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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.

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Presentation on theme: "Ideal Operational Amplifier analysis and design Ideal OP-Amps: an op-Amp is high gain dc differential amplifier. Ideal characteristics : 1- Gain infinity."— Presentation transcript:

1 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

2 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

3 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

4 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

5 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

6 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

7 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

8 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

9 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

10 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

11 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

12 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

13 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

14 14 Prepared by Dr. Ali Saad King Saud University


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