2 OPERATIONAL AMPLIFIERS THE IDEAL OPERATIONAL AMPLIFIER An ideal operational amplifier is a dependent voltage source whose output voltage outVrelative to ground is proportional to difference between its two input voltages 1inV and 2inV . ()21out V in inVAVV=− [0-1] 21in inVV−is referred to as differential input voltage and denoted asdV. 21din inVV V=− [0-2] The proportionality factorVAis the differential gain which also referred to as open-loop gain. The input terminal designated by minus sign ""−is called inverting terminal. The output of op-amp outVdue to signal which find its way to inverting terminal is 180out of phase with input signal. 2out V inVAV=− [0-3]2 OPERATIONAL AMPLIFIERS Chapter 2 The input terminal designated by plus sign ""+is called the non-inverting terminal. The output of op-amp outVdue to signal which find its way to non-inverting terminal is in phase with input signal. 1out V inVAV= [0-4] +−non inverting−invertingoutVdV++−−±±1inV2inV0VA< Figure 2-1: Ideal operational amplifier The operational amplifier, op-amp amplifies the difference between the voltage signals applied at its two input terminals and amplifies it by gain VA as the output voltage. 12inVVV=− [0-5] ()12out V in VVAVAVV== − [0-6] ±++−−inVVinAV−+−outV Figure 2-2 : Low frequency equivalent circuit of operational amplifier The open loop gain is very high and is frequency independent VA=∞ [0-7]Chapter 2 MICROELECTRONIC CIRCUITS 3 The voltage drop across the two terminals is zero. 21in inVV= [0-8] The input resistance is infinite inR=∞ [0-9] Since for an ideal op-amp, input resistance inR is infinite, the current flow to Inverting as well as non-inverting terminals is zero. 1200IandI== [0-10] The output resistance is negligible. 0outR= [0-11] The bandwidth is infinite BW=∞ [0-12] Power supply sensitivity is zero 0PSS= [0-13] Common mode rejection ratio is very large. CMRR=∞. [0-14] (common mode rejection ratio 0outV=when 12in inVV= Current Constraint: No current flows through any of the two op-amps input terminals. Voltage Constraint:4 OPERATIONAL AMPLIFIERS Chapter 2 No voltage drops across the two terminals. When 12in inVV= then 0outV = leads to output resistanceoutR,to be zero 0outR= [0-15] Ideal operational amplifier characteristics: Input resistance inR=∞ Output resistance 0outR= Voltage gain VA=∞ Bandwidth BW=∞ Output voltage 120outVwhenVV== Table 2-1: Ideal operational amplifier characteristic OPERATIONAL AMPLIFIER BASIC CONFIGURATION: The operational amplifier provides amplification, but the gain of operational amplifiers that are fabricated under the same condition widely varies. The gain of an op-amp changes as its operating temperature or its power supply changes. For example, the manufacturer nominal gain of 741 is 200,000 but can vary between 150,000 to 250,000. Also different applications need different gains. It is impractical to manufacture wide variety of operational amplifiers to accommodate large selection of gains. For these reasons it is desirable to build an amplifier circuit whose gain is independent of the gain of the operational amplifier and its gain will be determined by external components. A form of feedback amplifier should be employed. Operational amplifier circuits are classified into two basic configurations: inverting amplifier, and non-inverting amplifier, depending on the applied input voltages. The Inverting Amplifier: Non-inverting terminal of the inverting amplifier is grounded . The input voltage inVis applied through the resistor 1Rto the inverting terminal as shown in figure 2-3; and a resistor 2R connect the output to the inverting input that supplies negative feedback. Negative feedback is produced when some of the output signal is reintroduced back to the input out of phase with original input.Chapter 2 MICROELECTRONIC CIRCUITS 5 inV++−−2R1RoutV±0NV=loadRoutR0IV=2I1IinRoutILI Figure 2-3: The inverting amplifier configuration The closed loop gain is defined as; outinVGV [0-16] Since voltage drop across the inverting terminal IVand non-inverting terminal NVis zero. 0outNIVVVVA−=  [0-17] Then 0NIVV== and IVis virtual ground. The current flow through resister 1Ris 11in I inIVV VIRR−=  [0-18] Since the current cannot flow through inverting terminals,12II=.The output voltage is 22 210inout NVVVIR RR=− =− [0-19] The closed-loop gain6 OPERATIONAL AMPLIFIERS Chapter 2 21outinVRGVR==− [0-20] is independent of open loop gain VAof op-amp and load resistance loadR The input resistance inRis 11in ininininVVRRVIR=== [0-21] Output resistance is negligible,0outR= , because of ideal voltage source ()00VI NVAVV=−= at the output. The output current outIwhich is supplied by op-amp is 2out LIII=− [0-22] 2out outoutloadVVIRR=+ [0-23] outIis function of load resistance loadRas well as feedback resistor2R The inverting voltage amplifier equivalent circuit is shown in the figure 2-4 ±++−−1inRR=inVoutV21inRVR−0outR= Figure 2-4: The inverting op-amp equivalent circuit Example 2.1: In the circuit in figure 2-5. calculate the closed loop gain G, input resistance inRand output resistanceoutR.Chapter 2 MICROELECTRONIC CIRCUITS 7 inV++−−10kΩ1kΩoutV±0NV=10kΩoutR0IV=2I1IinRoutILI1kΩ1kΩ Figure 2-5: The inverting amplifier circuit Solution: 11inVIR= [0-24] 2121out inRVIR VR=− =− [0-25] 10101outinVkVVk=− =− [0-26] 1111in inininVVRRkVIR≡===Ω [0-27] 0outR= [0-28] Example 2.2: Find the high-gain of the high-gain circuit of Figure 2-6.8 OPERATIONAL AMPLIFIERS Chapter 2 inV++−−3R1RoutV±0NV=0IV=4I1I2R6R4R3I2I Figure 2-6: High gain realization op-amp circuit Solution: Invoking the voltage constraint which implies the voltage drop across the two terminals are zero. 0INVV== [0-29] 11inVIR= [0-30] 12II= [0-31] 23221inRVRI VR=− =− [0-32] 323313inVRIVRRR==− [0-33] 423III=− [0-34]Chapter 2 MICROELECTRONIC CIRCUITS 9 224113 1 31in ininVVRRIVRRR R R=+ = + [0-35] 44 3outVRIV=−+ [0-36] 42421131out in in inRRRRVVVVRRRR=− − − [0-37] 2441321outinVRRRGVRRR==− ++ [0-38] If resistance 4Ris short (40R=) and 3Ris open()3R=∞, then 21outinVRGVR==− [0-39] Comparison between equation 2-38 and 2-39 indicates that the gain of the circuit of figure 2-6 increases by factor 44321RRRR++ [0-40] Or in the other word the