US4087757A — Constant delay resonant tank circuit combination …

Claim 1

Independent Claim 475 words

A multitank filter including a signal receiving primary resonant tank (p) feeding signals to two secondary resonant tanks (l and h) whose outputs are combined and demodulated to form a single resultant signal and which have a low (ω 0l ) and a high (ω oh ) resonant frequency, respectively, as compared to the resonant frequency (ω op ) of the primary tank and also the center frequency (ω c ) of the band of frequencies passed by the multitank filter wherein the Q p and Q l , and Q h values of the filter tank circuits as well as their resonant frequencies (ω o ) are obtained in accordance with the following steps for providing a substantially constant delay τ a and a substantially linear amplitude response M over a given band of frequencies: (1) select initial trial values of Q and ω o , for each tank; (2) choose a value for f b and t to determine a point on each of two ultimate graphs of τ a and M wherein f b is a notation of convenience for determining the frequency of which the differential delay (τ a ) is measured with respect to the center frequency (ω c ) of a band of frequencies and t is the instantaneous time and specifies the instantaneous phase of f b and the graph of τ a having a "y" ordinate of time delay, the graph of M having a "y" ordinate of amplitude and both graphs having an x ordinate of frequency: (3) derive ω a1 , ω a2 , τ a1 , τ a2 from the values selected in the previous steps in accordance with the following formulas: ##EQU4## (4) determine the values of M 1 and M 2 (the instantaneous magnitude of an output signal obtained from the low and high tanks upon demodulation in the point determined by f b and t) in accordance with the following formulas: ##EQU5## (5) obtain the values of α and β in accordance with the following formulas: α = π f.sub.b (t - τ.sub.a1) β = 2π f.sub.b (t - τ.sub.a2) (6) obtain the composite magnitude (M) and delay (τ a ) from the previously obtained values in accordance with the following formulas for the point on the graph determined by the above-referenced f b and t: M.sup.2 = M.sub.1.sup.2 + M.sub.2.sup.2 - 2M.sub.1 M.sub.2 Cos (β - α) ##EQU6## (7) assign new values to f.sub.b and t and repeat steps 3 through 7 until enough graph points have been selected to provide an indication of the composite amplitude response and delay characteristics for the values of Q and ω selected in the first step; and (8) repeat steps 1 through 7 until an amplitude response and delay characteristic is obtained which is sufficiently linear and flat, respectively, to fulfill design requirements.

Claim 2

Dependent Claim 475 words

A multitank filter including a signal receiving primary resonant tank (p) feeding signals to two secondary resonant tanks (l and h) whose outputs are combined and demodulated to form a single resultant signal and which have a low (ω 0l ) and a high (ω oh ) resonant frequency, respectively, as compared to the resonant frequency (ω op ) of the primary tank and also the center frequency (ω c ) of the band of frequencies passed by the multitank filter wherein the Q p and Q l , and Q h values of the filter tank circuits as well as their resonant frequencies (ω o ) are obtained in accordance with the following steps for providing a substantially constant delay τ a and a substantially linear amplitude response M over a given band of frequencies: (1) select initial trial values of Q and ω o , for each tank; (2) choose a value for f b and t to determine a point on each of two ultimate graphs of τ a and M wherein f b is a notation of convenience for determining the frequency of which the differential delay (τ a ) is measured with respect to the center frequency (ω c ) of a band of frequencies and t is the instantaneous time and specifies the instantaneous phase of f b and the graph of τ a having a "y" ordinate of time delay, the graph of M having a "y" ordinate of amplitude and both graphs having an x ordinate of frequency: (3) derive ω a1 , ω a2 , τ a1 , τ a2 from the values selected in the previous steps in accordance with the following formulas: ##EQU4## (4) determine the values of M 1 and M 2 (the instantaneous magnitude of an output signal obtained from the low and high tanks upon demodulation in the point determined by f b and t) in accordance with the following formulas: ##EQU5## (5) obtain the values of α and β in accordance with the following formulas: α = π f.sub.b (t - τ.sub.a1) β = 2π f.sub.b (t - τ.sub.a2) (6) obtain the composite magnitude (M) and delay (τ a ) from the previously obtained values in accordance with the following formulas for the point on the graph determined by the above-referenced f b and t: M.sup.2 = M.sub.1.sup.2 + M.sub.2.sup.2 - 2M.sub.1 M.sub.2 Cos (β - α) ##EQU6## (7) assign new values to f.sub.b and t and repeat steps 3 through 7 until enough graph points have been selected to provide an indication of the composite amplitude response and delay characteristics for the values of Q and ω selected in the first step; and (8) repeat steps 1 through 7 until an amplitude response and delay characteristic is obtained which is sufficiently linear and flat, respectively, to fulfill design requirements.

Claim 3

Dependent Claim 423 words

A multitank filter comprising, in combination: a first tuned circuit means having a first amplitude response, a first Q value Q 1 and a resonance at a first frequency ω o1 ; a second tuned circuit means having a second amplitude response, a second Q value Q 2 and a resonance at a second frequency ω o2 ; a primary tank circuit means, including signal input means, having a third amplitude response and a third Q value Q 3 , and resonant at a frequency ω o3 intermediate ω o1 and ω 02 ; means connecting said primary tank circuit means to said first and second tuned circuit means for supplying filtered signals thereto; output means, connected to at least one of said first and second tuned circuit means, for providing output signals which, relative to signals supplied to said input means, have a substantially linear amplitude response (M) and a constant differential time delay (τ) over a given frequency band; and the linear amplitude response and constant delay at any frequency on a graph of M or τ respectively is defined by the equations: M = √M.sub.1.sup.2 + M.sub.2.sup.2 - 2M.sub.1 M.sub.2 Cos (β - α), and τ.sub.a = t - (γ/2πf.sub.b). where M is the linear amplitude response at a given frequency, M 1 is the instantaneous magnitude of the demodulated signal output by said first tuned circuit means, M 2 is the instantaneous magnitude of the demodulated signal output by said second tuned circuit means, α is a notation of convenience and equals 2πf b (t-τ a1 ), where f b is a notation of convenience for determining the frequency at which the differential time delay (τ a ) is measured with respect to the center frequency (ω c ) of a band of frequencies, t is the instantaneous time and specifies the instantaneous phase of f b , and τ a1 is the differential time delay referred to the band center delay of the carrier signal as it traverses through the primary tank and the (lower frequency) first tuned circuit means, β is a further notation of convenience used to simplify the writing of mathematical equations and equals 2πf b (t-τ a2 ) with the identical definitions applying as used in conjunction with α and with τ a2 being the time differential delay of the higher frequency or second tuned circuit means, τ is the differential time delay at any given frequency on the graph, and γ is defined as equaling arc sin(M 1 sin α-M 2 sin β/M).

Claim 4

Dependent Claim 423 words

A multitank filter comprising, in combination: a first tuned circuit means having a first amplitude response, a first Q value Q 1 and a resonance at a first frequency ω o1 ; a second tuned circuit means having a second amplitude response, a second Q value Q 2 and a resonance at a second frequency ω o2 ; a primary tank circuit means, including signal input means, having a third amplitude response and a third Q value Q 3 , and resonant at a frequency ω o3 intermediate ω o1 and ω 02 ; means connecting said primary tank circuit means to said first and second tuned circuit means for supplying filtered signals thereto; output means, connected to at least one of said first and second tuned circuit means, for providing output signals which, relative to signals supplied to said input means, have a substantially linear amplitude response (M) and a constant differential time delay (τ) over a given frequency band; and the linear amplitude response and constant delay at any frequency on a graph of M or τ respectively is defined by the equations: M = √M.sub.1.sup.2 + M.sub.2.sup.2 - 2M.sub.1 M.sub.2 Cos (β - α), and τ.sub.a = t - (γ/2πf.sub.b). where M is the linear amplitude response at a given frequency, M 1 is the instantaneous magnitude of the demodulated signal output by said first tuned circuit means, M 2 is the instantaneous magnitude of the demodulated signal output by said second tuned circuit means, α is a notation of convenience and equals 2πf b (t-τ a1 ), where f b is a notation of convenience for determining the frequency at which the differential time delay (τ a ) is measured with respect to the center frequency (ω c ) of a band of frequencies, t is the instantaneous time and specifies the instantaneous phase of f b , and τ a1 is the differential time delay referred to the band center delay of the carrier signal as it traverses through the primary tank and the (lower frequency) first tuned circuit means, β is a further notation of convenience used to simplify the writing of mathematical equations and equals 2πf b (t-τ a2 ) with the identical definitions applying as used in conjunction with α and with τ a2 being the time differential delay of the higher frequency or second tuned circuit means, τ is the differential time delay at any given frequency on the graph, and γ is defined as equaling arc sin(M 1 sin α-M 2 sin β/M).

Annuity Stage	Window Opens	Payment Deadline	Surcharge Period Until	Estimated Fee	Status
3.5 Years (Year 4)	1981-05-01	1981-10-31	1982-05-02	$2000.00	Window Closed / Lapsed
7.5 Years (Year 8)	1985-05-01	1985-10-31	1986-05-02	$3760.00	Window Closed / Lapsed
11.5 Years (Year 12)	1989-05-01	1989-10-31	1990-05-02	$7700.00	Window Closed / Lapsed

Constant delay resonant tank circuit combination for frequency discrimination

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