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: in the course of 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.
In radio engineering, it is often required to shift the signal spectrum along the frequency axis by a certain constant value while maintaining the signal structure. Such a shift is called a transformation
To clarify the essence of the frequency conversion process, let's return to the question of the impact on a nonlinear element of two voltages, briefly considered in § 8.4. However, in this case, only one of the oscillations, namely the one created by the auxiliary generator (local oscillator), will be considered harmonic. By the second oscillation, we mean the signal to be converted, which can be any complex but narrow-band process.
Thus, two voltages act on the nonlinear element: from the local oscillator
from signal source
The amplitude frequency and the initial phase of the heterodyne oscillation are constants. The amplitude and instantaneous frequency of the signal can be modulated, i.e., they can be slow functions of time (narrow-band process). The initial phase of the signal is a constant value.
The task of frequency conversion is to obtain the sum or difference frequency. As follows from expression (8.30), for this it is necessary to use a quadratic nonlinearity,
As a nonlinear element, we take, as in § 8.9, a diode, however, for a more complete identification of the products of the interaction of the signal and the heterodyne oscillation, we approximate its characteristic by a polynomial of the fourth degree (and not the second, as in § 8.4):
Terms containing different degrees only or only are of no interest. From the point of view of the transformation (shift) of the frequency, the terms that are products of the form of the right side of the expression (8.72) are of primary importance are framed.
Substituting (8.70) and (8.71) into these products and discarding all components whose frequencies are not the sum of the sum or the difference, after simple trigonometric calculations, we arrive at the following final result:
It can be seen from this result that the frequencies of interest to us arise only due to even powers of the polynomial approximating the characteristic of the nonlinear element. However, only the quadratic term of the polynomial (with a coefficient) forms components whose amplitudes are proportional only to the first degree. Higher even degrees (fourth, sixth, etc.) violate this proportionality, since the amplitudes of the oscillations they introduce also contain degrees higher than the first.
This shows that the amplitudes must be chosen in such a way that in the expansion (8.72) the terms not higher than the second degree have the predominant value. This requires the fulfillment of the inequalities
Then expression (8.73) becomes the following:
In radio receivers and many other devices in which the task of frequency conversion is closely related to the task of signal amplification, usually?,
The first term in curly braces with frequency (derivative of the cosine argument) corresponds to the shift of the signal spectrum to the high-frequency region, and the second term with frequency - to the low-frequency region. To select one of these frequencies - difference or sum - you need to apply the appropriate load at the output of the converter. Let, for example, the frequencies are very close and it is required to select a low frequency located near zero. Such a task is often encountered in measuring technology (the “zero beats” method). In this case, the load should be the same as for amplitude detection, i.e., it should consist of a parallel connection of R and C, which ensures filtering (suppression) of high frequencies and separation of the difference frequency. If the difference frequency lies in the high frequency range, then to select it a resonant oscillatory circuit should be used (Fig. 8.42). If the useful, to be selected, is the sum frequency, then the circuit must be tuned accordingly to the frequency
Typically, the bandwidth of the oscillating circuit, which is the load of the converter, is designed for the width of the spectrum of the modulated oscillation. In this case, all current components with frequencies close to pass through the circuit evenly and the structure of the signal at the output coincides with the structure of the signal at the input.
Rice. 8.42. Frequency converter equivalent circuit
Rice. 8.43. Signal spectrum at the input and output of the converter:
The only difference is that the output frequency is equal to or whatever the resonant frequency of the load circuit is.
So, when converting the frequency, the laws of change in the frequency amplitude and phase of the input oscillation are transferred to the output oscillation. In this sense, the signal conversion in question is linear, and the device is a linear converter or "mixer".
The spectrum of the signal over frequency without changing the shape of the spectrum. P. h. occurs when the oscillations of the signal n of the local oscillator act on a non-linear device, called. mixer; as a result, in the spectrum of the output signal, along with other frequencies, difference and sum frequencies are formed: the selection of one of them is the result of the operation of the mixer. The amount of shift is determined by the frequency of the auxiliary. generator (heterodyne).
P. h. is used in radio receivers, will measure. technique, reference generators, etc., since in this case the signal amplification in a wide range of tunable frequencies is replaced by the amplification of a non-tunable combination. frequencies, called intermediate. The constancy of the intermediate frequency = const when changing the frequency of the signal provides simultaneously. frequency tuning of the local oscillator T. o., signal amplification in devices with P. h. is carried out at a relatively low, usually standard frequency.
When transmitting information, radio frequency oscillations can be modulated according to dec. parameters: amplitude frequency p phase (see modulated fluctuations). In order for the h to be transferred to an intermediate frequency without distortion during P., it is necessary to perform. conditions: 1) a non-linear device (for example, ) must have a current-voltage characteristic close to quadratic or approximated by a polynomial of even degree; 2) the signal amplitude must be much less than the oscillation amplitude of the local oscillator 3) the frequency must be higher
Since there are dec. in the output circuit of the mixer. combin. frequency, then in order to isolate the difference or sum frequency, the output circuit must be selective, that is, resonant, tuned to the desired frequency.
Under P. frequency divider or frequency multiplier. FROM. F. Litvak.
Physical encyclopedia. In 5 volumes. - M.: Soviet Encyclopedia. Editor-in-Chief A. M. Prokhorov. 1988 .
See what "FREQUENCY CONVERSION" is in other dictionaries:
frequency conversion- The process of linearly shifting the bandwidth occupied by a signal to another region of the frequency spectrum, with or without inversion. [L.M. Nevdyaev. Telecommunication technologies. English Russian explanatory dictionary reference book. Edited by Yu.M. Gornostaev ...
frequency conversion- dažnio keitimas statusas T sritis automatika atitikmenys: engl. frequency conversion; frequency transformation vok. Frequenztransformation, f; Frequenzumsetzung, f; Frequenzumwandlung, f; Frequenzwandlung, f rus. frequency conversion, n pranc.… … Automatikos terminų žodynas
frequency conversion- dažnio keitimas statusas T sritis fizika atitikmenys: angl. frequency conversion vok. Frequenzumsetzung, f; Frequenzumwandlung, f; Frequenzwandlung, f rus. frequency conversion, npranc. conversion de la frequence, f … Fizikos terminų žodynas
radio frequency conversion- frequency conversion The process of transferring the radio frequency band occupied by a signal to another part of the frequency spectrum. [GOST 24375 80] Topics radio communication General terms radio reception Synonyms frequency conversion ... Technical Translator's Handbook
frequency conversion to number code- — [Ya.N. Luginsky, M.S. Fezi Zhilinskaya, Yu.S. Kabirov. English Russian Dictionary of Electrical Engineering and Power Industry, Moscow, 1999] Electrical engineering topics, basic concepts EN frequency to number conversion ... Technical Translator's Handbook
frequency conversion in the direction of its decrease- — [Ya.N. Luginsky, M.S. Fezi Zhilinskaya, Yu.S. Kabirov. English Russian Dictionary of Electrical Engineering and Power Industry, Moscow, 1999] Electrical engineering topics, basic concepts EN frequency down conversionFDC ... Technical Translator's Handbook
frequency to voltage conversion- — [Ya.N. Luginsky, M.S. Fezi Zhilinskaya, Yu.S. Kabirov. English Russian Dictionary of Electrical Engineering and Power Industry, Moscow, 1999] Electrical engineering topics, basic concepts EN frequency to voltage conversion ... Technical Translator's Handbook
frequency downconversion- — [Ya.N. Luginsky, M.S. Fezi Zhilinskaya, Yu.S. Kabirov. English Russian Dictionary of Electrical Engineering and Power Industry, Moscow, 1999] Electrical engineering topics, basic concepts EN frequency down conversion ... Technical Translator's Handbook
Radio Frequency Conversion- 163. Frequency conversion of a radio signal Frequency conversion Source: GOST 24375 80: Radio communication. Terms and definitions original document ... Dictionary-reference book of terms of normative and technical documentation
frequency conversion based on Raman scattering- Ramano dažnio keitimas statusas T sritis radioelektronika atitikmenys: engl. Raman frequency conversion vok. Raman Frequenzumwandlung, f rus. frequency conversion based on Raman scattering, n pranc. conversion Raman de frequence, f … Radioelectronics terminų žodynas
Books
- Radio engineering circuits and signals (set of 2 books), I. S. Gonorovsky. The book is a textbook for the new course "Radio Engineering Circuits and Signals" and corresponds to the program of this course for the specialty "Radio Engineering". In the first part, the spectral and ...
Frequency conversion - the shift of the signal spectrum on the frequency scale in one direction or another, i.e., in the region of both lower and higher frequencies. With such a shift or transfer, the shape of the spectrum should not change.
An example of frequency conversion (amplitude modulation, detection). When generating an AM signal, the spectrum of the modulating signal containing the transmitted message is transferred to the region of higher frequencies to enable the radiation of the receiving radio signal in the form of electromagnetic waves into the transmission line. When a radio signal is detected, its spectrum is also transferred, but in the opposite direction - to the low-frequency region, which makes it possible to again highlight the modulating signal, and, consequently, the transmitted message. In this case, of course, it is required that, with such transformations, the shape of the signal extracted during detection coincides with the shape of the modulating signal during modulation. Fulfillment of this requirement means that there is no distortion during the filing. A necessary condition for undistorted message transmission is the preservation of the spectrum shape of the control signal when it is transferred both to the high-frequency region (during modulation) and during reverse transfer to the low-frequency region (during detection).
The general principle behind frequency conversion is that the signal to be converted is multiplied by harmonic oscillations with a frequency r. This oscillation must be obtained using a special generator called heterodyne. If the signal spectrum contains a harmonic with a frequency of 0, then by multiplying these harmonic oscillations we get:
i.e., at the output of the multiplier, harmonic oscillations with sum and difference frequencies appear, therefore, each harmonic of the signal causes the appearance of two harmonic oscillations with sum and difference frequencies at the output of the multiplier.
In the figure of the AM signal spectrum conversion scheme:
a) AM signal
b) AM signal spectrum
c) local oscillator signal
d) local oscillator signal spectrum
e) signal spectrum at the output of the multiplier
f) frequency response of the difference frequency filter (or IF filter FPF)
g) signal at the output of the difference frequency filter.
Scheme of a transistor frequency converter.
In practical circuits of frequency converters, non-linear elements (semiconductor diodes, transistors, vacuum tubes) are used. In this multiplier circuit, the transistor performs, or rather, its input nonlinear circuit: the base-emitter transition. The best conditions for frequency conversion are obtained if the dependence i b \u003d (U b.e) is quadratic, i.e.
i b \u003d i b.e + a 1 U b.e + a 2 U b.e
In the converter, the voltage U b.e. is proportional to the sum of the voltages of the signal S (t) and the local oscillator U g (t), i.e. the variable component of this voltage:
U b.e (t) \u003d S (t) + U g (t)
Substituting this expression into (1) we get.
i b = i b. e + a 1 S(t) + a 2 U g (t) + a 2 S 2 (t) + 2a 2 U g (t) S (t) + a 2 U g (t)
Of all the terms in this formula, only one is of interest - the underlined one, which contains the products of the local oscillator voltage and signal.
For example, S(t) is described by the function
S AM (t)=Um sin(t+)
(amplitude modulated signal)
and U g (t) \u003d U m g sin (t +), then this term
2a 2 U g (t) S(t)= 2a 2 U m g sin(t+)*)=U m sin(t+)=
A 2 U m g U m (cos[- g)t+-]-cos[(- g)t++])
If the circuit in the collector circuit of the transistor is adjusted to an intermediate frequency pr \u003d - r, then all other oscillations with frequencies , r, - r, 2, 2 r will be filtered out. The current component of the difference frequency collector - r causes the appearance of voltage, on the resonant resistance of the circuit u, therefore, at the output of the converter
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 - hundreds of μV, 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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