Operational Amplifiers: Introduction, Models, and Applications

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Dive into the world of operational amplifiers with this comprehensive guide covering topics such as op-amp models, fundamental circuits, comparators, and various application and design examples. Explore why op-amps were originally designed for mathematical operations and how they have evolved to become essential components in modern electronics. Gain insights into ideal and non-ideal op-amp configurations through detailed examples and learn about operational amplifier circuits and their functionalities.

  • Operational Amplifiers
  • Op-Amp Models
  • Applications
  • Electronic Circuits
  • Amplifier Design
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  1. 1 Chapter 4. Operational amplifiers EMLAB

  2. Contents 2 1. Introduction 2. Op-Amp Models 3. Fundamental Op-Amp Circuits 4. Comparators 5. Application Examples 6. Design Examples EMLAB

  3. Why operational amplifiers ? 3 1. Originally, the op-amp was designed to perform mathematical operations such as addition, subtraction, differentiation, and integration. 2. By adding simple networks to the op-amp, we can create these building blocks as well as voltage scaling, current-to-voltage conversion, and myriad more complex applications. EMLAB

  4. 2. Op-amp model 4 Ideal op-amp : ?? , ?? 0, ?0 ??? 0, ??? 0 ??? EMLAB

  5. Example 5 ?? ?? ?? ?? = ?0 ?0 ??+ ?? 1 ??+ ?? EMLAB

  6. Example : unity gain buffer 6 ??= ?(??+ ??+ ??) + ?0??? ??= ???+ ?0??? ???= ??? ?? ?? ???+ ?0??? ???+ ?0??? = = 1 ?(??+ ??+ ??) + ?0??? ?(??+ ??+ ??) + ?0??? ?? ?? EMLAB

  7. Example 4.2 7 Let us determine the gain of the basic inverting op-amp configuration shown in the figure using both the non-ideal and ideal op-amp models ?1 ?? ?1 ?0 ?1 ?2 +?1 +?1 ?? ?2 = 0 ?? +?? ??? ?? = 0 ?0 ?? ?2/?1 1 ?2+1 ?2 ?1 = 1 ?1+1 ?2+1 1 ?2 1 ?2 ? 1 ?? ?? ?? EMLAB

  8. 8 Ideal model ? ? 0 [?] Virtual short ??= ??2 ?? = ?2 ??= ??1, ?? ?1 Step 1. Use the ideal op-amp model: Ao , Ri , Ro= 0. i+= i-=0, v+= v- Step 2. Apply nodal analysis to the resulting circuit. Step 3. Solve nodal equations to express the output voltage in terms of the op-amp input signals. EMLAB

  9. Example 4.3 9 Let us now determine the gain of the basic non-inverting op-amp configuration shown in the figure. ? ?+= ??? ??? ?? =?0 ??? ?? 1 ?? 1 =?0 ??? + ?? ?? ?0 ??? = 1 +?? ?? EMLAB

  10. Example 4.5 10 Consider the op-amp circuit shown in the figure. Let us determine an expression for the output voltage. ?4 ? ?+= ?2 ?3+ ?4 ?1 ? ?1 =? ?? ?2 ??= ? ?2 ?1(?1 ? ) = ?2 ?1?1+ 1 +?2 ?3+ ?4?2=?2 ?4 ?1(?2 ?1) ?1 ( ?4= ?2, ?3= ?1) EMLAB

  11. Example 4.6 11 The circuit shown in the figure is a precision differential voltage-gain device. It is used to provide a single-ended input for an analog-to-digital converter. We wish to derive an expression for the output of the circuit in terms of the two inputs. ?1 ?? ?2 ?2 ?? ?1 +?1 ?? ?1 +?2 ?1 ?? +?1 ?2 ?? +?2 ?2 = 0 = 0 ??= (?1 ?2) 1 +?2 +2?2 ?? ?1 EMLAB

  12. Example 4.7 12 ?1 ?? 10? + 30???=?? 10? ?1 ?2 10? ?1 ?2+ ?1 ??= 2?1 ?2 ?0 +?1 ?? 10? ??= 4 = 0 4= 0 ??= 8?1 4?2 EMLAB

  13. 4.4 Comparators 13 (a) An ideal comparator and (b) its transfer curve. (a) A zero-crossing detector and (b) the corresponding input/output waveforms. EMLAB

  14. Application example 4.11 14 An instrumentation amplifier of the form shown in Fig. 4.26 has been suggested. This amplifier should have high-input resistance, achieve a voltage gain Vo/(V1-V2) of 10, employ the MAX4240 op-amp listed in Table 4.1, and operate from two 1.5 V AA cell batteries in series. Let us analyze this circuit, select the resistor values, and explore the validity of this configuration. ?? 2 ?1 ?2 ?? ?? ?? ?? 2 ?? ?? =?2 ?? ?2 ?? ?1 ?1 =?1 ?2 2 = ??= ?? ?? ? EMLAB

  15. 15 ??= ?1+?1 ??= ?2 ?2 ?(?1 ?2), ?(?1 ?2) ??= 1 +?1 ?1 ?1 ??= ?2 ??1+ 1 +?2 ??2, ?2 ? ? ??= ?? ??= ??= 1 +?1+ ?2 (?1 ?2) ? ?? = 1 +2?1 = 10 ( ?1= ?2) ?1 ?2 ? ?1= 4.5? ??) ? = 100 ? , ?1= 450 ? EMLAB

  16. Design example 4.14 16 We wish to design a weighted-summer circuit that will produce the output Vo= - 0.9V1 - 0.1V2 The design specifications call for use of one op-amp and no more than three resistors. Furthermore, we wish to minimize power while using resistors no larger than 10k . ?? ?1+ ?2= ?? ?1 ?1 +?2 ?2 =0 ?? ? ??= ? ?1?1 ? ?2?2 ? ?+= 0 ? ?1 ? ?2 ? ? = 0.9, = 0.1 ?1= 0.9, ?2= 0.1 ??. ? = 270 [ ], ?1= 300 [ ], ?2= 2.7 [? ], EMLAB

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