Resistive solution for the output resistance of a controlled source

The output resistance of a basic amplifier circuit is a dynamic parameter, and the commonly used calculation method is the "pressure-to-current method". Among the several dynamic parameters of an amplifier circuit, the calculation of output resistance is the most complicated. For this reason, many electronic technology textbooks often only give the calculation formula for the output resistance without the derivation process. The new method introduced in this article 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 abstracted when people study the characteristics of certain circuit elements or components. Its characteristic is that its voltage or current is a function of the voltage or current of other parts of the circuit. In other words, it is controlled by the voltage or current of a certain branch, so it is called a controlled source.

Independent sources and controlled sources have completely different roles in circuits. The former is used as the input of the circuit, which represents the effect of the outside world on the circuit; the latter is used as a model of the physical phenomena occurring in certain circuit elements and components, which reflects the control relationship between the voltage or current at one point in the circuit and the voltage or current at another point.

The controlled source has two properties: power source and resistance. For the controlled source, as long as the control quantity is not zero, the controlled voltage source will have voltage output at both ends, and the controlled current source will be able to output current. They have the same external characteristics as independent sources in the circuit, which is its power source property. The resistance of the controlled source means that an equivalent resistor can be used to replace the controlled source in the circuit. For example: Find the equivalent circuit shown in Figure 1.

First, the controlled current source is transformed into a controlled voltage source. The circuit after transformation is shown in FIG2(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).

From this question, we can see that in this circuit CCUS is equivalent to a 100Ω resistor. The above shows that the controlled source has resistance, and in the circuit it is equivalent to a resistor of a certain value.

2 Using the resistivity of the controlled source to solve the output resistance

When solving the output resistance of various basic amplifier circuits, if the controlled source in the small signal equivalent circuit can be represented by an equivalent resistor, then the calculation of the output resistance becomes easy to understand and calculate. It only requires simple Ohm's law and series-parallel knowledge to solve it, and there is no need to use cumbersome and complicated circuit laws.

Example 1: Find the output resistance of the common-collector circuit in Figure 3.