Circuit materials are evaluated by a number of different parameters, including dielectric constant (Dk) and dissipation factor (Df). Those two parameters also have temperature-based variants that provide insight into the expected behavior of a circuit material with changes in temperature, notably the thermal coefficient of dielectric constant (TCDk) and the thermal coefficient of dissipation factor (TCDf). The parameters detail the amounts of change in a material’s Dk and Df, respectively, as a function of temperature, with less change representing a material that is more stable with temperature.

A circuit material with an ideal TCDk, with a Dk that would remain at a fixed value even as the temperature changes, would have a TCDk of 0 ppm/°C. In the real world, however, circuit materials exhibit some change in Dk with changing temperature. A circuit material considered to have stable Dk with temperature will have a very low value of TCDk, typically less than 50 ppm/°C. When an application requires that a circuit board be subjected to a wide operating-temperature range and deliver stable performance all the while, a circuit board’s TCDk parameter is one of the key specifications to consider after determining the required Dk for that application’s circuits.

Although circuit temperature stability requirements for military and aerospace applications are well documented, due to the typically hostile operating conditions of military circuits and systems in the field, commercial applications can also endure conditions of changing temperatures that can require better-than-average circuit-board TCDk performance. Power amplifiers for wireless base stations or outdoor-mounted microcells may not experience the wide temperature swings of military environments, but they depend on circuit Dk stability with temperature to maintain stable gain and output power. Their active devices are impedance matched to a typical 50-Ω circuit/system environment for optimum gain, output power, and power-added efficiency, and changes in Dk will cause variations in amplifier performance. In addition to environmental temperatures, the self-heating effects of amplifiers can further complicate changes in a material’s Dk characteristics with temperature, especially for materials with high values of TCDk.

 Similarly, passive components, such as filters, can suffer from unwanted frequency changes with changes in Dk, such as shifts in passbands and stopbands. Ideally, wireless base stations would be maintained in temperature-controlled environments but, again in the real world, this is often not the case, and circuit-board TCDk is then a key performance parameter of interest.

When performance with temperature is important, specifying a circuit-board material should be done deliberately and by taking a close look at available data sheets. Circuit designers should never assume that two materials from the same manufacturer or the same product line will have the same TCDk characteristics. Different materials based on PTFE, for example, can have widely different values of TCDk. PTFE, of course, is the basis for many excellent, low-loss, high-frequency circuit materials, but the TCDk characteristics of these materials can vary widely. Some PTFE-based circuit materials can suffer large changes in Dk with temperature, evidenced by TCDk values of 200 ppm/°C and even higher.

At the same time, some PTFE-based circuit based materials can provide near-ideal TCDk characteristics. PTFE-based RO3003™ circuit material from Rogers Corp. has outstanding TCDk of -3 ppm/°C, making it a strong candidate for temperature-sensitive circuit designs facing wide operating temperature ranges. The family of circuit laminates includes materials with Dk from 3.00 to just over 10.00 when measured through the z-axis (thickness) of the material at 10 GHz. The laminates are popular circuit choices for military and commercial applications through millimeter-wave frequencies of 77 GHz and higher, including in automotive radar systems which much maintain stable performance over wide temperature extremes.

Just as suppliers of circuit materials may test and specify the Dk values of their materials in different ways, such as at different test frequencies, any valid comparison of circuit materials for their TCDk performance levels calls for an understanding of the measurement methods used to determine TCDk for a particular material. Material measurements are often based on industry-standard IPC test methods for agreement of values among different material suppliers.

For example, measurements of circuit laminate TCDk at Rogers Corp. are performed by means of the clamped stripline test detailed in IPC test method IPC-TM-650 2.5.5.5c. Prior to testing a circuit laminate, all of the copper is etched from the substrate. The substrate is then clamped into a fixture which behaves like a loosely coupled stripline resonator. The fixture and its material to be tested are placed into a laboratory temperature-controlled environment, such as an oven. The temperature is changed in steps and the fixture and material are allowed to reach thermal equilibrium with each change in temperature before the Dk is measured. Many measurements are performed to cover a wide operating temperature range and to measure the Dk at different points across that temperature range. The end result is a curve of Dk versus temperature for that material, which is the TCDk of that material.

Temperature-Dependent Loss

Just as TCDk is a barometer of how a material’s Dk changes with temperature, TCDf is a measure of a circuit material’s dissipation factor (Df) or loss tangent and how it changes with changing temperature, typically with loss increasing as temperature increases. As with TCDk, the temperature effects of TCDf can impact the performance of both active and passive circuits. At higher temperatures, a circuit material with high value of TCDf can compromise the gain and output power of an amplifier, and increase losses in passive circuits, such as filters or passive antennas.

The TCDf values of circuit materials from Rogers Corp. are characterized with a measurement method that is the same as that used for testing TCDk. The measurements are complicated by the variations in the loss properties of the resonator circuit which is integral to the clamped stripline fixture and the fact that copper conductivity changes with temperature. Rather than attempting to measure and report Df versus temperature to derive a TCDf value for the material, loss versus temperature is measured, where it is the loss of the resonator in the form of its inverse quality factor (1/Q). As with TCDk, an ideal value of TCDf would be close to zero, to indicate little or no change in dissipation factor with temperature. In the real world, circuit materials with the lowest possible values of TCDf are to be preferred for temperature-sensitive circuit applications, whether for active or passive circuits.

All of the information shown above is in regards to the effect of temperature on the Dk and Df properties (TCDk and TCDf) of material when considering a short term thermal event.  How a laminate responds to long term thermal exposure is a different subject than TCDk and TCDf, even though these properties can be involved with long term thermal aging evaluations.   These aging evaluations are critical to understand if the circuit material is the proper choice for the conditions it will be exposed to in the end-use environment and that it will meet the needs of the intended application over the life of the product.  More information on long term thermal aging can be found a in two part series blog dated April 16^th 2013 and May 3^rd 2013.  The respective titles of these blogs are “Picking A PCB For High Reliability” and “PCB Formulated for Reliability”.

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