Frequency-agile bandstop filter with tunable attenuation

A frequency-agile bandstop filter technology with tunable stopband attenuation and constant absolute bandwidth is described. The technology is demonstrated by a six-resonator planar microstrip filter with simultaneous varactor-diode tuning of stopband attenuation from 30dB to 50dB and of operating frequency from 1.8 GHz to 2.2 GHz, with a stopband bandwidth of 60 MHz and absolute 3dB bandwidth of less than 390 MHz.


I. INTRODUCTION
Receiver applications sometimes call for discerning weak signals in the presence of much stronger signals. Unfortunately, the stronger signals can drive the receiver front-end amplifier into compression or saturationdistorting, compressing, and masking weaker signals, desensing the receiver. Recently, compact narrowband absorptive bandstop, or "notch", filters have been demonstrated that can selectively eliminate fixedfrequency or frequency-hopping interferers using lossy circuit components [1]- [6]. However, there are occasions when it is desirable to receive both weak and strong signals, attenuating the strong signals only just enough to keep the amplifier operating linearly. This paper addresses such a need by describing an extension of the circuit in [2] that enables tuning of the stopband attenuation level of a frequency-agile absorptive notch filter without the need for additional components. Although it is conventionally possible to tune attenuation by tuning bandwidth, the new approach allows tuning of stopband attenuation while preserving both stopband and passband bandwidths. This new circuit component could also be called a "frequencyagile frequency-selective variable attenuator." Due to their relative simplicity, "first-order" absorptive filters tend to be the most practical to use in frequencyagile applications, but attenuation characteristics of such first-order sections alone tend to lack sufficient stopband bandwidth to be of practical use. Consequently, first-order sections are cascaded to realize practical stopband bandwidths [2], [7]. This paper investigates such a "thirdorder", six-resonator, microstrip absorptive bandstop filter -composed of a properly phased cascade of three "firstorder" stages -with a 22% frequency tuning range and a 20dB stopband-attenuation tuning range. Unlike the filters of [8], attenuation is tuned by tuning varactor capacitance (i.e., resonator frequencies) rather than FET resistance. II. THE TUNABLE "ABSORPTIVE-PAIR" NOTCH FILTER Conventional bandstop filters reflect stopband signals, and resonator loss tends to reduce and limit their stopband attenuation and band-edge selectivity. In [2], a tworesonator bandstop filter topology, termed an "absorptivepair", was introduced that, to at least some extent, absorbs stopband signals -with resonator loss limiting minimum bandwidth rather than stopband attenuation. One of many possible electrically-equivalent circuit schematics of an absorptive pair is given in Fig. 1, in which ideal (frequency invariant) admittance inverters k 01 couple lossy lumped-element resonators, with admittances Y p and Y m , to the ends of a phase shift element of characteristic admittance Y s and frequency-invariant phase shift I, while ideal admittance inverter k 11 directly couples the two resonators. Although a more accurate analysis would require frequency dependent representations of couplings and phase shifts, including frequency dependence would lead to more complicated results which obscure understanding. Fig. 2 shows representative transmission responses of the highpass prototype of the filter of

A. Analysis of the Absorptive Pair
For the idealized a sorptive-pair notch filter in Fig. 1: , To better understand the behavior of the absorptive bandstop filter it is most convenient to work with its highpass prototype, with a minimum of attenuation L o at radian frequency Z = 0. The highpass prototype can be represented by Fig. 1(a), with Y p and Y m replaced by Y p´= g (1+ j (Z´q u + b/g)) and (5) as shown in Fig. 3, where b is a variable frequencyinvariant susceptance, g is a conductance, Z´ is the normalized highpass prototype radian frequency, q u =Z ´c /g is the unloaded Q of the shunt admittances of the highpass prototype, c is a capacitance, and Z ´= 1 is the band-edge radian frequency at which the attenuation is L s .
In terms of s´= jZ´, S 21 is given by with zeros at where the frequency of infinite stopband attenuation is (12) and from (10) and (11) the resonant frequencies are   Fig. 1 to form the first-order highpass prototype.

B. Frequency-Agile Absorptive-Pair Bandstop Filter
To demonstrate the capabilities of the absorptive-pair, an improved implementation of the frequency-agile bandstop filter demonstrated in [2] was designed using an iterative-analysis, manual-optimization approach, resulting in the layout of Fig. 5(a) and the manufactured unit of Fig.  5(b). The design process began by (a) characterizing the microstrip loss on the Rogers' RO4003 substrate (60-mil thick, 3.38 dielectric constant, 0.0021 dielectric loss tangent, 0.034 mm copper) by matching measurements of a conventional notch filter (with a single, open-circuited, half-wavelength resonator) to corresponding microstrip models in commercially-available circuit and 3D planar electromagnetic (EM) field simulators (by adjusting conductor resistivity) and (b) extracting the series-resistorinductor-capacitor (series-RLC) model of the varactors, in Fig. 6, from two-port s-parameter measurements of a 50: microstrip line with a shunt-connected reverse-biased varactor diode to ground. Then a microstrip circuit model, topologically representative of Fig. 1, was iterativelyoptimized at three operating frequencies: a lowest tuned frequency of about 1.5GHz, a highest tuned frequency of about 2.5GHz, and a mid-band tuned frequency of 2GHz. Experience with [2] indicated that the design should constrain the resonant frequencies of the resonators to be equal at the target lowest-tuned frequency and constrain one of the two bias voltages to be the highest acceptable voltage at the target highest-tuned frequency.
Once the circuit model's attenuation was greater than 60dB at each of the three operating frequencies for some set of bias voltage pairs, ad-hoc lowpass varactor bias networks, comprised of three sections of meandered (electrically quarter-wavelength) microstrip were added, with intervening 20pF shunt capacitors to ground. After the circuit had been re-optimized, subcircuits were gradually replaced by s-parameter files of corresponding EM-modeled microstrip layouts, and further re-optimized, until the entire circuit model (except varactors and capacitors) had been replaced by a collection of sparameter files corresponding to different portions of EMmodeled microstrip layouts (dielectric overlay sections, center section, bias lines, and varactor grounding vias).
It was beneficial to keep the varactor ground vias as far apart as practical to minimize their coupling, to design the isolation level of the bias networks to be similar to the maximum attenuation of the filter (about 60dB), and to mount the bypass capacitors vertically as substrate feedthroughs to minimize their inductance to ground and keep the associated series resonances above the frequency band of interest. Simulations and measurements of the filter's performance are compared in Fig. 7(a) and a plot of measured maximum-attenuation frequency versus the difference between the two bias voltages is given in Fig.  7(b) -corroborating the theory in section II(a).    Three of the frequency-agile, first-order, absorptive-pair bandstop filter stages of the preceding section were connected in cascade by two 52.7: microstrip lines, each approximately 30° long at 2GHz, resulting in the integrated third-order, six-resonator bandstop filter shown in Fig. 8. Superimposed plots of the measured characteristics of the filter are shown in Fig. 9, where the filter has been tuned to attenuation levels of 30, 35, 40, 45, and 50 dB at operating frequencies of 1.8, 2.0, and 2.2 GHz by bias voltages shown in Fig. 10. Stopband bandwidths are all tuned to 60 MHz and the resulting absolute 3dB bandwidths are all less than 390 MHz.

IV. CONCLUSION
A first-order (two-resonator) absorptive bandstop filter with tunable stopband attenuation has been introduced along with a theory of its design and operation. The circuit concept does not rely on particular tuning components or manufacturing technologies. A cascade of three first-order sub-circuits is used to make a third-order filter. Unlike the filters of [8], it exhibits useful levels of frequency selectivity, passband insertion loss, and stopband bandwidth, and demonstrates simultaneous and substantial tunability of operating frequency and stopband attenuation while maintaining constant stopband and 3dB bandwidths. Filters of this type may be useful in receivers that must simultaneously handle widely different signal levels.