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The authors of Analog's article Practical Techniques to Avoid Instability Due to Capacitive Loading correctly compute TF poles and zeroes of the inloop compensation circuit feedback, applying OCTC. What they do in error is that they use a pole zero cancellation method for computing the feedback capacitor value required to flatten the transfer function best.

The OCTC method used in the Practical Techniques.. article is an approximate analysis techniques used in electronic circuit design to determine the corner frequency of complex circuits (citing the Wikipedia article on OCTC). As for the criterion of the approximation validity, the Wikipedia article states that a fairly large ratio of \$τ_1/τ_2\$ is needed for accuracy.

From the Wiki article formulas one can see that the time constants \$τ_1, τ_2\$ are the inverse (and negated) values of the transfer function poles, $$ s_{1,2} = -1/τ_{1,2} $$ The article uses an imaginary variable \$j\omega\$, I use a Laplace domain variable \$s\$, which is more convenient for an analysis of capacitive circuits with their pure real poles/zeros.

For the circuit of the Practical Techniques.. article, the time constant ratio value is about two, so OCTC gives only coarse estimation. The pole and zero cancellation method, when used for calculation of the component values, solves some kind of an inverse problem and sowhich is not well conditioned as it is very sensitive to the precision of pole and zero values. For illustration of potential complications, look atnotice the transfer functionuncertainty of the feedback circuit discussed in the Practical Techniques.. article withTF zero positions easily shiftedlocated at potentially gradual TF curve slopes.

TF570p

Here, TF is computed for the inloop frequency compensation circuit with component values Rout = 50, Rx = 25, Rf = 20K, Rin = 10K, CL = 100n and Cf = 570p. Pole/zero pair values are -262839/-271047 and -133494/-129452. When Cf value tends to 561.096382331p, the pole values tend to -267000 and -133500, and the transfer function tend to become constant. Try and compare this exact pole/zero values with those computed by the formulas of the Practical Techniques.. article.

You can find an exact solution for the inloop frequency compensation feedback circuit in my answer to the electronics.SE question Understanding on frequency compensation on driving capacitive loads with an op-amp.

The authors of Analog's article Practical Techniques to Avoid Instability Due to Capacitive Loading correctly compute TF poles and zeroes of the inloop compensation circuit feedback, applying OCTC. What they do in error is that they use a pole zero cancellation method for computing the feedback capacitor value required to flatten the transfer function best.

The OCTC method used in the Practical Techniques.. article is an approximate analysis techniques used in electronic circuit design to determine the corner frequency of complex circuits (citing the Wikipedia article on OCTC). As for the criterion of the approximation validity, the Wikipedia article states that a fairly large ratio of \$τ_1/τ_2\$ is needed for accuracy.

From the Wiki article formulas one can see that the time constants \$τ_1, τ_2\$ are the inverse (and negated) values of the transfer function poles, $$ s_{1,2} = -1/τ_{1,2} $$ The article uses an imaginary variable \$j\omega\$, I use a Laplace domain variable \$s\$, which is more convenient for an analysis of capacitive circuits with their pure real poles/zeros.

For the circuit of the Practical Techniques.. article, the time constant ratio value is about two, so OCTC gives only coarse estimation. The pole and zero cancellation method, when used for calculation of the component values, solves some kind of an inverse problem and so it is very sensitive to the precision of pole and zero values. For illustration of potential complications, look at the transfer function of the feedback circuit discussed in the Practical Techniques.. article with zero positions easily shifted at potentially gradual TF curve slopes.

TF570p

TF is computed for the inloop frequency compensation circuit with component values Rout = 50, Rx = 25, Rf = 20K, Rin = 10K, CL = 100n and Cf = 570p. Pole/zero pair values are -262839/-271047 and -133494/-129452. When Cf value tends to 561.096382331p, the pole values tend to -267000 and -133500, and the transfer function tend to become constant. Try and compare this exact pole/zero values with those computed by the formulas of the Practical Techniques.. article.

You can find an exact solution for the inloop frequency compensation feedback circuit in my answer to the electronics.SE question Understanding on frequency compensation on driving capacitive loads with an op-amp.

The authors of Analog's article Practical Techniques to Avoid Instability Due to Capacitive Loading correctly compute TF poles and zeroes of the inloop compensation circuit feedback, applying OCTC. What they do in error is that they use a pole zero cancellation method for computing the feedback capacitor value required to flatten the transfer function best.

The OCTC method used in the Practical Techniques.. article is an approximate analysis techniques used in electronic circuit design to determine the corner frequency of complex circuits (citing the Wikipedia article on OCTC). As for the criterion of the approximation validity, the Wikipedia article states that a fairly large ratio of \$τ_1/τ_2\$ is needed for accuracy.

From the Wiki article formulas one can see that the time constants \$τ_1, τ_2\$ are the inverse (and negated) values of the transfer function poles, $$ s_{1,2} = -1/τ_{1,2} $$ The article uses an imaginary variable \$j\omega\$, I use a Laplace domain variable \$s\$, which is more convenient for an analysis of capacitive circuits with their pure real poles/zeros.

For the circuit of the Practical Techniques.. article, the time constant ratio value is about two, so OCTC gives only coarse estimation. The pole and zero cancellation method, when used for calculation of the component values, solves some kind of an inverse problem which is not well conditioned as it is very sensitive to the precision of pole and zero values. For illustration of potential complications, notice the uncertainty of TF zero positions located at gradual TF curve slopes.

TF570p

Here, TF is computed for the inloop frequency compensation circuit with component values Rout = 50, Rx = 25, Rf = 20K, Rin = 10K, CL = 100n and Cf = 570p. Pole/zero pair values are -262839/-271047 and -133494/-129452. When Cf value tends to 561.096382331p, the pole values tend to -267000 and -133500, and the transfer function tend to become constant. Try and compare this exact pole/zero values with those computed by the formulas of the Practical Techniques.. article.

You can find an exact solution for the inloop frequency compensation feedback circuit in my answer to the electronics.SE question Understanding on frequency compensation on driving capacitive loads with an op-amp.

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V.V.T
V.V.T
  • 4.6k
  • 9
  • 10

The authors of Analog's article Practical Techniques to Avoid Instability Due to Capacitive Loading correctly compute TF poles and zeroes of the inloop compensation circuit feedback, applying the time and transfer constant (TTC) methodOCTC. What they do in error is that they use a pole zero cancellation method for computing the feedback capacitor value required to flatten the transfer function best.

While the advanced methods of the accepted answer can provide a sufficient precision for computing pole/zero values, theThe OCTC and SCTC methodsmethod used in the Practical Techniques.. article areis an approximate analysis techniques used in electronic circuit design to determine the corner frequency of complex circuits (citing the Wikipedia article on OCTC). As for the criterion of the approximation validity, the Wikipedia article on OCTC)states that give only limited precision, especially for zeroes. This electronicsa fairly large ratio of \$τ_1/τ_2\$ is needed for accuracy.SE question

From the Wiki article formulas one can see that the time constants \$τ_1, τ_2\$ are the inverse (and negated) values of the transfer function poles, Understanding on frequency compensation on driving capacitive loads with an op-amp$$ s_{1,2} = -1/τ_{1,2} $$ discusses a technicalThe article uses an imaginary variable How to Drive Large Capacitive Loads with an Op-Amp Circuit by Dr\$j\omega\$, I use a Laplace domain variable \$s\$, which is more convenient for an analysis of capacitive circuits with their pure real poles/zeros. Franco

For the circuit of the Practical Techniques. This How To. article, instead of the time constant ratio value is about two, so OCTC gives only coarse estimation. The pole and zero cancellation method, useswhen used for calculation of the ratiocomponent values, solves some kind of OCTCan inverse problem and SCTCso it is very sensitive to the precision of pole frequencyand zero values in order to calculate. For illustration of potential complications, look at the transfer function of the feedback capacitor value providingcircuit discussed in the best TF flatteningPractical Techniques. That question asks how to rationalize the formula for this ratio. article with zero positions easily shifted at potentially gradual TF curve slopes.

In my answer to that question I went the other way round and derived the formulaTF570p

TF is computed for polethe inloop frequency ratio from an exact formula for feedback capacitance that flattens TF bestcompensation circuit with component values Rout = 50, Rx = 25, Rf = 20K, Rin = 10K, CL = 100n and Cf = 570p. I solvedPole/zero pair values are -262839/-271047 and -133494/-129452. When Cf value tends to 561.096382331p, the feedback circuit equationspole values tend to -267000 and received-133500, and the exact formula for feedback capacitancetransfer function tend to become constant.

The formula Try and compare this exact pole/zero values with those computed by the formulas of the Practical Techniques article: $$ C_f = \left(1+{1 \over {|A_{cl}|}}\right)\left({\frac {R_2+R_1} {{R_2}^2}}\right)C_L R_o $$

Dr. Franco's formula: $$ C_f = (R_o/R_2)(1 + R1/R_2)^2 C_L $$ TF computed with C_f of Dr. Franco's formula:article.

562_5 The "exact" formula: $$ C_f = {\frac {(1 + R_1/R_2)^2} {(R_1/R_2 + R_2/R_o)(1 + R_0 R_1/{R_2}^2)}} C_L $$ TF computed with C_f of the You can find an exact formula:

561.096382331

Dr. Franco's formula provides a TF flatness precision in agreement withsolution for the Ro<<R2,R1 approximation;inloop frequency compensation feedback circuit in my answer to the exact formula gives a perfectly flat TFelectronics.SE question Understanding on frequency compensation on driving capacitive loads with an op-amp.

The authors of Analog's article Practical Techniques to Avoid Instability Due to Capacitive Loading correctly compute TF poles and zeroes of the inloop compensation circuit feedback, applying the time and transfer constant (TTC) method. What they do in error is that they use a pole zero cancellation method for computing the feedback capacitor value required to flatten the transfer function best.

While the advanced methods of the accepted answer can provide a sufficient precision for computing pole/zero values, the OCTC and SCTC methods used in the Practical Techniques article are an approximate analysis techniques used in electronic circuit design to determine the corner frequency of complex circuits (citing the Wikipedia article on OCTC) that give only limited precision, especially for zeroes. This electronics.SE question Understanding on frequency compensation on driving capacitive loads with an op-amp discusses a technical article How to Drive Large Capacitive Loads with an Op-Amp Circuit by Dr. Franco. This How To article, instead of the pole zero cancellation method, uses the ratio of OCTC and SCTC pole frequency values in order to calculate the feedback capacitor value providing the best TF flattening. That question asks how to rationalize the formula for this ratio.

In my answer to that question I went the other way round and derived the formula for pole frequency ratio from an exact formula for feedback capacitance that flattens TF best. I solved the feedback circuit equations and received the exact formula for feedback capacitance.

The formula of the Practical Techniques article: $$ C_f = \left(1+{1 \over {|A_{cl}|}}\right)\left({\frac {R_2+R_1} {{R_2}^2}}\right)C_L R_o $$

Dr. Franco's formula: $$ C_f = (R_o/R_2)(1 + R1/R_2)^2 C_L $$ TF computed with C_f of Dr. Franco's formula:

562_5 The "exact" formula: $$ C_f = {\frac {(1 + R_1/R_2)^2} {(R_1/R_2 + R_2/R_o)(1 + R_0 R_1/{R_2}^2)}} C_L $$ TF computed with C_f of the exact formula:

561.096382331

Dr. Franco's formula provides a TF flatness precision in agreement with the Ro<<R2,R1 approximation; the exact formula gives a perfectly flat TF.

The authors of Analog's article Practical Techniques to Avoid Instability Due to Capacitive Loading correctly compute TF poles and zeroes of the inloop compensation circuit feedback, applying OCTC. What they do in error is that they use a pole zero cancellation method for computing the feedback capacitor value required to flatten the transfer function best.

The OCTC method used in the Practical Techniques.. article is an approximate analysis techniques used in electronic circuit design to determine the corner frequency of complex circuits (citing the Wikipedia article on OCTC). As for the criterion of the approximation validity, the Wikipedia article states that a fairly large ratio of \$τ_1/τ_2\$ is needed for accuracy.

From the Wiki article formulas one can see that the time constants \$τ_1, τ_2\$ are the inverse (and negated) values of the transfer function poles, $$ s_{1,2} = -1/τ_{1,2} $$ The article uses an imaginary variable \$j\omega\$, I use a Laplace domain variable \$s\$, which is more convenient for an analysis of capacitive circuits with their pure real poles/zeros.

For the circuit of the Practical Techniques.. article, the time constant ratio value is about two, so OCTC gives only coarse estimation. The pole and zero cancellation method, when used for calculation of the component values, solves some kind of an inverse problem and so it is very sensitive to the precision of pole and zero values. For illustration of potential complications, look at the transfer function of the feedback circuit discussed in the Practical Techniques.. article with zero positions easily shifted at potentially gradual TF curve slopes.

TF570p

TF is computed for the inloop frequency compensation circuit with component values Rout = 50, Rx = 25, Rf = 20K, Rin = 10K, CL = 100n and Cf = 570p. Pole/zero pair values are -262839/-271047 and -133494/-129452. When Cf value tends to 561.096382331p, the pole values tend to -267000 and -133500, and the transfer function tend to become constant. Try and compare this exact pole/zero values with those computed by the formulas of the Practical Techniques.. article.

You can find an exact solution for the inloop frequency compensation feedback circuit in my answer to the electronics.SE question Understanding on frequency compensation on driving capacitive loads with an op-amp.

deleted 285 characters in body
Source Link
V.V.T
V.V.T
  • 4.6k
  • 9
  • 10

The authors of Analog's article Practical Techniques to Avoid Instability Due to Capacitive Loading correctly compute TF poles and zeroes of the inloop compensation circuit feedback, applying the time and transfer constant (TTC) method. What they do in error is that they use a pole zero cancellation method for computing the feedback capacitor value required to flatten the transfer function best.

While the advanced methods of the accepted answer can provide a sufficient precision for computing pole/zero values, the OCTC and SCTC methods used in the Practical Techniques article are an approximate analysis techniques used in electronic circuit design to determine the corner frequency of complex circuits (citing the Wikipedia article on OCTC) that give only limited precision, especially for zeroes. This electronics.SE question Understanding on frequency compensation on driving capacitive loads with an op-amp discusses a technical article How to Drive Large Capacitive Loads with an Op-Amp Circuit by Dr. Franco. This How To article, instead of the pole zero cancellation method, uses the ratio of OCTC and SCTC pole frequency values in order to calculate the feedback capacitor value providing the best TF flattening. That question asks how to rationalize the formula for this ratio.

In my answer to that question I went the other way round and derived the formula for pole frequency ratio from an exact formula for feedback capacitance that flattens TF best. I solved the feedback circuit equations and received the exact formula for feedback capacitance.

The formula of the Practical Techniques article: $$ C_f = \left(1+{1 \over {|A_{cl}|}}\right)\left({\frac {R_2+R_1} {{R_2}^2}}\right)C_L R_o $$ The authors write that the factor \$\left(1 + {1 \over |A_{cl}|}\right)\$ is added "by experimenting". But \$A_{cl} = 1 + R_2/R_1\$ and, for moderate R_2/R_1 values, the "experimental" factor fails to compensate the extra \$(1 + R1/R_2)\$ of both Dr. Franco's and the exact formulas.

Dr. Franco's formula: $$ C_f = (R_o/R_2)(1 + R1/R_2)^2 C_L $$ TF computed with C_f of Dr. Franco's formula:

562_5 The "exact" formula: $$ C_f = {\frac {(1 + R_1/R_2)^2} {(R_1/R_2 + R_2/R_o)(1 + R_0 R_1/{R_2}^2)}} C_L $$ TF computed with C_f of the exact formula:

561.096382331

Dr. Franco's formula provides a TF flatness precision in agreement with the Ro<<R2,R1 approximation; the exact formula gives a perfectly flat TF.

The authors of Analog's article Practical Techniques to Avoid Instability Due to Capacitive Loading correctly compute TF poles and zeroes of the inloop compensation circuit feedback, applying the time and transfer constant (TTC) method. What they do in error is that they use a pole zero cancellation method for computing the feedback capacitor value required to flatten the transfer function best.

While the advanced methods of the accepted answer can provide a sufficient precision for computing pole/zero values, the OCTC and SCTC methods used in the Practical Techniques article are an approximate analysis techniques used in electronic circuit design to determine the corner frequency of complex circuits (citing the Wikipedia article on OCTC) that give only limited precision, especially for zeroes. This electronics.SE question Understanding on frequency compensation on driving capacitive loads with an op-amp discusses a technical article How to Drive Large Capacitive Loads with an Op-Amp Circuit by Dr. Franco. This How To article, instead of the pole zero cancellation method, uses the ratio of OCTC and SCTC pole frequency values in order to calculate the feedback capacitor value providing the best TF flattening. That question asks how to rationalize the formula for this ratio.

In my answer to that question I went the other way round and derived the formula for pole frequency ratio from an exact formula for feedback capacitance that flattens TF best. I solved the feedback circuit equations and received the exact formula for feedback capacitance.

The formula of the Practical Techniques article: $$ C_f = \left(1+{1 \over {|A_{cl}|}}\right)\left({\frac {R_2+R_1} {{R_2}^2}}\right)C_L R_o $$ The authors write that the factor \$\left(1 + {1 \over |A_{cl}|}\right)\$ is added "by experimenting". But \$A_{cl} = 1 + R_2/R_1\$ and, for moderate R_2/R_1 values, the "experimental" factor fails to compensate the extra \$(1 + R1/R_2)\$ of both Dr. Franco's and the exact formulas.

Dr. Franco's formula: $$ C_f = (R_o/R_2)(1 + R1/R_2)^2 C_L $$ TF computed with C_f of Dr. Franco's formula:

562_5 The "exact" formula: $$ C_f = {\frac {(1 + R_1/R_2)^2} {(R_1/R_2 + R_2/R_o)(1 + R_0 R_1/{R_2}^2)}} C_L $$ TF computed with C_f of the exact formula:

561.096382331

Dr. Franco's formula provides a TF flatness precision in agreement with the Ro<<R2,R1 approximation; the exact formula gives a perfectly flat TF.

The authors of Analog's article Practical Techniques to Avoid Instability Due to Capacitive Loading correctly compute TF poles and zeroes of the inloop compensation circuit feedback, applying the time and transfer constant (TTC) method. What they do in error is that they use a pole zero cancellation method for computing the feedback capacitor value required to flatten the transfer function best.

While the advanced methods of the accepted answer can provide a sufficient precision for computing pole/zero values, the OCTC and SCTC methods used in the Practical Techniques article are an approximate analysis techniques used in electronic circuit design to determine the corner frequency of complex circuits (citing the Wikipedia article on OCTC) that give only limited precision, especially for zeroes. This electronics.SE question Understanding on frequency compensation on driving capacitive loads with an op-amp discusses a technical article How to Drive Large Capacitive Loads with an Op-Amp Circuit by Dr. Franco. This How To article, instead of the pole zero cancellation method, uses the ratio of OCTC and SCTC pole frequency values in order to calculate the feedback capacitor value providing the best TF flattening. That question asks how to rationalize the formula for this ratio.

In my answer to that question I went the other way round and derived the formula for pole frequency ratio from an exact formula for feedback capacitance that flattens TF best. I solved the feedback circuit equations and received the exact formula for feedback capacitance.

The formula of the Practical Techniques article: $$ C_f = \left(1+{1 \over {|A_{cl}|}}\right)\left({\frac {R_2+R_1} {{R_2}^2}}\right)C_L R_o $$

Dr. Franco's formula: $$ C_f = (R_o/R_2)(1 + R1/R_2)^2 C_L $$ TF computed with C_f of Dr. Franco's formula:

562_5 The "exact" formula: $$ C_f = {\frac {(1 + R_1/R_2)^2} {(R_1/R_2 + R_2/R_o)(1 + R_0 R_1/{R_2}^2)}} C_L $$ TF computed with C_f of the exact formula:

561.096382331

Dr. Franco's formula provides a TF flatness precision in agreement with the Ro<<R2,R1 approximation; the exact formula gives a perfectly flat TF.

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V.V.T
V.V.T
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  • 9
  • 10