MAY MAY 11, 201 2016: 6: LECTUR LECTURE E NOTES NOTES 1
QUIZZAGAN, Harlee T.1 Department of Physical Sciences, College of Science, University of the Philippines Baguio
*Corresponding author:
[email protected] OPERATIONAL OPERATIONAL AMPLIFIERS: AMPLIFIERS: Golden Rules 1. Voltage Rule: The output attempts to do whatever is necessary to make the voltage difference between between the inputs zero. 2. Current Rule: The inputs draw no current, because they are high impedance. Negative Feedback Feedback - mostly resistors but can be inductors or capacitors. This is needed because without this, the gain is infinite or extremely high but we put negative feedback in order to be able to control the output or gain. The input is connected to the negative terminal of the Op-Amp. Noninverting Amplifier Amplifier - There is no phase shift because input phase is the same as ouput phase. Figure 1: Noninverting Amplifier
is input and it is connected to the positive terminal. terminal . V in is input
There is a negative feedback and a voltage divider. By voltage rule, the inputs should be equal to each other, no matter what happens, such that V f
=
Ri Ri + Rf
V out = V in
(1)
by golden rule. Hence, the voltage gain is: Av =
V out V in
=
Ri + Rf Ri
=1 +
Rf Ri
Voltage Follower Follower - The output is connected to the input which makes them the same. Figure 2: Voltage Follower Follower
1
(2)
This is a unity gain amplifier. Why is it used? Recall buffer circuits in transistor which isolates the left side or input from the right side or output. Similarly, this Op-Amp acts as a electrical isolator or buffer. Inverting Amplifier - Compared to the noninverting amplifier, input is connected to the negative terminal. Figure 3: Inverting Amplifier
By golden rule, the input in the negative terminal should be equal to the input in the positive terminal. Refer to Figure 12-29. The input in the positive terminal is zero (ground) and hence, there is 0 voltage. By current rule, input draws no current. By voltage rule, Op-Amp has to create a current through Rf to make the input difference zero. However, the current cannot proceed from the negative to positive terminal then to ground because the input should draw no current. So instead, it passes through Ri then to the ground since the junction is grounded. Figure 4: Inverting Amplifier: Path of Current
Hence, since the input draws no current: V out Rf
+
V in Ri
=0
⇒
V out V in
=−
Rf Ri
= A v
(3)
REVIEW UNTIL THIS PART OF THE CHAPTER AND LEARN THE CONCEPTS. Possible Applications of Op-Amps/Thesis Prospects 1. Use Op-Amps to amplify the voltages generated by triboelectric devices. 2. Zero Level Detector - Detects at what point does your current have zero signal. Every time there is change in the circuit, there is also a counterpart change in the level. Refer to the figure attached in the following page to analyze this circuit. 3. Non-zero Level Detector - You can have either a battery reference, voltage-divider reference, or a zener diode reference. From these detectors, we can make a function generator since it converts the signal into square waves. 2
Figure 5: Zero Level Detector
Application of Zero Level Detector: - A Wheatstone brdige connected to a non-zero level detector such that if the signal is above the reference voltage (based on a reference temperature from a calibration curve), then the transistor will be switched on but if it is below the reference voltage, it will be switched off. Example: Circuit to tell whether the temperature is exceeding or below a particular temperature. 4. Digitization of Signal Figure 6: Digitization of Signal
ADC circuit such that an input analog signal is converted to digital signal in order to be able to read by a computer. The reference is through the negative terminal. V ref
=
n
8
V in
(4)
5. Summing Amplifier - Inverting amplifier with two inputs such that V out =
(V 1,in + V 2,in )
−
3
(5)
Refer to the book for the derivation of this equation. Since this is an inverting amplifier, expect the output to be negative. More summing amplifiers can be created by adding more inputs. Figure 7: Summing Amplifier
6. Summing Amplifiers with Gain Greater than Unity - If the resistors in the circuit are not already equal, then V out =
−
Rf R
(V 1,in + V 2,in + ... + V n,in )
7. Averaging Amplifier -
Rf R
(6)
1
=
(7)
n
8. Scaling Adder - Each input is being scaled or has its own contribution or weight such that the general expression is given to be and can be applied to any circuit of its kind. V out =
−
Rf R1
V 1,in +
Rf R2
V 2,in + ... +
Rf Rn
V n,in
(8)
9. Integrators - The capacitor is the feedback. If we integrate a square wave, we expect a triangular wave. Recall basic graphing ang integration so as to understand how is this possible. If we integrate a sine signal, then we expect a shifted sine signal or a cosine signal. Since the capacitor is the feedback, it takes time for the current to be gone hence there is a slow response from minimum to maximum and then back to zero again. V C
=
I C C
(9)
t
The rate of the change is simply the slope ∆V out V in =− ∆t Ri C
(10)
10. Differentiator - The resistor and capacitor changed position and that the resistor is at the feedback and is still an inverting amplifier. A triangular wave will be differentiated as a square wave. V out =
−
V C t
Rf C
THE END FOR THE COVERAGE OF THE FOURTH LONG EXAM!! DATE: May 19, 2016, 5:00 - 8:00 p.m. REFERENCES: Electronic Devices by Thomas Floyd, 9th Edition
4
(11)
