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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 1 Measuring Zo in SPICE Preferred Test Circuits and Why? Brought to you by: The Wizard of Zo

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 2 Measuring Zo in SPICEAol Test

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 3 Measuring Zo in SPICEAol Test

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 4 Measuring Zo in SPICE Closed Loop Gain

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 5 Measuring Zo in SPICE Closed Loop Gain

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 6 Measuring Zo in SPICE 1/Beta Test

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 7 Measuring Zo in SPICE 1/Beta Test

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 8 Measuring Zo in SPICE Aol, 1/Beta, Closed Loop Gain

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 9 Measuring Zo in SPICE Final Zo Test Circuit - Unloaded

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 10 Measuring Zo in SPICE Final Zo (dB) Test Circuit - Unloaded Below fx Zo is not valid fx

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 11 Measuring Zo in SPICE Final Zo (ohms) Test Circuit - Unloaded fx Below fx Zo is not valid

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 12 Measuring Zo in SPICE Final Zo Test Circuit – Loaded Source

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 13 Measuring Zo in SPICE Final Zo Test Circuit – Loaded Source Below fx Zo is not valid fx

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 14 Measuring Zo in SPICE Final Zo Test Circuit – Loaded Sink

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 15 Measuring Zo in SPICE Final Zo Test Circuit – Loaded Sink fx Below fx Zo is not valid

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 16 Measuring Zo in SPICE Final Zo Test Circuit – Complete Zo Curves Below fx Zo is not valid fx

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 17 Appendix – Ro Derivation Op Amp Model for Derivation of R OUT

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 18 Appendix – Ro Derivation = V FB /V OUT = [V OUT (R I / {R F + R I })]/V OUT = R I / (R F + R I ) R OUT = V OUT /I OUT V O = -V E Aol V E = V OUT [R I /(R F + R I )] V OUT = V O + I OUT R O V OUT = -V E Aol + I OUT R O V OUT = -V OUT [R I /(R F + R I )] Aol+ I OUT R O V OUT + V OUT [R I /(R F + R I )] Aol = I OUT R O V OUT = I OUT R O / {1+[R I Aol/(R F +R I )]} R OUT = V OUT /I OUT =[I OUT R O / {1+[R I A OL /(R F +R I )]}]/I OUT R OUT = R O / (1+Aol ) Derivation of R OUT (Closed Loop Output Resistance)

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 19 Appendix – Ro Derivation OPA353 Specifications R O = 40 R OUT (@1MHz, G=10) = 10 Aol @1MHz = 29.54dB = x30

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 20 Appendix – Ro Derivation OPA353 R OUT Calculation R O = 40 R OUT (@1MHz, G=10) = 10 Aol @10mHz = 29.54dB = x30 V OUT = I OUT R O / {1+[R I Aol/(R F +R I )]}

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Tim Green, Linear Applications 520-750-2193 green_tim@ti.com 21 Appendix – Ro Derivation R OUT vs R O R O does not change when feedback is used to close the loop Closed loop feedback forces V O to increase/decrease The increase/decrease in V O appears at V OUT as a reduction in R O R OUT is the net effect of R O and closed loop feedback controlling V O

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