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)
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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 - + i
It is widely used in instrumentation
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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
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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 - + 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);
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5. Non Inverting Amplifiervi 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
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6. 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
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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
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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
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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.
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10. 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
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11. Bode plot and Bandwidth limitation
100 80
AMP(dB) 60 40 20 10
100 1k
10k
100k 1M
10M
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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 funity=Gain-Band width=10Mhz. GBW=gain(numerical)x frequency at any point of the curve (Bode plot).
GBW=Av (num) xBW;
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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/
Funity=frequency at which Aol(num)=1;
176K
1.76K vi - vo +
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