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

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

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

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 +I3 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

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

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

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

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

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

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

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

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

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

Prepared by Dr. Ali Saad King Saud University