Polyphase Gm-C filter using Gm cells

Abstract

Polyphase gm-C filters can use matching gm cell components for improved higher image rejection results. Polyphase gm-C filter cells all can be matched by incorporating a matching gmu value in each of the g.sub.m components. The matching gmu value used to replace different gm values can be determined for incorporation into each gm cell component of a filter by: calculating coupling of gmi, gmij by gmi=Ci0 and gmij=Czij0 for i,j; calculating K.sub.i=gmi/gmu; rounding K.sub.i to an integer number, Ni=round(Ki), KiNi and Nij=round(Kij), KijNij; calculating a scaling factor for circuit capacitors C.sub.i and Czijby i=(NiKi)/Ki and ij=(NijKij)/Kij; and adjusting circuit capacitors C.sub.i and Czij by CiCi*(1+i) and CzijCzij*(1+ij). Once the process is completed for i,j, the result can be implemented to match gm cell components of traditional and newly designed polyphase gm-C filters with the matching gmu value.

Claims

1. A method for operating a filter, comprising: receiving signals into a polyphase gm-C filter having a plurality of transconductance (gm) cell components that are an integer multiple of a unit transconductance cell (gmu); wherein the gm cell components have values that are an integer multiple of a g.sub.mu value; and filtering the signals through the polyphase gm-C filter; wherein the gm cell components are prefabricated gm components of a traditional gm-C filter with prior different gm values that are adjusted with the g.sub.mu value to cause the prefabricated gm components to be integer multiples of the g.sub.mu value.

2. The method of claim 1, wherein the gm cell components are matched with a capacitance value representing a gm value that is predetermined for incorporation into the gm cell components.

3. The method of claim 2, wherein the gm cell components are fabricated in an integrated circuit.

4. The method of claim 2, wherein the g.sub.mu value for the gm cell components is predetermined by:
calculating coupling of gmi,gmij by gmi=Ci0 and gmij=Czij0 for i,j;
calculating K.sub.i=gmi/gmu;
rounding K.sub.i to an integer number,Ni=round(Ki),KiNi and Nij=round(Kij),KijNij;
calculating a scaling factor for circuit capacitors Ci and Czij by i=(NiKi)/Ki and ij=(NijKij)/Kij; and
adjusting the capacitance value of capacitors Ci and Czij by CiCi*(1i) and CzijCzij*(1+ij).

5. The method of claim 4, wherein the process is completed for i,j and is implemented as the g.sub.mu value on the gm cell components.

6. The method of claim 4, wherein the process is completed for i,j and is implemented as the g.sub.mu value on the gm cell components, and the gm cell components are disposed on an integrated circuit.

7. The method of claim 4, wherein the process completed for i,j is implemented as the g.sub.mu value on prefabricated gm components of a traditional gm-C filter with disparate gm values to cause the prefabricated gm components to be integer multiples of the g.sub.mu value.

8. The method of claim 7, wherein the prefabricated gm-C cell components are disposed on an integrated circuit.

9. The method of claim 1, wherein the prefabricated gm cell components are fabricated in an integrated circuit.

10. A polyphase gm-C filter, comprising: an input for receiving signals; an output for outputting the signals; and a plurality of transconductance (gm) cell components that are an integer multiple of a unit transconductance cell (gmu) incorporating values that are an integer multiple of a g.sub.mu value and connected to the input for receiving signals and connected to the output for outputting the signals; wherein the g.sub.mu unit value is implemented on prefabricated gm components of a traditional gm-C filter with prior different gm values to cause all the prefabricated gm components of a traditional gm-C filter to be integer multiples of the g.sub.mu value.

11. A polyphase gm-C filter of claim 10, wherein the g.sub.mu value incorporated in the more than one gm component is predetermined by:
calculating coupling of gmi,gmij by gmi=Ci0 and gmij=Czij0 for i,j;
calculating K.sub.i=gmi/gmu;
rounding K.sub.i to an integer number,Ni=round(Ki),KiNi and Nij=round(Kij),KijNij;
calculating a scaling factor for circuit capacitors C.sub.i and Czij by i=(NiKi)/Ki and ij=(NijKi.sub.j)/Kij;
determining a capacitance value for the circuit capacitors C.sub.i and Czij by CiCi*(1+i) and CzijCzij*(1+ij); and implementing the capacitance value as adjustments for Ci and Czij on the more than one gm component as an integer multiplication of a gm cell, gmu unit value.

12. The polyphase gm-C filter of claim 11, wherein the value of i,j depends on filter order.

13. The polyphase gm-C filter of claim 10, wherein the more than one gm component incorporating the g.sub.mu unit value are disposed on an integrated circuit.

14. The polyphase gm-C filter of claim 10, wherein the prefabricated gm components are disposed on an integrated circuit.

15. A method of designing a filter, comprising: arranging gm components for a polyphase gm-C filter on an integrated circuit together with inputs to and outputs from the polyphase gm-C filter; and setting the components with a matching g.sub.mu value wherein the matching g.sub.mu value is determined by:
calculating coupling of gmi,gmij by gmi=Ci0 and gmij=Czij0 for i,j;
calculating K.sub.i=gmi/gmu;
rounding K.sub.i to an integer number,Ni=round(Ki),KiNi and Nij=round(Kij),KijNij;
calculating a scaling factor for circuit capacitors Ci and Czij by i=(NiKi)/Ki and ij=(NijKij)/Kij; and
adjusting circuit capacitors C.sub.i and Czij by CiCi*(1+i) and CzijCzij*(1+ij).

16. The method of claim 15, wherein the process completed for i,j is implemented as the g.sub.mu value on all of the gm components to cause all of the gm components to be integer multiples of the g.sub.mu value.

17. The method of claim 15, wherein the process completed for i,j is implemented as the g.sub.mu value on prefabricated gm components of a traditional gm-C filter with prior different gm values to cause all of the prefabricated gm components of a traditional gm-C filter to be integer multiples of the g.sub.mu value.

18. A polyphase gm-C filter, comprising: an input for receiving signals; an output for outputting the signals; and more than one gm component incorporating a matching gmu value and connected to the input for receiving signals and connected to the output for outputting the signals; wherein the matching g.sub.mu value incorporated in the more than one gm component is predetermined by:
calculating coupling of gmi,gmij by gmi=Ci0 and gmij=Czij0 for i,j;
calculating K.sub.i=gmi/gmu;
rounding K.sub.i to an integer number,Ni=round(Ki),KiNi and Nij=round(Kij),KijNij;
calculating a scaling factor for circuit capacitors C.sub.i and Czij by i=(NiKi)/Ki and ij=(NijKij)/Kij;
determining a capacitance value for the circuit capacitors C.sub.i and Czij by CiCi*(1+i) and CzijCzij*(1+ij); and implementing the capacitance value as adjustments for Ci and Czij on the more than one gm component as an integer multiplication of a gm cell, gmu unit value.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 depicts basic gm-C based building blocks, in accordance with the embodiments.

(2) FIG. 2 depicts RLC implementation of a 5.sup.th order Elliptic Low Pass filter, in accordance with the embodiments.

(3) FIG. 3a depicts AC response of a real and complex filter, in accordance with the embodiments.

(4) FIG. 3b depicts Capacitor transformation to shift frequency, in accordance with the embodiments.

(5) FIG. 4 depicts implementation of the image-reject filter using two coupled 5.sup.th order low-pass Elliptic filters with coupling transconductors, in accordance with the embodiments.

(6) FIG. 5 depicts adding coupling matching gm cell components, matched by gmu value, as transconductors to one node of the gm-C filter, in accordance with the embodiments.

(7) FIG. 6 depicts a flow diagram of the invented method for matching coupling gm cell components to make them an integer multiple of gmu for an N.sup.th order filter, and with N=5 as an example, in accordance with the embodiments.

(8) FIG. 7 depicts a flow diagram for a method of operating a filter, in accordance with the embodiments.

(9) FIG. 8 depicts a flow diagram for a method of designing a filter, in accordance with the embodiments.

(10) FIG. 9 depicts a block diagram of a polyphase gm-C filter, in accordance with the embodiments.

DETAILED DESCRIPTION

(11) It will be readily understood that the components of the embodiments as generally described herein and illustrated in the appended figures could be arranged and designed in a wide variety of different configurations. Thus, the following more detailed description of various embodiments, as represented in the Figures, is not intended to limit the scope of the present disclosure, but is merely representative of various embodiments. While the various aspects of the embodiments are presented in drawings, the drawings are not necessarily drawn to scale unless specifically indicated.

(12) The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the embodiments is, therefore, indicated by the appended claims rather than by this detailed description. All changes that come within the meaning and range of equivalency of the claims are to be embraced within their scope.

(13) Reference throughout this specification to features, advantages, or similar language does not imply that all of the features and advantages that may be realized with the present invention should be or are in any single embodiment. Rather, language referring to the features and advantages is understood to mean that a specific feature, advantage, or characteristic described in connection with an embodiment is included in at least one embodiment of the present invention. Thus, discussions of the features and advantages, and similar language, throughout this specification may, but do not necessarily, refer to the same embodiment.

(14) Furthermore, the described features, advantages, and characteristics of the invention may be combined in any suitable manner in one or more embodiments. One skilled in the relevant art will recognize, in light of the description herein, that the invention can be practiced without one or more of the specific features or advantages of a particular embodiment. In other instances, additional features and advantages may be recognized in certain embodiments that may not be present in all embodiments of the invention.

(15) Reference throughout this specification to one embodiment, an embodiment, or similar language means that a particular feature, structure, or characteristic described in connection with the indicated embodiment is included in at least one embodiment of the present invention. Thus, the phrases in one embodiment, in an embodiment, and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment.

(16) Low noise, moderate linearity and low power are the reasons to choose the gm-C method for the implemented filter in accordance with the disclosed embodiments. Referring to FIG. 1, depicted is implementation of an integrator 110, a resistor 120 and an inductor 130 using transconductance and capacitance, and the corresponding formulas that express them as functions of gm and C. To implement a gm-C filter derived from an RLC filter, all resistors and inductors can be replaced with the demonstrated building blocks. The building block could then be disposed onto an integrated circuit.

(17) Referring to FIG. 2, labeled as prior art, depicted is a standard RLC circuit 200 of a 5.sup.th order low pass filter. To implement a gm-C filter on an integrated circuit from the standard RLC circuit 200 shown in FIG. 2, resistors and inductors illustrated therein need to be replaced by basic building blocks that were described with respect to FIG. 1. The top portion of FIG. 4 illustrates the gm-C implementation of a 5.sup.th order filter (of FIG. 2) with R and L being replaced with gm cells. All the parasitic caps of input and output stages of gm cells can be absorbed in C.sub.1, C.sub.2, C.sub.3, C.sub.4 and C.sub.5. This means that they may need to be adjusted slightly, or otherwise reduced to compensate for the parasitic capacitors and keep the AC response equal to the original AC response.

(18) To make a polyphase (i.e., image reject) filter, a frequency transformation is needed. FIG. 3a depicts the responses of real 311 and complex 312 (polyphase) filters. A real filter is symmetric around f=0 Hertz (Hz) and can pass both the positive frequencies (e.g., the desired signal), and the negative frequencies (the image signal). FIG. 3b depicts the complex frequency shift operation that converts a real low-pass function 321 into the complex function 322 in accordance with a preferred embodiment. Applying the frequency shift of 0 to the current equation of a floating capacitor provides the following:
I=(jC)(V.sub.1V.sub.2)(j.sub.0C)(V.sub.1V.sub.2)(1)

(19) In a quadrature system, V1, V2, jV1 and jV2 are available. This function can easily be implemented in hardware as shown by complex function 322 by adding two coupling transconductors, 323, 324, whose inputs are connected to the quadrature nodes (i.e., one fully differential gm cell in fully differential implementation).

(20) Referring to FIG. 4, depicted is a 5.sup.th order polyphase gm-C filter using two low pass gm-C filters, 411, 412, and coupling gm 415 using the concept explained in FIG. 3 and utilizing equation (1). Referring to FIG. 3, coupling gm has been added to low pass gm-C filter to shift the center frequency to the desired frequency and to further create a complex (polyphase/image-reject) filter.

(21) Referring to FIG. 5, depicted is one node of a polyphase filter 500. As is shown in FIG. 5, a gm cell component 520 is connected to node V1 of a filter 510 between capacitors C1 and Cz. The gm cell component includes gm1 and gm12 with the values:
gm1=C1*0,gm12=Cz*0(2)

(22) To maintain easier implementation and good matching among the transconductance stages of the improved filter, all gm cell components 520 can be implemented using integer multiples of a unit transconductance stage, gmu. Value for each gm cell component 520 to match can be obtained via the determination of a unit gmu value for each of the gm cell components 520. With the main low pass filter already using gmu, the gm cell components 520 need to be scaled to match the same gmu. This means that the gm cell components 520 should be configured in the form of:
gm1=C1*0=K1gmu, gm12=Cz*0=K12gmu(3)
where K1 and K12 are not necessarily an integer number. K can be rounded to the closer integer number, which implies some adjustment on the values of the circuit capacitors connected in the circuit to the node V1. C1 and/or Cz may need to be adjusted slightly to make K an integer number. This adjustment is similar to a post layout adjustment of circuit capacitors for a high frequency gm-C filter that keeps the AC response of the overall filter unchanged, while the middle nodes can be slightly changed.

(23) Referring again to formulas (2) and (3), coupling gm values of nodes 1 to 5 of a polyphase filter provided in accordance with features of the embodiment can be calculated as follows:
gm1=0*C1=K1gmu(4)
gm2=0*C2=K2gmu(5)
g3=0*C3=K3gmu(6)
g4=0*C4=K4gmu(7)
g5=0*C5=K5gmu(8)
g13=0*Cz13=K13gmu(9)
g35=0*Cz35=K35gmu(10)

(24) The described method (e.g., equation 1) for achieving optimum coupling transconductors can be employed to change coupling gm values of gm cell components to multiples of a unit transconductance, gmu, where K1, K2, K3, K4, K5, K13 and K35 can be replaced with integer numbers, N1, N2, N3, N4, N5, N13 and N35. Furthermore, C1, C2, C3 (and Cz with extra percussion) can be adjusted iteratively to compensate for the rounding coupling gm multiplication factors.

(25) Referring to the flowchart of FIG. 6, depicted is a method for an N.sup.th order filter, where N=5 in the described case is only used as an example and should not be interpreted as a limitation of the embodiments. It should be noted that i,j(N) can depend on filter order. The process begins in Block 610, as an example, for i=1, 2, 3, 4, 5 and j=3, 5. As shown in Block 620, coupling of gmi, gmij can be calculated by: gmi=Ci0 and gmij=Czij0. Then as shown in Block 630, Ki=gmi/gmu can be calculated. Then as shown in Block 640, Ki can be rounded to the closest integer number, Ni=round(Ki), KiNi and Nij=round(Kij), KijNij. Referring to Block 650, the scaling factor for circuit capacitors can then be calculated by: i=(NiKi)/Ki and ij=(NijKij)/Kij. C.sub.i and Czij Caps can then be adjusted, as shown in Block 660, by: CiCi*(1+i) and CzijCzij*(1+ij). The process can then be completed as shown in Block 670. It should be noted that (i=1, 2, 3, 4, 5), ij=(13, 35), wherever applicable.

An Example

(26) Referring to FIGS. 3a and 3b, as an example, making the RLC prototype a realistic scenario with a bandwidth (BW) of 1.2 MHz, 1 dB in band ripple, stop band of 1.5*BW, 55 dB Stop band rejection can be provided (e.g., which can be suitable for a GPS receiver). In such case, the parameters would be as follows:

(27) TABLE-US-00001 R C1 Cz2 L2 C3 Cz4 L4 C5 1 228.00 nF 68.90 nF 105.30 nF 330.50 nF 24.97 nF 129.6 nF 262.20 nF
Equal gm-C filter parameters, (which can be the filter that has been shown in FIG. 4, with the same component name that has been used here) are gmu for gm=1 and gm=10. Equal gm-C filter parameters for gm=1 and gm=10 will be as follow:

(28) TABLE-US-00002 gmu C1 Cz13 L2 C3 Cz35 L4 C5 gm = 1 1 2.28E07 6.89E08 1.05E07 3.31E07 2.50E08 1.30E07 2.62E07 gm = 10 1.0g0E05 2.28E07 6.89E08 1.05E07 3.31E07 2.50E08 1.30E07 2.62E07
A frequency shift of fc=4.1 MHz (megahertz), defined as 0=2**fc which is good for an IF frequency of 4.1 MHz, is shown being applied. This can achieve gmi as shown in the following table. Ki (Kij) is being defined as gmi/gmu (gmij/gmu). Ni (Nij) can be derived from Ki (Kij) (i=1, 2, 3, 4, 5, ij=13, 35). A summary of numbers that can be obtained from the disclosed process is listed in the following table:

(29) TABLE-US-00003 gmu C1 Cz13 L2 C3 Cz35 L4 C5 gm = 1 1 2.28E07 6.89E08 .05E07 3.31E07 2.50E08 .30E07 2.62E07 gm = 10 .00E05 2.28E07 6.89E08 .05E07 3.31E07 2.50E08 .30E07 2.62E07 C Normalized 2.28E12 6.89E13 .05E12 3.31E12 2.50E13 .30E12 2.62E12 Node i V1 V13 V2 V3 V35 V4 V5 Ci C1 Cz13 CL2 C3 Cz35 CL4 C5 2.28E12 6.89E13 .05E12 3.31E12 2.50E13 1.30E12 2.62E12 Coupling gm gm1 gm13 gm2 gm3 gm35 gm4 gm5 5.87E05 .77E05 2.71E05 8.51E05 6.43E06 3.34E05 6.75E05 Ki = gmi/gmu K1 K13 K2 K3 K35 K4 K5 5.874 1.775 2.713 8.514 0.643 3.339 6.755 Ni = round(Ki) Ni N13 N2 N3 N35 N4 N5 6 2 3 8 1 3 7 i% 2.153 12.680 10.593 6.037 55.460 10.143 3.634 Ci scaling C1(1 + 1) Cz13(1 + 13) C2(1 + 2) C3(1 + 3) Cz35(1 + 35) C3(1 + 4) C3(1 + 5) Factor Adjusted Ci 2.329E12 7.764E13 1.165E12 3.105E12 3.882E13 1.165E12 2.717E12

(30) The embodiments simplify polyphase gm-C filter design because only one type of gm cell adapted by the process described herein needs to be used. The improved design can make frequency shifting modular for variable IF frequencies, if needed. The improved design can save area in the filter circuit by rounding coupling gm cells to an integer factor of a gm unit, and thereby achieving a matching gmu value. The improved design can also reduce the number of the coupling gm cells, which can translate into less parasitic effect and which can be important for MHz range applications while being able to use small size gm cells. The improved design provides less complexity in circuitry due to using one type of gm cell, gm cells with a matching gmu value, for the whole polyphase filter. The improved design can achieve better image rejection and less layout effort when incorporated on an integrated circuit.

(31) Referring to FIG. 7, illustrated is a flow diagram 700 for a method of operating a filter. Referring to Block 710, a first step is shown as receiving signals into a polyphase gm-C filter comprising gm cell components matched by a gmu value. Then as shown in Block 720, a next step includes filtering the signals through the polyphase gm-C filter.

(32) Referring to FIG. 8, illustrated is a flow diagram 800 for a method of designing a filter. Referring to Block 810, a first step includes arranging gm components for a polyphase gm-C filter on an integrated circuit together with inputs to and outputs from the polyphase gm-C filter. Then as shown in Block 820, a next step includes setting all of the components for the polyphase gm-C filter with a matching gmu value.

(33) Referring to FIG. 9, illustrated is a block diagram 900 of a polyphase gm-C filter. A polyphase gm-C filter can include an input 910 for receiving signals, and an output 920 for outputting signals. Disposed between the input 910 and output 920 are more than one gm component 930 incorporating a matching gmu value and connected to the input for receiving signals and connected to the output for outputting the signals. The more than one gm component 930 can be fabricated on an integrated circuit 940 with the input 910 and output 920. Other circuit components (not shown) that typically utilize polyphase gm-C filters can also be connected to the input 910 and the output 920. Such other circuit components can also be fabricated on the integrated circuit 940 with the more than one gm component making up the polyphase gm-C filter.

(34) In accordance with the embodiments, a device and methods have be disclosed that can provide a polyphase gm-C filter using one type of gm cell that includes gm cell components having a matching gmu value, for a polyphase gm-C filter. Gm cells components of the polyphase gm-C filter can all be matched by incorporating a matching gmu value obtained for each of the gm components incorporated in a polyphase gm-C filter. The gm value can be obtained via a number value for each of the gm components which can be determined by: calculating coupling of g.sub.mi, g.sub.mij by g.sub.mi=C.sub.i0 and g.sub.mij=Czij0 for i,j; calculating Ki=gmi/gmu; rounding Ki to an integer number, Ni=round(Ki), KiNi and Nij=round(Kij), KijNij; calculating a scaling factor for circuit capacitors by i=(NiKi)/Ki and ij=(NijKij)/Kij; and adjusting capacitors Ci and Czij by CiCi*(1+i) and CzijCzij*(1+ij). Once the process is completed for i,j, the result can be implemented in a preexisting (e.g., a traditional gm-C filter) or new polyphase filter to match its gm components with a matching gmu value.

(35) It should be appreciated that a matching gmu value can also be implemented in prefabricated gm cell components of a traditional gm-C filter with prior different gm values to cause all the prefabricated gm components of a traditional gm-C filter to match. It should be appreciated that the improvement can be applied to any gm-C filter to make all gm cells an integer multiplication of one gmu. It should also be appreciated that embodiments of the invention can be implemented entirely in hardware or in an implementation containing both hardware and software elements. In embodiments that use software, the software may include but is not limited to firmware, resident software, microcode, etc.

(36) Although specific embodiments of the invention have been described and illustrated, the invention is not to be limited to the specific forms or arrangements of parts so described and illustrated. The scope of the invention is to be defined by the claims appended hereto and their equivalents.