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
1
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
Rf
i
Ri
v1
v2
-
vo
+
It is widely used in instrumentation
Prepared by Dr. Ali Saad King Saud
University
2
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
Slope=-Rf/Ri
+VT
-VT
-13 V
Prepared by Dr. Ali Saad King Saud
University
3
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 OpAmp by individual resistor Rk, the conductance 1/Rk is
proportional to the desired weighting.
if
v1
R1
v2
v3
If=I1 +I2 +I3
Rf
R2
-
vo
+
R3
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
4
Non Inverting Amplifier
Ri
-
vi
i=vi/Ri ;
i
Rf
vo
+
V0=i(Rf+Ri); Vo/vi=i(Rf+Ri)/iRi = 1+ Rf/Ri;
vo +13 V
Input Output Plot
Slope=1+Rf/Ri
-VT
+VT
vi
-13 V
Prepared by Dr. Ali Saad King Saud
University
5
Differential Amplifiers
i
v1
R2
R1
v2
v3
+
R1
vo
R2
V3=V2 R2/(R1+R2); i=(V1-V3)/R1 = (V3-Vo)/R2;
Vo=(V2-V1)R2/R1; Differential Amplifiers
Prepared by Dr. Ali Saad King Saud
University
6
Comparators
R1
Vi
Vref
+
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
7
Non Inverting Configuration (Real Op-Amp)
Negative Feed Back on voltage Gain
Vin
+
Vf
Vid
Aol
Vo
-
B
Vid=Vin-Bvo =Vin -Vf;
Vo=Aol (Vin-Bvo);
Av=Vo/Vin=Aol/(1+BAol);
Ideal Case Aol→∞ which imply Av=1/B;
Prepared by Dr. Ali Saad King Saud
University
8
Non Inverting
i
Rf
Ri
Av=1+Rf/R1
-
vi
+
vo
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
9
Non Inverting Op-Amp input resistance
RinF=VinRin/Vid=Rin(1+BAol) → input resistance very High.
Voltage Follower:
Vid
+
Vo
vin
Vo=V1 ; the circuit operate like an emitter follower,
except that the gain is exactly 1.
Prepared by Dr. Ali Saad King Saud
University
10
Bode plot and Bandwidth limitation
100
AMP(dB)
80
60
40
20
10
100
1k
10k
100k
Prepared by Dr. Ali Saad King Saud
University
1M
10M
11
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
12
Example
Determine Av and BW?
vi
176K
1.76K
-
vo
+
The amplifier follow the bode plot of slide 11.
Solution : GBW=BWx Av
Av=-176/1.76=-100=40dB.
BW=fc=GBW/ Av
Funity=frequency at which Aol(num)=1;
Prepared by Dr. Ali Saad King Saud
University
13
Prepared by Dr. Ali Saad King Saud
University
14