Optimum dinamikli yüksek mertebeden aktif RC filtre sentezi ve simulasyon için bir paket program cafid

A Package program called cafid for the synthesis and the simulation and high order active RC filtres with the optimum dynamic range

Tez No: 39616
Yazar: ERSİN BAYRAMOĞLU
Danışmanlar: PROF.DR. ALİ NUR GÖNÜLEREN
Tez Türü: Yüksek Lisans
Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
Anahtar Kelimeler: Benzetim, Filtreler, Paket programlar, Simulation, Filters, Packaged softwares
Yıl: 1994
Dil: Türkçe
Üniversite: İstanbul Teknik Üniversitesi
Enstitü: Fen Bilimleri Enstitüsü
Ana Bilim Dalı: Belirtilmemiş.
Bilim Dalı: Belirtilmemiş.
Sayfa Sayısı: Belirtilmemiş.

Özet

(3). Suboptimum cascade sequence is found by ordering biquadratic sections from input to output by increasing d^ values. (4). Gain distribution is evaluated to avoid overloading. In the CAFID, the decomposition problem has been solved to maximize the dynamic range of the cascaded network. In the realization phase, any of the appropriate network may be used to realize the biquadratic transfer functions in the cascade. This step can also be achieved by using the CAFID. After the evaluation of the CAFID, some considerable results, in addition to the new methods for pole-zero pairing have been obtained. Several important aspects and results are summarized as follows. Since the classical approximations are used to form the transfer function, the construction of single d;j table is adequate for solving pole-zero pairing with an assumption of all zero pairings chosen as z(0,oo) for band-pass Butterworth and Chebyshev filters. From the discussion of four types of biquadratic functions, the measure of flatness d;j can be found by evaluating G^co) at the three points of frequency. The new pole-zero pairing method, used only the dSj table, has been suggested. The proposed method for the classical filter approximations and four types of filter functions has given the expected optimum solution. The method has been verified by comparing the results of the d;j graph with the filter program. A new rule of thumb has been introduced to solve pole-zero pairing problem. Using this approximation method, one can easily find optimum or suboptimum solution without using a computer program. Studying various types of filter designs for different classical approximations, some properties of d;j values on the d^ table have been found. (1). The d;j values on columns of the d^ table are equal to each other in the Butterworth and Chebyshev filters ( dn = di2 =... = d^ ). (2). For the same filter specification, like A^, A^, £lp and Qs, the d;j tables constructed for a lowpass and a highpass filter are equal to each other for all type of classical approximation. (3). Two of the d;j values from dtj table can be equal to each other in the bandpass and bandreject filters. (4). For different pole-zero pairings from d;j table, the d;j values can also be equal to each other in the Chebyshev and Elliptic filters with even order. XVII

Özet (Çeviri)

First objective may be met if the maximum amplitudes of all the voltages V“ V2,..., Vn are equal to V,^. Thus the gain constants distribution must be made such that, iv! =|v,| =... =|vl =v (8) I Umax I 2lmax I ”Imax T v ' In order for the signal-to-ratio to be as high as possible, we must maximize the minimum of in-band signal what this means is that the pole-zero pairing and the cascade sequencing must be done such that the magnitude of the intermediate transfer functions T;(s) is as flat as possible over the filter passband. Decomposition problem can be split into the following three steps to obtain simple solutions. (1). Determine the pole-zero pairing such that each h;(s) is as flat as possible over the filter passband. (2). Find a sequence such that each T;(s) is as flat as possible. (3). Assign gain constants Hi0 such that (8) is satisfied. A systematic method was proposed for solving the pole-zero pairing problem iture [3 be defined as, in literature [3,42,43]. In this method, a measure of flatness for any function H;j(s) can d“=21og where (G \ 10 ij max \^ ij min J and G^lH^/Hj (9) GijmiK=Max[GİJ(ö;)], 0<<y<co Gy min = Min[Gğ (©)], aL < co < <aH where coL and coH are the lower and upper passband edge frequencies. After evaluating all the d^ values, dy table is constructed. The entry d;j is the value of measure of flatness for the biquad obtained by pairing p; with z-. The dy graph is also plotted. Meanwhile, using a specific type of algorithm, pole-zero pairings can be determined from d;j graph. In this thesis, a package of filter design program called CAFID (Computer Aided Filter Deign) has been developed. In addition, up to 20th order cascaded active filter designs can be seen as an outcome of the CAFID. For designing active filters it can be used one of the classical approximation methods and one of the types of filter functions. If it is desired, the magnitude and phase responses of the filter vs. frequency may be calculated and plotted on the screen. The decomposition problem is solved in the following steps: (1). dy values are calculated and the dy table is constructed. (2). Optimum pole-zero pairing is directly determined from dy table using the new developed method. XVI(3). Suboptimum cascade sequence is found by ordering biquadratic sections from input to output by increasing d^ values. (4). Gain distribution is evaluated to avoid overloading. In the CAFID, the decomposition problem has been solved to maximize the dynamic range of the cascaded network. In the realization phase, any of the appropriate network may be used to realize the biquadratic transfer functions in the cascade. This step can also be achieved by using the CAFID. After the evaluation of the CAFID, some considerable results, in addition to the new methods for pole-zero pairing have been obtained. Several important aspects and results are summarized as follows. Since the classical approximations are used to form the transfer function, the construction of single d;j table is adequate for solving pole-zero pairing with an assumption of all zero pairings chosen as z(0,oo) for band-pass Butterworth and Chebyshev filters. From the discussion of four types of biquadratic functions, the measure of flatness d;j can be found by evaluating G^co) at the three points of frequency. The new pole-zero pairing method, used only the dSj table, has been suggested. The proposed method for the classical filter approximations and four types of filter functions has given the expected optimum solution. The method has been verified by comparing the results of the d;j graph with the filter program. A new rule of thumb has been introduced to solve pole-zero pairing problem. Using this approximation method, one can easily find optimum or suboptimum solution without using a computer program. Studying various types of filter designs for different classical approximations, some properties of d;j values on the d^ table have been found. (1). The d;j values on columns of the d^ table are equal to each other in the Butterworth and Chebyshev filters ( dn = di2 =... = d^ ). (2). For the same filter specification, like A^, A^, £lp and Qs, the d;j tables constructed for a lowpass and a highpass filter are equal to each other for all type of classical approximation. (3). Two of the d;j values from dtj table can be equal to each other in the bandpass and bandreject filters. (4). For different pole-zero pairings from d;j table, the d;j values can also be equal to each other in the Chebyshev and Elliptic filters with even order. XVIIFirst objective may be met if the maximum amplitudes of all the voltages V”V2,..., Vn are equal to V,^. Thus the gain constants distribution must be made such that, iv! =|v,| =... =|vl =v (8) I Umax I 2lmax I“Imax T v ' In order for the signal-to-ratio to be as high as possible, we must maximize the minimum of in-band signal what this means is that the pole-zero pairing and the cascade sequencing must be done such that the magnitude of the intermediate transfer functions T;(s) is as flat as possible over the filter passband. Decomposition problem can be split into the following three steps to obtain simple solutions. (1). Determine the pole-zero pairing such that each h;(s) is as flat as possible over the filter passband. (2). Find a sequence such that each T;(s) is as flat as possible. (3). Assign gain constants Hi0 such that (8) is satisfied. A systematic method was proposed for solving the pole-zero pairing problem iture [3 be defined as, in literature [3,42,43]. In this method, a measure of flatness for any function H;j(s) can d”=21og where (G \ 10 ij max \^ ij min J and G^lH^/Hj (9) GijmiK=Max[GİJ(ö;)], 0<<y<co Gy min = Min[Gğ (©)], aL < co < <aH where coL and coH are the lower and upper passband edge frequencies. After evaluating all the d^ values, dy table is constructed. The entry d;j is the value of measure of flatness for the biquad obtained by pairing p; with z-. The dy graph is also plotted. Meanwhile, using a specific type of algorithm, pole-zero pairings can be determined from d;j graph. In this thesis, a package of filter design program called CAFID (Computer Aided Filter Deign) has been developed. In addition, up to 20th order cascaded active filter designs can be seen as an outcome of the CAFID. For designing active filters it can be used one of the classical approximation methods and one of the types of filter functions. If it is desired, the magnitude and phase responses of the filter vs. frequency may be calculated and plotted on the screen. The decomposition problem is solved in the following steps: (1). dy values are calculated and the dy table is constructed. (2). Optimum pole-zero pairing is directly determined from dy table using the new developed method. XVI(3). Suboptimum cascade sequence is found by ordering biquadratic sections from input to output by increasing d^ values. (4). Gain distribution is evaluated to avoid overloading. In the CAFID, the decomposition problem has been solved to maximize the dynamic range of the cascaded network. In the realization phase, any of the appropriate network may be used to realize the biquadratic transfer functions in the cascade. This step can also be achieved by using the CAFID. After the evaluation of the CAFID, some considerable results, in addition to the new methods for pole-zero pairing have been obtained. Several important aspects and results are summarized as follows. Since the classical approximations are used to form the transfer function, the construction of single d;j table is adequate for solving pole-zero pairing with an assumption of all zero pairings chosen as z(0,oo) for band-pass Butterworth and Chebyshev filters. From the discussion of four types of biquadratic functions, the measure of flatness d;j can be found by evaluating G^co) at the three points of frequency. The new pole-zero pairing method, used only the dSj table, has been suggested. The proposed method for the classical filter approximations and four types of filter functions has given the expected optimum solution. The method has been verified by comparing the results of the d;j graph with the filter program. A new rule of thumb has been introduced to solve pole-zero pairing problem. Using this approximation method, one can easily find optimum or suboptimum solution without using a computer program. Studying various types of filter designs for different classical approximations, some properties of d;j values on the d^ table have been found. (1). The d;j values on columns of the d^ table are equal to each other in the Butterworth and Chebyshev filters ( dn = di2 =... = d^ ). (2). For the same filter specification, like A^, A^, £lp and Qs, the d;j tables constructed for a lowpass and a highpass filter are equal to each other for all type of classical approximation. (3). Two of the d;j values from dtj table can be equal to each other in the bandpass and bandreject filters. (4). For different pole-zero pairings from d;j table, the d;j values can also be equal to each other in the Chebyshev and Elliptic filters with even order. XVIIFirst objective may be met if the maximum amplitudes of all the voltages V“ V2,..., Vn are equal to V,^. Thus the gain constants distribution must be made such that, iv! =|v,| =... =|vl =v (8) I Umax I 2lmax I ”Imax T v ' In order for the signal-to-ratio to be as high as possible, we must maximize the minimum of in-band signal what this means is that the pole-zero pairing and the cascade sequencing must be done such that the magnitude of the intermediate transfer functions T;(s) is as flat as possible over the filter passband. Decomposition problem can be split into the following three steps to obtain simple solutions. (1). Determine the pole-zero pairing such that each h;(s) is as flat as possible over the filter passband. (2). Find a sequence such that each T;(s) is as flat as possible. (3). Assign gain constants Hi0 such that (8) is satisfied. A systematic method was proposed for solving the pole-zero pairing problem iture [3 be defined as, in literature [3,42,43]. In this method, a measure of flatness for any function H;j(s) can d“=21og where (G \ 10 ij max \^ ij min J and G^lH^/Hj (9) GijmiK=Max[GİJ(ö;)], 0<<y<co Gy min = Min[Gğ (©)], aL < co < <aH where coL and coH are the lower and upper passband edge frequencies. After evaluating all the d^ values, dy table is constructed. The entry d;j is the value of measure of flatness for the biquad obtained by pairing p; with z-. The dy graph is also plotted. Meanwhile, using a specific type of algorithm, pole-zero pairings can be determined from d;j graph. In this thesis, a package of filter design program called CAFID (Computer Aided Filter Deign) has been developed. In addition, up to 20th order cascaded active filter designs can be seen as an outcome of the CAFID. For designing active filters it can be used one of the classical approximation methods and one of the types of filter functions. If it is desired, the magnitude and phase responses of the filter vs. frequency may be calculated and plotted on the screen. The decomposition problem is solved in the following steps: (1). dy values are calculated and the dy table is constructed. (2). Optimum pole-zero pairing is directly determined from dy table using the new developed method. XVI(3). Suboptimum cascade sequence is found by ordering biquadratic sections from input to output by increasing d^ values. (4). Gain distribution is evaluated to avoid overloading. In the CAFID, the decomposition problem has been solved to maximize the dynamic range of the cascaded network. In the realization phase, any of the appropriate network may be used to realize the biquadratic transfer functions in the cascade. This step can also be achieved by using the CAFID. After the evaluation of the CAFID, some considerable results, in addition to the new methods for pole-zero pairing have been obtained. Several important aspects and results are summarized as follows. Since the classical approximations are used to form the transfer function, the construction of single d;j table is adequate for solving pole-zero pairing with an assumption of all zero pairings chosen as z(0,oo) for band-pass Butterworth and Chebyshev filters. From the discussion of four types of biquadratic functions, the measure of flatness d;j can be found by evaluating G^co) at the three points of frequency. The new pole-zero pairing method, used only the dSj table, has been suggested. The proposed method for the classical filter approximations and four types of filter functions has given the expected optimum solution. The method has been verified by comparing the results of the d;j graph with the filter program. A new rule of thumb has been introduced to solve pole-zero pairing problem. Using this approximation method, one can easily find optimum or suboptimum solution without using a computer program. Studying various types of filter designs for different classical approximations, some properties of d;j values on the d^ table have been found. (1). The d;j values on columns of the d^ table are equal to each other in the Butterworth and Chebyshev filters ( dn = di2 =... = d^ ). (2). For the same filter specification, like A^, A^, £lp and Qs, the d;j tables constructed for a lowpass and a highpass filter are equal to each other for all type of classical approximation. (3). Two of the d;j values from dtj table can be equal to each other in the bandpass and bandreject filters. (4). For different pole-zero pairings from d;j table, the d;j values can also be equal to each other in the Chebyshev and Elliptic filters with even order. XVIIFirst objective may be met if the maximum amplitudes of all the voltages V”V2,..., Vn are equal to V,^. Thus the gain constants distribution must be made such that, iv! =|v,| =... =|vl =v (8) I Umax I 2lmax I“Imax T v ' In order for the signal-to-ratio to be as high as possible, we must maximize the minimum of in-band signal what this means is that the pole-zero pairing and the cascade sequencing must be done such that the magnitude of the intermediate transfer functions T;(s) is as flat as possible over the filter passband. Decomposition problem can be split into the following three steps to obtain simple solutions. (1). Determine the pole-zero pairing such that each h;(s) is as flat as possible over the filter passband. (2). Find a sequence such that each T;(s) is as flat as possible. (3). Assign gain constants Hi0 such that (8) is satisfied. A systematic method was proposed for solving the pole-zero pairing problem iture [3 be defined as, in literature [3,42,43]. In this method, a measure of flatness for any function H;j(s) can d”=21og where (G \ 10 ij max \^ ij min J and G^lH^/Hj (9) GijmiK=Max[GİJ(ö;)], 0<<y<co Gy min = Min[Gğ (©)], aL < co < <aH where coL and coH are the lower and upper passband edge frequencies. After evaluating all the d^ values, dy table is constructed. The entry d;j is the value of measure of flatness for the biquad obtained by pairing p; with z-. The dy graph is also plotted. Meanwhile, using a specific type of algorithm, pole-zero pairings can be determined from d;j graph. In this thesis, a package of filter design program called CAFID (Computer Aided Filter Deign) has been developed. In addition, up to 20th order cascaded active filter designs can be seen as an outcome of the CAFID. For designing active filters it can be used one of the classical approximation methods and one of the types of filter functions. If it is desired, the magnitude and phase responses of the filter vs. frequency may be calculated and plotted on the screen. The decomposition problem is solved in the following steps: (1). dy values are calculated and the dy table is constructed. (2). Optimum pole-zero pairing is directly determined from dy table using the new developed method. XVI(3). Suboptimum cascade sequence is found by ordering biquadratic sections from input to output by increasing d^ values. (4). Gain distribution is evaluated to avoid overloading. In the CAFID, the decomposition problem has been solved to maximize the dynamic range of the cascaded network. In the realization phase, any of the appropriate network may be used to realize the biquadratic transfer functions in the cascade. This step can also be achieved by using the CAFID. After the evaluation of the CAFID, some considerable results, in addition to the new methods for pole-zero pairing have been obtained. Several important aspects and results are summarized as follows. Since the classical approximations are used to form the transfer function, the construction of single d;j table is adequate for solving pole-zero pairing with an assumption of all zero pairings chosen as z(0,oo) for band-pass Butterworth and Chebyshev filters. From the discussion of four types of biquadratic functions, the measure of flatness d;j can be found by evaluating G^co) at the three points of frequency. The new pole-zero pairing method, used only the dSj table, has been suggested. The proposed method for the classical filter approximations and four types of filter functions has given the expected optimum solution. The method has been verified by comparing the results of the d;j graph with the filter program. A new rule of thumb has been introduced to solve pole-zero pairing problem. Using this approximation method, one can easily find optimum or suboptimum solution without using a computer program. Studying various types of filter designs for different classical approximations, some properties of d;j values on the d^ table have been found. (1). The d;j values on columns of the d^ table are equal to each other in the Butterworth and Chebyshev filters ( dn = di2 =... = d^ ). (2). For the same filter specification, like A^, A^, £lp and Qs, the d;j tables constructed for a lowpass and a highpass filter are equal to each other for all type of classical approximation. (3). Two of the d;j values from dtj table can be equal to each other in the bandpass and bandreject filters. (4). For different pole-zero pairings from d;j table, the d;j values can also be equal to each other in the Chebyshev and Elliptic filters with even order. XVII

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