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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) 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 - + i It is widely used in instrumentation Prepared by Dr. Ali Saad King Saud University

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**Prepared by Dr. Ali Saad King Saud University**

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 Prepared by Dr. Ali Saad King Saud University

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**Prepared by Dr. Ali Saad King Saud University**

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 - + if R2 R3 If=I1 +I2 +I If=-Vo/Rf ; I1=V1/R1; I2=V2/R2; I3=V3/R3 Vo=-Rf (V1/R1+V2/R2+V3/R3); Prepared by Dr. Ali Saad King Saud University

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**Non Inverting Amplifier**

vi vo Ri Rf - + i i=vi/Ri ; V0=i(Rf+Ri); Vo/vi=i(Rf+Ri)/iRi = 1+ Rf/Ri; vo -13 V +13 V Slope=1+Rf/Ri +VT -VT Input Output Plot vi 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 i v1 v3 vo R1 R2 - + v2 R1 R2 Prepared by Dr. Ali Saad King Saud University

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**Prepared by Dr. Ali Saad King Saud University**

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

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**Prepared by Dr. Ali Saad King Saud University**

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. Prepared by Dr. Ali Saad King Saud University

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**Non Inverting Op-Amp input resistance Voltage Follower:**

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. - + Vid Vo vin Prepared by Dr. Ali Saad King Saud University

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**Bode plot and Bandwidth limitation**

100 80 AMP(dB) 60 40 20 10 100 1k 10k 100k 1M 10M 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 funity=Gain-Band width=10Mhz. GBW=gain(numerical)x frequency at any point of the curve (Bode plot). GBW=Av (num) xBW; Prepared by Dr. Ali Saad King Saud University

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**Prepared by Dr. Ali Saad King Saud University**

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/ Funity=frequency at which Aol(num)=1; 176K 1.76K vi - vo + Prepared by Dr. Ali Saad King Saud University

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**Prepared by Dr. Ali Saad King Saud University**

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