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Operazionnie ysiliteli ,ZAP/AZP & (продолжение)
milstar: 1941: First (vacuum tube) op-amp An op-amp, defined as a general-purpose, DC-coupled, high gain, inverting feedback amplifier, is first found in US Patent 2,401,779 "Summing Amplifier" filed by Karl D. Swartzel Jr. of Bell labs in 1941. This design used three vacuum tubes to achieve a gain of 90dB and operated on voltage rails of ±350V. ###################################################### It had a single inverting input rather than differential inverting and non-inverting inputs, as are common in today's op-amps. Throughout World War II, Swartzel's design proved its value by being liberally used in the M9 artillery director designed at Bell Labs. ######################################################################### This artillery director worked with the SCR584 radar system to achieve extraordinary hit rates (near 90%) that ####################################################################### would not have been possible otherwise.[3] ########################### http://en.wikipedia.org/wiki/Operational_amplifier
milstar: http://news.cqham.ru/articles/detail.phtml?id=519
milstar: https://www.analog.com/en/technical-articles/small-form-factor-satcom-solutions.html Traditional ground station satellite communication systems in the Ka-band have relied on an indoor to outdoor configuration. The outdoor unit includes the antenna and a block downconversion receiver that outputs an analog signal in the L-band. The signal is then passed to the indoor unit, which contains the filtering, digitization, and processing systems. Because there are typically few interfering signals in the Ka-band, the outdoor unit is focused on optimizing the noise figure at the expense of linearity. The indoor to outdoor configuration works well for ground stations, but is difficult to transition into a low size, weight, and power (SWaP) environment. Several new markets are driving the need for small form factor Ka-band access. Unmanned aerial vehicles (UAVs) and dismounted soldiers would benefit from having access to these communication channels. For both UAVs and dismounted soldiers, radio power consumption directly translates to battery life, which translates to mission length. Additionally, legacy Ka-band channels that used to be specific to airborne platforms are now being considered for wider access. This means that the airborne platform that traditionally only needed to downconvert a single Ka-channel may now need to operate on multiple channels. This article will outline the design challenges that are faced in Ka-band, as well as outline a new architecture that will allow for low SWaP radio solution for these applications. Example System with the AD9371
milstar: https://www.renesas.com/kr/en/www/doc/datasheet/isl5416.pdf
milstar: https://www.analog.com/media/en/training-seminars/design-handbooks/Data-Conversion-Handbook/Chapter2.pdf
milstar: https://www.e-ope.ee/_download/euni_repository/file/%203367/Elektrotehnika.zip/42_____.html Начальным фазовым углом, или начальной фазой, называют в электротехнике угол, который прошёл от начала периода до начала наблюдения и который обозначает действительную точку отсчёта (рис.4.4). В начальный момент времени (t = 0), с которого мы начали наблюдение, ЭДС прошла с начала периода 60˚ или π /3. Начальная фаза этой ЭДС 60˚, ω = 0 и начальное значение ЭДС: eo = Em∙sinψ. На рис.4.5 показаны две синусоидальные ЭДС с начальными фазами Ψ1 = 60˚ и Ψ2 = 30˚. Их мгновенные величины: e1 = Em∙sin(ωt +ψ1) и e2 = Em∙sin(ωt +ψ2). Фазовый сдвиг между ними: ψ = ψ1 - ψ2 = 60˚ - 30˚ = 30˚. Рис.4.5. Временная диаграмма двух ЭДС с различными фазовыми углами. По фазе опережает тот синус, период которого начинается раньше, а отстаёт по фазе тот, чей период начинается позже. Т.е. мы можем сказать, что e1 опережает по фазе e2, или e2 отстаёт по фазе от e1. Угол фазового сдвига между напряжением и током обозначается буквой φ (фи). Этот сдвиг фаз имеет смысл, как между их амплитудными, так и нулевыми значениями. Обобщая, получим: φ = ψ1 - ψ2 . φ - угол сдвига фазы; ψ1 - начальная фаза первой синусоидальной величины, напряжения; ψ2 - начальная фаза второй синусоидальной величины, тока. Когда две синусоидальные величины совпадают начальными фазами, то говорят, что они совпадают по фазе. Когда разница между начальными фазами ± π, то говорят, что они в противофазе ============ https://studopedia.ru/12_91248_izmerenie-fazovogo-sdviga.html
milstar: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19890010082.pdf NASA (3) Band-pass sampling with digital quadrature mixers (Fig. 3). The input signal is sampled at the rate of 4W samples/sec, and the input samples are then mixed with the samples of reference in-phase and quadrature components and then low-pass filtered to eliminate the double frequency images resulting from the mixing operation. This is performed by using a finite impulse response (FIR) low-pass filter. Since the output of the low-pass filter is bandlimited to 2W, the output is mated (undersampled) by a factor of 2, thereby reducing the subsequent processing rate by 1/2. For bandpass sampling of the input signal it is assumed that the input signal is centered at an odd multiple of the bandwidth frequency. In practice, this is not a restrictive assumption since the IF frequency is normally chosen by the hardware design engineer. (4) Band-pass sampling with digital Hilbert transform (Fig. 4). The input signal is sampled at the rate of 4W samples/sec, the input samples are then Hilbert transformed using a digital Hilbert transformer. The Hilbert transformed sequence and the input sequence are then mixed with the reference in-phase and quadrature components. For band-pass sampling of the input signal it is assumed that the input signal is centered at an odd multiple of the bandwidth frequency. Note that cases (1) and (2) are applications of the ShannonWhittaker theorem, while cases (3) and (4) are obtained from the band-pass sampling theorems discussed below
milstar: 111. Comparison of Sampling Methods In this section the advantages and disadvantages of each of the sampling techniques described in the previous section are considered. (1) I and Q baseband sampling with analog quadrature mixers. Advantages: (a) Since the sampling rate of each channel is 2W samples/sec, this technique requires the slowest possible A/D convertor and processing rate for the recovery of I and Q samples. (b) The analog anti-aliasing filter design for this sampling technique is an ideal low-pass filter with a two-sided bandwidth of 2W. Generally, low-pass analog filters are easier to build than their analog band-pass counterparts. (c) Due to cost considerations, in some applications it is desirable to demodulate the signal directly from RF frequency to baseband with no intermediate stages. In such cases, this sampling method is the only known technique for recovering the in-phase and quadrature components. Disadvantages: (a) It is very difficult to achieve phase and amplitude balance in both in-phase and quadrature reference signals with analog quadrature mixers. Sinsky and Wang have studied this effect when the input signal is simply a sinusoid at frequency fo, and they show that the effect of unmatched phase or gain is to create an image at -fo, where the power of this image is A2/4 for amplitude mismatch, and @/4 for the phase mismatch. Here A and 4 denote the fraction of amplitude imbalance and the phase difference in radians between the two channels, respectively. For example, to provide an image rejection ratio (IRR) of -50 dB due to the phase imbalance, the phase imbalance must be kept under 0.36 deg. In [2] a method is proposed for compensating for these imbalances. In applications where the signal-to-noise ratio is high, the consideration of IRR is not significant since the image power (at -fo) is dominated by the channel noise. (b) The appearance of spurious signals is another problem with analog implementation of quadrature mixers. Normally, high-speed analog mixers are high-speed choppers and produce odd and even harmonics of the carrier frequency. If these harmonics are not properly filtered, they could fold back into the baseband, and severely degrade the performance of the receiver. (c) This technique requires two A/D convertors. ================================= (2) I and Q sampling with analog Hilbert transform. Sometimes referred to as hybrids or 90-deg phase shifters, analog Hilbert transformers are hardly used in practice because of the difficulties inherent in their fabrication. The relative merits and disadvantages of this technique are similar to those of the previous case, except that here additional phase and amplitude imbalance is introduced by the analog Hilbert transformer if it exhibits non-ideal characteristics. ================================ (3) Band-pass sampling with digital quadrature mixers. Advan rages : (a) Since quadrature mixing is done in the digital domain, the phase or amplitude imbalance problems discussed earlier for the baseband satnpling with analog quadrature mixers do not appear here. (b) Low-pass filtering operation is done in the digital domain using FIR filters. These filters are linear phase filters, i.e., they introduce a constant group delay in the output I and Q samples. This is particularly important in applications where ranging or Doppler information must be extracted from the received signal. Digital filters are inherently more robust and flexible than their analog counterparts. The bandwidth of the filter can be easily modified by changing the coefficients of the discrete filter. Furthermore, a special class of filters [3] called half-band filters (HBF) reduces the computational complexity and the processing rate of this sampling technique by a factor of two. (c) Only one A/D convertor is required. (d) If the sampling period is exactly 1/(4 f,), then the reference in-phase and quadrature components reduce to an alternating sequence ============================= Disadvantages: Faster A/D conversion (e& aperture conversion time) is required since the sampling rate is at least at 4W, as opposed to 2W for the baseband sarnpling case. This translates into stricter design requirements for the A/D design parameters, such as the sample and hold, and aperture time. Requires a band-pass anti-aliasing filter prior to band-pass filters are more difficult to fabricate than their low-pass counterparts. A/D conversion. As pointed out earlier, analog band-pass filters are more difficult to fabricate than their low-pass counterparts. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19890010082.pdf
milstar: It has been found that band-pass sampling using digital quadrature mixers is the most robust technique for Deep Space Network (DSN) applications. ======================== In deep space applications the signal-to-noise ratio (SNR) is extremely low, eg, the Advanced Receiver performance threshold is at 0 dB with a carrier-to-noise power of -75 dB with a 15 MHz bandwidth. In DSN applications it is necessary to detect telemetry symbols and track signal phase very accurately for ranging and Doppler measurement in order to determine the deep space probe’s position and velocity. Thus, the receiving system cannot tolerate any significant loss due to filtering or phase distortion. Band-pass sampling with digital quadrature mixers can meet these requirements since it does not suffer from the phase and amplitude imbalance which is inherent in I and Q baseband sampling
milstar: d) If the sampling period is exactly 1/(4 f,), then the reference in-phase and quadrature components reduce to an alternating sequence alternating sequence. мат. знакопеременная последовательность.
milstar: https://www.efjohnson.com/resources/dyn/files/75832z342fce97/_fn/Digital_Phase_Modulation.pdf BPSK modulation
milstar: https://descanso.jpl.nasa.gov/DPSummary/Descanso4--Voyager_new.pdf
milstar: https://www.funkshop.com/media/files_public/fb23655a52a4699eab4effe515ebed3f/yaesu-FTDX101D.pdf The Down Conversion type receiver construction is similar to the FTDX5000. The first IF frequency is 9 MHz, and a low noise figure dual gate MOS FET, D-quad DBM (Double Balanced Mixer) with excellent intermodulation characteristics, is implemented in the mixer section. Narrow band SDR configuration makes it possible to use the narrow bandwidth crystal roofing filters that have the sharp shape factor. This achieves the amazing multi-signal receiving performance when confronted with the most challenging on-the-air interference situations. In addition to IF down-conversion, The FTDX101 receivers implement the YAESU legendary powerful RF Front-Ends, outstanding low-noise Local Oscillators, roofing filters with sharp shape factors, and the latest circuit configurations that we carefully selected for all circuit elements. Consequently, the proximity BDR (Blocking Dynamic Range) in the 14 MHz band reaches 150 dB or more, the RMDR (Reciprocal Mixing Dynamic range) reaches 123 dB or more, and the 3rd IMDR (third-order Intermodulation Dynamic Range) reaches 110 dB or more. The Narrow band SDR receiver removes strong out of band signals by using a superheterodyne method, with narrow band roofing filters which significantly attenuates unwanted out of band frequency components, and the wanted signals within the passband are converted to digital by a high resolution 18-bit A/D converter and sent to an FPGA (Field Programmable Gate Array) for signal processing. The FT DX 101 series uses a hybrid SDR configuration that integrates a direct sampling SDR receiver in order to view the entire band status in real time, with the excellent dynamic receiver performance achieved by the narrow band SDR receiver circuit. By using this hybrid SDR design, the overall performance of the entire FTDX101 receiver system is improved. The Direct Sampling SDR driving the real time Spectrum display with its large dynamic range enables the weakest signal to be observed on the display when it appears and the Narrow Band SDR enables that signal to be selected, filtered and then decoded. If there is powerful AM station near your location or in challenging operating situations where there are a lot of strong signals in the band from Contests, DX-pedition activities, those signals outside the pass band can be attenuated by the very effective roofing filter in the front stage of the A/D converter. This reduces the signal load on the A/D converter which is a bottleneck from the viewpoint of the entire receiving circuit. Therefore, interference is reduced making it is possible to continue to operate even under such difficult conditions. https://www.yaesu.com/indexVS.cfm?cmd=DisplayProducts&ProdCatID=102&encProdID=959169DE998192AB87295E90077D740D&DivisionID=65&isArchived=0
milstar: This table compares the performance of two methods of calculating the FFT of an N-point real sequence. Complex FFT refers to using an N-point complex FFT in the standard way, while Real FFT refers to using an N/2-point complex FFT as described in this topic. As expected, the Real FFT method yields superior performance. http://processors.wiki.ti.com/index.php/Efficient_FFT_Computation_of_Real_Input#
milstar: https://pdfs.semanticscholar.org/9cd4/d0cee6c22a65dd6e5ae51c9b6cdbaeb550df.pdf
milstar: it is possible to represent the FFT frequency domain results of strictly real input using only real numbers. Those complex numbers in the FFT result are simply just 2 real numbers, which are both required to give you the 2D coordinates of a result vector that has both a length and a direction angle (or magnitude and a phase). And every frequency component in the FFT result can have a unique amplitude and a unique phase (relative to some point in the FFT aperture). One real number alone can't represent both magnitude and phase. If you throw away the phase information, that could easily massively distort the signal if you try to recreate it using an iFFT (and the signal isn't symmetric). So a complete FFT result requires 2 real numbers per FFT bin. These 2 real numbers are bundled together in some FFTs in a complex data type by common convention, but the FFT result could easily (and some FFTs do) just produce 2 real vectors (one for cosine coordinates and one for sine coordinates).
milstar: https://www.analog.com/media/en/technical-documentation/dsp-book/dsp_book_Ch31.pdf It is painfully obvious from this chapter that the complex DFT is much more complicated than the real DFT. Are the benefits of the complex DFT really worth the effort to learn the intricate mathematics? The answer to this question depends on who you are, and what you plan on using DSP for
milstar: While this is true, it does not give the complex Fourier transform its proper due. Look at this situation this way. In spite of its abstract nature, the complex Fourier transform properly describes how physical systems behave. When we restrict the mathematics to be real numbers, problems arise. In other words, these problems are not solved by the complex Fourier transform, they are introduced by the real Fourier transform
milstar: 1.First, the real Fourier transform converts a real time domain signal, x [n], into two real frequency domain signals, ReX[k ] & ImX[k ]. By using complex substitution, the frequency domain can be represented by a single complex array, X[k]. In the complex Fourier transform, both x [n] & X[k] are arrays of complex numbers. A practical note: Even though the time domain is complex, there is nothing that requires us to use the imaginary part. Suppose we want to process a real signal, such as a series of voltage measurements taken over time. This group of data becomes the real part of the time domain 2. Second, the real Fourier transform only deals with positive frequencies. That is, the frequency domain index, k, only runs from 0 to N/2. In comparison, the complex Fourier transform includes both positive and negative frequencies. This means k runs from 0 to N-1. The frequencies between 0 and N/2 are positive, while the frequencies between N/2 and N-1 are negative. Remember, the frequency spectrum of a discrete signal is periodic, making the negative frequencies between N/2 and N-1 the same as Chapter 31- The Complex Fourier Transform 571 between -N/2 and 0. The samples at 0 and N/2 straddle the line between positive and negative. If you need to refresh your memory on this, look back at Chapters 10 and 12. 3. Third, in the real Fourier transform with substitution, a j was added to the sine wave terms, allowing the frequency spectrum to be represented by complex numbers. To convert back to ordinary sine and cosine waves, we can simply drop the j. This is the sloppiness that comes when one thing only represents another thing. In comparison, the complex DFT, Eq. 31-5, is a formal mathematical equation with j being an integral part. In this view, we cannot arbitrary add or remove a j any more than we can add or remove any other variable in the equation. 4, the real Fourier transform has a scaling factor of two in front, while the complex Fourier transform does not. Say we take the real DFT of a cosine wave with an amplitude of one. The spectral value corresponding to the cosine wave is also one. Now, let's repeat the process using the complex DFT. In this case, the cosine wave corresponds to two spectral values, a positive and a negative frequency. Both these frequencies have a value of ½. In other words, a positive frequency with an amplitude of ½, combines with a negative frequency with an amplitude of ½, producing a cosine wave with an amplitude of one. 5., the real Fourier transform requires special handling of two frequency domain samples: ReX [0] & ReX [N/2], but the complex Fourier transform does not. Suppose we start with a time domain signal, and take the DFT to find the frequency domain signal. To reverse the process, we take the Inverse DFT of the frequency domain signal, reconstructing the original time domain signal. However, there is scaling required to make the reconstructed signal be identical to the original signal. For the complex Fourier transform, a factor of 1/N must be introduced somewhere along the way. This can be tacked-on to the forward transform, the inverse transform, or kept as a separate step between the two. For the real Fourier transform, an additional factor of two is required (2/N), as described above. However, the real Fourier transform also requires an additional scaling step: ReX [0] and ReX [N/2] must be divided by two somewhere along the way. Put in other words, a scaling factor of 1/N is used with these two samples, while 2/N is used for the remainder of the spectrum. As previously stated, this awkward step is one of our complaints about the real Fourier transform. Why are the real and complex DFTs different in how these two points are handled? To answer this, remember that a cosine (or sine) wave in the time domain becomes split between a positive and a negative frequency in the complex DFT's spectrum. However, there are two exceptions to this, the spectral values at 0 and N/2. These correspond to zero frequency (DC) and the Nyquist frequency (one-half the sampling rate). Since these points straddle the positive and negative portions of the spectrum, they do not have a matching point. Because they are not combined with another value, they inherently have only one-half the contribution to the time domain as the other frequencies. signal, while the imaginary part is composed of zeros https://www.analog.com/media/en/technical-documentation/dsp-book/dsp_book_Ch31.pdf https://www.analog.com/media/en/technical-documentation/dsp-book/dsp_book_Ch10.pdf https://www.analog.com/media/en/technical-documentation/dsp-book/dsp_book_Ch12.pdf
milstar: http://publ.lib.ru/ARCHIVES/S/SMIT_Stiven_V/_Smit_S.V..html http://www.autex.spb.su/download/dsp/dsp_guide/ch10en-ru.pdf http://www.autex.spb.su/download/dsp/dsp_guide/ch12en-ru.pdf http://www.autex.spb.su/download/dsp/dsp_guide/ch31en-ru.pdf
milstar: https://cdn.rohde-schwarz.com/pws/dl_downloads/dl_common_library/dl_brochures_and_datasheets/pdf_1/Realtime_FFT_app-bro_en_3606-8308-92_v0100.pdf
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