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Hello everyone, I’m Fan Xiaowei who is sharing today. I am very happy to have this opportunity to share the basic knowledge of operational amplifiers. First of all, thanks to Ali for giving me such a sharing opportunity. Operational amplifiers are simple and very simple. They are very basic compared to other advanced and complex circuits, but they are also the soul of analog circuits. So here I'm going to do some introductions for everyone. Sharing this time I feel very helpful for beginners, but for those who have done analog circuitry for many years, these should be very familiar.
Op amps are the soul of analog circuits. Whether we are doing integrated circuit design or circuit applications, as long as it is related to electricity, it is inseparable from the operational amplifier. In school, we learn analog circuits or analog electronics. We are familiar with the concept of "virtuality, shortness, and weakness." But in fact, in the application of the amplifier, only knowing this is not enough, so here I will introduce the relevant knowledge in the field of analog amplifier and the basic knowledge needed to learn the amplifier.
Now we officially begin today’s sharing. First, let’s introduce why we need an amplifier such as an operational amplifier.
Prior to the advent of operational amplifiers, analog amplifiers were already present. Its structure is shown in the figure. This circuit uses a triode to implement inverting amplification. Earlier amplifier circuits were constructed using electronic tubes. The advantage of this circuit is its simple structure and low cost. However, it also has serious drawbacks. First of all, it requires a static operating point, and each circuit needs different operating points and requires separate debugging. Second, this circuit is open-loop amplified, so the gain stability of the circuit is poor.
The previous one is a mathematical model of an operational amplifier. This one shows an example of an actual operational amplifier. Corresponding to the previous PPT, the op amp provides a feed forward gain and the divider resistor provides a feedback network. Here, three main points are mentioned. First, since the feedback coefficient β<1 is constant, it is necessary to make A large in order to ensure that Aβ is much larger than 1 and that the ideal amplifier A can be regarded as infinity. Second, for a resistive feedback network, the feedback coefficient is written in the form of a voltage divider of R1 and R2. It assumes that the negative input of the amplifier should be open circuited. Because according to Kirchhoff's current law, if there is current flowing in the negative input of the amplifier, the feedback coefficient cannot simply be written as a voltage divider. This is what we often call "virtual disconnection." Third, from the forward path, the output voltage can be written as the product of the forward gain A and the error (Vin-βVout). In an actual circuit, the output swing of the amplifier must be limited, and the open loop gain A is infinite. Therefore, the voltages at the positive and negative input terminals of the amplifier can only be equalized. This is an imaginary short circuit.
The design goal of the op amp is this ideal device, but it is difficult to achieve in practice. The design of an actual amplifier is often a compromise of various parameters. Increasing one parameter will sacrifice another parameter.
The second part is about the analysis of the operational amplifier circuit. What knowledge is needed to analyze the operational amplifier? In fact, analog circuits are indeed more difficult to get into and require multidisciplinary intersections, including electronics, control theory, signals and systems, and calculus. But don't be afraid to learn analog circuits because of this, because analog circuit design only uses the basic knowledge of these disciplines at certain times and does not require proficiency.
1. Energy conservation
Energy conservation is a law that must be satisfied by the circuit system. In fact, many people in the work use a lot of complicated analysis methods to analyze the circuit. Finally, it is found that energy conservation is not satisfied. This is an obvious mistake. In fact, the most important conclusion of energy conservation applications in the circuit is the Kirchhoff voltage law.
2. Conservation of charge
Corresponding to the conservation of energy is the conservation of charge, which is often used when doing capacitance-related analysis. In the same way, the most important conclusion of charge conservation applications in the circuit is the Kirchhoff voltage law.
3. Ohm's law
Ohm's law describes the voltage-current relationship between two ports of a resistive device.
The basic method of circuit analysis is Kirchhoff's voltage law and Kirchhoff's current law plus Ohm's law to write the circuit equations and solve them. Of course, when the circuit is too complex, solving the circuit by using this method will be very complicated, so in the circuit analysis, people have also introduced tools such as Thevenin equivalent to simplify the circuit analysis.
5. Voltage Source and Current Source
The ideal voltage and current source is a commonly used model for analysis, but the actual voltage source and current source used have internal resistance.
6. Capacitance and inductance IV relationship
The capacitance-inductance IV relationship is actually the Ohm's law of the capacitive inductance, but due to the physical properties of the capacitive inductance, a differential occurs in the equation. But this is the result of time domain analysis. If we analyze the IV relationship of the capacitive inductor in the frequency domain, we will find that the impedance of the inductor is positive imaginary and the impedance of the capacitor is negative imaginary.
7. The basics of calculus
Sometimes we need to write the equations of the circuit in the time domain. Due to the presence of the capacitive capacitor elements, these equations are often differential equations, so understanding the basics of calculus is necessary.
Ohm's law equations through KCL, KVL, and capacitor resistance. Solve the system of equations. From the above derivation, it can be seen that if these equations are solved in the time domain, complex differential equations must be solved. Is there any way to get the answer simply by solving a simple algebraic equation?
Mathematicians provide a tool called Laplace transform. With Laplace transformation, the time domain differential equation becomes an algebraic equation in the frequency domain. As shown in the definition of the Laplace transform, the writing here is relatively simple. We want to learn more about the need to consult the signal and system books. The above diagram also shows some commonly used functions corresponding to the Laplace transform.
It can be seen that the IV relationship of the capacitive inductance in the time domain is described by a differential equation and in the frequency domain it can be described by an algebraic equation.
The same circuit, we are very simple in the frequency domain analysis. In comparison with the Laplace transformation correspondence table in the above figure, the operation result is returned to the time domain, and it can be found that the two operation methods are equivalent.
Here we introduce Bode diagram, another common tool for analyzing the circuit. Our commonly used Bode diagram consists of two curves—the amplitude-frequency curve and the phase-frequency curve.
Due to the presence of capacitive inductance, the relationship between the input and output of the circuit is often a complex number. We will pay more attention to the complex modes and phases. We often use VOUT/VIN to express the output function of the circuit. The mode of the result is the gain of the circuit. The phase is the phase difference between the phase of the output signal and the phase of the input signal.
In the third part, we introduce the application of operational amplifier circuit analysis.
When analyzing circuits that use operational amplifiers, we often think of an op amp as a black box. Apply the analysis of the short and virtual short circuit concept of the previous analysis circuit. In addition to these two points, in fact, one of the previous analysis is implicit, that is, no delay in input and output, which in some applications need to be focused.
Many circuits with different functions can be built using an operational amplifier.
By combining the concept of virtual short circuits, KCL, KVL, and Ohm's law can analyze these circuits. Non-inverting amplifiers, inverting amplifiers, adders, subtractors, and so on are all the same analytical methods. The difference between them is that the computational complexity has gradually increased, but the method is consistent.
The integrators and differentiators can also be built using op amps. If you look at the analysis in the time domain, you can see that the circuit differential equations are complex, but if you analyze them in the frequency domain using Laplace transforms, you can see that the equations are much simpler. In addition, we also noticed the duality in the integrator-differentiator circuit, and the integrator's capacitor resistance turned into a differentiator.
Finally, we discuss the non-ideal characteristics of op amps and the selection of op amps.
This page shows some of the amplifier classification and selection methods, the figure also shows the characteristics of each type of amplifier, but these parameters are not isolated but crossed together, such as low-power op amp certainly It is low speed.
Today's sharing is here. I would like to thank IC caffee and Yali for providing such a platform for me to share with everyone.
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