Advanced ceramic materials and a high-resolution circuit fabrication process can combine to provide excellent electrical performance in small sizes. As demonstrated in Part 1 of this white paper, the combination has been applied at Dielectric Laboratories, Inc. (DLI) to the production of XTREME-Q^? high quality-factor (Q) resonators at microwave and millimeter-wave frequencies. This concluding part of the article series will show that the high-Q nature of these materials can also be applied to microwave and millimeter-wave filters at frequencies exceeding 67 GHz. In recognition of the unconventional nature of these new filters, DLI refers to the departure with conventional frequency-management design and manufacturing approaches as a " disruptive technology."

These capabilities in ceramic resonators and filters are not the results of new-found knowledge but come from years of designing and manufacturing extensive lines of high-Q Single-Layer Capacitors (SLCs) and Multi-Layer Capacitors (MLCs). Manufactured to precise tolerances, these extremely stable capacitors maintain their values over time, temperature, and vibration in the most demanding commercial, industrial, and military applications. The capacitor expertise is a building block for the higher-level design and manufacturing services offered as part of DLI's disruptive technology.

The disruptive technology essentially uses capacitors, inductors, and other high-frequency structures and components to form high-performance components on ceramic substrates. DLI offers a variety of different proprietary ceramic formulations in support of the technology, including CG, CF, and FS materials. These low-loss materials feature excellent stability over temperature (see Fig. 1 in Part 1 of this White Paper), as judged by their temperature coefficients of frequency (a measure of the variations in frequency over a certain temperature range). For temperatures from ?20 to +120°C, the temperature coefficients of temperature for the CG, CF, and FS ceramic materials range from 2.3 to 8.8 PPM/°C. In terms of resonators and filters, these numbers translate into frequency shifts of less than one tenth of one percent at extremely wide temperature extremes.

Compare this to the temperature stability of alumina (Al2O3) substrates commonly used in microwave circuits, at about 120 PPM/°C. These ceramic materials offer greater miniaturization capabilities compared to alumina and other substrates as a result of the higher dielectric constants. And they are stable over time, having been proven for decades in the company's lines of SLCs and MLCs.

Understanding Filters
The design and production expertise detailed in Part 1 of this White Paper (Resonators) also serves the synthesis and fabrication of highperformance, extremely temperature stable microwave filters from 500 MHz to beyond 67 GHz. The disruptive ceramic technology, with the aid of precisely controlled photolithography, has been applied to a wide range of lowloss, high-rejection filters, including microstrip, cavity, ring, and symmetrical dual-mode resonator types. DLI has already produced lowpass, highpass, and bandpass filter designs, including Bessel, Chebyshev, edge-coupled, hairpin, interdigitated, and custom variations. With passbands as wide as 30 percent, typical performance levels include insertion loss of less than 2 dB, return loss of 15 dB and minimum rejection of 45 dB, with tight amplitude ripple and group-delay variations.

The performance of individual filters depends upon a number of factors, including the number of filter poles, the architecture, the resonator Q, and the percentage bandwidth. In order to appreciate the performance of the filters fabricated with DLI's disruptive ceramic technology, it might help to review the basics of how a filter's performance is evaluated. Although the essential function of an RF/microwave filter is simple—to remove unwanted signal energy across a specific band of frequencies while leaving remaining portions of the spectrum unaffected—the design and implementation of high-frequency filters with acceptable performance traits is often a challenge even for experienced engineers.

Filters come in essentially four types: bandpass, band-reject, lowpass, and highpass filters. A bandpass filter channels signals with minimal attenuation through a range of frequencies known as the passband, and rejects signals at frequencies above and below the passband. A band-reject filter (also known as a notch filter) is essentially the opposite of a bandpass filter. It rejects signals across one band (known as the stop band) and allows signals to pass with minimal attenuation at frequencies above and below the stop band. A lowpass filter channels signals with minimal attenuation below a specified cutoff frequency, while rejecting signals above that cutoff frequency. The cutoff frequency is commonly a point at which signal attenuation reaches 3 dB. A high pass filter is essentially the opposite of a lowpass filter, rejecting signals below the cutoff frequency and passing signals with minimal attenuation above the cutoff frequency.

Filters are judged in terms of a number of performance parameters, including insertion loss, return loss (or VSWR), rejection, ripple, amplitude-versusfrequency response (or selectivity), group delay (how long a signal takes to propagate through a filter), phase response, and even quality factor (or Q). In a bandpass filter, insertion loss is the amount of signal attenuation above a 0-dB level that would be represented by an ideal transmission line in place of the filter. Insertion loss occurs due to a filter's dissipative elements (the resistors, inductors, capacitors, and transmission lines). Rejection is the amount of signal attenuation at specified points above and below the passband or center frequency, including the insertion loss.

Every filter has characteristic impedance, measured in ohms, with 50 ohms being typical. While the characteristic impedance may be consistent across the passband, it tends to vary once stop-bands are approached. At a system level, matching the terminal impedances at the I/O of a filter is critical to achieving good filter performance.

Bandpass filters are defined in terms of their center frequency (CF) [i.e., a 10.5-GHz bandpass filter] and the width of their passband. But defining the CF of a bandpass filter is not obvious, since it can be done arithmetically or geometrically. Generally the geometric definition is employed in the filter design process, and the arithmetic definition is used to specify a filter. The arithmetic center frequency is simply the sum of the lower and upper bandedges divided by two. For example, for a bandpass filter with 3-dB frequencies of 900 and 1000 MHz, the arithmetic center frequency is found by (900 + 1000)/2 = 950 MHz.

Like a resonator, a bandpass filter exhibits a Q. In a filter, the Q is the ratio of the midband frequency to the bandwidth. A narrowband filter, for example, with 3-dB band edges of 950 and 1000 MHz (center frequency of 975 MHz) has a Q of 975/50 = 19.5. A bandpass filter with wider 3-dB bandwidth of 500 to 1000 MHz would have a much lower Q of 750/500 = 1.5. Essentially, filter Q is related to the bandwidth, with narrower filter bandwidths resulting in higher filter Q values.

In fabricating filters, high-Q circuit elements (such as transmission lines, capacitors and inductors) are desirable for high-performance filter responses. Low-Q circuit elements tend to yield higher passband insertion loss and lower stopband attenuation. And lower-Q elements lead to a rounding of a filter's response, with poorly defined filter skirts. In general, circuit elements should have a Q of 100 or better commensurate with filter Q. Filter insertion loss is proportional to the ratio of filter Q to the resonator unloaded Qu. Where Loss = Q/Qu.

With additional sections, the rejection of a given filter design can be increased, but with additional complexity and insertion loss (due to additional resonant elements). Historically this resulted in difficult and time-consuming tuning when a fabricated filter misses its design targets (such as CF or BW). Filters fabricated with DLI's disruptive ceramic technology provide excellent performance with no tuning and can be produced in large quantities with the repeatability of a photolithographic process.