Under frequency conversion understand the transfer process without any distortion of the signal spectrum to another frequency range.
Frequency conversion is used to place the signal spectrum in a given section of the frequency range of the communication channel, as well as to increase the sensitivity and selectivity of superheterodyne type receivers.
The principle of transformation is illustrated in Fig. 3.9, 3.10.
The signal at the input of the converter depends on the time and the primary signal:
In the multiplier, it is multiplied by the local oscillator signal
and then filtered bandpass filter.
The input signal can be modulated (continuously or discretely) in amplitude, phase, carrier frequency. Let the spectral density of any modulated signal consist of spectral components concentrated around frequencies + co 0 (Fig. 3.10, but):
Rice. 3.9. Structural diagram of the frequency converter:
1 - multiplier;2 - bandpass filter
Rice. 3.10.
The spectral density is characterized by the spectral density of the amplitudes and the phase response. If these characteristics are necessary for the corresponding calculations, they must be calculated using formulas and presented in the form of graphs.
In other cases, exact data are not required and spectral densities can be depicted arbitrarily: for example, in the form of bell-shaped spectra or triangles for continuous spectral densities, or arrows for discrete ones, as is done in this book.
Let us calculate the spectral density of the local oscillator signal using the expression (A.1.3) of the delta function:
Assuming we get
The spectral density of a harmonic cosine wave with a zero initial phase (Fig. 3.10, b) is determined by the product of the amplitude of this oscillation, increased by l times, and the sum of two delta functions located at the points of the frequency axis ω = + ω r. We also calculate the spectral density of the product of the input signal and the local oscillator using formula (2.51):
where 
- intermediate frequency; ? BX (/b), 5 g (/co) are the spectral densities of the input signal and local oscillator, respectively.
In the spectral density of the product shown in Fig. 3.10, in, contains a useful transformation product (spectral components near the values of the intermediate frequency
co = +(O pr), as well as interfering components near frequencies -co 0 - co g, COo + Wp
Useful components (see Fig. 3.10, c, d) pass to the output of the bandpass filter, and the interfering ones are significantly attenuated. Spectral components at the output of the bandpass filter (Fig. 3.10, d ) are determined by the expression
if the bandpass filter gain /C(/co) = 1 in a given frequency band. They are accurate to a constant factor equal to BUT/ 2 coincide with the spectral components of the signal at its input, and the spectrum of the converted signal is grouped around the new frequency values equal to ω = + ω pr.
Frequency conversion is used in modulation and signal detection.
The spectrum transformations considered above for various types of amplitude modulation consist in shifting the spectrum of the transmitted signal to the radio frequency region. Such a shift can be thought of as a special case of a more general linear operation called frequency conversion. Frequency conversion generally means the shift of the signal spectrum along the frequency scale in one direction or another, i.e. to both higher and lower frequencies.
When receiving signals, frequency conversion is understood as the conversion of a modulated high-frequency oscillation associated with the transfer of its spectrum from the vicinity of the carrier frequency 0 to the vicinity of a lower (so-called intermediate) frequency pr, performed without changing the modulation law.
The frequency converter is a device in which the received high frequency signals (c) are converted into signals of a lower intermediate frequency (pr).
The converter includes a local oscillator and a mixer.
The local oscillator is an autogenerator of electrical oscillations, the frequency of which changes in proportion to the change in the frequency of the received signals. The mixer can be implemented on non-linear (semiconductor diodes, transistors) or parametric (for example, analog multipliers) elements.
The received signals with a frequency c and electrical oscillations of a local oscillator with a frequency r are fed to a mixer, where complex oscillations are formed containing components with frequencies c + r and c - r.
Difference fluctuations ( intermediate) frequencies pr \u003d c - r are selected using a filter (tuned to pr). The single loop filter is the simplest. Typically, a system of two or more connected circuits, piezoelectric or electromechanical filters are used.
The choice of intermediate frequency is made taking into account a number of requirements. In particular, the intermediate frequency is selected in the range in which powerful radio stations do not operate, and outside the frequency range in which the input circuits of the receiver are tuned. For radio broadcast receivers, standard values of intermediate frequency are set f pr - 465 kHz and 10.7 MHz. in television receivers f pr image signals is 38.0 MHz, and for audio image signals - 31.5 MHz and 6.5 MHz.
As an example, consider the implementation of a mixer based on an analog multiplier, at the input X which receives the signal voltage and at the input Y- local oscillator voltage
The shifting process is similar to balanced amplitude modulation. The output voltage of the multiplier contains two components - with difference and sum frequencies:
With a bias, only the component with the difference frequency is important, i.e. with intermediate frequency
To select the intermediate frequency, either a narrow-band filter (for example, an oscillatory circuit) or a low-pass filter is included in the output circuit of the multiplier.
As a result, the output voltage of the mixer
In the frequency converter, the modulation of the input signal is transferred to the intermediate frequency voltage. For an amplitude modulated signal
intermediate frequency voltage
Frequency conversion is widely used in radio receivers called superheterodyne receivers, the block diagram of which is shown in fig. nine.
The signal received by the antenna is fed through the filtering input circuits and the radio frequency amplifier to the frequency converter. The output of the transducer is a modulated waveform with a carrier frequency equal to the intermediate frequency of the receiver. The main gain of the receiver and its frequency selectivity, i.e. the ability to isolate the useful signal against the background of interference with other frequencies is provided by a narrow-band intermediate frequency amplifier.
A great advantage of a superheterodyne receiver is the invariance of the intermediate frequency. To tune the receiver to the desired station within the specified frequency range, it is only necessary to tune the local oscillator frequency.
Note that the frequency converter responds equally to signals with frequencies and, i.e., as they say, reception is possible both on the main and on the mirror channel.
When using an intermediate frequency, the complete preservation of the structure of the converted signal is possible only if if then the signal spectrum is reversed, i.e. in the transformed spectrum, max and min are interchanged.
When converting the frequency of a conventional amplitude-modulated oscillation, the reversal of the spectrum does not appear outwardly in any way, just the upper and lower side bands are reversed.
FEDERAL AGENCY FOR EDUCATION
Krasnoyarsk State Technical University
Laboratory work on RTCiS No. 4
Frequency conversion.
completed:
student gr. R53-4: Titov D.S.
checked:
Kashkin V. B.
Krasnoyarsk 2005
Objective
The study of the basic laws of frequency conversion. In this paper, the dependence of the conversion coefficient on the bias voltage is removed, the spectra of signals at the output of the converter are studied at large and small amplitudes of the local oscillator.
Homework .
Frequency converter circuit
Dependence of the differential slope on the input voltage.
Known: local oscillator frequency fg, intermediate frequency filter frequency ff. Determine the signal frequencies at which the voltage at the output of the converter reaches its maximum.
A) If the amplitude of the local oscillator is small, then the converter operates in quadratic mode, therefore
B) If the amplitude of the local oscillator is large, then the mode will no longer be quadratic.
where m and n are some positive integers.
In this case, there will be a strong distortion of the signal at the output of the converter.
Dependence Uout(Ub0) in the frequency conversion mode i.e. with simultaneous input of Us and Ug and fc=|fg±ff|.
This dependence has the same non-linear character as the input characteristic of a transistor.
experimental part
Let's take the dependence of the voltage at the output of the converter on the bias voltage in the forward passage mode at Uc=10 mV and fc=fp and the local oscillator is off.
Estimated intermediate filter frequency f=121 kHz (C=2200pF L=780 µH).
Experimentally found local oscillator frequency f=261 kHz, intermediate filter frequency f=104 kHz.
The signal frequency is adjusted according to the maximum voltage at the output of the converter.
The resulting characteristic is clearly non-linear. the input characteristic of the transistor is non-linear.
Let us choose the operating point in the middle of the linear section of the Uout(Ub0) dependence. Ub0=0.5 V.
Let's take and build the dependence of the voltage at the output of the signal frequency converter at Uc=10 mV, put in the table the values of the voltage at the output of the converter in the maxima and the frequency of the maxima. (Local oscillator is on, synchronization is off)
With a small amplitude of the local oscillator Ag = 10 mV.
With a large amplitude of the local oscillator Ag = 250 mV.
Oscillogram of the AM voltage at the input of the converter.
Oscillograms of the AM voltage at the output of the converter with a large local oscillator amplitude and a bias Ub0=0.5 V, at the signal frequency
1) fc=fg+fp fc=365 kHz
2) fc=fg-fp fc=158 kHz
3) fc=3fg+fp fc=840 kHz
4) fs=3fg-fp fs=630 kHz
Let us take the dependence Uout(Ub0) at a large amplitude of the local oscillator.
From the data obtained, we calculate and plot the dependence of the conversion coefficient on the bias voltage.
Output: during the laboratory work, the processes occurring during the frequency conversion of the AM signal were investigated.
The dependence of the voltage at the output of the converter on the bias voltage in the direct passage mode was removed, this dependence is non-linear.
The frequencies and amplitudes of the maxima were measured at low and high amplitudes of the local oscillator. We found out that at the output of the frequency converter, the signal has a complex spectrum with maxima at several frequencies
Oscillograms of signals at the output of the transducer were obtained at different frequencies of the input AM signal. It turned out that the output signals are slightly distorted.
8.8.1. Principle of frequency conversion
Signal frequency conversion is a process that provides a linear transfer of the signal spectrum on the frequency axis without changing its structure. The signal envelope and its initial phase do not change in this case. In other words, frequency conversion does not distort the law of amplitude, frequency or phase of the modulated oscillations.
As can be seen from the definition, frequency conversion is accompanied by the appearance of new spectrum components, i.e. leads to signal spectrum enrichment. Therefore, such a process can be implemented only with the use of non-linear or parametric devices that provide multiplication of the converted signal by an auxiliary harmonic oscillation, followed by selection of the required frequency range.
Indeed, if two signals are applied to the input of the multiplier:
then at the output we get the signal of the sum and difference frequencies:
where is the multiplier transfer coefficient.
The output filter, tuned, for example, to the difference frequency, will highlight the component of the difference (intermediate) frequency. Such a non-linear device is called mixer, and the source of harmonic oscillation - local oscillator.
The block diagram of the frequency converter is shown in fig. 8.41.
Rice. 8.41. Structural diagram of the frequency converter
Frequency conversion is used in superheterodyne receivers to obtain an intermediate frequency signal. The value of the intermediate frequency should be such that a large gain can be achieved without much difficulty with a high selectivity of the receiver. In broadcasting receivers of long, medium and short waves, and in receivers with frequency modulation (in the meter wave range) -. Signal frequency conversion is also used in radar receivers, in measuring equipment (spectrum analyzers, generators, etc.).
8.8.2. Frequency converter circuits
As mentioned above, the frequency conversion process is implemented by multiplying the converted signal by an auxiliary harmonic oscillation, followed by selection of the required frequency range. This can be done in two ways, which form the basis for the construction of practical frequency converter circuits:
1. The sum of two voltages (useful signal and local oscillator signal) is applied to a nonlinear element with subsequent selection of the necessary components of the current spectrum. Diodes, transistors and other elements with a non-linear characteristic are used as non-linear elements.
2. The voltage of the local oscillator is used to change any parameter of the mixer (the slope of the I–V characteristic of the transistor, the reactive parameter of the circuit). The useful signal applied to the input of such a mixer is converted with the appropriate spectrum enrichment.
To clarify the main features of the frequency conversion process, consider some frequency converter circuits.
but. Frequency converters on diodes
The scheme of a single-circuit frequency converter on a diode is shown in fig. 8.42.
Rice. 8.42. Single-loop frequency converter on the diode
Two signals are received at the input of the converter:
modulated narrowband signal, the carrier frequency of which must be transferred, say, to the region of lower frequencies;
local oscillator signal with constant amplitude, frequency and initial phase.
Thus, a voltage is applied to the nonlinear element
We approximate the I–V characteristics of the diode with a polynomial of the second degree
Then the diode current can be represented as follows:
Terms containing only , , , correspond to components in the diode current spectrum with frequencies , , and . Therefore, they are of no interest from the point of view of frequency conversion. The last term is of primary importance. It is this that indicates the presence in the current spectrum of components with converted frequencies and:
The frequency component corresponds to the shift of the signal spectrum to the low frequency region, and the frequency component to the high frequency region.
The output voltage with the required frequency is formed using a filter (oscillatory circuit) at the output of the converter, tuned to the appropriate frequency. The filter should select one component out of seven. Assuming that the filter is tuned to the difference (intermediate) frequency , we get the voltage at the output of the converter, equal to
For or , the frequency detuning , and , is very small. In this case, components with signal or local oscillator frequencies will not be filtered out by the selective system. It is also undesirable to use this system when solving the problem of frequency conversion in the range of acoustic frequencies. In this case, it is advisable to use balanced schemes that provide self-destruction (compensation) of unnecessary components. On fig. 8.43, a and fig. 8.43,b shows diagrams of such converters on diodes.
Rice. 8.43. Balanced frequency converters
In the scheme of Fig. 8.43, and the output voltage is
When obtaining the expression for, it is taken into account that the signal voltage is applied to the diodes of the circuits in antiphase, and the local oscillator voltage is in phase.
Substituting the expressions for and into formula (8.5), we obtain
From this it can be seen that at the output of the balanced converter fig. 8.43,a there are no components with frequencies equal to 0, , , , which simplifies the solution of the problem of obtaining the output signal of the required frequency. However, it is also necessary to connect an electoral system to the output of such a converter in order to filter the signal with the required frequency.
Balance converter fig. 8.43, b is a circuit that combines two balanced converters. The diodes of different branches are supplied with signal and local oscillator voltages with different phases. The operation of such a converter is explained by the following formulas:
Substituting the expressions for , , and into formula (8.6), we obtain
At the output of the converter fig. 8.44,b there is no component with the signal frequency (components with frequencies 0, , , are also absent). The filter at the output of such a converter must select one of the two components.
b. Transistor frequency converters
Transistor-based frequency converters are widely used in the receiving channels of radio engineering systems. At the same time, converter circuits are distinguished, in which the functions of the mixer and local oscillator are combined, and converter circuits with a local oscillator signal supplied from the outside. More stable operation is provided by the last class of converters.
According to the way the transistors are turned on, they distinguish:
1. Converters with the inclusion of a transistor according to the circuit with a common emitter and according to the circuit with a common base.
Common-emitter converters are more commonly used because have better noise characteristics and higher voltage gain. The local oscillator voltage can be applied to the base circuit or to the emitter circuit. In the first case, a higher gain is achieved, in the second case, better gain stability and good decoupling between the signal and heterodyne circuits.
2. Converters on amplifiers with cascode switching of transistors.
3. Converters on a differential amplifier.
4. Converters on field-effect transistors (with one and two gates).
The main properties and characteristics of the last three groups of converters are determined by the properties of the amplifiers on the basis of which they are built.
On fig. 8.44 shows diagrams of frequency converters on planar transistors.
In the scheme of Fig. 8.44, and the signal voltage is supplied to the base circuit of the transistor, the local oscillator voltage to the emitter. The circuit in the collector circuit is tuned to an intermediate frequency. Resistance and provide the necessary mode of operation of the amplifier (position of the operating point), resistance and capacitance - thermal stabilization of the position of the operating point. The frequency conversion is carried out by changing the frequency of the local oscillator signal of the transfer coefficient of the amplifying stage (the I–V characteristic of the transistor).
Rice. 8.44. Schemes of frequency converters on planar transistors
The transistorized frequency converter shown in fig. 8.44, b, built using a differential amplifier. A converted signal is applied to its input, and a local oscillator signal is applied to the base of the transistor of the stable current generator. The gain and noise figure of such converters are approximately equal to the corresponding coefficients of the amplifying stage.
Schemes of frequency converters on field-effect transistors are shown in fig. 8.45, a - a circuit with a combined local oscillator and fig. 8.45, b - a circuit using a field-effect transistor with two insulated gates.
Rice. 8.45. Schemes of frequency converters on field-effect transistors
On fig. 8.45, and a field-effect transistor with a gate in the form pn-transition acts as a mixer and local oscillator at the same time. The signal is sent to the gate of the transistor. The local oscillator voltage from part of the heterodyne circuit is fed into the source circuit of the transistor. The required transistor mode is ensured by the appropriate selection of the operating point using an automatic bias circuit. The resistor in the gate circuit allows the charges accumulated on the gate to drain. The load of the converter is a band-pass filter tuned to the required combination frequency of the drain current. Since the input and output resistances of the field-effect transistor are quite large, the input circuit to the gate and the band-pass filter circuit to the drain are connected completely.
In the circuit of a transistor frequency converter on a field-effect transistor with two insulated gates (Fig. 8.45, b), both gates are used as control electrodes. Essentially, the transistor operates under the influence of the sum of two voltages. The voltage is generated by the converted signal applied to the first gate, and the voltage is generated by the local oscillator signal applied to the second gate. An oscillatory circuit tuned to the difference frequency is connected to the drain of the transistor. The advantage of this circuit is the negligible capacitive coupling between the converted signal supply circuit and the local oscillator signal circuit. In the presence of such a connection, the local oscillator oscillation frequency can be captured by the signal. In this case, the frequency of the local oscillator signal becomes equal to the frequency of the converted signal, as a result of which there will be no frequency conversion.
Frequency conversion can also be carried out using parametric circuits. In such circuits, the local oscillator voltage is applied to a nonlinear capacitance (varicap), the value of which varies according to the law of the heterodyne voltage.
CONCLUSION
The current state of radio engineering is characterized by the intensive development of methods and means of signal processing, the widespread use of the achievements of digital and information technologies. At the same time, it is impossible to absolutize the variability of the basic fragments of the general theory of radio engineering, which form the basis of methods for solving problems of analysis and synthesis of modern radio engineering and information systems. Just as knowledge and free orientation in a variety of mathematical axioms allow one to come to new conclusions and results, so knowledge of the fundamental concepts in the field of signal modeling, methods and technical means of their processing makes it easy to understand new, even at first glance, very complex technologies. Only with such knowledge, a researcher or designer can count on the practical effectiveness of the well-known "know-how" principle (I know how).
Many issues directly related to "deterministic" radio engineering remained outside the scope of this book. First of all, these are the issues of signal generation, discrete and digital filtering, methods of analysis and construction of parametric and optoelectronic devices. Special attention and separate discussion deserve the problems of statistical radio engineering, the solution of which is unthinkable without a broad outlook in the field of methods for analyzing random signals and their transformations, methods for solving classical problems of optimal signal processing during their detection and measurement.
In the future, it is planned to publish a textbook devoted to the consideration of these problems, taking into account the latest theoretical and practical results.
LITERATURE
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2. Baskakov, S. I. Radio engineering circuits and signals: a textbook for universities. - M .: Higher. school, 2000.
3. Radio engineering circuits and signals / D.V. Vasiliev, M.R. Vitol, Yu.N. Gorshenkov and others; / Ed. A.K.Samoylo - M. Radio and communication, 1990.
4. Nefedov V.I. Fundamentals of radio electronics and communications: Textbook for universities. - M .: Higher. school, 2002.
5. Sergienko A.B. Digital signal processing. - St. Petersburg: 2003.
6. Ivanov M.T., Sergienko A.B., Ushakov V.N. Theoretical foundations of radio engineering. Proc. allowance for universities. - M .: Higher. school, 2002.
7. Manaev E.I. Fundamentals of radio electronics. - M .: Radio and communication, 1990.
8. Bystrov Yu.A., Mironenko I.G. Electronic circuits and devices. - M .: Higher. school, 1989.
9. Kayackas A.A. Fundamentals of radio electronics. - M:. Higher school, 1988.
10. Bronstein I.N., Semendyaev K.A. Handbook of mathematics for engineers and students of VTUZ. – M.: Science. Head. ed. Phys.-Math. Literature, 1986.
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With the simultaneous action of a signal and a local oscillator on a nonlinear element, currents of combination frequencies of the form 
, where m and n are integers of the natural series and determine the non-linearity of the conversion element with respect to the signal and local oscillator. If the converter is linear with respect to the signal, then m=1, if the local oscillator generates a harmonic signal, then n=1.
At all three inputs of the frequency converter, selective systems are connected, tuned accordingly to resonance at the input with the signal frequency. In this case, a heterodyne system is connected to terminals 3-3 (set n=1), and a selective system is connected to terminals 2-2 in the form, for example, of a simple oscillatory circuit.
The main equations that describe the operation of a 6-pole network are equations of the form:
(1)
(2)
Expressions (1) and (2) do not include time, since we consider the 6-pole to be inertial-free. When deriving equations that describe the frequency conversion process, we will assume that the signal voltage U c is of the order of tens to hundreds of microvolts, which allows us to consider the frequency converter linear. At the same time, the voltage with the local oscillator frequency U g has the order of tenths and units of V. Therefore, neither U c nor U pr cause a change in the parameters of the nonlinear element, this does U g. This allows the functions f 1 and f 2 to be expanded into a series Taylor in powers of small variables U c and U pr, that is, limiting to taking into account the terms of the expansion with U c and U pr in the first degree.
(3)
The derivatives, which are the coefficients of the series, are determined at and, that is, under the action of only the local oscillator voltage;
at
Physical meaning:
This is the input current under the action of U g.
- input conductivity.
- conductivity of the reverse conversion.
Output current during the action of the local oscillator, in the absence of a signal.
- steepness.
- output conductivity.
Since the heterodyne voltage is considered harmonic, for example, cosine: 
, then the steepness S(t), as a periodic function of time, can be represented as a Fourier series:
After substitution into (3) and (4), we obtain the equation of direct and inverse transformation:
a) direct conversion 
,
where I pr - intermediate frequency current;
b) inverse transformation 
.
Converter parameters.
1. Transducer slope:
(short circuit at the output)
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