Active polyphase filter with transconductor cross-coupling of filter sections

This application claims priority of provisional application Ser. No. 60/167,557, filed Nov. 23, 1999, entitled QUADRATURE BANDPASS FILTER COMBINING RC LEAPFROG & GM-C TECHNIQUES, which is incorporated herein by reference.

The present invention relates to the field of active polyphase filter design. More particularly, the invention relates to the use of transconductors to cross-couple active polyphase filters sections.

Polyphase filters receive an N-phase (or polyphase) input signal and create an N-phase output signal. A quadrature filter is a four-phase polyphase filter. In a quadrature filter, the input will consist of four signal voltages of mutually equal value. These four input signals jointly constituting a signal vector group with the individual signal vectors succeeding one another in a given direction of rotation through phase angles of 90 degrees. Dependent on direction of rotation, counter-clockwise or clockwise, the frequency of the polyphase signal is positive or negative. The I degree and 180 degree signal vectors are designated the +1 and −I signals. The 90 degree and 270 degree signal vectors are designated the +jQ and −jQ signals. Such a polyphase filter is known from the article “Asymmetric Polyphase Networks” by M. J. Gingell, published in “Electrical Communication”, Vol. 48, no. 1 and 2, 1973, pp. 21-25.

Passive LC filters are limited by the difficulty of incorporating inductors into integrated circuits. To replace inductors and reduce sensitivity to component variations, active-RC filters were introduced. Operational amplifiers and, in some designs, gyrators are the reactances in an active-RC design. Active-RC filter circuits are easier to design and manufacture than passive filters. Feedback loops between the inputs and outputs of the active-RC reactances replace the need for inductive elements and reduce sensitivity to component variation.

The conversion of passive-LC filters designs to active-RC filter designs, termed “filter design,” is the subject of many publications. Filter design begins with the choice of a passive filter. The most common types of passive filters are the gaussian, Butterworth, Bessel, and Chebyshev filters. The type of passive filter is chosen based upon its characteristics, such as ripple, stopband rejection, pole quality factor, noise figure, and sensitivity. The order of the filter, an indication of the number of poles in the filter, is also chosen. The choice of filter type and order is based on the constraints of the intended manufacturing process and end-use. After a filter type and order are chosen, nodal transfer functions (generally represented in Laplace notation) for the filter are derived. e nodal transfer functions allow a signal flow graph of the passive filter to be mapped. The noaltransfer functions of the passive filter are then replaced with active elements, resistors, and capacitors. The resulting active-RC filter network has a filter transfer function equivalent to the passive filter.

Three books that demonstrate filter design techniques are: (i) Handbook of Filter Synthesis, by Anatol I. Zverev, published 1967 by John Wiley & Sons; (ii) Electronic Filter Design Handbook, by Arthur B. Williams, published 1995 by McGraw Hill; and (iii) Analog MOS Integrated Circuits for Signal Processing, by Roubik Gregorian and Gabor C. Temes, published 1986 by John Wiley & Sons. In these books, schematics and tables of figures detail XT the configuration and component values for a broad range of filter types and orders. A detailed example of filter design can also be found in the following U.S. Patents: (i) “Symmetrical Polyphase Networks Utilizing Constant Reactances” by Michael John Gingell, number 3,618,133, issued 1971; and (ii) “Asymmetric Polyphase Filter” by Johannes O. Voorman, number 4,914,408, issued 1990 (hereafter “Voorman Patent”). Computer programs for filter design are also available.

An example of filter design is illustrated in FIGS. 1A and 1B. FIG. 1A shows a low-pass third-order passive LC filter 1 with four nodes, N 1 , N 2 , N 3 , and N 4 , numbered sequentially clockwise from the top left. The input voltage Vin is applied across N 1 and N 4 . The output voltage Vout is measured across N 3 and N 4 . A first resistor RP 1 is connected between N 1 and N 2 . A first capacitor CP 1 is connected between N 2 and N 4 . An inductor LP 1 is connected between N 2 and N 3 . A second capacitor CP 2 and a second resistor RP 2 are connected in parallel across N 3 and N 4 .

FIG. 1B shows a low-pass third-order active-RC filter block (hereafter “FB”) that approximates the transfer function of the low-pass third-order passive LC filter shown in FIG. 1 A. FB includes: two input terminals IA and IB; two output terminals OA and OB; three reactances X 1 , X 2 , and X 3 ; and fourteen matched resistors R. Each reactance is an active balanced integrating circuit than includes: one balanced differential amplifier 2 , a reactance input pair 3 ; a reactance output pair 4 ; and a matched capacitor pair C 1 , C 2 , and C 3 . In each matched capacitor pair: one capacitor is shunted between the first input of a reactance input pair 3 and the first output of the reactance output pair 4 ; and the other capacitor is shunted between the second input of the reactance input pair 3 and the second output of the reactance output pair 4 .

The internal nodes of FB can be identified by their associated terminal 5 , as set forth in below Table I below.

Note also that output terminal OA is attached to terminal T 3 C and that output OB is attached to terminal T 3 D. The Table II netlist below indicates the location of the fourteen matched resistors R. In table II, one matched resistor R is connected between the first node and the second node.

While resistors R are shunted across X 1 and X 3 , no resistors R are shunted across X 2 .

FIG. 1C shows a block diagram of FB. The block diagram has two inputs IA and IB. The block diagram has two outputs OA and OB. The block diagram also has three sets of four-lead terminals T 1 -T 3 for a total of twelve terminals. The first set is labeled T 1 and is composed of four terminals T 1 A, T 1 B, T 1 C, and T 1 D. The second set is labeled T 2 and is composed of four terminals T 2 A, T 2 B, T 2 C, and T 2 D. The third set is labeled T 3 and is composed of four terminals T 3 A, T 3 B, T 3 C, and T 3 D. Figure IC also demonstrates how FB can be attached to a 2-phase input +Iin and −Iin, by input terminals IA and IB respectively, to generate a 2-phase output +Iout and −Iout, through output terminals OA and OB respectively.

A second example of filter design is shown in FIGS. 1D and 1E. FIG. 1D shows a low-pass sixth-order passive LC filter 6 with six nodes, NZ 1 , NZ 2 , NZ 3 , NZ 4 , NZ 5 , and NZ 6 , numbered sequentially clockwise from the top left. The input voltage Vzin is applied across NZ 1 and NZ 6 . The output voltage Vzout is measured across NZ 5 and NZ 6 . A first resistor RPZ 1 is connected between NZ 1 and NZ 2 . A first capacitor CPZ 1 is connected between NZ 2 and NZ 6 . A first inductor LPZ 1 is connected between NZ 2 and NZ 3 . A second capacitor CPZ 2 is connected between NZ 3 and NZ 6 . A second inductor LPZ 2 is connected between NZ 3 and NZ 4 . A third capacitor CPZ 3 is connected between NZ 4 and NZ 6 . A third inductor LPZ 3 is connected between NZ 4 and NZ 5 . A second resistor RPZ 2 is connected between NZ 5 and NZ 6 .

FIG. 1E shows a low-pass sixth-order active-RC filter block (hereafter “FBZ”) that approximates the transfer function of the low-pass sixth-order passive LC filter shown in FIG. 1 D. FBZ includes: two input terminals IZA and IZB; two output terminals OZA and OZB; six reactances XZ 1 , XZ 2 , XZ 3 , XZ 4 , XZ 5 , and XZ 6 ; and twenty-six matched resistors RZ. Each reactance is an active balanced integrating circuit than includes: one balanced differential amplifier 2 , a reactance input pair 3 ; a reactance output pair 4 ; and a matched capacitor pair CZ 1 , CZ 2 , CZ 3 , CZ 4 , CZ 5 , and CZ 6 . In each matched capacitor pair: one capacitor of each matched pair is shunted between the first input of a reactance input pair 3 and the first output of the reactance output pair 4 ; and the other capacitor is shunted between the second input of the reactance input pair 3 and the second output of the reactance output pair 4 .

The internal nodes of FBZ can be identified by their associated terminal 5 , as set forth in Table III below.

Note also that the output terminal OZA is attached to TZ 6 A and that the output terminal OZB is attached to TZ 6 B. The Table IV netlist below indicates the location of the twenty-six matched resistors RZ. In the table, one matched resistor RZ is connected between the first node and the second node.

While resistors RZ are shunted across XZ 1 and XZ 6 , no resistors RZ are shunted across XZ 2 , XZ 3 , XZ 4 , or XZ 5 .

FIG. 1F shows a block diagram of FBZ. The block diagram has two inputs IZA and IZB. The block diagram has two output terminals OZA and OZB. The block diagram also has six sets of four-lead terminals for a total of twenty-four terminals. The first set is labeled TZ 1 and is composed of four terminals TZ 1 A, TZ 1 B, TZ 1 C, and TZ 1 D. The second set is labeled TZ 2 and is composed of four terminals TZ 2 A, TZ 2 B, TZ 2 C, and TZ 2 D. The third set is labeled TZ 3 and is composed of four terminals TZ 3 A, TZ 3 B, TZ 3 C, and TZ 3 D.

The fourth set is labeled TZ 4 and is composed of four terminals TZ 4 A, TZ 4 B, TZ 4 C, and TZ 4 D. The fifth set is labeled TZ 5 and is composed of four terminals TZ 5 A, TZ 5 B, TZ 5 C, and TZ 5 D. The sixth set is labeled TZ 6 and is composed of four terminals TZ 6 A, TZ 6 B, TZ 6 C, and TZ 6 D. FIG. 1F also demonstrates how FBZ receives a 2-phase input +Iin and −Iin, by input terminals IZA and IZB respectively, to generate a 2-phase output signal +Iout and −Iout, through output terminals OZA and OZB respectively.

FIGS. 2A and 2B demonstrate how low-pass quadrature filters can be constructed from a first filter section 7 for the I signals and a second filter section 8 for the Q signals. FIG. 2A shows a first filter section FB and a second filter section FB′. Both FB and FB′ are identical to the third-order low-pass active RC filter illustrated in FIGS. 1B and 1C. The first filter section FB is attached to a 2-phase input +Iin and −Iin, by FB input terminals IA and IB respectively, to generate a 2-phase output +Iout and −Iout, through FB output terminals OA and OB respectively. The second filter section FB′ is attached to a 2-phase input +Qin and −Qin, by FB′ input terminals IA′ and IB′ respectively, to generate a 2-phase output +Qout and −Qout, through FB′ output terminals OA′ and OA′ respectively. The terminals of FB and FB′ are not used in this configuration.

FIG. 2B shows a first filter section FBZ and a second filter section FBZ′. The first filter section FBZ and the second filter section FBZ′ are both identical to the low-pass sixth-order active RC filter illustrated in FIGS. 1E and 1F. The first filter section FBZ is connected to inputs +Iin and −Iin by input terminals IZA and IZB, respectively, and to outputs +Izout and −Izout by ouput terminals OZA and OZB, respectively. The second filter section FBZ′ is connected to inputs +Qin and −Qin by input terminals IZA′ and IZB′, respectively, and to outputs +Qzout and −Qzout by output terminals OZA′ and OZB′, respectively. The terminals of FBZ and FBZ′ are not used in this configuration.

Though the circuit path for the I and Q signal inputs never intersect each other in the circuits shown in FIGS. 2A and 2B, the two filter sections perform as a low-pass sixth-order quadrature filter and low-pass twelfth-order quadrature filter, respectively. Since the bandpass of the quadrature filter includes both low positive frequencies and low negative frequencies, the quadrature filters shown in FIGS. 2A and 2B act like band-pass filters with a center frequency of zero hertz.

The Voorman Patent (U.S. Pat. No. 4,914,408) discloses that a quadrature band-pass filter can be created by cross-coupling the reactances of two filter sections with matched resistors. Application of this approach can be accomplished by shunting matched resistors between the terminals 5 of the first filter section FBZ and the terminals 5 of the second filter section FBZ′.

To simplify representation of the matched resistors, FIGS. 3A to 3 D describe two resistor coupling blocks and their contents. FIG. 3A shows three sets of four matched resistors, R 1 , R 2 and R 3 . Each resistor has a node on either end. The node netlist for each resistor is set forth in Table V below.

FIG. 3B shows the resistor coupling block diagram labeled “R block.” The R block has 24 leads. The leads are grouped into sets of four leads labeled RC 1 , RC 2 , RC 3 , RC 1 ′, RC 2 ′, and RC 3 ′. Each set has an A, B, C, and D lead. RC 1 , for instance, has leads RC 1 A, RC 1 B, RC 1 C, and RC 1 D. And RC 1 ′ has leads RC 1 A′, RC 1 B′, RC 1 C′, and RC 1 D′.

FIGS. 3C and 3D describe the resistor block for FBZ. FIG. 3B shows six sets of four matched resistors, RZ 1 , RZ 2 , RZ 3 , RZ 4 , RZ 5 , and RZ 6 . Each resistor has a node on either end. The node netlist for each resistor is set forth in Table VI below.

FIG. 3D shows the resistor coupling block diagram labeled “RZ block.” The RZ block has forty-eight leads. The leads are grouped into sets of four leads labeled RZC 1 , RZC 2 , RZC 3 , RZC 4 , RZC 5 , RZC 6 , RZC 1 ′, RZC 2 ′, RZC 3 ′, RZC 4 ′, RZC 5 ′, and RZC 6 ′. Each set has an A, C, and D lead.

FIGS. 4A shows a first filter section FB and a second filter section FB′ coupled together through an R block. Excluding the addition and coupling of the R block, FIG. 4A shows the same quadrature filter configuration as in FIG. 2 A. Corresponding R block leads are connected to the terminals of the first filter section FB and the section filter section FB′. RC 1 A and RC 1 A′, for instance, are connected to T 1 A and T 1 A′ respectively. The coupling of the first filter section FB to the second filter section FB′ in FIG. 4B follows the same method as FIG. 4A, except that the RZ block is used to couple FBZ and FBZ′.

Coupling the filter sections of a low-pass quadrature filter changes the quadrature filter in two ways. First, the coupling reduces the quadrature filter's sensitivity to component variations between the first filter section FBZ and the second filter section FBZ′. As the I and Q signals share many components, component variations effects have approximately the same impact upon each signal's transfer function. A second result of the cross-coupling is that the center frequency of the quadrature filter is moved from zero hertz to a new center frequency. As disclosed in the Voorman Patent, the center frequency of the coupled filter is equal to 1/R i C i , where R i is the value of an individual cross-coupling resistor between two corresponding reactances and C i is the capacitance of an single matched capacitor shunted between the input and output of the corresponding reactances. During design of integrated circuits containing these active quadrature band-pass filters, the center frequency can be adjusted by adjusting the value of R i and C i .

The resistor cross-coupling disclosed in the Voorman Patent has some limitations. First, the center frequency cannot be altered post-manufacture, as resistors and capacitors are passive elements with non-adjustable values. Second, component variations between the first filter section and the second filter section can degrade output signal quality. The resistors are shunted across operational amplifiers, which are susceptible to variation in common mode voltage or DC offset voltage. A mismatch between corresponding operational amplifiers can result in larger than expected or smaller than expected currents through a coupling resistor. Larger than expected and smaller than expected currents can also result from component variations between matched capacitor and resistors.

The invention is an improved implementation of an active-RC polyphase band-pass filter with transconductor cross-coupling between filter sections. The polyphase filter has first to fourth inputs, first to fourth outputs, two filter sections, and a block of transconductor pairs. The four input signals to the polyphase filter succeed one another in phase by 90 degrees. The two filter sections have reactances comprised of active balanced operational amplifiers with matched capacitors in their feedback loops. Each transconductor pair of the block is coupled between corresponding reactances of each filter. The transconductance value of each transconductor pair is set as the product of a desired radian center frequency and the capacitance of the corresponding matched capacitors. In the preferred embodiment, the transconductors are Gm cells and the transconductance value of at least one Gm cell is field adjustable. This means that the transconductance value can be adjusted after the filter has been constructed or placed in service. The filter sections of the preferred embodiment can be a pair of low-pass, third-order, active-RC gaussian filters or a pair of low-pass sixth-order active-RC gaussian filters.

The first filter section has X-reactances and M-terminals. The second filter section has Y-reactances and N-terminals. The filter sections are coupled by the block of transconductors with a total of M plus N terminals. The X-reactances are coupled to the first input, the third input, the first output, and the third output. The Y-reactances are coupled to the second input, the fourth input, the second output, and the fourth output of the output. The M-terminals are coupled to select ones of the X-reactances. The N-terminals are coupled to select ones of the Y-reactances. In the preferred embodiment: X and Y are equal and M and N are equal; one half of the M-terminals are coupled to reactance input terminal pairs of the first filter section and the other half are coupled to reactance output terminal pairs of the first filter section; and one half of the N-terminals are coupled to reactance input terminal pairs of the second filter section and the other half are coupled to reactance output terminal pairs of the second filter section.

The reactances of each filter section are comprised of active balanced integrating circuits. Each active balance integrating circuit has a balanced differential operational amplifier with matched capacitors in their feedback loop. The balanced differential operational amplifier has a reactance input terminal pair and a reactance output terminal pair. The first matched capacitor is shunted between the first input of the reactance input terminal pair and the first output of the reactance output terminal pair. The second matched capacitor is shunted between the second input terminal of the reactance input terminal pair and the second output of the reactance output terminal pair. The matched capacitors of the first to Xth reactance and the corresponding matched capacitors of the first to Yth reactance are of equal capacitance.

The block of transconductors is composed of Z-transconductor pairs composed of Gm cells. Each of the Z-transconductor pairs cross-couple a reactance of the first filter section through its M-terminals and the correspoding reactances of the second filter section through its N-terminals. Each Gm cell has one transconductor input terminal pair and one transconductor output terminal pair. The transconductance value of each Gm cell is set as the product of a desired radian center frequency and the capacitance of the nearest matched capacitors. In the preferred embodiment, the transconductance value of at least one Gm cell is field adjustable, permitting adjustment of the center frequency in the field.

In each Z-transconductor pair, one Gm cell is coupled by its transconductor input terminal pair to a reactance output terminal pair of a corresponding X-reactance through a selected pair of M-terminals and by its transconductor output terminal pair to a reactance input terminal pair of a corresponding Y-reactance through a selected pair of N-terminals. The second Gm cell in each Z-transconductor pair is coupled by its transconductor input terminal pair to a reactance output terminal pair of a corresponding Y-reactance through a selected pair of N-terminals and by its transconductor output terminal pair to a reactance input terminal pair of a corresponding X-reactance through a selected pair of M-terminals. As the inputs of each Gm cell are a differential voltage from a single reactance, variation in the common mode voltage or DC offset between the filter sections does not adversely affect the polyphase filter's transfer function.

FIG. 1A is a schematic of a low-pass third-order passive LC filter;

FIG. 1B is a schematic of an active-RC filter design of the low-pass third-order passive LC filter shown in FIG. 1A;

FIG. 1C is a block diagram of the low-pass third-order active-RC filter shown in FIG. 1B;

FIG. 1D is a schematic of a low-pass sixth-order passive LC filter;

FIG. 1E is a schematic of an active-RC filter design of the low-pass sixth-order passive LC filter shown in FIG. 1D;

FIG. 1F is a block diagram of the low-pass sixth-order active-RC filter shown in FIG. 1E;

FIG. 2A illustrates a low-pass third-order quadrature filter constructed from two of the low-pass third-order active-RC filter blocks shown in FIG. 1C;

FIG. 2B illustrates a low-pass sixth-order quadrature filter constructed from two of the low-pass sixth-order active-RC filter blocks shown in FIG. 1F;

FIG. 3A shows the nodal connections for the R block;

FIG. 3B shows the block diagram of the R block;

FIG. 3C shows the nodal connections for the RZ block;

FIG. 3D shows the block diagram of the RZ block;

FIG. 4A shows a band-pass sixth-order quadrature filter constructed from two low-pass third-order active-RC filters coupled together by one R block;

FIG. 4B shows a band-pass twelfth-order quadrature filter constructed from two low-pass sixth-order active-RC filters coupled together by one RZ block;

FIG. 5A is a schematic of a reactance from the first filter section, a reactance from the second filter section, a transconductor pair, and a set of resistors;

FIG. 5B is a schematic of a transconductor pair used in the coupling of FB pairs;

FIG. 5C is a schematic of a G block used in the coupling of FB pairs;

FIG. 5D is a block diagram of the G block shown in FIG. 5C;

FIG. 5E is a schematic of a transconductor pair used in the coupling of FBZ pairs;

FIG. 5F is a schematic of a GZ block used in the coupling of FBZ pairs;

FIG. 5G is a block diagram of the GZ block shown in FIG. 5F;

FIG. 6A shows a b and-pass sixth-order quadrature filter constructed from two low-pass third-order active-RC filters coupled together by one G block;

FIG. 6B shows a band-pass twelfth-order quadrature filter constructed from two low-pass sixth-order active-RC filters coupled together by one GZ block.

The invention cross-couples a first 2-phase filter section and a second 2-phase filter section with transconductors to create a band-pass quadrature filter. This implementation reduces the filter's sensitivity to component variations and permits the center frequency of the filter to be field adjusted.

In the preferred embodiment of the present invention there is an interaction of paired reactances between the first filter section FB and the second filter section FB 1 . FIG. 5A shows four items: the first reactance of the first filter section, X 1 ; the first reactance of the second filter section, X 1 ′; the nodal connections between the matched resistors 9 and the two filter sections; and the nodal connections between the transconductors 10 and the two filter sections. Each reactance X 1 , X 1 ′ includes a balanced differential operational amplifier 2 , a reactance input pair 3 , a reactance output pair 4 , and a feedback path between the output pairs and the input pairs. The feedback path consists of a resistor R and a matched capacitor C 1 in parallel. The nodal connection information for the matched resistors 9 can be identified by their associated terminal 5 and by the node netlist. The nodal connection information for the transconductors is derived below. A view of X 1 in the context of FB can be seen in FIG. 1 B.

The transconductors each have a transconductor input terminal pair 11 and a transconductor output terminal pair 12 . The first transconductor 13 receives its input signals from the reactance output pair of X 1 ′ and the second transconductor 14 receives its input signals from the reactance output pair of X 1 . The first transconductor 13 has two output currents, I 1 and I 2 , and the second transconductor 14 has two output currents, I 3 and I 4 . In the first transconductor 13 , the voltage across the transconductor output terminal pair 12 is V 1 and the voltage across the transconductor input terminal pair 11 is V 2 ′. In the second transconductor 14 , the voltage across the transconductor output pair 12 is V 1 ′ and the voltage across the transconductor input terminal pair 11 is V 2 . The transconductance of both transconductors is G 1 .

The transconductors 13 , 14 shown in FIG. 5A, are operational transconductor amplifiers, also known as Gm cells. It is well known that Gm cells convert a differential voltage into proportional differential current. As used in the invention, the Gm cells create equivalent currents between the first filter section 7 and the second filter section 8 . In FIG. 5A, the currents of the replaced resistors R 1 are labeled i 1 , i 2 , i 3 , and i 4 . For the transconductors, 13 and 14 , to properly replace the resistors R 1 : I 1 should be equal to i 1 ; 12 should be equal to i 2 ; I 3 should be equal to i 3 ; and I 4 should be equal to i 4 . The below Equation 1 and Equation 2 are derived from Ohm's Law. Equation 1 and Equation 2 state the differential current across the matched resistors 9 . V 1 and V 1 ′ are not variables in Equation 1 and Equation 2 because the feedback loop across each operational amplifier 2 drives V 1 and V 1 ′ to a much smaller voltage than V 2 and V 2 ′.

i 1 − i 2 = V 2 ′/R 1   Equation 1

i 3 − i 4 = V 2 /R 1   Equation 2

Gm cells operate according to the below equations, where Vd is the differential input voltage, G is the transconductance, and +Ig and −Ig are the differential output currents.

+I g =( Vd×G )/2  Equation 3

−I g =−( Vd×G )/2  Equation 4

Applying these equations to the FIG. 5A circuit elements we obtain:

I 1 − I 2 = V 2 ′× G 1   Equation 5

I 3 − I 4 = V 2 × G 1   Equation 6

If G 1 is set equal to 1/R 1 , Equation 5 and Equation 6 become:

I 1 − I 2 = V 2 ′/ R 1   Equation 7

I 3 − I 4 = V 2 / R 1   Equation 8

To simplify representation of the Gm cells 13 , 14 , FIGS. 5B to 5 D describe a Gm coupling block and its contents for a sixth-order band-pass quadrature filter. FIG. 5B shows a transconductor pair including a first transconductor 13 and a second transconductor 14 . Each Gm cell has a transconductor input terminal pair 11 , including input leads GIA and GIB, and a transconductor output terminal pair 12 , including output leads GOA and GOB. FIG. 5C shows three sets of matched transconductor pairs 13 , 14 with transconductance G 1 , G 2 , and G 3 . The node netlist for each Gm cell in FIG. 5C is set forth in Table VII below.

FIG. 5D shows a transconductance coupling block diagram labeled “G block.” The G block has twenty-four leads. The leads are grouped into sets of four leads labeled GC 1 , GC 2 , GC 3 , GC 1 ′, GC 2 ′, and GC 3 ′. Each set has an A, B, C, and D lead. GC 1 , for instance, has leads GC 1 A, GC 1 B, GC 1 C, and GC 1 D. And GC 1 ′ has leads GC 1 A′, GC 1 B′, GC 1 C′, and GC 1 D′.

FIGS. 5E to 5 G describe a Gm coupling block and its contents for the sixth-order band-pass quadrature filter. FIG. 5E shows a transconductor pair with a first transconductor 13 and a second transconductor 14 . Each Gm cell has a transconductor input pair 11 , with input leads labeled GZIA and GZIB, and a transconductor output pair 12 , with output leads labeled GZOA and GZOB. FIG. 5F shows six sets of matched transconductor pairs with transconductance GZ 1 , GZ 2 , GZ 3 , GZ 4 , GZ 5 , and GZ 6 . The node netlist for each Gm cell is set forth in Table VIII below.

FIG. 5G shows the transconductance coupling block diagram labeled “GZ block.” The GZ block has forty-eight leads. The leads are grouped into sets of four leads labeled GZC 1 , GZC 2 , GZC 3 , GZC 4 , GZC 5 , GZC 6 , GZC 1 ′, GZC 2 ′, GZC 3 ′, GZC 4 ′, GZC 5 ′, and GZC 6 ′. Each se an A, B, C, and D lead.

FIGS. 6A shows a first filter section 7 and a second filter section 8 coupled together through an G block. Excluding the addition and coupling of the G block, FIG. 6A shows the same quadrature filter configuration as in FIG. 2 A. Corresponding G block leads are connected to the terminals of the first filter section 7 and the second filter section 8 . GC 1 A and GC 1 A′, for instance, are connected to T 1 A and T 1 A′ respectively. The coupling ofthe first filter section 7 to the second filter section 8 in FIG. 6B follows the same method as FIG. 6A, except that the GZ block is used to couple FBZ and FBZ′.

The present invention has the advantage of reducing imbalances between filter section from common mode voltage and DC offset of each filter section's operational amplifier 2 outputs. In contrast, in the prior art arrangement of FIGS. 1-4, differences in the common mode voltage or DC offset of pair reactances can result in currents across the cross coupling resistors that are larger or smaller than expected. As current magnitudes stray from the desired theoretical values, the transfer function of the active-RC filter can be altered unpredictably. As used in the present invention, Gm cells are unaffected by mismatched common mode voltages and mismatched DC offsets. Unlike the prior art arrangement, the Gm cell current is not based upon the voltage potential between a first filter section 7 node and a second filter section 8 node. The output current of a Gm cells is based upon the differential input from the output pair of one balanced operational amplifier of one filter section. The common mode and DC offset voltages, therefore, are subtracted out.

The present invention also permits the center frequency of the quadrature filter to be field adjustable. Unlike an integrated resistor or capacitor, the conductance value of the Gm cells can be easily adjusted in the field by electronic means. The center frequency of the quadrature filter is equal to the transconductance value of a matched pair divided by its associated capacitance value. By altering the transconductance value electronically, the center frequency of the quadrature filter can be moved at will to a selected frequency. A field adjustable center frequency means that components can be tuned after manufacturing or being placed in service. A field adjustable architecture also allows the manufacturer to make one part for applications requiring different center frequencies or for applications requiring center frequencies adjustable during operation of the end-user device.

Using the present invention, it is possible to individually transform each reactance in a filter. The transformation can take place by scaling each resistance associated with a reactance in a filter by a scaling factor and by likewise scaling each capacitance and the associated Gm by the inverse of the scaling factor. Using such a transformation maintains the reactance. The transformation can be performed to optimize the signal handling capability of the filter. The transformation can also be performed to allow the selection of more convenient values for resistors and capacitors. Considering FIG. 5A, the reactance labeled X 1 can be transformed by scaling its resistors R and the associated resistors R 1 by a scaling factor. The capacitors C 1 for this reactance are scaled by the inverse of the scaling factor. Also the Gm of the transconductor 13 is scaled by the inverse of the scaling factor.

The present invention has been described in terms of specific embodiments incorporating details to facilitate the understanding of principles of construction and operation of the invention. References to specific embodiments and details of the invention are not intended to limit the scope of the appended claims. It will be apparent to those skilled in the art that modifications may be made in the illustrated embodiment without departing from the spirit and scope of the invention. Specifically, it will be apparent to those skilled in the art that while the preferred embodiment of the present invention is used with third-order and sixth-order low-pass gaussian 2-phase filter sections, the present invention could also be implemented on other types of filters, filters sections of different orders, or filters section of more than two phases.