#### What is in this article?:

Printed-circuit-board (PCB) materials with high dielectric constants can help miniaturize microwave circuits, but engineers using these materials must be aware of the impact of loss and dispersion on their designs.

## Filter Layouts

**Figure 3** shows the layouts of the filter designs. As this figure shows, the higher Dk value results in about a 37% reduction in PCB area for the same filter. The filters were not optimized, but slightly modified to ensure that both had about the same return loss (15 dB or better) within the passband. The center frequencies and bandwidths were within a few percent of each other, so optimization was not needed for those parameters. **Figure 4** shows the output of the filter performance levels according to the Sonnet software.

Both filters were nearly the same in terms of center frequency and bandwidth. A main difference is improved stopband characteristics for the filter using the material with Dk value of 3. There is some slight difference in passband insertion loss, although some of that is due to the difference in dissipation factor (Df) between the two materials. The material with Dk of 3 had a dissipation factor of 0.0016 while the material with Dk of 10.8 had a Df of 0.0027. Insertion loss was 0.61 dB for the filter on material with Dk of 3 while the insertion loss was 1.05 dB for the filter on material with Dk of 10.8. Both filters were not modeled with rough copper configurations so that simulated insertion loss would probably be higher on actual circuits.

Microwave circuits may incorporate slow-wave propagation design to reduce the size of a circuit; when combined with high Dk materials, this size reduction can be dramatic. Microwave circuits in which the size of the circuit is related to the wavelength can be reduced in size by means of slow-wave propagation since the wavelength is shortened as the wave is slowed. A reduction in the phase velocity directly relates to a decrease in wavelength, and this property can be used to shrink the size of microwave circuits.

The concept of slow-wave propagation can be examining a small section of microstrip transmission line via the Sonnet Software simulator. **Figure 5** shows two microstrip transmission-line circuits used for this evaluation, on 30-mil-thick substrate having a Dk value of 3. One is a normal microstrip transmission line and the other uses a ladder configuration. The ladder pattern of the conductor causes the electric and magnetic stored energies to separate in distance and that separation slows the phase velocity.

**Figure 6** offers a comparison of group-delay characteristics across the passband frequency range of the filters modeled in **Figs. 3 and 4**. As can be seen, the group delay is slower for the microstrip transmission line using the ladder pattern for the signal conductor than for the normal microstrip transmission line.

**Related Articles**

• Materials Support High-Speed Circuits

• Corralling Materials For Microwave Circuits

• Absorbers Highlight Material Showcase

If the conductors for the filters in **Fig. 3** were not solid copper patterns, but used the ladder effect, the geometries of these circuits could be reduced even further. However, an EM simulation model for ladder patterned conductors is extensive. Rather than perform that simulation, a general calculation was performed for the change in phase velocity/wavelength for filter size reduction.

Using the filter design of **Fig. 3** as a reference, which is based on material with Dk value of 3, and comparing this to a filter on the material with Dk of 10.8 and using the ladder pattern conductors, the higher Dk value filter would be reduced in size by 41% compared to the filter using the material having a Dk value of 3. Of course, the ladder structure would affect the even- and odd-mode characteristics of the filter, so the reduction of size for this filter is reference only and the actual filter performance may be altered from what is shown in **Fig. 4**.

These simulation examples show just a sampling of the many uses for high Dk circuit materials in microwave applications. They can bring reductions in circuit size but, as noted, there are always tradeoffs when choosing a circuit material. When considering the use of high-Dk circuit materials to achieve a size reduction or some other benefits, a designer is advised to consult their circuit material supplier for detailed information.

### References

1. John Coonrod, “Using High Frequency PCB Laminates for Improving Thermal Management Issues,” PCB West 2011 Conference & Exhibition, Santa Clara, CA, September 2011.

2. Jia-Sheng Hong and M.J. Lancaster, Microstrip Filters for RF/Microwave Applications, Wiley, New York, 2001.

Note: RO4000, RO4350B, RO4450F, RO4360G2, RO3006, and RO3210 are licensed trademarks of Rogers Corp.