Linear Analysis of Amplified Line AC Signals

The amplifier circuit is a nonlinear circuit. This is because the electronic components that make up the circuit are nonlinear. To use it to amplify the signal without distortion, it is necessary to set an appropriate operating point so that the electronic device works in an approximately linear region. This determines that the analysis of the amplifier includes DC analysis and AC analysis. The performance of nonlinear devices for DC signals and AC signals is different. This is the difference between amplifier analysis and general linear circuit analysis. When performing small signal analysis on the amplifier, its circuit model is linear. However, the nonlinearity of electronic devices has always played an important role in the analysis of amplifiers.

Keywords: amplifier circuit; electronic device; linearity; nonlinearity

"Basics of Electronic Technology" is an important technical foundation course for electronic majors. Analog circuits are a difficult course for students to learn and teachers to teach. Amplifiers are the entry basis of analog circuits, and are also the focus and difficulty of "Basics of Electronic Technology". Only by solving this problem can we enter the field of electronic technology. Through teaching practice, the author gradually formed the analysis ideas and principles of amplifiers with the main contradictions of nonlinear devices, linear devices and linear amplification, linear nonlinearity as the main line, and DC analysis and AC analysis as the main content. This has better solved the transition from "Circuits" to "Electronic Technology" and solved the problem of difficulty in getting started with electronic technology.

1 From linear to nonlinear

Electronic circuits are a branch of electric circuits. They are circuits that contain electronic devices. Electronic devices are nonlinear devices, so electronic circuits are nonlinear circuits. "Circuits" generally include a chapter on nonlinear circuits, but the content is small and only briefly introduced, which does not attract enough attention from students. Therefore, the transition from linear circuits to nonlinear circuits must be made at the beginning of the "Basics of Electronic Technology" course.

"Basics of Electronic Technology" starts with the PN junction, which is the basis of semiconductor devices. After discussing the working principle of the PN junction and obtaining the volt-ampere characteristics of the PN junction, we enter the nonlinearity: its volt-ampere characteristic curve is a nonlinear function. Here we must first give the definition of linear resistance, introduce the concepts of DC (static) resistance and AC (dynamic) resistance, and compare linear resistance (the volt-ampere characteristic curve is a straight line passing through the origin, and its DC resistance and AC resistance are equal and a constant) to draw the following important conclusions:

(1) The DC resistance and AC resistance of a nonlinear element at any point on the volt-ampere characteristic curve are generally not equal.

(2) The DC resistance and AC resistance of a nonlinear element are not constants, but vary with different static operating points.

The forward resistance of a PN junction is very small, while the reverse resistance is very large. Therefore, its nonlinearity is often summarized as unidirectional conductivity. A diode is a PN junction, and a transistor is composed of two PN junctions. When it works in the amplification state, the input characteristic is equivalent to the forward characteristic of the PN junction, while the output characteristic is equivalent to the reverse characteristic of the PN junction under the control of minority carrier injection into the base region.

The above is about the nonlinearity of electronic devices. Only with the nonlinear characteristics of electronic devices can we distinguish electronic circuits from general linear circuits, and only then can we understand the working principle of the amplifier, the setting of the static operating point, and the difference between DC analysis and AC analysis.

2 Characteristics of the amplifier circuit caused by nonlinearity

Nonlinear elements often generate new frequency components, that is, nonlinear distortion. This is the primary issue that must be considered in electronic circuits. If the AC signal is directly added to the emitter junction of the transistor (that is, without static bias), due to the unidirectional conductivity of the emitter junction, even if its dead zone voltage and the nonlinearity of the forward characteristics are ignored, serious nonlinear distortion will occur, so that only the positive half cycle is turned on, and the negative half cycle is cut off (Class B working state). Only by shifting the center position of the AC signal upward along the voltage axis, that is, adding a forward bias to the emitter junction, and making the forward bias value greater than the amplitude value of the AC signal, can the PN junction be turned on in both the positive and negative half cycles of the AC signal (Class A working state), and undistorted amplification can be obtained, and two conclusions can be drawn from this:

(1) In order to overcome the nonlinear distortion caused by the unidirectional conductivity of the PN junction, a DC bias signal must be added to the amplifier before the AC signal is added.

(2) There are both DC and AC signals in the amplifier circuit; the circulation loops of the two signals may be different, that is, there are both DC and AC paths; the voltage and current at each point in the amplifier have both DC and AC components, that is, the instantaneous quantity is equal to the DC quantity plus the AC quantity, which determines that the analysis of the amplifier includes two parts: DC analysis and AC analysis. DC analysis is to determine the DC operating point of the amplifier, and AC analysis is to calculate the performance indicators such as the amplification factor, input and output resistance, output power and efficiency, and frequency response. The paths of DC signals and AC signals are different, especially the performance of nonlinear devices to DC signals and AC signals is different (DC resistance and AC resistance), so DC analysis and AC analysis should use different circuit networks and parameters. These are often overlooked by some students and should be paid special attention to.

3 Linear equivalent circuit analysis of slightly changing signals

In the analysis method of the amplifier, the slightly changing signal is transformed into an analysis problem of the linear circuit, thus completing the whole process of linear-nonlinear-linear. But this is not a return to the original place, but a qualitative leap and improvement. Although the AC analysis of the amplifier circuit is also a linear analysis, the AC parameters of the nonlinear device at a given static operating point must be used. The nonlinear characteristics still play a role here. In many electronic circuits, the DC resistance and AC resistance of electronic devices are different. This concept can be used to understand and explain the working principles of many circuits. For example, the active load uses this feature to obtain a larger AC equivalent resistance under the condition of lower DC power supply voltage or larger static working current. In the differential amplifier circuit, through the analysis of the emitter resistance function of the long-tail differential amplifier, it is known that it can effectively reduce the common-mode amplification factor without any effect on the differential signal, so the larger it is, the better. If a linear resistor is used, under a certain working current, the selection of a large resistor must be limited by the emitter DC power supply voltage. In this way, it is natural to select an active load with a large AC resistance and a small DC resistance.

4 Conclusion

In the course of "Circuits", we have gone from general linear circuit analysis to nonlinearity of electronic devices, and then to linear analysis of AC signals in amplifying circuits. At this point, the task of analyzing amplifying circuits has been basically completed, because circuits are loops composed of circuit elements. Analyzing circuits means first replacing these elements with models of circuit elements, and then using basic circuit laws and basic analysis methods to solve the network composed of circuit element models. The only difference between electronic circuits and general circuits is that they contain electronic devices. Now, when electronic devices are also replaced with their circuit models, electronic circuits become general circuits, and their analysis becomes the analysis of general circuits. This is to make students understand that electronic circuits are a branch of circuits, and "Basics of Electronic Technology" is a continuation and expansion of "Circuits", and their basic laws and analysis methods are the same, thus establishing a unified and complete concept of circuit analysis.