Condition of stable operation of the amplifier

The condition of self-excitation is equality

the first of which is the phase balance condition, and the second the amplitude balance condition.

The amplifier will not be self-excited if the conductance of the circuit at its input, taking into account the feedback, will be positive:

But the absence of self-excitation does not mean the invariance of the amplifier.

We introduce the stability coefficient

If a , the amplifier can be self-excited. With no feedback, which corresponds to the maximum stability of the amplifier. Usually take . In this case, the change of the gain and bandwidth under the action of the OS does not exceed 10 ... 20%. the closer to one, the more stable the amplifier.

Similar reasoning is true for a negative OS: the properties of the amplifier should not undergo significant changes, so choose .

Let us find the stability condition of the amplifier with a given stability margin. When considering the previous question, we received

        .

Where - the function that determines the dependence from disorder and argument .

The nature of this dependence, and consequently, the active component of the input dynamic conductivity from shown in the figure (solid line). As a function of the argument , it will change (dashed lines), approaching or . At pic negative, with OOS - positive.

Figure 10.7.

Substitute the expression for in the expression for

At the last lesson, we obtained an expression for the resonant gain

In this expression entered the signs of the absolute value and to combine both cases of OS in one formula, since with pic and , and at OOS , .

Multiplying both sides of the resulting equality by get

Solving this equation for get

Sustainability is ensured if

With identical circuits at the input and output of the amplifier ; and the expression for take the form

This expression shows that to obtain a large, stable gain, an amplifying device must be chosen with the maximum value of the ratio . This relationship simultaneously characterizes the amplification capabilities of an electronic device and spurious feedback. Gain is possible if . Expression Study by shows that it has extreme points:

When studying the effect of the internal OS on the performance of the amplifier, it is necessary to proceed from the largest absolute value of the active component of the input dynamic conductivity.

Then

In a multi-stage amplifier, the output circuit of this stage is the input of the next stage. In the presence of an OS, it is shunted by the input dynamic conductivity of the next cascade. Because of this, its equivalent conductivity changes, which entails a change in the input dynamic conductivity and parameters of the input circuit of this cascade to an even greater degree. Thus, a multi-stage amplifier is less stable than a single-stage amplifier. However, if in each cascade the condition

then the decrease in stability is insignificant.