by accident when they were characterizing the channel using a VNA and saw an unexpected resonant null in the SDD21 insertion loss plot. When all was said and done, it turned out there was a glitch in the fabricator’s software controlling the backdrilling process. There is no practical way to find these faults; short of doing VNA measurements on 100% of the backdrilled holes. With hundreds of them in a typical highspeed backplane, the cost would be prohibitive. Thus we have to trust the fabrication process of the vendor(s).
If only there was a way to terminate the stub and get rid of all this backdrilling. Well there just might be a solution. After returning from last year’s DesignCon2010, I was intrigued by a paper presented by Dr. Nicholas Biunno on a new matched terminated stub technology developed by SanminaSCI Corporation. They call this technology MTSvia^{TM}^{ }and it allows the embedding of metal thinfilm or polymer thick film resistors within a PCB stackup during its fabrication. I like to call it “The Stubinator”. They developed this technology as an alternative to backdrilling. The beauty of this is you can terminate all the highspeed via stubs on just one resistive layer at the bottom of the PCB.
Of course, for this to work, we need to terminate the vias with a resistance equal to the differential via impedance to be most effective. But how do we determine the via differential impedance without going through a bunch of trial and error builds? In a DesignCon2009 paper titled, “Practical Analysis of Backplane Vias” I coauthored with Eric Bogatin from Bogatin Enterprises L.L.C., Sanjeev Gupta and Mike Resso from Agilent Technologies, we showed how you can model and simulate differential vias as simple twinrod transmission line structures using simple transmission line circuit models as shown in Figure 1. You can download a copy of this awardwinning paper from my web site at: Lamsimenterprises.com .
After determining fo (either by measurement of a real structure or through 3D modeling) and solving for Dkeff by rearranging equation (1), the differential via impedance calculated using the following equation:
(2)
Where:
s = the center to center spacing of the vias
D = Drill diameter.
Example:
The differential vias used in the model of Figure 1 has the following parameters:
s = 0.059 in.
D = 0.028 in.
stub_length = 0.269 in.
Dkeff = 6.14 by Equation (1) and fo=4.4GHz ;
Zdiff = 66 Ohms by Equation (2).
By adding a 66 Ohm resistor across the bottom of each via stub in the model, the blue trace in the plot shows the stub resonance has completely disappeared at the expense of an additional flat loss of about 10dB. The eye has opened up nicely.
This “Stubinator” technology looks like it could be a promising alternative to backdrilling. It resolves many of the issues and limitations highlighted above. Combined with silicon that can accommodate the additional signal loading, it may extend the life of traditional copper interconnections for next generation of Ethernet standards beyond 10GB/s.
Backplane Architecture and Design
According to Wiktionary, an Architect is: “A person who plans, devises or contrives the achievement of a desired result.” Because the backplane is the key component in any system architecture, the sooner you consider the backplane’s physical architecture near the beginning of a project, the more successful the project will be. If you think about it in the same way as designing a building, you would never consider building it without first engaging a building architect to plan and oversee the detailed design. Likewise, the backplane architect plans and oversees the physical backplane design before any layout is ever started. He or she works closely with a systempackaging engineer to satisfy the system requirements before any concept becomes final. Sometimes the original system architecture needs revisions due to physical limitations the backplane imposes. This can only be established with due diligence and planning during the highlevel design stage.
Unlike other circuit pack designs used in the system, the backplane is much like the keel of a ship of which the rest of the ship’s construction depends on for support and structural integrity throughout its lifetime. Backplanes need to be right the first time so that circuit packs can interoperate together day one and be capable of supporting future system upgrades as technology advances. Once the system has been deployed into the field, it is next to impossible to change the backplane to correct any deficiencies or to upgrade for performance like you can by redesigning the plugin circuit packs.
The seasoned backplane architect is a unique individual usually tasked to turn the system architect’s ideas and dreams, like the system block diagram example shown to the left, into reality. An oftenmisunderstood profession, backplane architects wear many hats to accomplish their goals. Often they must juggle the design requirements from many disciplines and decide on the best tradeoffs for the final design. They must converse fluently with system architects, mechanical designers, circuit pack designers, connector suppliers, PCB layout designers, ASIC/FPGA and software engineers. They must be organized and meticulous in their documentation and design. But, most importantly, they must have a sound knowledge of mechanical, PCB layout/fabrication, signal integrity, power and EMC issues.
The greatest danger in leaving the backplane design as an afterthought is the connector selection and pinout definition. If left to system packaging engineers and board designers to define, they may not be optimum for either performance or system cost. Many times system architects and packaging engineers will merely take the total number of signals and choose a connector with the highest pin density per inch without considering PCB routing or signal integrity implications. Inefficient routing of the traces leads to an increase in layer count and results in a thicker board. Thicker boards leads to higher hole aspect ratios and longer vias affecting high speed performance. Additional layer count impacts common equipment cost.
The highlevel design stage is where the physical backplane architecture starts to take shape. It uncovers potential layout routing issues and gives you the confidence the design will work the first time. The importance of this stage cannot be overstated. It primarily drives these key activities:

Sanitizes the system architecture.

Defines the final selection of appropriate connectors.

Defines the connector signal partitioning and circuit pack pinouts.

Provides the routing plan and design rules for layout.

Defines the net topologies for signal integrity analysis and link budgeting.

Facilitates the mechanical design of shelf and system packaging.

Defines the minimum slot pitch for optimum routing channels.

Facilitates early circuit pack floor planning and final card size.

Facilitates ASIC and FPGA pin selection for optimum routing to backplane connectors.

Estimates PCB layer count and board thickness.

Establishes an estimate for system cost of goods to support the business case.
Proper route planning and connector pinout definition is vital for optimum performance. When done correctly, the final schematic capture and actual PCB layout will flow smoothly with no surprises. As an example, the left half of the figure (labeled HLD Plan) shows a sample of an inner layer highlevel design route plan I did using Framemaker as the drawing tool on a design before any schematic was ever captured or pinouts defined. Everything was planned from the number of layers to how the tracks needed to break out of the connector fields. The right half of the figure is the actual layout done in Cadence Allegro showing the inner layer routing of the artwork. The due diligence done in the highlevel design stage made the actual layout fairly trivial. If you forgo this step, the worstcase scenario is the project will need to be reset to redesign shelf mechanicals or redefine card pinouts causing delay in meeting time to market objectives and ballooning R&D costs. It’s a classic case of pay me now or pay me later.
At Lamsim Enterprises Inc., we can help you with these or any other design challenges you may have by providing innovative signal integrity and backplane solutions. Visit us at our web site at: lamsimenterprises.com .
Backplane Architecture Terms and Definitions
The following is a list of common terms and definitions associated with system architecture and backplane design:
Backplane
A backplane is a multilayered printed circuit board assembly serving as the backbone of a system. Its purpose is to interconnect several printed circuit board assemblies called circuit packs or cards using plug in connectors to form a complete system. These cards plug into one side of the shelf assembly. Usually in mission critical system applications like central office telco or data centers, the backplane is passive meaning it does not contain active semiconductor devices permanently attached as part of the final assembly. Usually only connectors are the only components, but occasionally capacitors and resistors are also used. Active backplanes on the other hand, contains active components and often found in enterprise or consumer grade applications
Midplane
A midplane is similar to a backplane in function except that the circuit packs plug into both sides of the shelf assembly. In these systems, cards with I/O cabling from the faceplate plug into one side of the shelf, while nonI/O circuit pack plug in on the other side. Some midplane architectures have the front card plugged in orthogonally to the rear cards for high speed applications.
Parallel Bus Topologies
Parallel bus topologies carry data words in parallel on multiple traces from cardslot to cardslot across a backplane or from chip to chip on a circuit pack. Up until the late 1990’s, most system architectures used this form of interconnect. Due to signal integrity and timing issues associated with some parallel bus architectures with 10 to 16 card slots, the speed of the bus was limited to 2566 MHz Two popular industry standard systems still using parallel busses today are CompactPCI and VMEbus.
The main issue with a parallel bus topology is fault tolerance where a single point of failure on the bus can bring down the entire system. Mission critical systems often had to employ redundant busses to guard against single point failures.
As performance demand increased, newer high speed system architectures were designed using serial technology in a pointtopoint or pointtomultipoint switched fabric topologies.
Switched Fabric
Switched fabric, or just plain fabric, is the term most popular used in telecommunications and highspeed networks, including InfiniBand, Fiber Channel, PCIe, ATCA and other proprietary fabric based architectures. In these architectures, all data passes through the fabric before continuing to its destination. It offers better total throughput than parallel busses because traffic is spread across multiple physical links. It manages and controls all functions of the network and acts as a repeater for the data flow.
Single Star Topology
Star topologies are one of the most common highspeed serial topologies used in networks today. The advantage is it reduces the chance of network failure by connecting all of the systems to a central node. A failure of a link from any peripheral node to the central node results in the isolation of that peripheral node from all others. As a result, the rest of the systems remain unaffected.
In its simplest form, a single star topology consists of one central hub node interconnected pointtopoint to other peripheral nodes resembling a spoke wheel or star configuration. When implemented in a backplane, the central node is usually the switched fabric card and the peripheral nodes are line cards. The fabric card switches messages between the other line cards in the network. The line cards usually have faceplate I/O connectors to connect to other shelves in a network.
The main disadvantage with a single star topology is high dependence of the system on the functioning of the central fabric. Failure of the fabric card can bring down the entire system. Because of this, mission critical systems employ two fabric cards for redundancy in a dual star topology configuration.
Dual Star/Multistar Topology
The dual star or multistar topology is similar to the star network topology except it has two or more central hub nodes interconnected pointtopoint to other peripheral nodes. When implemented in a backplane application, these central nodes are usually the switched fabric cards and peripheral nodes are the line cards. The additional fabric(s) provides redundancy in mission critical system applications in case of failure, or for upgrading fabric card hardware.
Fully Connected Mesh Topology
A fully connected mesh topology, when applied to a backplane application, does not have one central fabric node(s) as in the case of star topologies. Instead, each line card node connects with all other line card nodes forming a mesh. Its major disadvantage is the number of connections grows significantly with the number of nodes. This requires additional backplane connector pins and layers to interconnect them. Because of this, it is impractical for large systems and only used when there are a small number of cards needing to be interconnected.
Fiber Weave Effect Timing Skew
Fiber weave effect timing skew is becoming more of an issue as bit rates continue to soar upwards. For signaling rates of 5GB/s and beyond, it can actually ruin your day. For example, the figure on the left shows a 5GB/s received eye is totally closed due to 12.7 inches of fiber weave effect. It was modeled and simulated using Agilent ADS software.
So what is fiber weave effect anyways and why should we be concerned about it? Well, it’s the term commonly used when we want to describe the situation where a fiberglass reinforced dielectric substrate causes timing skew between two or more transmission lines of the same length. Since the dielectric material used in the PCB fabrication process is made up of fiberglass yarns woven into cloth and impregnated with epoxy resin, it becomes nonhomogeneous.
The speed at which a signal propagates along a transmission line depends on the surrounding material’s relative permittivity (e_{r}), or dielectric constant (Dk). The higher the Dk, the slower the signal propagates along the transmission line. When one trace happens to line up over a bundle of glass yarns for a portion of its length, as illustrated by the top trace in the figure on the left, the propagation delay is different compared to another trace of the same length which lines up over mostly resin. This is known as timing or phase skew and is due to the delta Dk surrounding the respective traces.
Fiber weave effect is a statistical problem. It is not uncommon for PCB designs to have long parallel lengths of track routing without any bends or jogs. This is particularly true in large passive backplane designs. Because the fiber weave pattern tends to run parallel to the xy axis, any traces running the same way will eventually encounter a situation of worst case timing skew if you build enough boards. This was demonstrated by Intel after compiling more than 58,000 TDR and TDT measurements over two years. In 2007, Jeff Loyer et al presented a DesignCon paper “Fiber Weave Effect: Practical Impact Analysis and Mitigation Strategies” where they published the data and proposed techniques to mitigate the effect of fiber weave skew. They showed statistically it is possible to have a worst case timing skew of approximately 16ps per inch representing a delta Dk of approximately 0.8.
In high speed differential signalling this is an issue because any timing skew between the positive (D+) and negative (D) data converts some of the differential signal into a common signal component. Ultimately this results in eye closure at the receiver and contributes to EMI radiation.
You can calculate the timing skew using the following equation:
Where:
t_{skew} = total timing skew due to fiber weave effect length (sec)
Dk_{max}= dielectric constant of material predominated by fiberglass.
Dk_{min}= dielectric constant of material predominated by resin.
c = speed of light = 2.998E+8 m/s (1.18E+10 in/s)
A practical methodology you can use to estimate the minimum and maximum values of Dk is by studying the material properties available from PCB laminate suppliers. Consider two extreme styles of fiberglass cloths used in modern PCB laminate construction as illustrated by the figure on the left. The loose weave pattern of 106 has the highest resin content of all the most popular weaves, while the tight weave pattern of 7628 has the lowest. Therefore, you could use the specified values of Dk for cloth styles 106 and 7628 to get Dk_{min} and Dk_{max }respectively. Once you have these and apply a tolerance, you can estimate the t_{skew }.
Example:
Assume Fr4 material; one inch of fiber weave effect; Dk_{106}= 3.34(+/0.05) and Dk_{7628}= 3.97(+/0.05), then timing skew is calculated as follows:
Modern serial link interfaces use differential signalling on a pair of transmission lines of equal length for interconnect between two points. In a DesignCon 2007 paper, “Losses Induced by Asymmetry in Differential Transmission Lines” by Gustavo Blando et al, they showed how intrapair timing skew between the positive (D+) and negative (D) data caused an increase in the differential insertion loss profile due to timing induced resonances. These resonances appear as dips in the differential insertion loss profiles of the channel as shown in the following figure:
This figure presents the results from an ADS simulation I did recently of a PCIe Gen2 channel running at 5GT/s. The eye diagrams are at the receiver after approximately 30” of track length chip to chip. The channel model was parameterized to allow for adjusting the fiber weave effect length as required.
As you can see, when the length of the fiber weave effect induced skew increases from 0 to 12.7 inches, the fundamental frequency nulls in the differential insertion loss plots decrease. These nulls occur at the fundamental frequency (fo) and every odd harmonic.
Also, the eye shows some degradation at 5.6 inches of fiber weave effect and starts to distort significantly after 7.8 inches. At 12.7 inches, fo equals the Nyquist frequency of the data rate (in this case 2.5GHz) and the eye is totally closed.
You can predict the resonant frequency ahead of time and use it to gain some intuition before you simulate and validate the results. If you know the total intrapair timing skew, fo is calculated using the following equation:
Where:
f_{o }= resonant frequency
t_{skew} = total intrapair timing skew
Example:
Using t_{skew} = 16 ps/in we calculated above and using 12.7 inches from the last simulation results in the figure above, the fundamental resonant frequency null is:
You can find more details of this phenomena plus a novel way to model and simulate it from a recent White Paper I published titled, “Practical Fiber Weave Effect Modeling”. It, along with other papers, is found on my website at LamsimEnterprises.com.
PCB Laminate Construction
Present day FR4style laminates used for PCB fabrication rely on woven glass fiber yarns to maintain the structural integrity of the finished product. These yarns are made up of electronic or EGlass material. Because it is the same glass used in everything from Corvette bodies to boat hulls, it is a very inexpensive reinforcement material. NEGlass has improved electrical and mechanical performance over EGlass. It is used for higher performance laminate products such as Park Nelco 400013SI.
The table on the left shows five of the most common fiberglass styles used for laminate construction today. When glass fiber yarns are woven into fabric, the “Warp” yarns run the length of the roll, while the “Fill or Weft” yarns run the width. Yarn count refers to the number of warp threads per inch by the number of fill threads per inch.
Prepreg is the term we commonly use for a weave of glass fiber yarns preimpregnated with resin which is only partially cured. The glass to resin thickness ratio defines the overall thickness of a prepreg mat. You can see from the table above, the typical resin content is a function of the thread count and yarn diameter. For example, the figure on the far left illustrates styles like 106 and 1080 having smaller diameter yarns and higher resin content. The right hand figure is indicative of yarns with larger diameter and lower resin content like style like 2116 or 7628.
When copper foil is attached to one or both sides of fully cured prepreg mats, the finished laminated panel is called a core. Both cores and prepreg mats are available in various panel sizes and thicknesses.
There are several different kinds of resin systems in use today to form prepreg and cores. The general specification FR4 is the most common. It refers to a specific fireretardant level rather than specific resin chemistry. Since you have a choice of many laminates that meets the FR4 fire specification, there is no such thing as “standard FR4”. That being said, most of us consider “standard FR4” to mean a laminate having a typical dielectric constant (Dk) of about 4.3 and dissipation factor (Df) of 0.020 – 0.025 at 1MHZ and 50% resin content.
Each family of resin systems have their unique electrical and mechanical characteristics depending on the fiberglass style and resin chemistry. For example, Nelco 40006 at 50% resin content has a typical Dk of 4.0 and Df of 0.023 at 2.5GHz. A higher performance resin system like Nelco N400013 on the other hand, has a Dk of 3.7 and Df of 0.009 for the same resin content and frequency. This tells us two things:

A lower Dk means we can ultimately achieve an overall thinner board for the same characteristic impedance.

A lower DF means less high frequency attenuation allowing us to run at a higher bit rate or have longer traces.
When designing your board stackup, it is best to refer the manufactures data sheet for exact values. The Park Electrochemical Corp. (Nelco) website is an excellent resource to explore when trying to decide on the best dielectric material to use for your next highspeed design.