Dual-circuit parametric amplifier. Power balance in multi-circuit parametric systems

The ability of controlled reactive two-terminal networks, under certain conditions, to play the role of active circuit elements served as the basis for the creation of a special type of radio engineering devices called parametric amplifiers. These amplifiers are used mainly in the microwave range as input stages of highly sensitive radio receiving devices. The main advantage of parametric amplifiers is their low noise level, which is due to the absence of shot current fluctuations in them.

Implementation of parametrically controlled reactive elements.

The possibility of parametric amplification of signals was theoretically predicted at the beginning of the century.

However, the plastic implementation of this idea became possible only in the 50s after the first successful designs of parametric semiconductor nodes were created. The operation of these diodes, also called varactors, is based on the following effect. If a voltage of reverse polarity is applied to the -junction of the diode, then the separated charge q in the blocking layer is a nonlinear function of the applied voltage u. The dependence is called the volt-coulomb characteristic of such a nonlinear capacitor. When the voltage changes in the locked bottom junction, a bias current appears

Here is the differential capacitance of the varactor, which is approximately described by the formula

where k is the size coefficient; - contact potential difference.

The more a junction is blocked, the lower its differential capacitance.

Modern varactors have very advanced characteristics and are capable of operating up to frequencies of several tens of gigahertz, which corresponds to the millimeter wavelength range.

An element with parametrically controlled inductance can also be created. It is an inductive coil having a core made of ferromagnetic material with a pronounced dependence of induction B on the biasing current I. Such elements have not found widespread use at radio frequencies due to the high inertia of the processes of magnetization reversal of the material.

Single-circuit parametric amplifier.

Let us consider a signal generator formed by parallel connection of an element with active conductivity and an ideal source of harmonic current with amplitude and frequency . A resistive load having conductivity is connected to the generator. There is a voltage at the generator terminals with an amplitude and active power is released in the load

As is known from circuit theory, in the load matching mode with the generator, when the value reaches its maximum value:

(12.37)

Obviously, the power in the load can be increased by somehow reducing the conductivity of the generator. This can be achieved, for example, by connecting a parametric capacitor (varactor) in parallel with the generator.

Rice. 12.4. Circuits of a single-circuit parametric amplifier: a - principle; b - equivalent

The varactor capacitance should vary with frequency. The initial phase of the pump oscillator should be chosen so that the resistance [see formula (12.34)] was negative.

In Fig. 12.4, a, b shows the circuits of the simplest single-circuit parametric amplifier that implements this principle.

Inductive element L together with a capacitor [see formula (12.27)] form a parallel oscillatory circuit tuned to the signal frequency. The input resistance of this circuit is so high that it practically does not shunt the negative active conductivity

introduced by the varactor.

Referring to Fig. 12.4, b, we note that the power released in the load will also be maximum in the matching mode, i.e., when

The ratio of this quantity to that determined by formula (12.37) in the absence of a parametric element is usually called the nominal gain

For example, let . Then or in logarithmic units.

Parametric amplifier stability.

If the negative conductivity of the varactor completely compensates for the sum of the conductivities of the generator and the load, then the parametric amplifier becomes unstable and self-excites.

From the equivalent circuit shown in Fig. 12.4, b, it follows that the critical value of the introduced negative conductivity

Assuming that the phase relationships between signal and pump oscillations are optimal in the sense that from formulas (12.34), (12.41) we find the critical depth of capacitance modulation:

Example 12.3. A single-circuit parametric amplifier operates at frequency ), the signal generator and the load have the same conductivity, varactor capacitance Determine the limiting limits of capacitance change, upon reaching which the amplifier self-excites.

Using formula (12.42) we determine

Thus, a parametric amplifier is self-excited if the varactor capacitance, changing with time according to a harmonic law, fluctuates in the range from to

Parametric gain in detuning mode.

In real conditions, it is difficult, and sometimes impossible, to accurately fulfill the synchronism condition. If the signal frequency is somewhat out of tune relative to the required value, that is, then the parametric amplifier is said to operate in asynchronous mode. In this case, the value Ф, which determines, according to (12.34), the active introduced resistance, depends on time: The introduced resistance, changing according to the law

periodically acquires different signs. As a consequence of this, profound changes in the level of the output signal are observed, similar in nature to beats. This disadvantage of single-circuit amplifiers largely prevents their practical use.

Dual-circuit parametric amplifier.

Work aimed at improving the performance characteristics of parametric amplifiers has led to the creation of fundamentally different devices, free from the above disadvantage. The so-called double-circuit amplifier is capable of operating at an arbitrary ratio of signal and pump frequencies, and regardless of the initial phases of these oscillations. This effect is achieved through the use of auxiliary oscillations that occur at one of the combination frequencies.

The circuit of a two-circuit parametric amplifier is shown in Fig. 12.5.

The amplifier consists of two oscillatory circuits, one of which, called the signal circuit, is tuned to the frequency and the other, the so-called idler circuit, is tuned to the idler frequency. The connection between the circuits is carried out using a parametric varactor capacitance, which changes over time according to a harmonic law with the pump frequency:

Rice. 12.5. Circuit of a two-circuit parametric amplifier

Typically, the quality factors of the signal and idle circuits are high. Therefore, in a stationary mode, the voltages on these circuits are quite accurately described by harmonic functions of time:

with certain amplitudes and initial phases.

Taking into account the signs of the stresses indicated in Fig. 12.5, we find that the voltage on the varactor, whence the current through the varactor

(12.44)

Let us analyze the spectral composition of this current. Using the formula we have already encountered, we are convinced that the current contains components at the signal frequency, at the idle frequency, and also at the combination frequencies

In order to find the conductivity introduced into the signal circuit by a series connection of a varactor and an idler circuit, one should first of all isolate in formula (12.44) the current component at the signal frequency:

(12.45)

Here the first term is in time quadrature with the voltage and therefore is not associated with the introduction of active conductivity into the circuit. The second term is proportional to the voltage amplitude on the idle circuit. To find this value, we select in (12.44) the useful component of the current at the idle frequency, proportional to the amplitude

If is the resonant resistance of the idle circuit, then the voltage on it, caused by oscillations at the signal frequency,

whence it follows that

(12.47)

Substituting the values ​​into the second term of formula (12.45), we obtain the expression for the useful component of the current at the signal frequency, which is due to the influence of the varactor and the idle circuit:

Thus, the conductivity introduced into the signal circuit by the series connection of the varactor and the idle circuit turns out to be active and negative:

The nominal gain is calculated using formula (12.40). Stability analysis is carried out in the same way as in the case of a single-circuit amplifier.

Comparing formulas (12.38) and (12.49), it can be noted that in a two-circuit amplifier the introduced negative conductivity is not associated with the initial phases of the signal and pump. In addition, a two-circuit parametric amplifier is not critical to the choice of frequencies and the inserted conductivity will always be negative if

Power balance in multi-circuit parametric systems.

The insensitivity of parametric amplifiers using Raman oscillations to the phase relationship between the useful signal and the pump makes it possible to study such systems on the basis of simple energy relationships. Let us turn to the general diagram presented in Fig. 12.6.

Here, three circuits are connected in parallel with a capacitor with a nonlinear capacitance. Two of them contain signal and pump sources, the third is passive and serves as an idle circuit tuned to the combination frequency ( - integers). Each circuit is equipped with a narrow-band filter that passes only vibrations with frequencies close to respectively. For simplicity, it is assumed that the signal and pump circuits have no ohmic losses.

Let one of the sources (signal or pump) be absent. Then the current flowing through the nonlinear capacitor will not contain components with combination frequencies. The idle circuit current is zero and the system as a whole behaves like a reactive circuit, consuming no power on average from the source.

If both sources are present, then a current component appears at the combination frequency; this current can only be closed through the idle circuit.

Rice. 12.6. To the derivation of energy relations in a two-loop parametric system

The load present here consumes power on average, and positive or negative resistances are introduced into the signal and pump circuits, the value and sign of which determine the redistribution of power between the sources.

The system under consideration is closed (autonomous), and based on the law of conservation of energy, the average powers of the signal, pumping and Raman oscillations are related by the relation

The power averaged over the oscillation period T can be expressed in terms of the energy E released during this time interval:

( - frequency in hertz). Thus,

or, given that

As is customary, we will consider the power released in the load to be positive and the power supplied by the generator to be negative. From relations (12.54) it is clear that since then So, if the idle circuit of the amplifier is tuned to the frequency, then both sources (signal and pump) give power to the idle circuit, where it is consumed in the load. Since then the power gain

The advantage of this method of parametric amplification lies in the stability of the system, which is unable to self-excite at any signal or pump power. The disadvantage is due to the fact that the frequency of the output signal is higher than the frequency of the input signal. In the microwave range this causes certain difficulties in further processing of oscillations.

Regenerative parametric amplification.

Let i.e., the tuning frequency of the idle circuit. The Manley-Rowe equations take the form

As follows from the first equation, in this mode both powers are positive. Thus, some of the power taken from the pump generator enters the signal circuit, i.e., regeneration at the signal frequency is observed in the system. Output power can be extracted from both the signal and idle circuits.

Equations (12.56) do not make it possible to determine the gain of the system, since the power contains both the part consumed from devices connected to the amplifier input and the part arising due to the regeneration effect. It can be noted that such amplifiers are capable of self-excitation, since under certain conditions non-zero power will develop in the signal circuit even in the absence of a useful signal at the input.

A parametric amplifier is a device containing an oscillatory circuit in which, under the influence of an external source (pump generator), an energy-intensive parameter (capacitance or inductance) changes and, due to the appropriate organization of the oscillatory system, the signal is amplified.

There are semiconductor, ferrite and electron beam parametric amplifiers.

Semiconductor parametric amplifiers (SPA) due to a number of positive properties (low required power of the pump generator,

the possibility of microminiaturization, etc.) have received the greatest application. The main element of the PPU is a parametric diode, which is a reverse-biased p-n junction, suitably connected to the oscillatory system, to which constant mixing and voltage are supplied from the pump generator, creating capacitance modulation. The dependence of the diode capacitance on the applied bias voltage is described by the expression:

where is the contact potential difference;

n is a parameter characterizing the nonlinear properties of the capacitance (for welded diodes n = 1/2, for diffusion diodes - n = 1/3).

If a pump voltage is applied to a reverse-biased p-n junction, then the change in diode capacitance can be described

where , , is the modulation depth of the capacitance at the corresponding harmonic of the pump frequency.

Due to the nonlinear dependence of the capacitance of a parametric diode on the applied voltage, currents of various combination frequencies can arise in it

Where m, n- integers ranging from to .

If the capacitance has no losses, then the power distribution over combination frequencies is determined by the Manly-Rowe relation

where is the power at frequency.

It should be noted that the Manly-Rowe relations follow from the law of conservation of energy for a parametric amplifier.

The most interesting cases are when the system operates at three frequencies - the signal and pump frequencies and one of the combination frequencies. Typically the combination frequency is either the sum frequency or the combined frequency.

Let's consider a parametric amplifier operating at a sum frequency, i.e. combination frequency is the sum of frequencies

signal and pump generator. In relation to the Manly-Rowe equations, these three frequencies can be represented as

Then, based on the relations, Menly Row can be written

The operating mode is non-regenerative, because at . The power gain from the second equation is defined as

This type of parametric amplifier is powered by a stable boost converter. Their use is limited by the fact that when amplifying microwave signals it is difficult to achieve sufficiently large gain factors.

Let's consider an example when oscillatory circuits tuned to frequencies , , , are connected through a nonlinear capacitance.

In accordance with the Manly-Rowe relations, we have

It follows that the frequency chains, from the point of view of parametric influence, are energetically equivalent, the power of the pump generator is pumped into both of these chains or, in other words, negative conductivity is introduced both at the signal frequency and at the difference frequency.

Therefore, parametric amplifiers of this type are regenerative.

Depending on the ratio of frequencies, resonances can be either in different oscillatory systems, or, if in one oscillatory system.

In the first case, the parametric amplifier is called a double-circuit amplifier (circuits tuned to the pump frequency are not taken into account); in the second case, it is called a single-circuit amplifier.

The most widely used are double-circuit reflective-type PPUs, since, unlike single-circuit PPUs, they do not require strict phasing of signal and pump frequencies and allow low noise temperatures combined with good broadband.

The block diagram of a parametric amplifier can be presented as follows (Fig. 5.9).

The schematic diagram of a dual-frequency or, as it is often called, a dual-circuit amplifier is shown in Fig. 10.16. The first, signal, circuit is tuned to the central frequency of the signal spectrum (resonant frequency), and the second, “idler” circuit is tuned to the sor frequency, which is quite different from .

The pumping frequency is selected from the condition

(10.43)

When choosing a frequency, it is based on the condition that the signal frequency is outside the transparency band of the auxiliary contour. But the combination frequency must be outside the operating band of the signal circuit.

If these conditions are met, only one frequency voltage will exist on the signal circuit, and only one frequency voltage will exist on the auxiliary circuit. Considering the amplitudes of these voltages to be small compared to it is possible to replace the nonlinear capacitance , together with the pump generator, with a linear parametric capacitance that varies with frequency, as was done in § 10.5.

Rice. 10.16. Dual frequency parametric amplifier

Then, under the influence of the signal voltage, a current arises in the variable capacitance circuit (in addition to other components that are not of interest in this case)

[cm. 10.36)]. Here .

The current across the open circuit resistance creates a voltage drop

We write down the equivalent EMF acting on capacitance C, as in § 8.16 [see. (8.99)], in the form

The combination current due to this EMF, by analogy with expression (10.44), will be

Note that the pumping phase and frequency (it) are absent in expression (10.45).

Taking into account the above relation for the last equality can be written in the form

As we see, in relation to the signal circuit, the nonlinear capacitance, together with the pump generator and the idle circuit, can be replaced by conductivity, taking into account the found current

The complex amplitude of this current

Complex voltage amplitude on the signal circuit Therefore, the conductivity shunting the signal circuit will be

(10.46)

where is the complex conjugate function

For resonance, when, therefore, the resistance of the auxiliary circuit will be and formula (10.46) takes the form

In the equivalent circuit shown in Fig. 10.17, the elements located to the left of the dashed line correspond to the signal circuit of the amplifier, and to the right - the nonlinear capacitance along with the auxiliary circuit. The resulting circuit essentially coincides with the circuit of a single-circuit amplifier (see Fig. 10.15). The only difference is in the method of determining the equivalent negative conductivity.

The details related to the definition of combination oscillations are given in order to draw attention to the following advantages of a two-circuit amplifier:

a) the equivalent negative conductance, and therefore the power gain, does not depend on the phase of the pump voltage.

b) compliance with a certain relationship between frequencies is not required

Both of these properties of a two-circuit amplifier are explained by the fact that the total phase of the combination current in expression (10.45), which determines the nature of the equivalent conductivity, is essentially the phase difference of the pump voltages. The first of them has the form and the second (without taking into account ). When the difference is formed, the difference drops out, and the difference frequency in any case coincides with the signal frequency (since ).

The gain of a two-circuit amplifier at the resonant frequency can be determined from an expression similar to formula (10.40):

where is calculated by formula (10.46), is the load conductivity of the signal circuit.

When the signal frequency deviates from the resonant frequency and, accordingly, the frequency from the resistance module decreases, which leads to a decrease in the module and, consequently, the power gain.

Based on expression (10.46), the frequency response and bandwidth of the dual-circuit amplifier can be calculated.

The stability condition of the amplifier in this case can be written in the form

Let us consider the energy balance in a dual-frequency amplifier depending on the frequency ratio. Let the frequency and power of the signal at the amplifier input be given. Since with increasing auxiliary frequency the module of the negative value increases [see. (10.46)], then it also increases [see. (10.48)]. Amplifier output signal power

To determine the required power of the pump generator Pson, as well as the power allocated in the auxiliary circuit, we will use the Manly-Rowe theorem. Based on expression (7.104), the following relations can be written:

(The minus sign in the last expression is omitted, since it is obvious that this power is taken from the pump generator.) The power relationship is illustrated in Fig. 10.18. From this figure it is clear that more power is released on the auxiliary circuit than on the signal circuit. Thus, although the power increases with increasing frequency, the distribution of power taken from the pump generator changes in favor of the frequency. Despite this, they often operate in the mode since when amplifying a weak signal, the main importance is not the degree of power utilization, but the power ratio

To illustrate the quantitative relationships in a two-frequency parametric amplifier, we give the following example.

Let it be necessary to amplify a signal at a frequency with a spectrum width

Initial data of the first (signal) circuit: characteristic resistance Ohm; internal resistance of the signal source, shunt circuit, ; load resistance .

Initial data of the second (idle) circuit: resonant frequency; characteristic resistance Ohm; load resistance .

Before calculating the required variation of the varicap capacitance, we will find the limiting conductivity value that can be connected to the signal circuit for a given signal spectrum width

The maximum quality factor of the signal circuit (when shunted with negative conductivity), obviously, should not exceed

When the resulting conductivity shunting the first circuit must be at least

In conclusion, we note the main advantages and disadvantages of a parametric amplifier.

An important advantage of a parametric amplifier is its relatively low noise level compared to transistor or tube amplifiers. In § 7.3 it was noted that the main source of noise in transistor and tube amplifiers is the shot effect, caused by the chaotic transfer of discrete charges of electrons and holes (in the transistor). In a parametric amplifier, a similar effect occurs in a device that modulates a parameter. For example, a change in the capacitance of a varicap occurs due to the movement of electrons and holes. However, the intensity of the flow of electrical carriers in a varicap is many times less than in a transistor or lamp. In the latter, the flow intensity directly determines the power of the useful signal released in the load circuit, and in a varicap it is just the effect of parameter modulation. The weakening of the influence of the shot effect is so significant that in a parametric amplifier the noise level is determined mainly by thermal noise. In this regard, cooling the parametric diode to 5 ... 10 is often used.

The disadvantage of a parametric amplifier is the complexity of decoupling the pump and signal circuits.

In the circuit presented in Figure 10.14, a, typical for parametric amplifiers of the meter range, decoupling is carried out using isolation capacitors and blocking chokes. In the microwave range, where parametric amplifiers are especially widely used, it is necessary to resort to very complex designs that combine in one unit a two-frequency oscillatory circuit in the form of hollow resonators, a varicap and special decoupling elements (circulator, directional coupler, absorber, barrier filter). These issues are discussed in special courses.

It was found that, under certain conditions, parametric elements are capable of playing the role of active elements in a circuit. This allows you to create based on them parametric amplifiers, which have a low level of intrinsic noise, since there is no current noise due to the shot effect. Parametric amplifiers are mainly used in the microwave range as input stages of radio receiving devices with high sensitivity.

In the 50s of the 20th century, the first semiconductor parametric diodes were designed ( varactors). Parametrically controlled nonlinear capacitances and inductances were studied in section 2.3.

Single-circuit parametric amplifier. The schematic diagram of such an amplifier is shown in Fig. 6.8, a, and the equivalent is in Fig. 6.8, b.

Dependence of parametric capacitance on the harmonic pump signal at frequency
:

Conductivity
is introduced into the equivalent circuit of the amplifier by a parametric change in capacitance by the pump signal. Input signal – harmonic current generator with amplitude , frequency and internal conductivity
.,
- load conductivity. To implement parametric amplification with maximum power release on the load conduction, the following conditions must be met:

(6.27)

Where
;

(6.29)

since the voltage amplitude at the generator terminals is equal to , and active power is released in the load
.

If there is no pump signal, then power is released in the load

(6.30)

and
, because
.

Nominal power gain of a parametric amplifier is called the quantity

(6.31)

for example if
Cm,
See then.

The critical value of the introduced negative conductivity, when the parametric amplifier loses stability and self-excites,

(6.32)

Under conditions (6.32), the negative conductivity of the varactor completely compensates for the sum of the conductivities of the input generator and load. The parametric amplifier operates stably if
, if
, then the amplifier self-excites and turns into a parametric self-oscillator.

Let the phase relationships of the input signal and pump oscillations be optimal so that in (6.27)
. Then from (6.27) and (6.32) we find the critical depth of modulation of the parametric capacitance by the pump signal:

(6.33)

Let's consider parametric amplification in detuning mode. Synchronism condition:
, it is almost impossible to perform accurately. Let
- frequency detuning of the input signal, that is
. If
, then the amplifier operates in asynchronous mode. Then the magnitude of the phase shift
, which determines the conductivity introduced into the circuit, depends on time:. The introduced resistance changes as

(6.34)

periodically changing sign to the opposite one over time.

As a result, profound changes in the output signal level, similar to beats, are observed. This drawback prevents the use of single-circuit amplifiers in practice.

Dual-circuit parametric amplifier. Free from the specified disadvantage two-circuit parametric amplifier, the diagram of which is shown in Fig. 6.9.

The amplifier consists of two oscillating circuits, one of which is tuned to the frequency . This circuit is called signal. Another circuit called single, set to idle frequency
. The connection between the circuits is achieved through a parametric varactor capacitance. The pump signal changes the parametric capacitance according to the harmonic law at the pump frequency
:

Both oscillatory circuits - signal and idle - are high-Q. Therefore, in stationary mode, the voltages on these circuits are approximately harmonic:

(6.36)

According to Fig. 6.9, voltage on the varactor
. Then the current through the varactor

(6.37)

Since , the signal spectrum (6.37) contains components at the signal frequency
, at idle frequency
, as well as at combination frequencies
And
. The varactor and idler circuit connected in series to the signal circuit can be replaced in the equivalent circuit by the conductivity introduced into the signal circuit. To find this conductivity, it is necessary to isolate in (6.37) the current component at the signal frequency:

In (6.38), the first term is shifted relative to the voltage
in phase on
. Therefore, due to it, there is no introduction of active conductivity into the signal circuit. Second term at signal frequency proportional to amplitude
voltage on the idle circuit. Let's find the value
. To do this, let us isolate in the varactor current (6.37) a useful component at the idle frequency, proportional to
:

(6.39)

Let
- resonant resistance of the idle circuit. The voltage on it caused by oscillations at frequency
,

whence, comparing with the second expression in (6.36), we obtain:

(6.41)

Let us substitute expressions (6.41) into the second term in (6.38). We obtain the expression for the useful component of the current at the signal frequency due to the influence of the varactor and the idle circuit:

The conductivity introduced into the signal circuit by the series connection of the varactor and the idler circuit is

(6.43)

turns out to be active and negative.

Next, you can calculate the nominal gain of a two-circuit parametric amplifier using formula (6.31). The stability analysis of a double-circuit amplifier is carried out in the same way as for a single-circuit amplifier. Let's compare the expression

(6.27)

for a single-circuit amplifier and (6.43) for a double-circuit amplifier, we find that in a double-circuit amplifier the introduced conductivity, unlike a single-circuit amplifier, does not depend on the initial phases of the input signal and pumping. In addition, a double-circuit amplifier, unlike a single-circuit amplifier, is not critical to the choice of signal frequencies and pumping
. The introduced conductivity will be negative if
.

Conclusion.A two-circuit amplifier is capable of operating at an arbitrary ratio of signal and pump frequencies, regardless of the initial phases of these oscillations. This effect is due to the use of auxiliary oscillations that occur at one of the combination frequencies.

Power balance in multi-loop parametric systems. Insensitivity to phase relationships allows you to study: multi-loop parametric systems based on energy relationships. The equivalent circuit of a two-circuit parametric amplifier is shown in Fig. 6.10.

Here parallel to the nonlinear capacitance
three two-terminal networks are included. Two of them contain signal and pump sources, and the third forms an idler circuit tuned to the combination frequency
, Where
And - integers. Each of the three two-terminal networks contains a narrow-band filter tuned to frequencies ,
And
, respectively. Simplifying the problem, we assume that the signal and pump circuits do not have ohmic losses. If one of the sources (signal or pump) is missing, then there are no components at combination frequencies in the current flowing through the nonlinear capacitor. The idle circuit current is zero. The system behaves as a reactive system, that is, on average it does not consume source power.

If both sources are present, then a current component appears at the combination frequency
. This current can be closed through an idle circuit. The idle circuit load consumes power on average. Active parts of resistances appear in the signal and pump circuits. Their values ​​and signs are determined by the redistribution of power between sources. Let us apply to the autonomous (closed) system Fig. 6.10 law of conservation of energy: the average (over the periods of the corresponding oscillations) powers of the signal, pumping and combination oscillations are related as

(6.44)

Average power expressed through energy allocated for the period:

Where
- frequency.

Where
,
And
, or

Execution of (6.45) regardless of the choice of frequencies And
is possible only when

(6.47)

In (6.47) we move from energies to powers, we get Manly-Rowe equations:

(6.48)

The Manly-Rowe equations make it possible to study the patterns of power conversion in multi-circuit parametric systems. Let us study two typical cases.

Parametric amplification with frequency up-conversion. Let in (6.48)
. We have:

(6.49)

The power released in the load is positive, and the power supplied to the circuit by the generator is negative. Since in (6.49)
, That
And
(see Fig. 6.11).

Conclusion. If the idle circuit of the parametric amplifier is tuned to the combination frequency
, then both sources - signal and pump, supply power to the idle circuit, where it is consumed in the load. Because
, then the power gain

(6.50)

The advantage of the system under study is that it is so stable that it cannot be excited at any signal or pump power. Disadvantage – the frequency of the output signal is higher than the frequency of the input signal. In the microwave range this leads to difficulties in signal processing.

Regenerative parametric amplification. Let
,
. Then the idle circuit frequency
, And
. The Manly-Rowe equations are:

(6.51)

From the first equation in (6.51) it follows that
And
. This means that some of the power taken from the pump generator enters the signal circuit. That is, in the system there is regeneration at signal frequency. Output power can be extracted from both the signal and idle circuits (see Fig. 6.12).

Great Soviet Encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .

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