Resistive solution of the controlled source

The output resistance of the basic amplifier circuit is a dynamic parameter, and the commonly used calculation method is the "pressurization flow method". In the several dynamic parameters of the amplifying circuit, the juice of the output resistor is the most complicated. It is for this reason that many electronic technical textbooks often only give the calculation formula for the output resistance without a derivation process. The new method introduced in this paper is easy to understand, simple and practical, and has certain theoretical value.

1 controlled source and its resistance

A controlled source is a circuit model that is abstracted when people study the characteristics of certain circuit components or components. Its characteristic is that its voltage or current is a function of voltage or current in other parts of the circuit. In other words, it is subject to a certain The branch voltage or current is controlled, so it is called a controlled source.

Independent sources and controlled sources have completely different roles in the circuit. The former is the input to the circuit, which represents the external action on the circuit; the latter is a model of the physical phenomena occurring in certain circuit components and components, which reflects that one voltage or current in the circuit is subjected to another voltage. Or the control relationship of the current.

The controlled source has duality: power and resistance. For the controlled source, as long as the control amount is not zero, there is a voltage output across the controlled voltage source, and the controlled current source can output the current. They have the same external characteristics in the circuit as independent sources, which is its power supply. The resistivity of a controlled source means that an equivalent resistance can be used in the circuit instead of the controlled source. An example is as follows: Find the equivalent circuit shown in Figure 1.

First, the controlled current source is transformed into a controlled voltage source. The transformed circuit is shown in Figure 2(a).

According to Figure 2 (a), the following circuit equation can be written:

U=-100I+1000I+2000I+10=2900I+10

According to the above circuit equation, the original circuit diagram 1 can be finally simplified to Fig. 2(b).

As can be seen from this question, CCUS is equivalent to a 100Ω resistor in this circuit. The above indicates that the controlled source has resistance, and it is equivalent to a certain value of resistance in the circuit.

2 Solve the output resistance with the resistivity of the controlled source

When solving the output resistance of various basic amplifying circuits, if the controlled source in the small signal equivalent circuit can be represented by an equivalent resistance, the calculation of the output resistance becomes easy to understand and easy to calculate, only A simple Ohm's law and a series-parallel knowledge are needed to solve the problem, and there is no need to use complicated and complicated circuit laws.

Example 1 Find the output resistance of the common circuit of Figure 3.

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