Dielectric and Insertion Loss Measurement Part 1: The Problem in High Frequency, High Data Rate Designs

by | Dec 21, 2021 | High Frequency/High Data Rate Designs

As onboard data rates have increased, the industry has run up against challenges of ever shrinking insertion loss budgets on transmission lines. There has been a lot of work done to recover the signal even after the amplitude has degraded by >=28dB; techniques such as DFE, FEC, and hardware such as phased lock loops, re-timers have enabled these high data rates. Moving from PAM-2 (NRZ) to PAM-4 signaling is also helping the advance to higher data rates at the same Nyquist frequency. However, all of this has come at a cost, as the eye height and width margins are reduced, in addition to tighter jitter and skew budgets. However, with data rates pushing 112 Gbps at 28 GHz Nyquist frequency, the challenge is to find dielectric material and metal conductor solutions that can address these challenges. Achieving 0.7dB/inch (28 dB for a 40-inch line) on 4-5 mil traces is a major challenge, if not an impossible goal, with the current conductor technology. Building Test Vehicles to select the copper, oxide and materials is not a suitable option, as the number of combinations becomes very large and unwieldy and extremely time consuming for the technology to push forward. Normally, simulation would be considered a reliable alternative to building TVs, but the industry has built the belief that the Dielectric properties data from the material suppliers cannot be trusted. The source of the mistrust stems from the nature of the measurement systems.

Dielectric Measurements

Measuring dielectric properties should be straightforward, but in practice it is not. Let us start with Dielectric Constant. The velocity of an electromagnetic wave is slowed down, as it enters a medium, by a factor of the square root of its Dielectric Constant (refractive index is the analog of this quantity in optical frequencies). This is clearly understood in the realm of visible light, which lies between 405 and 790 THz. The same reduction of velocity phenomena occurs at lower frequencies such as in the microwave regime. The measurement of this quantity should not be fraught with as much controversy as is seen in the electronics industry, writ-large, let alone as is seen particularly in the Printed Circuit Board industry.

Dissipation Factor, or loss tangent, as it is also called, is the amount of energy dissipated in a material as EM waves travel through it. It is the same property that allows us to use a microwave oven to cook – this is done through the heat generated due to the orientation polarization of water molecules present in the food being warmed. This property is responsible for attenuation through a dielectric and is, therefore, central to the study of loss, but, again, given how fundamental it is, its measurement should also be far less controversial.

While there are a number of accurate techniques available to measure Dk and DF, there is a lot of confusion about these properties, mainly arising from the fact that materials used in PCBs are anisotropic – that is, the dielectric properties are not the same in the planar and perpendicular directions. The most repeatable and accurate method for testing Dk and DF is the use of resonant metal cavities or dielectric resonators. To get a reliable measurement with the cavity method, one must use the TE mode EM waves. The TE mode means “transverse electric”, implying that the field is transverse to the direction of propagation. This mode is preferred for measuring the dielectric properties because the Q- factor is high. The Q-factor, or Quality factor, is a number that indicates how slowly or quickly the oscillations die out after excitation without any external damping. A high Q factor means that the oscillations die out slowly or that a cavity, in such a case, is substantially lossless.

The resonant frequency of a cavity is the frequency at which the magnetic energy stored equals the electrical circuit energy stored. In circuit theory, this is analogous to when the inductance and capacitance of a circuit equal each other.

Energy stored in a cavity is given as:

(1)   \[ W_{magnetic} = W_{electrical} = \frac{\varepsilon}{2}\ \times \iiint |E|^2\, d\tau  \]

Where E is the electrical field, \tau is time, and \epsilon is the permittivity. When the cavity has non-zero loss, then Q is given as:  

(2)   \[ Q= \frac{\omega W}{P_d}  \]

where \omega is the angular frequency, W is the stored energy, and P_d is the average power dissipated.

For the dielectric losses:

(3)   \[ Q_d = \frac{\omega \varepsilon' \iiint |E|^2\, d\tau}{\omega \varepsilon'' \iiint |E|^2\, d\tau} = \frac{\varepsilon'}{\varepsilon''}  \]

where \varepsilon' is the real part of the permittivity and \varepsilon'' is the imaginary part of the permittivity.

Similarly, as the cavity material is not a perfect conductor:

(4)   \[ Q_c = \frac{\omega W}{P_d} , P_d = R \oiint\limits_{walls} |H|^2\, ds  \]

where H is the magnetic field, R is the intrinsic resistance of the material, and the contour integral is taken over the cavity walls.

The solution to these equations can be computed using the shape and dimensions of the cavity. The overall Q of the cavity is defined as:

(5)   \[ \frac{1}{Q} = \frac{1}{Q_{conductive}} + \frac{1}{Q_{dielectric}}  \]

So, the basic principle of dielectric properties measurement is simple: measure the Q of the empty cavity/resonator, create a perturbation through the introduction of the sample or MUT (Material-Under-Test). This shifts the resonant frequency. Variational principle techniques such as the Rayleigh method are then used to compute the Dielectric constant (\varepsilon_r) and \tan\delta , on the basis of the Q-factor and resonant frequency of the cavity before and after the introduction of the MUT. The above-described methods are very direct and are considered quite reliable and highly accurate.

 Dk Mismatch

The mismatch between impedance and propagation delay measurements and reported Dk’s mainly stems from the fact that appropriate measurement methods are not used to characterize dielectric properties. These discrepancies might seem strange, given that cavity and resonator methods are very reliable and accurate. In fact, Krupka et. al. have shown that the uncertainty on Dk measurement can be as low as 0.15-0.3% and the resolution on the DF can be as low as  with these methods [4]. This is orders of magnitude below the discrepancy found from measurement vs simulation gap in DF. So, what is the driver behind these discrepancies?

The Dk gap between simulation and measurement is because TE mode is not the propagation mode in a printed circuit board transmission line. The properties measured using the cavity method using TE mode are in the X and Y or the planar direction. This would be fine if the material had the same properties in all directions, but this is not the case with the composite materials used in printed circuit boards. The properties in the XY plane tend to show higher Dk values, due to the effect of glass, and a higher DF if the resin material loss is below that of the Glass and vice versa, if the resin has a higher DF.

Figure 1. Modes of propagation shown in a parallel plate waveguide. (a) Top. TE Mode propagation; (b) Middle. TM Mode propagation; and (c) Bottom. TEM Mode propagation. Adapted from [11].

In transmission lines TEM mode is the mode for propagation. This mode is not possible generally in wave guides and cavities, save for some special cases, such as in a parallel plate waveguide. Using TM mode is an option using a cavity method. The TM mode being the mode where the magnetic fields are transverse to the direction of the propagation. The measurements in TM mode are closely related to the actual dielectric constant experienced by the transmission line – in fact, TM_0 mode in parallel plate waveguide is identical to TEM mode [11].

The problem with using TM cavities is that these have a much lower Q factor, which leads to lower granularity/resolution. Therefore, TM mode resonators do not have the ability to discern loss numbers accurately. TM mode measurement systems still produce reasonable results for Dk, but have very large variability for dissipation factor.

A reasonable alternative is a stripline resonator, such as the Bereskin method, which attempts to measure dielectric properties by exciting a stripline and measuring the Q factor with and without the material under test. Since copper is used in the measurement, the loss is an aggregate of the conductor loss and the Dielectric loss. The Dielectric loss is extracted by subtracting the calculated copper loss. The Stripline is wide enough to minimize the skin depth, a smooth copper is chosen (rolled annealed), and the loss is computed as a function of the resistance of the stripline. Since rolled annealed copper is not perfectly smooth, resulting in roughness loss that is not accounted for, the method does tend to slightly overestimate the dissipation factor. The issues commonly seen with this method are related to the subjective way the resonant peaks are chosen leading to errors. There are other methods available such as open resonator (Fabry-Perot, Free-space) methods, but these are typically not used, due to limited availability of equipment or test facilities, low relevance, high expense, and long lead times.

Mechanism for Dielectric Loss

Before going deeper into a discussion on the bridge between simulation and measurement of loss, it is important to understand the mechanisms behind loss. Here, we explore the mechanism for dielectric loss. Polarization is a phenomenon that refers to the displacement of the positive and negative charges of atoms, ions, or molecules. This could be due to impurities, interfacial charge, dipoles that align themselves with the field, or other defect boundaries.

Figure 2. Polarization of Dielectrics as a function of frequency.

As shown in figure 2, there are four main types of Polarization in Dielectric Materials. [7]

  1. Electronic Polarization / Optical Polarization: The electric fields cause shifting or deformation of the electron clouds. Mainly the outer electron clouds are shifted.
  2. Atomic or Ionic Polarization: This is also called vibration polarization. The electric field causes the atoms or ions of a molecule to be displaced with respect to one another.
  3. Dipolar Polarization: Materials with permanent dipoles move in alignment with the fields, causing the reorientation of the dipoles towards the direction of the electric field.
  4. Interfacial Polarization: mainly relevant for non-homogenous materials, this is when charge accumulates at the interface of two dissimilar materials.

For high-speed applications below 100 GHz, almost all of the polarization is due to the dipolar polarization, also known as orientation polarization. The most accurate methods for Dk and DF measurement are only available at discrete frequencies and, in most cases, only operate at frequencies below 10 GHz [4]. The data rates, however, are moving up substantially and frequencies in the mmWave range are not uncommon for RF applications and are starting to become more common for even High-Speed Digital applications. This is driving a search for reliable test methods to characterize materials at higher frequencies. So far, the data at higher frequencies has proven to be noisy and unreliable when using techniques, such as the Fabry Perot Open Resonator or newer TM cavity methods.

The best available alternative is to use the Dk and DF at sub 10 GHz frequencies [4] and use a suitable model to extrapolate these properties to higher frequencies. The expected error on the extrapolation is very small. For many dielectrics, the highest loss numbers are actually in the sub 10 GHz range due to resonances around 5 GHz or so. Normally there are not many resonance peaks associated with a higher Df but there may be resonances generated due to the periodic nature of the glass weave when the traces are rotated but that is a different phenomenon, an artifact of routing the traces at an angle leading to resonance due to periodicity.

Since the most accurate characterization can be done at below 10 GHz and since most materials do not exhibit major resonances below 100 GHz, until more reliable methods can be developed or emerging methods can be refined for high frequency dielectric measurement, it is best to rely on data at 5 or 10 GHz measured by reliable methods such as Bereskin or the Cavity methods and then extrapolate these to higher frequencies. Extrapolation models, like the Debye Infinite Pole model are very accurate and highly representative of the actual phenomena. Some other methods, such as multi-pole models are not very useful, since the knowledge of these poles is required “a priori”.  The Debye Infinite Pole model (9,3) is a Causal model that uses a single frequency to build a model for a wide frequency range:

(6a)   \[ \sum\limits_{i=1}^{n} \frac{\Delta\varepsilon'}{1+j(\frac{\omega}{\omega_{2i}})} \rightarrow \frac{\Delta\varepsilon'}{m_2-m_1} \int_{m_1}^{m_2} \frac{1}{1+j(\frac{\omega}{10^x})} \, dx = \frac{\Delta\varepsilon'}{m_2-m_1} \frac{\ln \frac{\omega_2 + j\omega}{\omega_1+j\omega}}{\ln 10}  \]

(6b)   \[ \varepsilon' - j\varepsilon'' = \varepsilon_{\infinity} + \frac{\Delta\varepsilon'}{m_2-m_1} \frac{\ln \frac{\omega_2 + j\omega}{\omega_1+j\omega}}{\ln 10}  \]

Several commercial software products have the Debye Infinite Pole model built-in.

DF Mismatch: The Gap Between Measurement and Simulation

Traditionally, simulations using data provided by material suppliers show lower insertion loss when compared to the measurements. Because of this, the dielectric data is seen as suspect, hence the search for alternatives to direct measurement, i.e., extraction from S-parameters. Conductivity of copper is seen as another variable, where the effect of copper treatment, presence of other metals such as nickel etc., and the resulting effect on conductivity is being studied. It is not uncommon to see a 10-15% variation in conductivity values between different copper foils. Oxide roughness is seen as another contributing factor and oxide suppliers are developing solutions for lower roughness. The end-users therefore desire a new method to characterize the dielectric properties and the impact of various factors such as oxide roughness etc.


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