Double balanced mixer with 8 diodes. Powerful high frequency mixers

Any radio receiving device contains signal converters from HF to IF and IF to LF (there may be several intermediate frequencies). In the PPP there is only one such converter, from HF directly to LF. They are called mixers and are located immediately after the antenna and the DPF, or further - after the UHF, IF, thus “connecting” the main components of the receiver with the GPA, OG. Therefore, the parameters of the entire receiver largely depend on the efficiency and quality of signal conversion. There are two main types of mixers - passive and active. The former have a transmission coefficient of less than 1, and the latter provide a signal amplification greater than unity, however, to maintain the dynamic range, the amplification is not made large, usually no more than 10 times the voltage.

Any mixer, especially the very first one, in addition to the transmission coefficient, must also have a low noise level (to increase sensitivity). An equally important indicator is the ability to suppress powerful out-of-band signals, which can result in direct detection and “clogging” of the main signal.

Active type mixers will not be considered in this article, because This is a separate independent topic. The article is devoted to passive mixers made on passive elements - semiconductor diodes, as they are most widely used in various amateur radio designs. Passive mixer circuits based on field-effect, including high-power, transistors operating in key modes, as well as mixer circuits on electronic switches, have also become widespread. various types multiplexers/demultiplexers). However, this is also a topic for a separate article.

First of all, balanced mixers of various types are symmetrical circuits in which two signals (RF input and heterodyne) are mixed. Double balanced mixers are widely used in radio receiver circuits. They are balanced not only with respect to local oscillator oscillations, but also with respect to the input signal. This type of mixer attenuates both the local oscillator and input signals at the output. Naturally, the output also produces a lower level of conversion by-products compared to conventional balanced mixers.

At HF frequencies of amateur radio bands (up to 30 MHz), ordinary high-frequency silicon diodes, for example, types KD503, KD509, KD514, KD521, KD522 and germanium type GD508, also have fairly good conversion properties.

In double balanced mixers, it is advisable to use Schottky diodes (for example, type KD922). A fairly common mistake is to consider KD514 silicon diodes to be Schottky diodes. These are not Schottky diodes, but according to some characteristics they are quite close to them. Sometimes in the old reference books This error occurs because According to the technology, a diode with a METAL-SEMICONDUCTOR contact was previously called a diode with a Schottky structure (according to the author of this technology). Its production technology is a cross between a conventional diode with a pn junction and a diode with a Schottky barrier. According to physics (not technology!), the forward voltage of silicon Schottky diodes is noticeably lower than that of conventional silicon diodes (using any other technology). In addition, there is a large ratio of reverse to forward resistance and insignificant capacitance at zero bias. Schottky diodes have a very short switching time, which expands the frequency range of their application (up to several hundred GHz).

The use of silicon, pulsed, epitaxial-planar, high-speed, short-recovery diodes KD514 (that’s what it’s correct to call them!) in high-speed switches, which include ring diode mixers, increases sensitivity by reducing the noise figure and, thus, can increase the gain of the IF path (and ultimately the sensitivity). Sometimes in practice, installing KD514 has a noticeable, audible effect, without selecting diodes, which cannot be said about KD503 and other types of diodes.

The amount of loss in a diode mixer is usually 6-10 dB. This is not much, but most designers want to have less losses. This suggests the need to use an active mixer in the receiver circuit. But the dynamic range (DR) of a receiver with a passive mixer is often greater than that of a receiver with an active mixer. In addition, DD is needed when the radio receiver is intended to work with powerful neighboring radio stations, or in the conditions of amateur radio contests, when in the general air dump, weak stations are adjacent to powerful neighbors. Under normal conditions, this almost never happens. Thus, the magnitude of the receiver's dynamic range should not particularly concern us.

If the mixer is the first stage of the receiver, and this happens quite often, then all the main characteristics of the receiver practically depend on the quality of the mixer. The level of the mixer's own noise is important. The smaller it is, the higher the achievable sensitivity of the receiver becomes. From the above, it becomes clear that among diodes, preference should be given to those with the smallest direct internal p-n resistance transition. The smaller it is, the less noise is generated in the diode at the same current through the diode. It should be borne in mind that the stage following the mixer must also have a low noise figure. This is very important to realize the benefits of a passive mixer.

Figure 1 shows the circuits of a simple balanced mixer and a ring (double balanced) mixer made using diodes.

These mixers use balun transformers T1 and T2, wound on ring ferrite cores with a twist of three wires.

To achieve maximum sensitivity, when setting up the mixer, you need to select the local oscillator voltage. Insufficient voltage reduces the transmission coefficient and increases the input resistance, and excessive voltage increases the noise of the mixer itself. In both cases, sensitivity decreases. The optimal voltage ranges from fractions of a volt to 1-1.5 V (amplitude value) and depends on the type of diode.

In mixers with back-to-back diodes (VPD), voltage is supplied simultaneously through the coupling coil - the signal from the input circuit and the local oscillator voltage (Fig. 2).

The local oscillator voltage is significantly greater than the signal voltage. For normal operation For such a mixer on silicon diodes, the local oscillator voltage should be 0.6-0.7 V (amplitude value). One of the diodes opens at the peaks of the positive half-waves of the local oscillator signal, and the other - at the peaks of the negative ones. As a result, the resistance of parallel-connected diodes decreases twice during the heterodyne voltage period. Hence such advantages of this mixer as the absence of direct current (the mixer does not detect either the signal or the local oscillator voltage). And the local oscillator frequency is chosen to be half the signal frequency, which improves frequency stability and significantly reduces local oscillator interference to the input circuits of the mixer, because the emission of its signal is 30-60 dB lower (half the signal frequency) than with conventional mixers.

In a VPD mixer, it is best to use silicon diodes with a threshold voltage of about 0.5 V - they provide slightly greater noise immunity than germanium diodes. In any case, it is necessary to select the optimal local oscillator voltage for the maximum transmission coefficient. In general, all types of diode mixers require careful selection of the GPA voltage to obtain the best mixer parameters.

For more information about the operation of mixers, we also recommend that you refer to the works of V.T. Polyakov, G. Tyapichev, links to which are indicated at the end of the article.

Summarizing the above, it should be noted that in the above circuits of diode mixers, it is required (in addition to the correct choice of diode type) both symmetry (identical characteristics) of the diodes themselves, or their arms (in ring circuits), and symmetry of the design. Thus, for normal operation of diodes in mixer circuits, we can talk about the need for their correct selection and installation on the circuit board (the design of installing mixers on diodes will be discussed at the end of the article).

Without selecting diodes, it is difficult to ensure the required symmetry of the bridge, especially in those circuits where no balancing elements are provided, as in the circuits in Fig. 1 and 2. The required symmetry of the heterodyne voltage is achieved by the fact that the coupling coil (or broadband transformers) is wound simultaneously by two others twisted wires and is placed on a ferrite ring strictly symmetrically. Failure to follow this simple rule leads to the fact that some radio amateurs installing modern types of diodes do not select them during the initial debugging of the mixer design, believing that the asymmetry of the remaining home-made elements reduces the gain from their selection to zero. Naturally, the reasons for the asymmetry may be associated not only with the transformers themselves, so it is not recommended to rush to redo them.

When choosing diodes for a mixer based on reference materials, it should be noted that their capacitances should be the same (and as small as possible) at the same voltage. It is advisable to select a minimum switching (recovery) time. V.T.Polyakov, RA3AAE in his works indicates that preference should be given to diodes with a lower capacitance (no more than 1...3 pF) and the shortest reverse resistance recovery time (no more than 10...30 ns). This data can be found in reference books. When working on VHF, the requirements increase even more.

In many cases, the optimal choice may be to use ready-made diode microassemblies with selected characteristics. For example, the often recommended KDS523A, B, or diodes selected for the assembly (KDS523VR). However, in a number of cases, it is necessary to check these assemblies at least in the most in a simple way, since the permissible spread in them can reach 10% and this can negatively affect the operation of the mixers and will require adding balancing resistors and/or capacitors to the mixer circuit, which is generally useless, since it increases losses in the mixer. And this is always undesirable.

Received in Lately Widespread selection of diodes based on direct resistance does not seem to be so relevant, since an imperfect transformer (as mentioned above) will still introduce an imbalance in the arms of the bridge. Of course, if you are confident in the complete symmetry of the windings and their equality of total (complex) resistances, then using a conventional digital multimeter (in the “testing” mode) you can reject diodes with large deviations in direct resistances. There is a second reason, even more significant. It's about the fact that the equality of direct resistances only means that with the same amplitude of the local oscillator, the same current will flow through the diode. But this is important for high voltages from the GPA, but for input signals, the amplitude of which is much smaller and lies at the microvolt level, the most important thing is the same I-V characteristics of the diodes precisely in the region of low voltages, i.e. at the very beginning of the current-voltage characteristic, and not in the region of high voltages.

Unfortunately, domestic diodes, even from the same batch, not to mention just the same type, have a very large spread of parameters, so simple selection by resistance (forward voltage) at one point of the current-voltage characteristic is ineffective. An explanation of why such a selection is not effective is given in the figure below. In fact, the spread of the I-V characteristics of diodes can be quite large, but by chance, at the measurement point, the internal resistance of the diodes will be the same with a fairly high accuracy. In fact, this is possible quite often. However, this is only the appearance of the identity of the current-voltage characteristics of the diodes. Selection using 2 points is more accurate. But such a selection is also only a check of the coincidence of static characteristics, and not dynamic ones.

Therefore, it is often recommended to use imported ones - the same 1N4148 (analogous to KD522). They have a significantly smaller spread, which guarantees good operation of the mixer even without selection. Although it is very simple to select the current-voltage characteristic at one point with a digital multimeter (in testing mode). It should be noted that in this circuit for selection (and in others too!) diodes must be connected using alligator clips or the like, but in no case by soldering. Even after connecting with clamps, you need to wait a while - heating the diodes by hand changes the measurement results (not to mention soldering). And they need to come to room temperature...

You can select diodes based on “direct voltage” by assembling the simplest scheme: from a stable source with a voltage of at least 10 V through a resistor, a forward current through a diode is set (for example, 1 mA). And they measure the voltage drop with any voltmeter with a high input impedance (tube, type VK7-9, or any digital, which is better). Select diodes that have the closest measured voltage values. You can check two points, for example, by setting currents of 1 mA and 0.1 mA.

A common technique is recommended for selecting diodes for a ring balanced mixer and is described B. Stepanov, RU3AX. It is used to compare the current-voltage characteristics of diodes in the forward direction. Since a semiconductor diode is a nonlinear element, direct measurement of its direct resistance with an ohmmeter does not allow such a comparison. This must be done at several (at least two) points current-voltage characteristics diode, measuring the voltage drop across the diode at fixed forward current values. The diagram of the simplest device that allows you to select diodes is shown in the figure.

To select diodes exact values stabilized current are not significant - all diodes will be compared at the same current values. It is only necessary that these values ​​differ by about ten times... Details of the assembly and operation of this device are given .

As we discussed earlier, it is necessary to multiply the input signal by the sinusoidal voltage of the local generator (local oscillator). Devices that multiply two analog signals in radio receiving and radio transmitting devices are called mixers. Typically, the operation of multiplying two analog signals is carried out due to the current-voltage characteristic of the nonlinear element. An example of the current-voltage characteristic of a nonlinear element is shown in Figure 1.

Figure 1 Multiplication of two analog signals due to the current-voltage characteristic of a nonlinear element

In real mixer circuits, the signal amplitude of the local oscillator (local oscillator) is many times greater than the amplitude of the input signal. Therefore, the dynamic resistance (or transmission coefficient) of a nonlinear element can be considered as a function of the local oscillator voltage. The transmission coefficient of a nonlinear element is determined by the formula:

therefore, the transconductance can be considered as a derivative of the current-voltage characteristic of the nonlinear element. Then the voltage at the mixer output will be written as follows:

This formula shows that the described change in the operating mode of a nonlinear element under the influence of the local oscillator voltage is equivalent to multiplying the input signal by this voltage. If the current-voltage characteristic is quadratic dependence current from voltage, then its derivative will be linear function, and in this case, the transconductance of the nonlinear element will linearly depend on the local oscillator voltage, which means that no useful signal will appear in the mixer.

Now let's determine the transmission coefficient of the mixer (frequency converter). To do this, we will use the dependence of the slope of a nonlinear element with a quadratic characteristic on the input voltage. A graph of the slope versus input voltage for a nonlinear element with a quadratic characteristic is shown in Figure 2.

Figure 2. Graph of transconductance versus input voltage for a nonlinear element with a quadratic characteristic

Unfortunately, in addition to the useful transformation described, additional spectrum components will be present at the output of the nonlinear element. First of all, this is the voltage of the local oscillator itself and its harmonics. After all, a nonlinear element also has a static transmission coefficient. The same can be said for the input signal. In the case of a quadratic characteristic of a nonlinear element, the voltage of the first and second harmonics of both the local oscillator and the input signal will be present at its output.

When discussing the principles of operation, we have already discussed that to transfer the spectrum of the useful signal to an intermediate frequency, the formula is used:

However, in the situation under consideration, the nonlinear element contains harmonic signals of the input signal and the local oscillator. An intermediate frequency can be formed not only by the first harmonics, but also by harmonics of higher orders. As a result, this formula is modified to the following form:

As a result, additional side reception channels are formed in the receiver. Where these channels are located and the mechanism of their occurrence is illustrated in Figure 2.

Figure 2. Mechanism of formation of side channels due to second- and third-order nonlinearity products

Closest side channel is the channel f with ", spaced halfway intermediate frequency. It is formed by multiplying its second harmonic and the second harmonic of the local oscillator. The frequency difference between them exactly corresponds to the intermediate frequency. As a result of conversion, the signal of this channel passes to the output of the intermediate frequency filter without attenuation. The appearance of this side channel results in stricter requirements for the RF filter.

To combat this reception side channel, symmetrical mixer circuits such as and mixers are used. In addition, the local oscillator signal level plays a significant role. As the local oscillator signal level increases, the harmonic level of the received signal decreases. This is due to the fact that the nonlinear element actually goes into the key operating mode.

In exactly the same way, a side channel is formed by multiplying the third harmonic of the side channel f c "and local oscillator. Usually in a mixer the level of third-order conversion products is higher than the level of second-order conversion products, however, this side reception channel is further away from the useful signal (2/3 f IF), and therefore can be more easily suppressed using a preselector bandpass filter.

When designing a mixer, the number of signal and local oscillator harmonics taken into account depends on the type of current-voltage characteristic of the nonlinear element and the shape of the local oscillator signal. Mixers built on nonlinear elements with quadratic current-voltage characteristics have the smallest number of harmonics, and, consequently, the smallest number of side channels.

Recently, frequency converters with a rectangular local oscillator voltage have become widely used. The active elements of the mixer (diodes or transistors) operate practically in switching mode. Moreover, both in the open and closed states, they represent almost linear resistance. As a result, practically no harmonics of the useful signal are formed. The nonlinear properties of active elements appear only when switching operating modes, and the shorter this interval, the better. As a result, the local oscillator harmonics have nothing to interact with

To suppress unwanted spectrum components, bandpass filters are used, tuned to the frequency of the working channel. In addition, some mixer circuits use different methods for compensating local oscillator and signal voltages and currents. Mixers based on diodes and transistors are most widely used in superheterodyne receivers. Let's start studying the operation of frequency converters with the simplest circuit - a diode mixer

Literature:

Together with the article “The principle of operation of a mixer (frequency converter)” read:

Real mixers are difficult to analyze, and therefore their performance characteristics are determined by many parameters...
http://site/WLL/ParSmes.php

In a diode converter, two signals are simultaneously supplied to the input of a nonlinear element, which is a diode...
http://site/WLL/DiodSmes.php

In order to remove the local oscillator voltage from the output signal, a push-pull circuit called a balanced mixer is usually used...
http://site/WLL/BalSmes.php

A ring mixer circuit allows you to reduce the level of the radio signal at the output of the frequency converter...
http://site/WLL/KolSmes.php

In some cases, in a superheterodyne receiver it is very difficult to satisfy the requirements for suppressing the frequency of the mirror channel and the adjacent channel simultaneously...
http://site/WLL/kvSmes.php

Based on their circuit design, microelectronic mixers are usually divided into three types: a mixer based on one diode, the so-called single-cycle mixer. (OS); balanced mixer (BS) and double balanced mixer (DBS). We will not consider mixers that are more complex in functionality.

Rice. 4.2. Mixer circuit: a - on one diode; b - balanced; c - DBS on a bridge circuit; d - DBS according to the “star” scheme

The diagrams are shown in Fig. 4.2. Structurally, the output of the IF signal for the ring-type circuit is made using a configuration called and is a combination of a hybrid connection and a “four-diode star”. The advantage of the star circuit (Fig. 4.2, d) over the ring one (Fig. 4.2, c) is the presence of a central node (connection of four diodes), through which a direct connection is made to the IF circuit. All three types of mixers differ significantly more in the nature of the output signal spectrum than in the electrical configuration of their circuits. During frequency conversion, combinational components arise, the frequencies of which lie in the passband of the output filters of the mixers tuned to the IF. In Fig. 4.3 a nomogram has been constructed to determine possible combinations of signal and local oscillator harmonics

In table Figure 6 shows the combination frequencies at the output of the BS and It should be remembered that the suppression occurs using the phase principle, so its value strongly depends on the balance of the mixers and the correct matching of the diodes. In table 7 shows the parameters of various mixers.

Rice. 4.3. Nomogram for determining possible combinations of harmonics in the useful IF band

DBS has the following advantages: reducing the density of harmonics of input signals and combination frequencies in the output spectrum; increasing the dynamic range and maximum permissible power; reducing the requirements for diode breakdown voltage; eliminating or limiting filter requirements due to isolation between all pole pairs. However, DBS also have disadvantages: for example, the required local oscillator power increases compared to BS in the absence of bias; inconvenient placement of diodes. Despite these disadvantages, DBS is widely used. Let's consider the characteristics of the DBS.

The bandwidth of a star mixer in the microwave range is approximately two octaves, but it is usually limited to short-circuit quarter-wave stubs up to an octave. Based on this circuit, mixers with a bandwidth of an octave and an isolation between any pairs of poles of at least 20 dB in the frequency range up to and at least 17 dB in the range of Fig. 4.4. shows the main characteristics of mixers in the frequency band from 1 to 1. Combination frequencies in such a mixer can be divided into two types: signals with fixed and

(click to view scan)

dependent levels. Signals of the first type are obtained by mixing the harmonics of the local oscillator and the input signal: . The amplitudes of these signals remain fixed relative to the side frequencies of the first order and on the graphs of the dependence of the output power on the input they have the same slope as the latter (Fig. 4.5, a). The harmonics of the input signal, mixing with the local oscillator signal or its harmonics, create combination frequency signals with dependent levels having frequencies. The amplitudes of these signals with respect to the first-order side frequencies depend on the level of the local oscillator signal. In the graphs, the dependence of the output power on the input has a slope equal to the order of the harmonic of the input signal. The most interesting of them are frequencies that are multiples of the IF, since with a wide band of input frequencies they can fall into it, for example, frequencies where (Fig. 4.5, b).

As noted, suppression of harmonics of input signals and signals at combination frequencies in the output spectrum is one of the most important characteristics mixer Therefore, to ensure a given amount of suppression, it is necessary to correctly select the mixer circuit, the loads on its poles, as well as the DC bias mode 185, 191. Although, from a theoretical point of view, DBSs have an advantage, in practice, when implementing mixers in the form of integrated circuits, BSs have better performance, in particular lower noise figure and SWR. This is due to the difficulty of implementing DBS in an integrated version, so BS are widely used in micro-design.

Rice. 4.4. Dependence of noise figure losses and star decoupling

Rice. 4.5. Amplitudes of signals of combination frequencies: a - with a fixed level relative to the component; with dependent level

Let us consider the values ​​of suppression of combinational components in a BS to assess the effectiveness of their use when it is necessary to suppress combinational components of the frequency spectrum. Expressions for suppression in the particular case when the frequency of the Raman signal where , are given

at work. More general expressions for calculating the amount of suppression of combinational components with frequency for a BS were obtained in the work. In Fig. 4.6, a shows an equivalent circuit in which the combination frequency voltages are at the outputs of the mixing diodes (before the addition circuit); and - voltage of the useful inverter at the same points of the circuit; signal voltage at the inputs of the first and second diodes; the total voltages of the combination frequency and the useful inverter at the input of the addition circuit. Let us write a formula connecting the amount of suppression of combinational components in the BS with the amount of suppression of the same components in the OS:

where is the suppression in the diode of a given mixer; M is the ratio of the voltage transfer coefficient of the first diode for the output useful intermediate frequency to the same coefficient of the second diol; - ratio of transmission coefficients for the output combination frequency;

Rice. 4.6. Equivalent circuit of a balanced mixer (a) and block diagram of phase suppression of the mirror channel (b)

Angles between output voltage vectors

where is the phase change in the local oscillator (signal) voltage introduced by the loaded coupler; change in voltage phase from the coupler output to the diode input; angle that takes into account the polarity of the diode. The amount of suppression of combinations only due to balance for the following coefficients: characteristic of real mixers, is 13.4 dB.

When designing mixers, it is necessary to take into account the method beneficial use mirror frequency. Conversion loss and noise figure can be minimized by proper selection of reactive loads at the sum and mirror frequencies. However, this is often very difficult to achieve, especially if the mirror and signal frequencies are close. There are two ways to solve this problem: using frequency-selective circuits and using phase relationships between signals. A circuit assembled based on the first method can operate in a narrow frequency band. In addition, if the difference between the mirror frequency and the frequency

signal is small, very high-quality filters with low losses are required, which are difficult to manufacture in an integrated design. There are known examples of the implementation of such circuits, which made it possible to obtain conversion losses of up to 3.5 dB.

It should be noted that in the mixer there are two signals at the mirror frequency: the signal arriving at the mixer input from the antenna, and the signal generated in the mixer by converting the input signal. If an external signal with a frequency is supplied to the diode via the signal input, then, interacting with the oscillations of the local oscillator, an intermediate frequency signal is formed

This phase is not correlated with the phase of the useful signal, although in frequency it is no different from the useful signal and is an interference that cannot be eliminated without the use of special measures.

Let's consider phase methods for suppressing the mirror frequency, which are most suitable for microelectronic mixers. In Fig. Figure 4.6, b shows a block diagram of a mixer with suppression of the mirror signal arriving at the input of the mixers. The circuit uses two balanced mixers, to which the signal is supplied through hybrid connection 1, and the local oscillator signal is supplied through common-mode power divider 2 without phase shift. In this case, at the outputs of the mixers, such phase relationships are achieved between the IF signals converted from the input signals at the mirror and carrier frequencies that, when added at the output hybrid connection 3, we have on one output arm only the IF signal obtained by converting the carrier signal, and on the other - a mirror frequency signal that is absorbed by a matched load. The prototype in-band has a noise figure of 10 dB (including dB noise figure) at local oscillator power and a constant diode forward bias of 0.1 V. The isolation between the poles of the signal and the local oscillator is more than 16 dB, and the amount of signal suppression along the mirror channel is 20-25 dB.

Of interest is the circuit of a low-noise mixer (LSM) with phase suppression of the mirror receiving channel and with the return of the energy of the mirror frequency arising in the mixer. If significant suppression of the mirror frequency of more than 30 dB is required, then use a mixer with double frequency conversion, i.e. two mixers connected in series: the first “transfers” the signal to a high (first) intermediate frequency, at which it is easy to suppress the mirror frequency with filters, and then the second mixer converts the high intermediate frequency into a low IF, at which it goes further processing signal.

The described method makes it possible to improve the characteristics of a two-balanced active mixer in terms of intermodulation components by introducing a negative feedback, thus reducing the nonlinearity of the active elements. As a result, in terms of its characteristics, the two-balance active mixer becomes comparable to such previously known 1,2 mixer circuits as a ring diode mixer and a mixer based on powerful switching field-effect transistors with an insulated gate ( MOSFET).

Introduction

Mixers and modulators are an important component in the construction of radio frequency communication systems. To implement functions necessary in communication systems such as frequency conversion, modulation and demodulation, many different mixer circuits are used, built using diodes, powerful key field-effect transistors with an insulated gate ( MOSFET), double-gate field-effect transistors, as well as the very popular so-called “transistor tree” or “Gilbert Cell” developed at one time by Barry Gilbert. But in all these circuits, the nonlinearity of the semiconductor devices used, directly or indirectly, causes distortion when two or more different signals interact in the mixer - a phenomenon known to professionals as the occurrence of intermodulation distortion (IMD).

The sources of intermodulation distortion are the subject of a separate discussion, which has received a lot of attention in the specialized literature, and the continuation of which is not the subject of this article. More precisely, the reader will be offered a brief discussion of the two most famous mixer circuits, such as the ring diode mixer and the transistor tree, to identify their main characteristics and then compare them with the previously mentioned new negative feedback mixer circuit, in which the desired signal is undistorted can be achieved by using simple negative feedback circuitry, known from the transistor amplifier circuit with parallel negative voltage feedback, which significantly improves the characteristics of the mixer in terms of 3rd order intermodulation components (IIP 3) and compression point (P 1dB).

Ring diode mixer

Ring diode mixers came into use with the widespread use of semiconductor diodes in the late 1940s, and their non-linearity characteristics immediately became apparent 3,4. This phenomenon continues to be the object of close study in the specialized literature 5,6,7.

The construction of a class I ring diode mixer is illustrated by the diagram on Fig.1. Here four diodes are connected in a ring and alternately switch to the state "ON" And "OFF" signal supplied from the local oscillator (LO).

Fig.1. A typical Class I ring diode mixer.

The local oscillator signal power required for normal operation of such a mixer is usually +7 dBm, for circuits of ring diode mixers of subsequent classes, the required power of the local oscillator signal reaches +17 dBm and more, which is due to the desire for higher quality indicators for intermodulation components.

For the purpose of subsequent comparative analysis consider quality characteristics by intermodulation components and compression point of a common class I type ring diode mixer SBL-1 produced by the company Mini-Circuits. This mixer is widely popular among amateur radio developers, and its commercial “double” SBA-1 distributed even more widely, which is why it was chosen for this study.

According to the testing conditions, the local oscillator signal level with frequency 10 MHz compiled the required +7 dBm, and the other input of the mixer received two signals with frequencies 500 kHz And 510 kHz. These frequencies were selected based on the operating frequency range of the mixer SBL-1 and will also be used for subsequent comparative testing of other mixer circuits.

Mixer quality parameters SBL-1 illustrates Fig.2, and their numerical values ​​are summarized in table 1.

Fig.2. Intermodulation distortion of the SBL-1 ring diode mixer, 10 dBm/div.

These are objectively typical characteristics of a Class I ring diode mixer, but, as will be shown below, higher levels of IIP 3 and P 1dB parameters can be achieved with significantly lower local oscillator signal power in an active mixer built on the basis of two amplifiers with negative feedback .

Table 1.

Mixer based on high-power switching field-effect transistors with an insulated gate (MOSFET)

Fig.3.

High quality ring mixers use insulated gate field effect transistors instead of diodes ( MOSFET). A typical diagram of such a mixer is shown in Fig.3.

Mixers of this type are characterized by an intersection point for 3rd order intermodulation products (input intercept points - IIP 3) above +40 dBm, but at the cost of a very high power level of the local oscillator signal, usually +17 dBm and higher, which in practice often prevents their use in portable radio equipment. However, its performance is superior to that of a Class III ring diode mixer.

In professional and amateur radio literature 8,9,10,11,12,13,14 the topic of constructing ring mixers using powerful switching field-effect transistors is very widely discussed, and it is quite difficult to pay enough attention to this topic without being distracted from the actual purpose of this article.

Mixer according to the “transistor tree” scheme

On Fig.4 The functional diagram of a “transistor tree” type mixer is shown. Originally patented in 1966 by Howard Jones as a synchronous detector 15, this very popular active mixer is better known as the "Gilbert Cell", according to a later patent and the use of this circuit as the basis for construction. analog multipliers 16. This mixer in its design is a derivative of the family of tube synchronous demodulators 17.

Fig.4. A transistor tree mixer, also known as a Gilbert Cell.

Here is the input intermediate frequency (IF) signal through a transformer T 2 controls a differential current source on transistors in antiphase VT 2 And VT 5. To stabilize the mixer conversion coefficient over a wide range of input signal levels, as well as to reduce the influence of transistor nonlinearity VT 2 And VT 5 Serial negative current feedback resistors are included in the emitters and between them R 4 ..R 6.

Output currents of a differential current source, that is, collector currents of transistors VT 2 And VT 5, are switched in antiphase by transistors of differential pairs VT 1:VT 3 And VT 4:VT 6, alternately switched to the “ON” state. and "OFF" signal supplied from the local oscillator LO through a transformer T 1. The collectors of the transistor pairs are mutually cross-connected, therefore, due to the summation of the currents on the load resistors R 3 And R 7, the local oscillator and intermediate frequency signals are suppressed, and the products of their mixing, including the useful RF radio signal, are separated on the primary winding of the transformer T 3.

In order to check the characteristics shown in Fig.4 the mixer was assembled by a manufacturer Harris microcircuit CA3054(now it is produced by the company Intersil— approx. translator) containing two identical differential amplifiers. With a supply voltage equal to +12 V and resistor resistance R 4 ..R 6 equal 100 Ohm(a resistor assembly of three resistors was used) voltage at the bases of the transistors VT 2 And VT 5 was set equal +2.1 V, while the collector bias current of these transistors was 15 mA. Transistor base voltage VT 1, VT 3, VT 4 And VT 6 was set equal +4.7 V. Thus, the operating point of the transistors VT 2 And VT 5 remained in the linear portion of their characteristics throughout the entire range of input signal levels 18 . All transformers T 1, T 2 And T 3 Fair-Rite 2843-002-402(binocular-transfluctor). With a winding ratio 1:1:1 The input and output impedances of the mixer are 50 ohm.

The test conditions for the mixer were the same as for the ring diode mixer, with the exception of the local oscillator signal level, which was 0 dBm (1 mW). This level was set for all active mixers considered in this article, which work quite satisfactorily even at such low local oscillator signal levels as -6 dBm (0.25 mW).

Fig.5 And table 2 illustrate the quality characteristics of the mixer according to the “transistor tree” scheme. Compression point P 1dB The characteristics of such a mixer are higher than those of a ring diode mixer, and the intersection point for intermodulation components of the 3rd order ( IIP 3) - below. However, despite the fact that the local oscillator signal level required for operation of a “transistor tree” type mixer is significantly lower than for a ring diode mixer, its quality characteristics in terms of the level of intermodulation distortion are slightly inferior to the ring diode mixer.

Fig.5. Intermodulation distortion of the mixer according to the “transistor tree” scheme, 10 dBm/div.

Table 2.

For a long time it was believed that the main obstacle to obtaining higher characteristics in terms of the level of introduced intermodulation distortion in a mixer using a “transistor tree” scheme was the control transistors VT 2 And VT 5, operating as voltage-controlled current sources. 19,20 A number of methods described in the literature have been successfully used to correct this deficiency. 19,21,22 But all these methods ignore other sources of intermodulation distortion, such as nonlinearity of the current transfer coefficient h fe control transistors, as well as the nonlinearity of the characteristics of the four transistors switching their current VT 1:VT 3 And VT 4:VT 6. These disadvantages can be overcome by using a combined series-parallel negative feedback circuit ( series/shunt feedback), covering all transistor nodes of the mixer, by analogy with transistor amplifier stages.

Amplifier with combined series-parallel negative feedback ( series/shunt feedback)

On Fig.6 The diagram of a transistor amplifier with a combined series-parallel negative feedback (NFB) is shown.

Fig.6.

Sequential OOS ( series feedback) formed by a resistor R 2 included in the emitter circuit of the transistor VT 1. Parallel OOS ( shunt feedback) formed by a resistor R 1 connected between the collector and the base of the transistor VT 1.

The input and output impedance of such an amplifier is determined by the ratio 23.24:

and power gain:

This negative feedback topology allows simple means to increase the linearity of a transistor amplifier and, in addition, is easily implemented in a transistor tree mixer circuit.

(option 1)

The diagram of a linearized active mixer according to the “transistor tree” scheme, covered by deep feedback, is shown in Fig.7. The first linearized “amplifier” with a combined series-parallel feedback loop is formed by connecting individual resistors of the parallel feedback loop ( shunt feedback) R 2:R 3 between the collectors of the transistors of the key transistor pair VT 1:VT 3 and the base of the control transistor VT 2 via decoupling capacitor C 1. Sequential OOS ( series feedback) is formed by a circuit of three resistors R 5:R 9:R 13. As a result, the “amplified” intermediate frequency signal IF, which is suppressed in the basic “transistor tree” circuit, is here isolated as common mode across the load resistors and through the parallel OOS circuit R 2:R 3:C 1 supplied to the base of the control transistor VT 2. At the same time, the local oscillator LO and the resulting radio frequency RF signals are based on the transistor VT 2 are suppressed. Thus, the circuit acts as an amplifier only for the intermediate frequency signal IF, and since the combined series-parallel OOS circuit covers all three transistors, the distortions they introduce due to their nonlinearity are compensated.

Fig.7.

Similarly, the second transistor pair VT 4:VT 6 with a second control transistor VT 5 and the corresponding circuits of parallel and serial OOS form a second linearized “amplifier”. Note that three resistors R 5:R 9:R 13 play the same role as a resistor R 2 in the diagram on Fig.6 and expressions and .

Output transformer T 3 connected to the collectors of transistors of transistor pairs VT 1:VT 3 And VT 4:VT 6 via four 100 ohm resistors R 7:R 8:R 10:R 11 in such a way that signals with the local oscillator frequency LO and the intermediate frequency IF on its primary winding are suppressed and only the products of their mixing are present at the mixer output.

To test the active mixer linearized in this way, a circuit was assembled from the same elements as the previous mixer circuit, with the same modes DC. With the resistance of parallel OOS resistors R 2, R 3, R 15 And R 16 equal 330 Ohm the input and output impedance of both “amplifiers” was approximately 100 Ohm, and the gain by each “amplifier” of the intermediate frequency signal IF was about +6.7 dB.

Fig.8. Intermodulation distortion of linearized active mixer (option 1), 10 dBm/div.

Table 3.

Given on Fig.8 and in table 3 test results show that, in comparison with the previously discussed “transistor tree” type mixer, the circuit of which is shown in Fig.4, collected according to the Fig.7 circuit, a linearized active mixer with a combined feedback loop has higher characteristics in terms of the level of introduced intermodulation distortion and is superior to a ring diode mixer SBL-1 companies Mini-Circuits at a significantly lower signal level of the local oscillator LO. The compression point suffers somewhat P 1dB, - this is caused by incomplete suppression of the local oscillator signal LO at the collectors of the transistors VT 1:VT 3 And VT 4:VT 6, which leads to their saturation too early. This happens because of four 100 -ohm resistors R 7:R 8:R 10:R 11 in the crosshairs between the collectors of these transistors, while in the mixer “transistor tree” on Fig.4 the corresponding collectors of the transistors are connected to each other directly and the local oscillator signal on them is suppressed almost completely. In addition, this chain of resistors introduces excessive attenuation of the output signal - about 6 dBm. This drawback was avoided by combining the output signals of the mixer not with resistors, but with the help of a so-called “hybrid” transformer.

Combining signals using a “hybrid” transformer

Hybrid transformers 25,26,27 (also known as bridge transformers or symmetrical transformers) were previously widely used in telephone amplifiers, but with the use of appropriate ferromagnetic materials they have easily found their way into high-frequency circuits.

In the diagram on Fig.9 A hybrid transformer is used to separate the difference signal from two signals with an in-phase component. Signals having a common-mode component are fed to opposite terminals primary winding transformer, which has a tap from the middle and is isolated from the secondary. With this connection, the common-mode component appears at the midpoint of the primary winding of the transformer, and the difference signal is released at its secondary winding. This happens because the current in the primary winding flows only at different potentials at the opposite terminals of the winding.

Fig.9 Isolating the difference signal using a “hybrid” transformer.

Let the primary and secondary windings of such a transformer each have 2N And M turns accordingly. Then, to match the load, the resistance values ​​in the circuit are Fig.9 must be related by the following relationships:

Use for combining output signals in a mixer circuit on Fig.7 circuit of four resistors R 7:R 8:R 10:R 11 led to a decrease in the mixer transmission coefficient by 6 dBm. The use of a hybrid transformer for the same purpose reduces these losses to nothing, therefore, when speaking about such a circuit topology, the term “lossless” is often used (i.e. “without losses” or “without attenuation”).

Linearized active mixer without loss of useful signal (option 2)

On Fig.10 shows a diagram of a linearized active two-balance mixer, in which the following is used to combine the output signals: lossless- topology using hybrid high-frequency transformers. The circuit contains two identical balanced active mixers, so it is enough to consider the operation of one of them.

Fig. 10.

To begin with, let's imagine that the mixer as a whole is loaded by the RF output to the load resistance R L(not shown in the diagram). Then the reduced value of the load resistance for each of its component balanced mixers will be equal to 2R L. Moreover, if the windings of hybrid transformers T 3 And T 4 made with the ratio of the number of turns 1:1:1 , then the resistance at the midpoint of their primary winding will also be 2R L, and the resistance at the ends of this winding will be equal 4R L.

Periodic antiphase switching of transistors VT 1 And VT 3 the local oscillator signal LO modulates the collector current of the transistor VT 2, thereby creating a differential signal in the primary winding of the transformer T 3. Load resistance in the collector circuit of the transistor VT 2- a constant value equivalent to parallel-connected resistances in the collector circuits of transistors VT 1 And VT 3 and equal to the resistance at the midpoint of the hybrid transformer, i.e. 2R L. Thus, in this circuit it is possible to implement an “amplifier” with a combined series-parallel OOS ( series/shunt feedback).

Let us assume that the secondary windings of both output hybrid transformers are disconnected from each other and each loaded with its own load resistance. In this case, the voltages on the collectors of four transistors VT 1, VT 3, VT 4 And VT 6 are determined by the expressions , , and , respectively:

AIF— amplitude of the intermediate frequency signal;
G— the gain of the “amplifier” determined by the expression;
— local oscillator frequency value;
— intermediate frequency value;
I bias— collector bias current of the transistor VT 2.

The rightmost term in the equalities represents the differential carrier signal of the local oscillator in the primary winding of the transformer T 3. It is equivalent to the signal in the primary winding of the transformer T 4, but opposite in phase (equal to and ). The balance of these two signals, with the corresponding connection of the secondary windings of these two transformers (see. Fig.10), provides effective suppression of the local oscillator signal and separation of mixing products, including the useful RF radio signal, at the output of the mixer. In the ideal case (i.e., in the absence of losses), the expressions describing the voltages on the collectors of the same four transistors take the following form:

Reconstructed intermediate frequency signals at the midpoints of the primary winding of output hybrid transformers T 3 And T 4 are described by expressions:

and the signal at the mixer output is described by the expression:

which, provided that M=N is equal, takes the form:

The circuit for testing was assembled, again, from the same elements as the previous mixer circuit, with the same DC modes. Two hybrid transformers T 3 And T 4 had the same design as input transformers T 1 And T 2, and with the winding ratio 1:1:1 contained four turns of trifilar winding on a core of the type Fair-Rite 2843-002-402. Therefore, the input and output resistance of each of the balanced mixers was 100 Ohm. Accordingly, taking into account the parallel connection of the secondary windings of transformers T 3 And T 4, the input and output resistance of the mixer is 50 ohm.

The circuit was tested on Fig.10 at the same frequencies and local oscillator signal level as the previous one. Fig.11 And table 4 illustrate the quality indicators of the mixer. As a result of the fact that the level of third-order intermodulation products was -53 dBc, intersection point IIP 3 accordingly reaches a completely satisfactory level +29.5 dBm. Also the compression point P 1dB rose to +10.5 dBm. Thus, the use of a hybrid transformer in the circuit made it possible to design an active mixer that competes in its low level of intermodulation distortion with a Class III ring diode mixer, but requires much less local oscillator signal power.

Fig. 11. Intermodulation distortion of linearized active mixer (option 2), 10 dBm/div.

Table 4.

Sensitivity to reactive load

In view of the above, a lumped selection bandpass filter with a central frequency was assembled 10.7 MHz and bandwidth 500 kHz, the diagram of which is shown in Fig.12. The measured intrinsic attenuation of the filter was 5.5 dB and was taken into account in the results of subsequent measurements.

Fig. 12.

From those given in table 5 The measurement results show that the ring diode mixer SBL-1 is indeed very sensitive to the connection at its output instead of a purely active matched load of a notch IF filter: the third-order intermodulation product intercept IIP 3 while falling on 11.5 dB, and the compression point P 1db on 3 dB. Active mixers, without exception, showed essentially less sensitivity to frequency-dependent loading, compression point P 1db at the same time, it remained in the same place, and the intersection point for third-order intermodulation products IIP 3 fell no more than 1 dB in all three cases.

Table 5.

The results obtained are not surprising. In the case of a ring diode mixer, the signal energy from the unloaded output is reflected back into diode circuit, where it can then interact with the nonlinearity of the diode junctions. Conversely, the signal energy reflected back into the active mixer is extinguished in the load resistances of the switching transistors, and the nonlinear base-emitter junctions are isolated due to the low current feedback coefficients of the transistors.

Conclusion

So, an active mixer with a combined series-parallel OOS circuit has shown such quality characteristics that are also desirable when developing high-quality radio frequency transceiver systems. Further improvements, including the use of alternative negative feedback topologies to improve the noise performance of the mixer, will provide a mixer with a very wide dynamic range without requiring excessive power levels from the local oscillator.

©Christopher Trask, 1998.

Translation ©Zadorozhny Sergey Mikhailovich, 2006

Literature:

1. Trask, Chris, "Feedback Technique Improves Active Mixer Performance"; RF Design, September 1997.
2. Patent pending.
3. Belevitch, V., “Non-Linear Effects in Ring Modulators”; Wireless Engineer, Vol.26, May 1949, p.177.
4. Tucker, D. G., "Intermodulation Distortion in Rectifier Modulators"; Wireless Engineer, June 1954, pp.145-152.
5. Gardiner, J.G., "An Intermodulation Phenomenon in the Ring Modulator"; The Radio and Electronics Engineer, Vol.39, No.4, April 1970, pp.193-197.
6. Walker, H.P., "Sources of Intermodulation in Diode-Ring Mixers"; The Radio and Electronics Engineer, Vol.46, No.5, May 1976, pp.247-253.
7. Maas, Stephen A., "Two-Tone Intermodulation in Diode Mixers"; IEEE Transactions on Microwave Theory and Techniques, Vol.MTT-35, No.3, March 1987, pp.307-314.
8. Evans, Arthur D. (ed), "Designing with Field-Effect Transistors"; McGraw-Hill/Siliconix, 1981.
9. Rohde, Ulrich L., "Recent Developments in Circuits and Techniques for High-Frequency Communications Receivers"; Ham Radio, April 1980, pp.20-25.
10. Rohde, Ulrich L., "Key Components of Modern Receiver Design"; QST, May 1994, pp.29-31 (pt.1), June 1994, pp.27-31 (pt.2), July 1994, pp.42-45 (pt.3).
11. Rohde, Ulrich L., "Recent Advances in Shortwave Receiver Design"; QST, November 1992, pp.45-55.
12. Rohde, Ulrich L., "Performance Capability of Active Mixers"; Ham Radio, March 1982, pp.30-35 (pt.1), April 1982, pp.38-44 (pt.2).
13. Rohde, Ulrich L., "Performance Capability of Active Mixers"; Proceeding WESCON 81, pp.24/1-17.
14. Rohde, Ulrich L. and T.T.N. Bucher, Communications Receivers: Principles and Design, 1st ed.; McGraw-Hill, 1988.
15. Jones, Howard E., "Dual Output Synchronous Detector Utilizing Transistorized Differential Amplifiers"; U.S. Patent 3.241.078, March 15, 1966.
16. Gilbert, Barrie, "Four-Quadrant Multiplier Circuit"; U.S. Patent 3.689.752, 5 September 1972.
17. Schuster, N.A., “A Phase-Sensitive Detector Circuit Having High Balance Stability”; The Review of Scientific Instruments, Vol.22, No.4, April 1951, pp.254-255.
18. Sullivan, Patrick J. and Walter H. Ku, "Active Doubly Balanced Mixers for CMOS RFICs"; Microwave Journal, October 1997, pp.22-38.
19. Chadwick, Peter, "The SL6440 High Performance Integrated Circuit Mixer"; WESCON 1981 Conference Record, Session 24, pp.2/1-9.
20. Chadwick, Peter, "More on Gilbert Cell Mixers"; Radio Communications, June 1998, p.59.
21. Heck, Joseph P., "Balanced Mixer With Improved Linearity"; U.S. Patent 5.548.840, 20 August 1996.
22. Gilbert, Barrie, “The MICROMIXER: A Highly Linear Variant of the Gilbert Mixer Using a Bisymmetric Class-AB Input Stage”; IEEE Journal of Solid-State Circuits, Vol.32, No.9, September 1997, pp.1412-1423.
23. Meyer, Robert G., Ralph Eschenbach, and Robert Chin, “Wide-Band Ultralinear Amplifier from 3 to 300 MHz”; IEEE Journal of Solid-State Circuits, Vol. SC-9, No. 4, Aug 1974, pp. 167-175.
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Original text:

Trask, Chris, “A Linearized Active Mixer,” Proceedings RF Design 98, San Jose, California, October 1998, pp. 13-23.

At the output of the balanced mixer, the local oscillator voltage is suppressed, but the voltage of the received operating signal is present. As was discussed when considering the principles of operation, in principle these components should not be present at the output of an ideal multiplier. A ring mixer (frequency converter) circuit allows you to reduce the level of the radio signal at the output of the frequency converter. This circuit is often called a double balanced mixer. diode ring mixer is shown in Figure 1.

Suppression of the input signal at the output of the ring mixer (frequency converter) is carried out by subtracting the currents of the balanced mixer assembled on diodes VD1, VD4 and the currents of the balanced mixer assembled on diodes VD2, VD3.

The signal spectrum at the output of the ring balanced mixer (frequency converter) is shown in Figure 2.

Please note that the spectrum of the signal at the output of the ring mixer (frequency converter) is already similar to the spectrum of an ideal multiplier. Insufficiently suppressed components of the output signal spectrum must be suppressed by bandpass filters at the input and output of the mixer.

At the output of the ring mixer circuit (frequency converter), not only the signal present at the input of the frequency converter is suppressed, but also all components formed by odd degrees of the polynomial approximation of the slope of the nonlinear elements used in the mixer. The process of suppressing the input signal at the output of the ring mixer (frequency converter) is illustrated in Figure 3.

This figure shows the situation when the frequencies of the received signal and the local oscillator are equal. The timing diagram of the output current resembles the timing diagram of a rectified signal. As a result, the even half-waves of the received signal suppress the odd ones. This results in all odd harmonics in the output signal spectrum being suppressed. The spectrum of the output signal mainly contains components of even harmonics:

If the current-voltage characteristic of the nonlinear element is approximated by a quadratic function (second-order polynomial), then we will obtain a converter that is as close as possible to an ideal multiplier. Approximation of the shape of the current-voltage characteristic of mixing diodes to a quadratic polynomial can be obtained by appropriate selection of the volume resistance of the semiconductor.

Currently, ring diode mixers (frequency converters) are made in the form of ready-made integrated circuits. In this case, the input and output resistance is equal to 50 Ohms. The input impedance of the local oscillator input is also made equal to 50 Ohms. The integral design of the ring mixer (frequency converters) allows you to achieve a high degree of symmetry of the mixer arms, which allows you to get enough good characteristics suppression of local oscillator signals in radio and intermediate frequency circuits. An example of such ring mixers (frequency converters) is the mixers manufactured by Mini-Circuits. The parameters of some of them are given in Table 1.

Table 1 Parameters of ring mixers (frequency converters)

The dimensions of these mixers are quite small, suitable for surface mounting. Figures 4 and 5 show photographs of these microcircuits.

Figure 5. Appearance and dimensions of MBA mixers

Since the input and output resistances of the selected mixers are equal to 50 Ohms, the circuit diagram for connecting these radio receiver components is quite simple. It is shown in Figure 6.

When building modern industrial or cellular radio communication systems, it should be kept in mind that these communication systems use fairly high frequencies. Therefore, when implementing high-frequency radio equipment components, including frequency mixers, you should Special attention give them design features. For example, all communication lines must be made in the form of microstrip lines, and individual receiver and transmitter nodes must be shielded from electromagnetic radiation. Figure 7 shows a microstrip line design in which the signal conductor passes over the ground surface of the printed circuit board.

In this figure, W is the width of the signal wire; T—thickness of copper deposition; H is the thickness of the dielectric of the printed circuit board, which has electrical permeability ε . It should be noted that for a specific printed circuit board, all parameters are fixed with the exception of the width of the signal conductor. The characteristic impedance of a microstrip line can be found using the empirical formula:

In this formula, the values ​​of H are divided by W and T, resulting in a dimensionless coefficient. Therefore, these values ​​can be entered in both millimeters and inches. For example, when using FR-4 fiberglass laminate with a thickness of 0.5 mm and a value of 4.0, to achieve a characteristic impedance of 50 Ohms, the transmission line must be made in a strip with a width of 0.5 mm. The thickness of the copper coating should be equal to 0.04 mm. To realize a characteristic impedance of 75 Ohms under the same conditions, the width of the conductor must be equal to 0.2 mm. More accurate calculations can be performed using the wave impedance calculator provided on the website.

An example of the design of a mixer based on the ADE-1L IC is shown in Figure 8.

The figure clearly shows the strict adherence to the width of the conductors supplying input signals. It can be seen how sharp changes in direction are structurally removed in order to avoid reflection from the inhomogeneity of the strip line.

date last update file 10.10.2018

Literature:

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