*This post authored by John Coonrod originally appeared on the Rog-Blog hosted by Microwave Journal*.

Dielectric constant (Dk) is one of the most essential of printed-circuit-board (PCB) material parameters. Circuit designers rely on it for determining such things as impedances and the physical dimensions of microstrip circuits. Yet, it is not unusual to see a laminate data sheet with different values of Dk for the same material, such as a process Dk and a specification Dk. A material supplier may even recommend an additional value of Dk, to be used in computer-aided-engineering (CAE) software simulators. Why all the different numbers and is there one value of Dk that is the one to trust when designing a circuit?

As detailed in the last several blogs, there are more than a few ways to determine the Dk of a microwave laminate, and these different measurement methods often yield different results for the same material. Some of the measurement techniques are based on the use of “raw” PCB materials—without circuits on them—while some of the methods use a well characterized circuit with predictable performance to then determine the Dk for the material. Materials suppliers may use terms like “process Dk” to refer to the target value for the material when it is being processed, and “specification Dk” to mean a value determined by means of one or more of the measurement methods described in the two previous blogs. Often, the process and specification Dk values are the same for a given laminate.

A more meaningful version of Dk is the “Design Dk” that is currently published in the Rogers’ Product Selector Guide and serves as the values for Dk in the MWI-2010 Impedance Calculator, available for free download (note that it does require sign-up). The Design Dk is a value that provides the most accurate and repeatable results when used for circuit design purposes, notably in commercial CAE circuit and system simulation programs.

For some materials, the process or specification Dk may have the same value as the Design Dk. For Rogers’ popular RT/duroid® 6002 microwave laminate, for example, the process Dk and the Design Dk are both 2.94 in the z-axis. One difference is that the process Dk is specified at 10 GHz on the data sheet, while the Design Dk is given for frequencies from 8 to 40 GHz. The values were determined using two different test methods.

At the same time, the Dk values may differ appreciably. Rogers RO3010™ laminate has a process Dk of 10.2 in the z-axis at 10 GHz, but a Design Dk value of 11.2 is recommended for use with commercial CAE software simulators for more accurate modeling purposes.

If process and specification Dk values are determined by measurements, why should there be a need for a “Design Dk” value? As mentioned in the previous two blogs, there are many test methods for determining the Dk of a laminate. As an example, the global trade organization IPC lists 13 different test methods to determine a material’s Dk. Materials suppliers use any number of these measurement methods for their own determinations of Dk, while laminate users may have their own, and different, methods for determining the Dk of a laminate before using it for design purposes. In the two materials mentioned above as examples, a different measurement was used in each case to find the process/specification Dk and the Design Dk: the clamped stripline method was used for the process/specification Dk and the differential phase length method was used for the Design Dk.

Within Rogers, for example, the X-band clamped stripline resonator test is used for standard quality assurance (QA) testing of specification or process Dk, although the full-sheet-resonator (FSR) measurement method may also be used for QA testing. The split post dielectric resonator (SPDR) method may also be used to characterize materials within Rogers. For determining the Design Dk, the microstrip differential phase-length method will be used for all materials.

While none of the test methods is ideal, the differential phase-length method is elegant in its simplicity. It relies on fabricating two microstrip circuits of significantly different lengths on the same laminate material, using the same connectors or test fixture to determine the phase angle differences between the circuits for a given test frequency. A value of Dk can be determined from simple calculations based on the differences between physical lengths and phase angles. The process is repeated for as many frequencies as is practical. It is not a fast method, but it does provide accurate results for Dk in the z-axis, with anisotropic material effects (Dk values in the x and y axes) having little impact on the measurements.

This test method uses microstrip circuits commonly used in actual applications. It is also performed at the high frequencies often used in applications, to account for “copper effects,” in which a laminate with rougher copper surface can test for a higher apparent Dk value than a laminate with smoother copper surface. Test methods using lower frequencies may not reveal the effects of the copper roughness on measured Dk value.

The Design Dk values have been determined for all of Rogers’ high-frequency laminates and are being reported to all major developers of CAE simulation software tools. In addition, those values are now included in the MWI-2010 Microwave Impedance Calculator, the Product Selector Guide, and in the Slide Rule published in the November 2010 issue of Microwave Journal.

The **Rogers ACS Division** has introduced a new design program that is free to download called the **MWI-2010 Microwave Impedance Calculator**, a transmission line modeling tool for electronics engineers (setting up an account is required).

The MWI-2010 Microwave Impedance Calculator software doesn’t replace sophisticated suites of modeling tools, such as the Advanced Design System (ADS) from Agilent Technologies or Microwave Office from AWR. Nor can it challenge the prediction capabilities of a planar or 3D electromagnetic (EM) simulator such as the Sonnet suites from Sonnet Software. But what it does, it does well, which is to calculate key parameters for most common microwave transmission lines, including microstrip, stripline, and coplanar-waveguide transmission lines. The software is downloaded as an executable (.exe) file and runs on most Windows-based personal computers, including those with Windows XP, Windows Vista, and Windows 7 operating systems. To speed and simplify the use of the software, Rogers also offers a 22-page operator’s manual in PDF file format.

**Using the Transmission-Line Modeling Tool**

The MWI-2010 program is based on closed-form equations derived from Poisson’s wave equations. The simple-to-use software can determine key parameters for a selected transmission-line type and laminate material, such as the conductor width and conductor metal thickness needed to achieve given impedance at a target frequency. The software’s intuitive graphical user interface (GUI) screen allows a user to select from a variety of different transmission-line types, including conventional microstrip, edge-coupled microstrip, conventional stripline, offset stripline, and conductor-backed coplanar-waveguide (CPCPW) transmission lines. The on-screen menus allow a user to select a transmission-line technology and a laminate material. Once a material, such as Rogers RT/duroid® 6035HTC material, is selected, its pertinent characteristics are also shown on the screen, including relative dielectric constant (permittivity), dissipation factor (loss), thermal conductivity, and thermal coefficient of dielectric constant. Moving a mouse cursor over any material name reveals additional information about the material.

**Enter Parameters such as Thickness, Operating Frequency and RF Power Level**

With a material in place, the next step is to pick a standard dielectric thickness from a menu, or enter a custom thickness. A standard copper cladding thickness must also be selected from a menu, or a custom thickness entered manually. Copper conductor roughness is also accounted for, either selected from a menu as a standard value, or entered manually as a nonstandard value. Similarly, a standard value for copper conductivity can be used in a calculation, or a custom value entered, although any change in the value for copper conductivity will affect all metal layers in a multilayer circuit.

The MWI-2010 software allows an operator to enter parameters pertinent to a specific application, such as operating frequency and RF power level. Once a user has selected the desired transmission-line type, dielectric material, material thickness, conductor width, thickness of the conductive metal cladding, etc., a calculation will provide results in terms of such transmission-line parameters as conductor width and conductor spacing for a selected impedance. The software can generate insertion loss tables of data that can be used to create plots of loss versus frequency, and these plots can then be compared to actual measured results from a microwave vector network analyzer (VNA).

This exact procedure was performed to evaluate the accuracy of the MWI-2010 software for calculations of conventional microstrip parameters. MWI-2010 calculations performed for conventional microstrip transmission lines have proven to be extremely accurate since they include the effects of dispersion as well as copper roughness. For example, calculations performed on RT/duroid 6035HTC laminates have compared quite closely with actual measurements. These are ceramic-filled PTFE composite materials with a dielectric constant of 3.5 at 10 GHz and dissipation factor of 0.0013 at 10 GHz. In a comparison of MWI-2010 predictions versus measurements for a 20-mil-thick microstrip transmission line on RT/duroid 6035HTC with 1-oz. copper cladding, predicted and measured data matched almost exactly through 6 GHz. The predictions do not maintain the same accuracy above 7 GHz for this particular model, but still track the measured data very closely even at those higher frequencies.

The MWI-2010 software may not be able to match the accuracy of an EM simulator for a given prediction, but it is considerably faster, providing results almost instantaneously. It has been found to be most accurate for calculations on conventional microstrip and stripline, very accurate with edge-coupled microstrip and offset stripline transmission lines, and fairly accurate with conductor-backed coplanar-waveguide (CBCPW) transmission lines, although in the case of CBCPW transmission lines, vias must be properly placed to ensure accurate results.

Calculating the impedance of transmission lines is not trivial, since a number of factors can affect impedance. In microstrip, the width of the conductor and thickness of the dielectric substrate impact impedance. In CBCPW, not only the conductor width and dielectric thickness, but the spacing on the signal plane between the signal conductor and the adjacent ground planes will affect impedance. The MWI-2010 software is free, and provides results fairly quickly that are accurate and can be saved for use in other programs, including in word processors or in spreadsheets for creating x-y plots. In addition to calculating the impedance and loss of a transmission line, the MWI-2010 software provides information on a laminate’s effective dielectric constant, signal wavelength, skin depth, the electric length for a transmission line at a selected frequency, and propagation delays. It can even calculate the temperature rise above ambient temperature for a selected laminate based on an input RF power level.

For anyone needing a quick impedance calculation for designing a filter, coupler, or other high-frequency circuit, the MWI-2010 software provides usable results. And the price is right!

We are always on the lookout for interesting engineer communities, and we recently found one by following the Twitter stream just after DesignCon 2011 ended. The community we found was the SemiWiki project, a few folks from DesignCon had shared their trip reports from the show. The community is described as:

The SemiWiki Project provides in-demand content for semiconductor design and manufacturing, facilitating peer-to-peer communications using Web 2.0 technologies.

This group is serious about collaboration and creating a valuable community for semiconductor engineers. What is cool is that they are running a contest to encourage and reward participation for becoming a “top influencer“, and the prize is an Android Tablet. Winners will be revealed at the Design Automation Conference (DAC) June 5-12 2011 so there is still time! There is a running list of those “influencers” with their points accumulated so far. Nothing like a little competition!

Beyond encouraging participation, this appears to be a growing, active community with Forums, various Wikis that includes a wealth of information being shared. Check it out if you’re a semiconductor engineer…