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General theory of frequency conversion

Lecture



The purpose of the analysis.

In the analysis of the inverter solve two main tasks:

1) determine the input voltage   General theory of frequency conversion Why find a useful component of the current   General theory of frequency conversion intermediate frequency, which coincides with the resonant frequency of the filter, and then calculate the main indicators of the converter - gain, frequency response, phase response, etc .;

2) find the component of the inverter input current at a frequency   General theory of frequency conversion that loads the signal source.

To simplify the analysis is carried out under the following assumptions:

a) The mixer of any frequency converter is considered as a non-linear six-port circuit, the output of which includes a selective load   General theory of frequency conversion tuned to intermediate frequency.

  General theory of frequency conversion

Figure 11.3.

b) We assume that three harmonic voltages act on a nonlinear element:

- signal voltage   General theory of frequency conversion ;

- intermediate frequency voltage   General theory of frequency conversion ;

- the voltage of the local oscillator   General theory of frequency conversion .

c) We believe that   General theory of frequency conversion and   General theory of frequency conversion i.e. we assume a nonlinear element operating in a linear mode with respect to the signal voltage; relative to the voltage of the heterodyne, the nonlinear element always operates in a nonlinear mode.

d) We assume that the nonlinear element of the mixer is a spinless device that does not contain capacitive and inductive elements. Therefore, its current does not depend on the derivatives or integrals of the voltages applied to the nonlinear element. For inertia-free NE, the input and output currents are determined by the static current-voltage characteristic:

  General theory of frequency conversion ,

  General theory of frequency conversion .

Determination of the useful component of the output current (direct frequency conversion).

Because   General theory of frequency conversion and   General theory of frequency conversion small then current

  General theory of frequency conversion

can be decomposed into a Taylor series in two variables, by limiting the number of members with   General theory of frequency conversion and   General theory of frequency conversion in the first degree:

  General theory of frequency conversion . (**)

The first term is a component of the output current, which is caused by the action of the heterodyne voltage at   General theory of frequency conversion . We introduce the notation

  General theory of frequency conversion .

Second term   General theory of frequency conversion characterizes the input current increment, which is caused by the action of the signal.

  General theory of frequency conversion - the instantaneous value of the direct conduction or the steepness of the non-constant periodically varying in time under the action of the voltage of the local oscillator.

Third term   General theory of frequency conversion is the increment of the output current of the mixer as a result of the action of the intermediate frequency voltage at its output.

  General theory of frequency conversion - the instantaneous value of the output conductivity of the mixer, changing in time under the action of the voltage of the local oscillator.

According to the linear theory of frequency converters, the first three terms are taken into account in the expression (**); at the same time current   General theory of frequency conversion linearly dependent on   General theory of frequency conversion and   General theory of frequency conversion . Taking into account the accepted notation, you can write

  General theory of frequency conversion .

Since the magnitudes   General theory of frequency conversion ,   General theory of frequency conversion and   General theory of frequency conversion are determined when there is a local oscillator voltage and periodically with a frequency   General theory of frequency conversion vary in time, they can be represented by Fourier series:

  General theory of frequency conversion ;

  General theory of frequency conversion ;

  General theory of frequency conversion .

The obtained series contain only cosine terms, since   General theory of frequency conversion , and we consider non-inertia.

Substituting the resulting relations in the expression for   General theory of frequency conversion , we get:

  General theory of frequency conversion .

or using the cosine multiplication rule, we get

  General theory of frequency conversion . (*)

It is clear from the last two relations that the output current of the mixer contains components with frequencies   General theory of frequency conversion and combination components with frequencies

  General theory of frequency conversion and   General theory of frequency conversion .

Frequency conversion is possible on any harmonic of a slope:

  General theory of frequency conversion ;

  General theory of frequency conversion at   General theory of frequency conversion ;

  General theory of frequency conversion at   General theory of frequency conversion .

Of these values, only one is used. If at   General theory of frequency conversion   General theory of frequency conversion , the frequency conversion is called simple. If at   General theory of frequency conversion   General theory of frequency conversion , the frequency conversion is called Raman, it is possible because of the appearance of harmonics of the slope.

Thus, of all the components of the output current, only the component with the frequency   General theory of frequency conversion .

We define in the expression (*) the current component with frequency   General theory of frequency conversion . Due to the second term with   General theory of frequency conversion and the third term at   General theory of frequency conversion will have

  General theory of frequency conversion ;

or

  General theory of frequency conversion . (-)

Turning to the complex amplitude, this expression can be written

  General theory of frequency conversion (+)

Where   General theory of frequency conversion ;   General theory of frequency conversion

This relationship is called the direct frequency conversion equation. The first term of the equations (-) and (+) characterizes the process of frequency conversion. The second term is due to the load response, since   General theory of frequency conversion depends on load resistance   General theory of frequency conversion .

Determination of the useful component of the input current (inverse frequency conversion).

In the mixer, along with direct and possibly reverse frequency conversion. Its physical meaning is that if an intermediate frequency voltage is applied to the input terminals of the mixer, then if there is a heterodyne voltage, a current with a signal frequency will flow through the input terminals of the mixer. Such frequency conversion is possible only if the mixer has nonlinear inverse-conductivity, periodically changing with the frequency of the local oscillator. Inverse frequency conversion changes the input and output conductance of the mixer. this is most pronounced in the diode frequency converter.

The inverse frequency conversion equation can be obtained by representing the input current   General theory of frequency conversion as a function of the local oscillator voltage   General theory of frequency conversion and two small variables   General theory of frequency conversion and   General theory of frequency conversion .

  General theory of frequency conversion .

By expanding this function in a Taylor series in two variables   General theory of frequency conversion and   General theory of frequency conversion . and limited to linear members, get

  General theory of frequency conversion .

Where   General theory of frequency conversion - the current at the input of the ne due to the action of the voltage of the local oscillator;

  General theory of frequency conversion - the instantaneous value of the input conductance NE;

  General theory of frequency conversion - instantaneous value of the conductance of the feedback NE.

Acting as in the case of direct frequency conversion, in the end, for the reverse frequency conversion, you can get

  General theory of frequency conversion ,

Where   General theory of frequency conversion - amplitude of the kth conduction harmonic of the inverse transform   General theory of frequency conversion for intermediate frequency voltage;

  General theory of frequency conversion - constant component of input conductance   General theory of frequency conversion for voltage signal.

Internal parameters of the frequency converter.

Based on the equations of direct and inverse transformations, we define the internal parameters of the converter, i.e. Parameters independent of load impedance and source impedance.

a) Direct-acting internal conductivity (direct conversion slope) is defined as the ratio of the amplitude of the intermediate-frequency current to the amplitude of the voltage of the input signal with a shorted output (   General theory of frequency conversion ):

  General theory of frequency conversion ;

b) The internal output conductance of the converter is equal to the ratio of the amplitude of the intermediate frequency current to the amplitude of the voltage of the same frequency with a short-circuited input (   General theory of frequency conversion ):

  General theory of frequency conversion ;

c) Internal conduction of the reverse action (steepness of the inverse transformation   General theory of frequency conversion ) is calculated as the ratio of the amplitude of the current component to the frequency of the signal to the amplitude of the intermediate-frequency voltage with a short-circuited input (   General theory of frequency conversion ):

  General theory of frequency conversion ;

d) Internal input conductance is equal to the ratio of the amplitude of the current component with the frequency of the signal to the amplitude of the voltage of the same frequency, with shorted output terminals (   General theory of frequency conversion ):

  General theory of frequency conversion .

In the general case, with the inertial nature of the conductivity of the nonlinear element, the internal parameters of the mixer are complex quantities. Therefore, the equations characterizing the operation of the mixer should be written in the form:

  General theory of frequency conversion .

Thus, the transforming element together with the local oscillator can be represented as a quasilinear quadrupole, characterized by four y-parameters — the transforming parameters.

External parameters of the converter.

Equivalent equivalent circuits of amplifying elements of the amplifying and converting cascades do not outwardly differ. The difference is only in the value of the parameters. Therefore, similarly to the amplifying (resonant) cascade, we define the external parameters of the converter.

  General theory of frequency conversion

Figure 11.4.

a) Gain

  General theory of frequency conversion .

b) input conductance

  General theory of frequency conversion .

c) output conductivity

  General theory of frequency conversion .

Where   General theory of frequency conversion - signal source conductivity;

  General theory of frequency conversion - load conductivity.


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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