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Ideal Operational Amplifier analysis and design Ideal OP-Amps: an op-Amp is high gain dc differential amplifier. Ideal characteristics : 1- Gain infinity Vo=0 when v1=v2 Rd=infinite (input impedance Ro=0 (output impedance is zero) Equivalent Op-Amp circuit Ro Rd A(v2-v1) 1 Prepared by Dr. Ali Saad King Saud University

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Two Basic Rules for design of OP-Amp Rule1: When the Op-Amp output is in its linear range the two inputs are the same voltage. Rule 2: No current flows into either input terminal of the Op-Amp. Inverting Amplifiers vi v1 v2 Ri Rf vo- + It is widely used in instrumentation i 2 Prepared by Dr. Ali Saad King Saud University

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Equation : v2=0; v1=0 by using rule 1. Ohm’s Law: Vi=I. Ri Rule 2 : Vo=-I. Rf=-ViRf/Ri; imply that Vo/Vi=-Rf/Ri; Input output plot of inverting amplifier : The input output plot shows an slope of –Rf/Ri. In the central portion but the output saturate at about ±13 volts. -13 V +13 V Slope=-Rf/Ri +VT -VT 3 Prepared by Dr. Ali Saad King Saud University

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SUMMING Amplifier The Inverting Amplifier may be extended to for m a circuit that yields sum of several input voltages. Each input voltage V1, V2, V3, …Vk is connected to the negative input of the Op- Amp by individual resistor Rk, the conductance 1/Rk is proportional to the desired weighting. v1 v2 v3 R1 Rf vo- + R2 R3 if If=I1 +I2 +I3 If=-Vo/Rf ; I1=V1/R1; I2=V2/R2; I3=V3/R3 Vo=-Rf (V1/R1+V2/R2+V3/R3); 4 Prepared by Dr. Ali Saad King Saud University

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Non Inverting Amplifier i=vi/Ri ; V0=i(Rf+Ri); Vo/vi=i(Rf+Ri)/iRi = 1+ Rf/Ri; -13 V +13 V Slope=1+Rf/Ri +VT-VT vi vo Input Output Plot vi vo Ri Rf - + i 5 Prepared by Dr. Ali Saad King Saud University

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Differential Amplifiers V3=V2 R2/(R1+R2); i=(V1-V3)/R1 = (V3-Vo)/R2; Vo=(V2-V1)R2/R1; Differential Amplifiers v3 vo R1 R2 - + v1 v2 R1 R2 i 6 Prepared by Dr. Ali Saad King Saud University

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Comparators Vi Vref R1 Rf R2 R3 - + Comparator is a circuit that compares the input voltage with some reference voltage. -Vref If R3 =0; V0=+13V if Vi=-Vref Vo flip when Vi+Vref=0; Vi >Vref → Vo=-13V; Vi< Vref → V0=+13V. Vo Vi -13V +13V 7 Prepared by Dr. Ali Saad King Saud University

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Non Inverting Configuration (Real Op-Amp) Negative Feed Back on voltage Gain Vid=Vin-Bvo =Vin -Vf; Vo=Aol (Vin-Bvo); Av=Vo/Vin=Aol/(1+BAol); Ideal Case Aol→ ∞ which imply Av=1/B ; B Aol - + Vo Vin Vf Vid 8 Prepared by Dr. Ali Saad King Saud University

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Non Inverting vi vo Ri Rf - + i Av=1+Rf/R1 Effect of Negative Feed Back on Output Resistance RoF =Ro/(1+B.Aol). For inverting B=R1/Rf; For Non-inverting amplifier B=R1/(R1+Rf); Inverting Amplifier input resistance Rinf=R1 (Without feed back) With Feed Back R’F=Rinf/(Aol+1)≈Rinf/Aol. If Aol very big → R’F≈ Very Small can be neglected. 9 Prepared by Dr. Ali Saad King Saud University

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Non Inverting Op-Amp input resistance RinF=VinRin/Vid=Rin(1+BAol) → input resistance very High. Voltage Follower: Vo=V1 ; the circuit operate like an emitter follower, except that the gain is exactly 1. vin Vo - -+-+ Vid 10 Prepared by Dr. Ali Saad King Saud University

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Bode plot and Bandwidth limitation 10 1001k 10k 100k 1M10M 80 60 40 20 100 AMP(dB) 11 Prepared by Dr. Ali Saad King Saud University

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fc: corner frequency, Break frequency or critical frequency. fc : is defined as frequency at which the gain of the amplifier reduced by 3dB from the zero frequency gain or mid frequency. Midband ranges : from mid frequency to fc : [0,fc]. Example : A certain Op-Amp has Aol =120,000 fc= 100Hz; Determine Amid (dB) and Ac (numerical). Solution : Amid(dB)=20logAol= 20x5,08=101,6dB. Ac(dB)=101,6-3=98.6dB Ac(num)=log-1(Ac(dB)/20)=85000. Ac=0.707 Amid. Unity Gain : When the bode plot cross zero, the frequency at that position is equal to the unity gain. For the OP-Amp of the previous slide f unity =Gain-Band width=10Mhz. GBW=gain(numerical)x frequency at any point of the curve (Bode plot). GBW=Av (num) xBW; 12 Prepared by Dr. Ali Saad King Saud University

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Example Determine Av and BW? The amplifier follow the bode plot of slide 11. Solution : GBW=BWx Av=-176/1.76=-100=40dB. BW=fc=GBW/ F unity =frequency at which Aol(num)=1; vi 1.76K 176K vo- + 13 Prepared by Dr. Ali Saad King Saud University

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