1The operational amplifier• The operational amplifier or op amp is very important element in low to moderate-frequency amplifier applications.• A simple model can be used to this complex device.• The model can be applied in calculating input impedance, output impedance, and voltage gain of the popular inverting and non inverting amplifier stages.• An operational amplifier or op amp might include 20 BJT or MOS transistors and 20 resistors.• An understanding of the complex circuitry within the op amp is not necessary to use this amplifying circuit in the construction of an amplifier.23−4Ideal Op-Amp Characteristics1. Internal differential gain Aodis infinite.2. Differential input voltage (v2-v1) is zero.3. Effective input resistance is infinite (i1and i2are zero).4. Output resistance is zero so output voltage is connected directly to dependent voltage source.5Chapter Goals• Understand behavior and characteristics of ideal operational amplifiers (op amps)• Study non-ideal op-amp behavior• Demonstrate circuit analysis techniques for ideal and non-ideal op amps• Characterize inverting, non-inverting, summing and instrumentation amplifiers, voltage follower and integrator• Learns factors involved in circuit design using op ampsIdeal Operational Amplifier• The ideal op amp is a special case of an ideal differential amplifier with infinite gain, infinite Ridand zero Ro.– If A is infinite, vidis zero for any finite output voltage.– Infinite input resistance Ridforces input currents i+and i-to be zero.• The ideal op amp has the following assumptions:– Infinite common-mode rejection, power supply rejection, open-loop bandwidth, output voltage range, output current capability and slew rate– Zero output resistance, input-bias currents and offset current, input-offset voltage.vid=vOA and limA→∞ vid=0Close loop6i1 = i2V0=V1-i2R2=0 - (VI/R1)R2If the op amp open loop gain is finite (non ideal op amp)7ExampleFor the circuit given in Fig., design an inverting op-amp such that Av= -15 and the input resistance Ri= 20 kΩ. Assume an ideal voltage source.8i1i1i1=VI/R1, this current also flow through the capacitor, causing charge to accumulate on VC.At time t, the charge Q at the capacitance equal to dttit)(01∫Because i=Q/t and the voltage acrossthe capacitor is dttict)(101∫Because Q=CV. If initial voltage (t=0) on C is denoted VCdtticVtVtCC)(1)(01∫+=Now the output voltage VO=-VC(t)dttiCVVtCO)(101∫−−=dttVCRVVtICO)(10∫−−=In terms of the voltageThus the circuit provides an output voltage that is proportional to timeintegral of the input.9Noninverting Op-Amp121RRvvAiov+==Between (1) and (2) there is a virtual short circuit (v1 = v2)We know the current I is the rate of change of chargeiii=dQ/dt, also Q=CVdtdvCvCdtdiII 11)( ==Since A is a virtual groundAdRdtdvCiRvIO)(.22−=−=dttdvCRvIO)(12−=Voltage Follower11112=∞⇒+==viovARIfRRvvA Voltage follower is used as an impedance transformer or a buffer, where Zin⇒ ∞, Zout≅ 0Voltage Follower010.RRRvvSLLIO≅+=1≅IOvvSever loading effect Almost zero loading effect10Chapter FifteenApplications and Design of Integrated CircuitsPassive and active filters• Filters are building blocks of communication and instrumentations.• The oldest technology based on inductors and capacitors are called passive LC filters, which are incompatible with any of the modern techniques for assembling electronic systems.• Active-RC filters utilize op amp together with resistors and capacitors.• At present, the most viable approach for realizing fully integrated monolithic filters is the switch capacitance techniques.Active filters11Uses of the filters• Some of the uses are listed below:• in electronic power supply ripple smoothing• as tuned circuits in RF stages• for selection of particular sideband as in SSB transmitters• for harmonic frequency suppression in transmitters• As wave trap for eliminating undesirable signal from radio and TV receivers• for improving high and low frequency response in video amplifier• for restricting audio frequency band pass in SSB transmitters• For eliminating undesirable frequency from motors, generators and other electrical and electronic equipment.One pole active filters• Usually, passive filters suffers from loading effects, substantially reducing the maximum gain from the unity.• Loading effect can be reduced by using active filters.12(cont.)13(cont.) (cont.)14above equationBasic principle of the switched-capacitor filter technique. (a) Active-RC integrator. (b) Switched-capacitor integrator. (c) Two-phase clock (nonoverlapping). (d) During φ1, C1charges up to the current value of viand then, during φ2, discharges into C2.15There are number of ways to solve this problem; perhapsthe easiest is using the principle of superposition and virtual short concept.To apply superposition we first reduce VI2=0(cont.)Next, we reduce the VI1=0 and evaluate the corresponding output voltageVO2R3 and R4 form a voltage divider. Therefore,orThe superposition principle tells us that the output voltage VO is equal to the sum ofVO1and VO2.16What is the condition under which this circuit will act as a difference amplifier?Let VI1=VI2⇒VO=0⇒Which is clearly that of a difference amplifierwith a gain of R2/R1Differential input resistanceWe know the condition for difference amplifier⇒ R1=R3and R2=R4V2-V1=Since two input of the op amp track each other in potential, we may write a loop equationExampleFor the difference amplifier shown in Fig. if R1= R3= 10 kΩ, R2= 20 kΩ, and R4= 21 kΩ, determine vowhen (a) vI1= +1 V, vI2= -1 V, (b) vI1= vI2= +1 V,17• An electronic oscillator may be define in any one of the following four ways:i) It is a circuit which convert dc energy into ac energy at a very high frequencyii) It is an electronic source of alternating current or voltage having sine, square or sawtooth or pulse shapesiii) It is circuit which generates an ac output signals without requiring any externally applied input signal.iv) It is an unstable amplifier.Classification of Oscillators• Electronic oscillators may be broadly divided into following two groups:i) sinusoidal (or harmonic) oscillators-which produce an output having sine wave formii) non- sinusoidal (or relaxation) oscillators-they produce an output which has square, rectangular or sawtooth wave form, employ circuit building blocks known as multivibrators.18oscillationsThe