Abstract:
A plurality of passive filters in combination with a corresponding plurality of operational amplifiers form an individual series of quasi low-pass, bandpass, and quasi high-pass filters which when their outputs are summed in an operational amplifier summer, constitute a &#34;semi-active&#34; notch filter having a low frequency phase shift of substantially zero, and a notch frequency which can be adjusted independently of the low frequency phase shift. The existence of the notch is also independent of the properties and limitations of the operational amplifiers used.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the invention 
     The present invention relates to a hybrid notch filter arrangement which employs a unique combination of active and passive elements, but more specifically the present invention relates to a &#34;semi-active&#34; notch filter wherein the low frequency phase shift and the value of the notch frequency thereof can be controlled independently. 
     2. Description of the Prior Art 
     In the prior art, a need has been established, in certain phase-locked-loop applications (in modeling the temperature and frequency dependence of the Josephson effects for example), for a low-pass filter or notch filter having minimal phase shift at low frequencies and good rejection characteristics at high frequencies. As is well known, the foregoing two properties are inter-related. Accordingly, in general, optimization of one property can only be accomplished at the expense of the other property. Hence, there is a need in the prior art for a notch filter which allows independent control of the low-frequency phase shift and the high frequency attenuation, i.e., the notch frequency. 
     Prior art techniques of stability control, in phase-locked-loops, include the use of low-pass filters (active and passive) and notch filters (active and passive). The major disadvantage of these filters is their excessive phase shift at low frequencies. For example, the well known twin-T filter has a low frequency phase shift 2 to 3 times greater than the acceptable low frequency phase shift in a phase-locked-loop for simulating the Josephson effects. Consequently, there is a need in the prior art to configure a filter having a frequency response with many of the characteristics of the twin-T, but yet having a low frequency phase shift of substantially zero. 
     In addition, it has been found that active low-pass and notch filters, built using conventional operational amplifiers, do not function properly at the frequencies of interest for Josephson effects simulation (0-300 kHz) because the gain of the operational amplifiers is so small at those frequencies. The design of most of these active filters is based on the assumption that the gain of the operational amplifier used therewith is approximately infinite, while in actual practice it is finite. It has also been found that, in general, the input impedance of passive filters is generally not as high as desired; nor is their output impedance as low as generally desired. Thus, there is a need in the prior art to configure a notch filter so as to provide a &#34;semi-active&#34; notch filter wherein the notch frequency is controlled primarily by the passive filters and the low frequency phase shift is controlled primarily by the properties of the operational amplifiers used. 
     As additional background material, a Josephson effects simulator in which the present invention can be used is disclosed, inter alia, in a Navy Technical Disclosure Bulletin Article to Jablonski, entitled &#34;Improved Josephson Analogue System For Modeling Superconductive Tunneling&#34;, Vol. 7, No. 4, June 1982, pgs. 82-85. 
     The prior art include some advances in low-pass and notch filter design, but as far as can be determined, no prior art filter incorporates all of the features and advantages of the present invention. 
     OBJECTS OF THE INVENTION 
     Accordingly, an important object of the present invention is to configure a notch filter in an improved manner so as to allow independent control of its low frequency phase shift and its high frequency attenuation, i.e., the notch frequency. 
     Another important object of the present invention is to configure a notch filter having a low frequency phase shift of substantially zero. 
     A further important object of the present invention is to configure a notch filter using a combination of passive and active circuits, i.e., a &#34;semi-active&#34; notch filter, in an improved manner. 
     Still a further important object of the present invention is to configure a notch filter using a combination of passive filters and conventional operation amplifiers so as to fabricate the &#34;semi-active&#34; notch filter such that the notch frequency is controlled primarily by the passive filters and the low frequency phase shift is controlled primarily by the properties of the operational amplifiers used. 
     SUMMARY OF THE INVENTION 
     In accordance with the above stated objects, other objects, features and advantages, the present invention has as a primary purpose to operate on signal components in three frequency ranges FR1, FR2, and FR3, where FR2 and FR3 are much larger than FR1, so as to eliminate signal components in the frequency range FR2 and greatly attenuate signal components in the frequency range FR3 with minimal phase shift and amplitude changes to the remaining signal components in the frequency range FR1. Typically, frequency range FR1 is 0 to 5 kHz, frequency range FR2 is 195 kHz to 205 kHz and frequency range FR3 is 390 kHz to 410 kHz. 
     The essence of the present invention is in the use of passive filter networks in combination with active circuits, i.e., operational amplifiers, in such a way that the low frequency phase shift of the resulting &#34;semi-active&#34; notch filter is independent of the location of the notch frequency or the frequency range of the notch. In other words, the notch frequency and/or range of the notch is controlled primarily by the properties of the passive filter networks, i.e., passive circuitry, and the low frequency phase shift is controlled primarily by the properties of the operational amplifiers used in the active circuits. 
     The purpose of the present invention is carried out by configuring a &#34;semi-active&#34; filter to comprise a plurality of passive filter networks, each of the passive filter networks being driven in parallel by signal components of an input signal(s) corresponding to and situated in a predetermined bandwidth. A plurality of voltage followers, i.e., buffer amplifiers, are each connected at their inputs to corresponding outputs of each of the passive filter networks. The outputs of the plurality of voltage followers are summed in a summer amplifier thereby giving the desired notch filter response in the overall predetermined bandwidth. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The foregoing, other objects, novel features and advantages of the present invention will be more apparent from the following more particular description of a preferred embodiment as illustrated in the accompanying drawings, in which: 
     FIG. 1 is a schematic diagram representation of a &#34;semi-active&#34; notch filter according to the present invention; and 
     FIGS. 2A and 2B are amplitude response and phase response graphs, respectively, of the &#34;semi-active&#34; notch filter of FIG. 1 according to the present invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     FIG. 1 shows a &#34;semi-active&#34; notch filter 10 in which the present invention is employed so as to allow independent control of low frequency phase shift and high frequency attenuation, i.e., the notch frequency. &#34;Semi-active&#34; notch filter 10 comprises a passive quasi low-pass filter portion 12 connected to an input signal line 14 driven by signal components of an input signal(s) V in . Passive quasi low-pass filter portion 12 includes an inductor L 1  connected in parallel to input signal line 14 and in series with a resistor R 1  and a capacitor C 1  connected in parallel to ground. Quasi low-pass filter portion 12 differs from a simple low-pass filter in that its phase response exhibits variations typical of a second order low-pass filter, as opposed to those of a simple first order low-pass filter. &#34;Semi-active&#34; notch filter 10 also comprises a passive band-pass filter portion 16, connected to input signal line 14, which includes a resistor R 2  connected in parallel to input signal line 14 and in series with a resistor R 3 , an inductor L 2  and a capacitor C 2   connected in parallel to ground. A passive quasi high-pass filter portion 18 completes the passive filter portions of &#34;semi-active&#34; filter 10. Passive quasi high-pass filter 18 includes a resistor R 4  and a capacitor C 3  connected in parallel between input signal line 14 and a resistor R 5  connected to ground. Unlike a simple high-pass filter, quasi high-pass filter portion 18 has non-zero signal gain at zero signal frequency. 
     Still referring to FIG. 1, a low-pass buffer/voltage follower amplifier 20 is connected, at its input, across resistor R 1  of passive quasi low-pass filter portion 12 so as to generate a non-inverted unity-gain signal at its output. Also, a band-pass buffer/voltage follower 22 is connected, at its input, across resistor R 3  of band-pass filter portion 16 so as to generate a non-inverted unity-gain signal at its output. Likewise, a high-pass buffer/voltage follower amplifier 24 is connected, at its input, across resistor R 5  of passive quasi high-pass filter portion 18 so as to generate a non-inverted unity-gain signal at its output. 
     To continue, the outputs of buffer/voltage followers 20, 22 and 24 are connected to the inverting input of summer amplifier 26, via resistors R 6 , R 7  and R 8 , respectively, and a resistor R 9  is connected from the output of summer amplifier 26, at output signal terminal 28, to the inverting input thereof so as to generate an inverted unity-gain output signal V out  at output signal terminal 28. 
     STATEMENT OF THE OPERATION 
     Details of the operation, according to the present invention, are explained in conjunction with FIGS. 1 and 2A and 2B viewed concurrently. 
     The three frequency ranges of interest FR1, FR2, and FR3, depicted in FIGS. 2A and 2B, are provided, inter alia, by passive filters 12, 16, and 18 as shown in FIG. 1. In frequency range FR1, from 0 to 5 kHz, for purposes of the present invention, the gain should be unity and the phase shift should be minimal, i.e., less than 2°. In frequency range FR2, from 195 to 205 kHz, the gain should be minimal. In frequency range FR3, which ranges from 390 to 410 kHz and represents the second harmonics of the frequencies in frequency range FR2, the gain should be small. However, for the present use in a phase-locked-loop and associated circuitry for simulating the Josephson effects, the gain in frequency range FR3 need not be as small as the gain in frequency range FR2. 
     For purposes of the present invention, &#34;semi-active&#34; notch filter 10 of FIG. 1 comprises 741 type operational amplifiers having a unity-gain bandwidth of approximately 815 kHz. The components for passive filters 12, 14 and 16 were chosen so as to create a notch at 200 kHz as shown in FIG. 2A. It should be noted that conventional operational amplifiers do not generally operate well at frequencies greater than 20 kHz. Nevertheless, as shown in FIG. 2A, the filter of the present invention can be used to filter out frequencies of several hundred kilohertz. This is because, according to the present invention, the existence of the notch is independent of the properties and limitations of the operational amplifiers used. However, the frequency limitations of the operational amplifiers used will affect the shape of the notch, often in a beneficial manner, e.g., the sides of the notch will become less steep. 
     The actual choice of operational amplifier type depends on the exact requirements for the phase shift in frequency range FR1 and the gain in frequency ranges FR2 and FR3. The choice also depends on such factors as operational amplifier cost and stability. It should be noted that as the gain and phase shift performance of an operational amplifier improves, the cost increases and the relative stability decreases. If the operational amplifiers used in the filter of the present invention were perfect, the phase shift in frequency range FR1 would decrease and the gain in frequency range FR3 would increase. The notch in frequency range FR2 would remain substantially as shown in FIG. 2A. The response peak between frequency ranges FR1 and FR2 would increase slightly. It should be noted further that the response peak is of no consequence in the application at hand, i.e., simulation of the Josephson effects. 
     Still referring to FIGS. 1 and 2A and 2B, as viewed concurrently, passive quasi low-pass filter portion 12 of &#34;semi-active&#34; notch filter 10 does not operate as a simple low-pass filter. As shown, it includes, inter alia, an inductor as well as a capacitor. This creates the second order response necessary to provide the phase inversions to signal components of the input signal(s) V in  which, when passive quasi low-pass filter portion 12 is operated in concert with filter portions 16 and 18, provide a notch filter response in frequency range FR2 and essentially zero phase shift in frequency range FR1. On the other hand, passive band-pass filter portion 16 is a standard band-pass filter containing both an inductor and a capacitor. For purposes of the present invention, the components comprising the foregoing filters are chosen so as to make the resonant frequencies thereof equal. Also, this common resonant frequency is chosen to be approximately equal to one-half the frequency value of the notch frequency of &#34;semi-active&#34; notch filter 10, i.e., one-half of 200 kHz, or 100 kHz. 
     Likewise, passive quasi high-pass filter portion 18 of &#34;semi-active&#34; notch filter 10 does not operate as a simple high-pass filter in that a resistor is connected in parallel across the capacitor so as to also pass low frequencies, i.e., the gain at zero frequency is non-zero. The characteristic frequency, i.e., half-power frequency, of this section is chosen to be approximately equal to one-third the frequency value of the notch frequency of &#34;semi-active&#34; notch filter 10. Consequently, at the notch frequency, the sum of the responses of the individual passive filter portions 12, 16 and 18 is equal to zero as shown in FIG. 2A. 
     To continue, the overall transfer function of &#34;semi-active&#34; notch filter 10 is given by: ##EQU1## f 0  being the notch frequency and j being equal to √-1. The first term of the right side of the equation is determined by the components of passive filter portions 12, 16 and 18 of &#34;semi-active&#34; notch filter 10. The second term results from buffer/voltage follower amplifiers 20, 22 and 24, where A 0  is the ratio of the unity-gain bandwidth of the particular operational amplifier used to the notch frequency of &#34;semi-active&#34; notch filter. The third term in the equation results from summer amplifier 26 which adds the outputs of the aforementioned buffer/voltage followers to generate the output voltage V out  (f). A 0  &#39; is determined by the choice of operational amplifier used and the notch frequency value. Typically, a single type operational amplifier is used so that A 0  =A 0  &#39;. The factor of four in the determinator of the third term is a consequence of the resistors R 6 , R 7  and R 8  at the input of summer amplifier 26 and the R 9  used for feedback therein. Note that for a perfect operational amplifier having a unity-gain bandwidth of infinity, the second and third terms on the right side of the equation reduce to one, and in this limit will not deleteriously affect the response of &#34;semi-active&#34; notch filter 10 according to the present invention. 
     To those skilled in the art, many modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that the present invention can be practiced otherwise than as specifically described herein and still be within the spirit and scope of the appended claims.