Differential Amplifiers and Frequency responseD. W. ParentEE 122EE 122The single opamp difference amplifier is a good place to start tlki btdiff lifi bt t ti ltalking about difference amplifiers, but not practical• Some signals have a large common part to the signal that does not contain information.Some times the common signal has a frequency component!1 V common signal1 volt with .1 AC signalThe single opamp difference amplifier is a good place to start tlki btdiff lifi bt t ti ltalking about difference amplifiers, but not practical• Looks perfect, but this is sensitive to matching of R2 to R4 and R3 to R1.1 V common signalSome times the common signal has a frequency component!1 volt with .1 AC signal1V common removed, AC amplified by 10Use superposition to derive circuit’s functionUse superposition to derive circuit s functionVout=vI2(1+R2/R1)‐vI1R2/R1The difference is not amplified!First take out R4 Short vI2, then Vout=‐vI1xR2/R1 Short vI1, then Vout=vI2(1+R2/R1)No ChangeIf R4=R2, and R1=R1 then Vout=vI2xR2/R1 Voltage DividerVout=R2/R1(vI2‐Vi1)What is the low est CMRR if the Resistors can vary by 10%?10%?• Looks perfect, but this is sensitive to matching of R2 to R4 and R3 to R1.CMRR=20log(|Ad|/|Acm|) Ad=R2/R1Acm=(R4/(R4+R3))(1‐R2R3/R1R4)If each resistor can have two states (+10% of nom or ‐10% of nom), and there are 4 resistors,There will be 16 different combinations to try.What is the low est CMRR if the Resistors can vary by 10%?10%?• Looks perfect, but this is sensitive to matching of R2 to R4 and R3 to R1.R1 tol R2 tol R3 tol R4 tol R1 nom R2 nom R3 nom R4 nom R1 R2 R3 R4 AD ACM CMRR‐10 ‐10 ‐10 ‐10 1.00E+04 1.00E+05 1.00E+04 1.00E+05 9.00E+03 9.00E+04 9.00E+03 9.00E+04 1.00E+01 0.00E+00 #DIV/0!‐10 ‐10 ‐10 10 1.00E+04 1.00E+05 1.00E+04 1.00E+05 9.00E+03 9.00E+04 9.00E+03 1.10E+05 1.00E+01 1.68E‐01 35.49034‐10 ‐10 10 ‐10 1.00E+04 1.00E+05 1.00E+04 1.00E+05 9.00E+03 9.00E+04 1.10E+04 9.00E+04 1.00E+01 ‐1.98E‐01 34.06583‐10 ‐10 10 10 1.00E+04 1.00E+05 1.00E+04 1.00E+05 9.00E+03 9.00E+04 1.10E+04 1.10E+05 1.00E+01 1.01E‐16 339.9196‐10 10 ‐10 ‐10 1.00E+04 1.00E+05 1.00E+04 1.00E+05 9.00E+03 1.10E+05 9.00E+03 9.00E+04 1.22E+01 ‐2.02E‐01 35.63511‐10 10 ‐10 10 1.00E+04 1.00E+05 1.00E+04 1.00E+05 9.00E+03 1.10E+05 9.00E+03 1.10E+05 1.22E+01 0.00E+00 #DIV/0!‐10 10 10 ‐10 1.00E+04 1.00E+05 1.00E+04 1.00E+05 9.00E+03 1.10E+05 1.10E+04 9.00E+04 1.22E+01 ‐4.40E‐01 28.87308‐10 10 10 10 1.00E+04 1.00E+05 1.00E+04 1.00E+05 9.00E+03 1.10E+05 1.10E+04 1.10E+05 1.22E+01 ‐2.02E‐01 35.6351110 ‐10 ‐10 ‐10 1.00E+04 1.00E+05 1.00E+04 1.00E+05 1.10E+04 9.00E+04 9.00E+03 9.00E+04 8.18E+00 1.65E‐01 33.892110 ‐10 ‐10 10 1.00E+04 1.00E+05 1.00E+04 1.00E+05 1.10E+04 9.00E+04 9.00E+03 1.10E+05 8.18E+00 3.06E‐01 28.5545910 ‐10 10 ‐10 1.00E+04 1.00E+05 1.00E+04 1.00E+05 1.10E+04 9.00E+04 1.10E+04 9.00E+04 8.18E+00 0.00E+00 #DIV/0!10 ‐10 10 10 1.00E+04 1.00E+05 1.00E+04 1.00E+05 1.10E+04 9.00E+04 1.10E+04 1.10E+05 8.18E+00 1.65E‐01 33.892110 10 ‐10 ‐10 1.00E+04 1.00E+05 1.00E+04 1.00E+05 1.10E+04 1.10E+05 9.00E+03 9.00E+04 1.00E+01 ‐2.02E‐16 333.89910 10 ‐10 10 1.00E+04 1.00E+05 1.00E+04 1.00E+05 1.10E+04 1.10E+05 9.00E+03 1.10E+05 1.00E+01 1.68E‐01 35.4903410 10 10 ‐10 1.00E+04 1.00E+05 1.00E+04 1.00E+05 1.10E+04 1.10E+05 1.10E+04 9.00E+04 1.00E+01 ‐1.98E‐01 34.06583101010101 00E+041 00E+051 00E+041 00E+051 10E+041 10E+051 10E+041 10E+051 00E+010 00E+00#DIV/0!101010101.00E+041.00E+051.00E+041.00E+051.10E+041.10E+051.10E+041.10E+051.00E+010.00E+00#DIV/0!Lowest CMRRWhat is the low est CMRR if the Resistors can vary by 5%?%?• Looks perfect, but this is sensitive to matching of R2 to R4 and R3 to R1.What is the low est CMRR if the Resistors can vary by 5%?%?• Looks perfect, but this is sensitive to matching of R2 to R4 and R3 to R1.R1 tol R2 tol R3 tol R4 tol R1 nom R2 nom R3 nom R4 nom R1 R2 R3 R4 AD ACM CMRR‐5 ‐5 ‐5 ‐5 1.00E+04 1.00E+05 1.00E+04 1.00E+05 9.50E+03 9.50E+04 9.50E+03 9.50E+04 1.00E+01 0.00E+00 #DIV/0!55551 00E 041 00E 051 00E 041 00E 059 50E 039 50E 049 50E 031 05E 051 00E 018 73E0241 17611‐5‐5‐551.00E+041.00E+051.00E+041.00E+059.50E+039.50E+049.50E+031.05E+051.00E+018.73E‐0241.17611‐5 ‐55‐5 1.00E+04 1.00E+05 1.00E+04 1.00E+05 9.50E+03 9.50E+04 1.05E+04 9.50E+04 1.00E+01 ‐9.48E‐02 40.46505‐5 ‐5 5 5 1.00E+04 1.00E+05 1.00E+04 1.00E+05 9.50E+03 9.50E+04 1.05E+04 1.05E+05 1.00E+01 0.00E+00 #DIV/0!‐55‐5 ‐5 1.00E+04 1.00E+05 1.00E+04 1.00E+05 9.50E+03 1.05E+05 9.50E+03 9.50E+04 1.11E+01 ‐9.57E‐02 41.25164/!‐55‐5 5 1.00E+04 1.00E+05 1.00E+04 1.00E+05 9.50E+03 1.05E+05 9.50E+03 1.05E+05 1.11E+01 0.00E+00 #DIV/0!‐555‐5 1.00E+04 1.00E+05 1.00E+04 1.00E+05 9.50E+03 1.05E+05 1.05E+04 9.50E+04 1.11E+01 ‐2.00E‐01 34.86824‐5 5 5 5 1.00E+04 1.00E+05 1.00E+04 1.00E+05 9.50E+03 1.05E+05 1.05E+04 1.05E+05 1.11E+01 ‐9.57E‐02 41.251645 ‐5 ‐5 ‐5 1.00E+04 1.00E+05 1.00E+04 1.00E+05 1.05E+04 9.50E+04 9.50E+03 9.50E+04 9.05E+00 8.66E‐02 40.382335 ‐5 ‐5 5 1.00E+04 1.00E+05 1.00E+04 1.00E+05 1.05E+04 9.50E+04 9.50E+03 1.05E+05 9.05E+00 1.66E‐01 34.709985 ‐55‐5 1.00E+04 1.00E+05 1.00E+04 1.00E+05 1.05E+04 9.50E+04 1.05E+04 9.50E+04 9.05E+00 0.00E+00 #DIV/0!5 ‐5 5 5 1.00E+04 1.00E+05 1.00E+04 1.00E+05 1.05E+04 9.50E+04 1.05E+04 1.05E+05 9.05E+00 8.66E‐02 40.3823355‐5 ‐5 1.00E+04 1.00E+05 1.00E+04 1.00E+05 1.05E+04 1.05E+05 9.50E+03 9.50E+04 1.00E+01 0.00E+00 #DIV/0!55‐5 5 1.00E+04 1.00E+05 1.00E+04 1.00E+05 1.05E+04 1.05E+05 9.50E+03 1.05E+05 1.00E+01 8.73E‐02 41.17611555‐5 1.00E+04 1.00E+05 1.00E+04 1.00E+05 1.05E+04 1.05E+05 1.05E+04 9.50E+04 1.00E+01 ‐9.48E‐02 40.465055 5 5 5 1.00E+04 1.00E+05 1.00E+04 1.00E+05 1.05E+04 1.05E+05 1.05E+04 1.05E+05 1.00E+01 0.00E+00 #DIV/0!Lowest CMRRInput impedance fixed!Input impedance fixed!BetterBetterBestBestFrequency dependence is easy to understand if we th d it ith idswap the words resistance with