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General analysis of the resonant amplifier

Lecture



Equivalent circuit amplifying device.

In the mode of small signals, a transistor or a lamp can be represented by an active linear quadrupole with a dependent current generator.

General analysis of the resonant amplifier

Figure 9.4.

Such a quadrupole is described by two linear equations connecting the voltages and currents at its input and output. Positive directions of currents and voltages are indicated in the figure by arrows. We will use the system of y-parameters, since at high frequencies it is most convenient. In the system of y- parameters, the equations of the quadrupole are:

General analysis of the resonant amplifier .

Recall that the y- parameters are determined during a short circuit at the input and output:

General analysis of the resonant amplifier - input conductance of a quadrupole with a short circuit at the output;

General analysis of the resonant amplifier - reverse conduction at input short-circuit;

General analysis of the resonant amplifier - direct conduction at short-circuit at the output (slope);

General analysis of the resonant amplifier - output conductance at the input short-circuit.

The analysis of specific amplifier circuits is more illustrative if we use the equivalent circuits obtained on the basis of the theory of two-port networks. The most common is the following equivalent circuit amplifying device.

General analysis of the resonant amplifier

Figure 9.5.

For further analysis, y- parameters are conveniently presented in the form:

General analysis of the resonant amplifier ; General analysis of the resonant amplifier ;

General analysis of the resonant amplifier ; General analysis of the resonant amplifier .

Where General analysis of the resonant amplifier ; General analysis of the resonant amplifier - the frequency at which General analysis of the resonant amplifier i.e. slope decreases in General analysis of the resonant amplifier time.

General analysis of the resonant amplifier where General analysis of the resonant amplifier .

Equivalent amplifier circuit.

The complete equivalent circuit of the amplifier contains the signal source and load.

General analysis of the resonant amplifier

Figure 9.6.

For this scheme

General analysis of the resonant amplifier ;

General analysis of the resonant amplifier the sign "-" in this expression appears due to the fact that the voltage on the load of the quadrupole (at points 2-2 ') from the current General analysis of the resonant amplifier will be opposite in sign to stress General analysis of the resonant amplifier ;

Where General analysis of the resonant amplifier - the total conductivity of the circuit and the load, converted to the output of the quadrupole, i.e. to points 2-2 '.

The diagram shows the incomplete inclusion of the contour. Inclusion rates

General analysis of the resonant amplifier ; General analysis of the resonant amplifier .

The main characteristics of the amplifier.

We define the main characteristics of the amplifier. Cascade ratio

General analysis of the resonant amplifier ;

General analysis of the resonant amplifier ;

General analysis of the resonant amplifier ;

General analysis of the resonant amplifier .

Attitude General analysis of the resonant amplifier find from the second equation of the quadrupole

General analysis of the resonant amplifier .

Substitute here General analysis of the resonant amplifier

General analysis of the resonant amplifier ,

from here

General analysis of the resonant amplifier .

Substitute the resulting relation in the expression for

General analysis of the resonant amplifier .

or if we substitute the value General analysis of the resonant amplifier

General analysis of the resonant amplifier ,

Where General analysis of the resonant amplifier - total equivalent circuit conductivity.

The total equivalent conductivity of the circuit can be expressed in terms of the equivalent resonant conductivity of the circuit and the generalized detuning

General analysis of the resonant amplifier ;

General analysis of the resonant amplifier ,

General analysis of the resonant amplifier - equivalent resonant conductivity of the circuit;

General analysis of the resonant amplifier - generalized detuning.

Then

General analysis of the resonant amplifier .

Gain module

General analysis of the resonant amplifier .

With General analysis of the resonant amplifier find the resonance gain

General analysis of the resonant amplifier .

Insofar as General analysis of the resonant amplifier depends on the coefficients General analysis of the resonant amplifier and General analysis of the resonant amplifier then there should be optimal values ​​of these coefficients for which General analysis of the resonant amplifier will be the maximum.

Expression research for General analysis of the resonant amplifier maximum allows to find the optimal values ​​of the coefficients

General analysis of the resonant amplifier ;

General analysis of the resonant amplifier ,

Where General analysis of the resonant amplifier .

Substituting the values ​​obtained General analysis of the resonant amplifier in the expression for General analysis of the resonant amplifier find the maximum gain

General analysis of the resonant amplifier .

It is clear from the last expressions that the resonant gain reaches its maximum value with the same contour shunting on the output side of the active element of this stage and on the load side, i.e. when

General analysis of the resonant amplifier .

Expression for General analysis of the resonant amplifier shows that with a small proper (constructive) attenuation of the contour, i.e. at D >> 1, the gain reaches its limit for the active element value

General analysis of the resonant amplifier .

If the structural attenuation of the contour is large, close to the equivalent, given from the condition of obtaining the required selectivity, then the gain is small, because at General analysis of the resonant amplifier , General analysis of the resonant amplifier . Hence it is clear that the contour should be sought to perform with the least possible own attenuation.

We derive the equation of the resonant curve of the amplifier:

General analysis of the resonant amplifier .

Those. the resonant characteristic of the amplifier in addition to the actual resonant properties is affected by the dependence of the coefficients General analysis of the resonant amplifier , General analysis of the resonant amplifier and toughness General analysis of the resonant amplifier from disorder. At small detuning, the change can be neglected. General analysis of the resonant amplifier , General analysis of the resonant amplifier and General analysis of the resonant amplifier . Then

General analysis of the resonant amplifier .

From here you can find the bandwidth of the amplifier for a given non-uniformity General analysis of the resonant amplifier .

General analysis of the resonant amplifier .

With General analysis of the resonant amplifier General analysis of the resonant amplifier .

Phase characteristic of the amplifier has the form

General analysis of the resonant amplifier .

Let us determine the input conductance of the amplifier stage (at points 1-1 'of the full equivalent circuit).

From the first equation of the quadrupole we get

General analysis of the resonant amplifier .

Substituting here the value we found earlier General analysis of the resonant amplifier get

General analysis of the resonant amplifier (+)

or, given that General analysis of the resonant amplifier and General analysis of the resonant amplifier get

General analysis of the resonant amplifier .

In the resulting expressions for General analysis of the resonant amplifier the second term is due to the conductivity of the internal feedback of the active element General analysis of the resonant amplifier .

Similarly, you can find the output conductivity of the active element (at points 2-2 'full equivalent circuit):

General analysis of the resonant amplifier . (*)

The structure of the expressions (+) and (*) is the same due to the equations of the quadrupole with respect to the input and output voltages and currents. From the obtained expressions it is clear that due to the internal OS, due to conductivity General analysis of the resonant amplifier , input conductance depends on the conductivity of the load, and output - on the conductivity of the signal source.

See also


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Devices for the reception and processing of radio signals, Transmission, reception and processing of signals

Terms: Devices for the reception and processing of radio signals, Transmission, reception and processing of signals