**1 Calculation model of series feedback transistor voltage regulator circuit**

There are many kinds of components in the series feedback transistor voltage regulator circuit, which is the object of our research, which makes the research results universal. The series feedback transistor voltage regulator circuit is shown in Figure 1. In the figure, Ui is the output voltage value after the grid voltage is transformed, rectified and filtered; VT1 is the adjusting tube, VT2 is the amplifier tube, VD is the voltage regulator tube, and the internal resistance is r. Suppose, the parameters of VT1 are rbe1, β1; the parameters of VT2 are rbe2, β2.

According to the circuit diagram, it can be seen that the circuit has 5 independent nodes, the input is node 1, the output is node 5, and the remaining nodes are marked in the figure in order.

According to the establishment method of the admittance matrix of the amplifying circuit, the calculation model of this circuit can be established.

(1) First remove the transistors VT1 and VT2, and write the admittance matrix of the remaining part of the circuit.

(2) According to the actual number in the circuit, write the node admittance matrix of transistors VT1 and VT2.

(3) Fill YVT1 and YVT2 into Y0 according to the row and column positions where their elements are located, to obtain the node admittance matrix of the series feedback transistor voltage regulator circuit:

This admittance matrix is the mathematical model used to describe the series feedback transistor voltage regulator circuit. For the regulated power supply, what we care about is whether the output voltage of the regulated power supply is constant, whether the output resistance is small, and whether the voltage regulation coefficient is small. With the mathematical model of the regulated power supply, the next step is how to solve the mathematical model.

**2 Solving the Performance Index of the Series Feedback Transistor Voltage Regulator Circuit**

2.1 Solving the performance index of the series feedback transistor voltage regulator circuit

For the DC voltage regulator circuit, it can be assumed that there are two external constant current source currents, denoted as Iω1 and Iωn, respectively, and the direction of the inflow from the external node is positive. In this way, the equation system of the whole circuit includes one equation for reflecting the signal source and one for the load. Since there are only two external nodes, it can be described by two equations, and then consider the two equations of the relationship between the external constant current source and the branch current, and a total of 6 equations can be described. Using the node admittance matrix of the DC regulated power supply, the port equation can be obtained:

Since the voltage regulator circuit has a common point, the node voltage column vector can be obtained:

In the formula, △ is the determinant of the node admittance matrix of the voltage regulator circuit; The algebraic cofactor corresponding to the element in row n, column 1; Δ1n is the algebraic cofactor corresponding to the element in row 1, column n in the admittance matrix; Δnn is the algebraic cofactor corresponding to the element in row n in the admittance matrix The algebraic cofactor corresponding to the element in the nth column.

With three equations, the quality index of the regulated power supply can be determined.

2.2 Voltage regulation coefficient of regulated power supply

2.3 Determine the output resistance of the regulated power supply

When calculating the output resistance, the load should be open circuit (RL=∞). If the signal source at the input end is a fixed potential source, it should be regarded as a short circuit at the signal source (Us=0, but Rs is reserved); if it is a constant current source, it should be regarded as a signal source. open circuit (Is=0, but keep Rs). The voltage Us is applied to the output terminal to obtain the current Is, so the output resistance can be obtained as:

Equations (11) and (13) are the analytical expressions describing the quality index of the voltage stabilized circuit, which are used as the basis for solving the quality index of the stabilized power supply. For the DC regulated power supply, as long as the node admittance matrix of the form (3) is established, and its determinant and the corresponding algebraic cofactors △, △11, △15, △55, △11, 55 are calculated , Substitute into formula (11) or formula (12) and formula (13) or formula (14), the voltage regulation coefficient and output resistance of the voltage regulator circuit can be obtained.

**3 The influence of parameter changes and circuit structure changes on the performance indicators of the regulated power supply**

The index used to measure the voltage regulation characteristics of the regulated power supply is the quality index. Commonly used quality indicators in Electronic circuits are voltage regulation coefficient output resistance and ripple voltage. For the regulated power supply, the more stable the output voltage of the regulated power supply, the smaller the output resistance, and the lower the voltage regulation coefficient, the better the voltage regulation effect of the regulated power supply. Through the analysis of the regulated power supply, different methods can be used to change the corresponding quality indicators according to different needs. The analytical expressions of the corresponding performance indicators are given below for several different methods.

3.1 Influence of parameter changes on performance indicators of regulated power supply

There are roughly two reasons for the change of circuit parameters: the first is caused by changes in natural conditions. Common changes in ambient temperature will cause changes in transistor input resistance rbe, current amplification coefficient β, etc., which will inevitably cause changes in element values in the transistor node admittance matrix; the second is caused by human factors, such as changing resistance. value, replacing transistors, etc., will also change the corresponding element value in the transistor node admittance matrix. In these two cases, only changing the value of some elements in the admittance matrix of the amplifier circuit does not change the number of nodes of the amplifier circuit. When analyzing the influence of parameter change on the performance index of the regulated power supply, the relative analytical formula can be used to obtain the corresponding value and the relative change rate of the performance index after the parameter change.

Here, take the replacement of the regulating tube as an example to illustrate its influence on the performance of the regulated power supply. In order to improve the output current of the regulated power supply, we can use high-power transistors as the adjustment tube of the regulated power supply. At this time, the number of nodes of the circuit does not change, and the additional matrix Yδ of the amplifier circuit is the node admittance matrix YVT1 of the adjustment tube, which includes:

The row number, column number b, c, and e in formula (15) should correspond to the actual numbers of the base, collector and emitter of the transistor in the regulated power supply, respectively. For the series DC regulated power supply shown in Figure 1, b, c, e correspond to node 2, node 1 and node 50, respectively. In formula (15), the second-order and higher-order higher-order The determinants of the subforms are all zero, and only 6 first-order subforms are non-zero values, and the incremental value of the corresponding algebraic cofactor caused by Yδ can be found:

With Equation (16), the effect of replacing the transistor on the performance index of the regulated power supply can be obtained:

3.2 The influence of the change of circuit structure on the performance index of regulated power supply

In order to improve the performance of the electronic circuit, it may be necessary to add a branch, or change the position of the contact of an existing branch, or insert a link. Or short-circuit two nodes, etc., which all make certain changes in the circuit structure. This change not only changes the position of the elements in the admittance matrix, but even expands or shrinks the order of the admittance matrix. In order to facilitate the analysis of the problem, it is assumed that the number of nodes of the amplifier circuit remains unchanged, so as to study the influence of certain changes in the circuit structure on the performance indicators of the regulated power supply.

3.2.1 The effect of adding capacitors at different nodes on the ripple coefficient

For the series feedback transistor voltage regulator circuit shown in Figure 1, in order to reduce the ripple factor, it is often realized by connecting a large capacitor to the ground. As for how big the capacitance of this capacitor is and which node it is connected to, we have to verify and determine it through theoretical calculations and actual physical experiments. Next, for this circuit, solve the analytical formula for the ripple coefficient when the same capacitor is connected across different nodes. (1) Connect capacitor C1 at i=2, k=0, and the additional matrix is:

Among them, △11, 22 is the algebraic cofactor left by removing the 1st row, 1st column, 2nd row and 2nd column in Y; The remaining algebraic cofactors in column 2. From this, the ripple coefficient after adding capacitor C1 to the ground at node 2 can be obtained:

(2) Connect the capacitor C2 at i=3, k=0 and connect the capacitor C3 at i=4, k=0. At this point, the additional matrices are:

Compare the ripple coefficients in the three cases, and select the one with the smaller value.

3.2.2 The effect of adding capacitors at different nodes on the output resistance

Compare the output resistances in the three cases, and select the one with the smaller value.

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