❤️ Corner reflector 🐞

"A corner reflector is a retroreflector consisting of three mutually perpendicular, intersecting flat surfaces, which reflects waves directly towards the source, but translated. The three intersecting surfaces often have square shapes. Radar corner reflectors made of metal are used to reflect radio waves from radar sets. Optical corner reflectors, called corner cubes or cube corners, made of three-sided glass prisms, are used in surveying and laser ranging. Principle Working principle of a corner reflector The incoming ray is reflected three times, once by each surface, which results in a reversal of direction. To see this, the three corresponding normal vectors of the corner's perpendicular sides can be considered to form a basis (a rectangular coordinate system) (x, y, z) in which to represent the direction of an arbitrary incoming ray, [a, b, c]. When the ray reflects from the first side, say x, the ray's x component, a, is reversed to −a while the y and z components are unchanged, resulting in a direction of [−a, b, c]. Similarly, when reflected from side y and finally from side z, the b and c components are reversed. Therefore, the ray direction goes from [a, b, c] to [−a, b, c] to [−a, −b, c] to [−a, −b, −c], and it leaves the corner reflector with all three components of direction exactly reversed. The distance travelled, relative to a plane normal to the direction of the rays, is also equal for any ray entering the reflector, regardless of the location where it first reflects. Animation showing the reflected rays in a corner of a cube (corner reflector principle). In radar Radar corner reflectors are designed to reflect the microwave radio waves emitted by radar sets back toward the radar antenna. This causes them to show a strong "return" on radar screens. A simple corner reflector consists of three conducting sheet metal or screen surfaces at 90° angles to each other, attached to one another at the edges, forming a "corner". These reflect radio waves coming from in front of them back parallel to the incoming beam. To create a corner reflector that will reflect radar waves coming from any direction, 8 corner reflectors are placed back-to-back in an octahedron (diamond) shape. The reflecting surfaces must be larger than several wavelengths of the radio waves to function. In maritime navigation they are placed on bridge abutments, buoys, ships and, especially, lifeboats, to ensure that these show up strongly on ship radar screens. Corner reflectors are placed on the vessel's masts at a height of at least 4.6 meters (15 feet) above sea level (giving them an approximate minimum horizon distance of 8 kilometers or 4.5 nautical miles). Marine radar uses X-band microwaves with wavelengths of 2.5 - 3.75 cm, so small reflectors less than 30 cm across are used. In aircraft navigation, corner reflectors are installed on rural runways, to make them show up on aircraft radar. In optics Corner cube reflector Apollo 15 Lunar Laser Ranging RetroReflector (LRRR) installed on the Moon In optics, corner reflectors typically consist of three mirrors or reflective prism faces which return an incident light beam in the opposite direction. In surveying, retroreflector prisms are commonly used as targets for long-range electronic distance measurement using a total station. Five arrays of optical corner reflectors have been placed on the Moon for use by Lunar Laser Ranging experiments observing a laser's time-of-flight to measure the Moon's orbit more precisely than was possible before. The three largest were placed by NASA as part of the Apollo program, and the Soviet Union built two smaller ones into the Lunokhod rovers. Automobile and bicycle tail lights are molded with arrays of small corner reflectors, with different sections oriented for viewing from different angles. Reflective paint for visibility at night usually contains retroreflective spherical beads. Thin plastic with microscopic corner reflector structures can be used as tape, on signs, or sewn or molded onto clothing. Other examples Corner reflectors can also occur accidentally. Tower blocks with balconies are often accidental corner reflectors for sound and return a distinctive echo to an observer making a sharp noise, such as a hand clap, nearby. Similarly, in radar interpretation, an object that has multiple reflections from smooth surfaces produces a radar return of greater magnitude than might be expected from the physical size of the object. This effect was put to use on the ADM-20 Quail, a small missile which had the same radar cross section as a B-52. See also References * * External links *Corner Reflector Antennas *Corner Reflector for WiFi Category:Mirrors Category:Radar "

❤️ Cosmic noise 🐞

"Cosmic noise and galactic radio noise is random noise that originates outside the Earth's atmosphere. It can be detected and heard in radio receivers. Cosmic noise characteristics are similar to those of thermal noise. Cosmic noise is experienced at frequencies above about 15 MHz when highly directional antennas are pointed toward the sun or to certain other regions of the sky such as the center of the Milky Way Galaxy. Celestial objects like quasars, super dense objects that lie far from Earth, emit electromagnetic waves in its full spectrum including radio waves. We can also hear the fall of a meteorite in a radio receiver; the falling object burns from friction with the Earth's atmosphere, ionizing surrounding gases and producing radio waves. Cosmic microwave background radiation (CMBR) from outer space, discovered by Arno Penzias and Robert Wilson, who later won the Nobel Prize for this discovery, is also a form of cosmic noise. CMBR is thought to be a relic of the Big Bang, and pervades the space almost homogeneously over the entire celestial sphere. The bandwidth of the CMBR is wide, though the peak is in the microwave range. See also *Intergalactic space *Interplanetary space *Interstellar medium *Radio astronomy References * Category:Astronomical radio sources Category:Noise "

❤️ Costas loop 🐞

"A Costas loop is a phase-locked loop (PLL) based circuit which is used for carrier frequency recovery from suppressed-carrier modulation signals (e.g. double-sideband suppressed carrier signals) and phase modulation signals (e.g. BPSK, QPSK). It was invented by John P. Costas at General Electric in the 1950s. Its invention was described as having had "a profound effect on modern digital communications". The primary application of Costas loops is in wireless receivers. Its advantage over other PLL-based detectors is that at small deviations the Costas loop error voltage is \sin(2(\theta_i-\theta_f)) as compared to \sin(\theta_i-\theta_f). This translates to double the sensitivity and also makes the Costas loop uniquely suited for tracking Doppler-shifted carriers especially in OFDM and GPS receivers. Classical implementation Costas loop working in the locked state. In the classical implementation of a Costas loop, a local voltage-controlled oscillator (VCO) provides quadrature outputs, one to each of two phase detectors, e.g., product detectors. The same phase of the input signal is also applied to both phase detectors and the output of each phase detector is passed through a low-pass filter. The outputs of these low-pass filters are inputs to another phase detector, the output of which passes through noise-reduction filter before being used to control the voltage-controlled oscillator. The overall loop response is controlled by the two individual low-pass filters that precede the third phase detector while the third low-pass filter serves a trivial role in terms of gain and phase margin. The above figure of a Costas loop is drawn under the condition of the "locked" state, where the VCO frequency and the incoming carrier frequency have become the same as a result of the Costas loop process. The figure does not represent the "unlocked" state. Mathematical models = In the time domain = Time domain model of BPSK Costas loop In the simplest case m^2(t) = 1. Therefore, m^2(t) = 1 does not affect the input of noise-reduction filter. Carrier and voltage-controlled oscillator (VCO) signals are periodic oscillations f_{ref,vco}(\theta_{ref,vco}(t)) with high- frequencies \dot\theta_{ref,vco}(t). Block \bigotimes is an analog multiplier. From the mathematical point of view, a linear filter can be described by a system of linear differential equations :\begin{array}{ll} \dot x = Ax + b u_{d}(t),& u_{LF} = c^*x. \end{array} Here, A is a constant matrix, x(t) is a state vector of filter, b and c are constant vectors. The model of a VCO is usually assumed to be linear : \begin{array}{ll} \dot\theta_{vco}(t) = \omega^{free}_{vco} + K_{vco} u_{LF}(t),& t \in [0,T], \end{array} where \omega^{free}_{vco} is a free-running frequency of voltage-controlled oscillator and K_{vco} is an oscillator gain. Similarly, it is possible to consider various nonlinear models of VCO. Suppose that the frequency of master generator is constant \dot\theta_{ref}(t) \equiv \omega_{ref}. Equation of VCO and equation of filter yield : \begin{array}{ll} \dot{x} = Ax + bf_{ref}(\theta_{ref}(t))f_{vco}(\theta_{vco}(t)),& \dot\theta_{vco} = \omega^{free}_{vco} + K_{vco}c^*x. \end{array} The system is non-autonomous and rather difficult for investigation. = In phase-frequency domain = Equivalent phase-frequency domain model of Costas loop VCO input for phase- frequency domain model of Costas loop In the simplest case, when : \begin{align} f_{ref}\big(\theta_{ref}(t)\big) = \cos\big(\omega_{ref} t\big),\ f_{vco}\big(\theta_{vco}(t)\big) &= \sin\big(\theta_{vco}(t)\big) f_{ref}\big(\theta_{ref}(t)\big)^2 f_{vco}\left(\theta_{vco}(t)\right) f_{vco}\left(\theta_{vco}(t) - \frac{\pi}{2}\right) &= -\frac{1}{8}\Big( 2\sin(2\theta_{vco}(t)) + \sin(2\theta_{vco}(t) - 2\omega_{ref} t) + \sin(2\theta_{vco}(t) + 2\omega_{ref} t) \Big) \end{align} the standard engineering assumption is that the filter removes the upper sideband with frequency from the input but leaves the lower sideband without change. Thus it is assumed that VCO input is \varphi(\theta_{ref}(t) - \theta_{vco}(t)) = \frac{1}{8}\sin(2\omega_{ref} t - 2\theta_{vco}(t)). This makes a Costas loop equivalent to a phase-locked loop with phase detector characteristic \varphi(\theta) corresponding to the particular waveforms f_{ref}(\theta) and f_{vco}(\theta) of input and VCO signals. It can be proved that filter outputs in time domain and phase-frequency domain are almost equal. Thus it is possible to study more simple autonomous system of differential equations :\begin{align} \dot{x} &= Ax + b\varphi(\Delta\theta), \Delta\dot{\theta} &= \omega_{vco}^{free} - \omega_{ref} + K_{vco}c^*x, \Delta\theta &= \theta_{vco} - \theta_{ref}. \end{align}. The Krylov–Bogoliubov averaging method allows one to prove that solutions of non-autonomous and autonomous equations are close under some assumptions. Thus the block-scheme of Costas Loop in the time space can be asymptotically changed to the block-scheme on the level of phase-frequency relations. The passage to analysis of autonomous dynamical model of Costas loop (in place of the non-autonomous one) allows one to overcome the difficulties, related with modeling Costas loop in time domain where one has to simultaneously observe very fast time scale of the input signals and slow time scale of signal's phase. This idea makes it possible to calculate core performance characteristics - hold-in, pull-in, and lock-in ranges. Frequency acquisition { style="float:center; margin:auto" Costas loop before synchronization Costas loop after synchronization } { style="float:center; margin:auto" Carrier and VCO signals before synchronization VCO input during synchronization Carrier and VCO signals after synchronization } The classical Costas loop will work towards making the phase difference between the carrier and the VCO become a small, ideally zero, value. states, "The local oscillator must be maintained at proper phase so that the audio output contributions of the upper and lower sidebands reinforce one another. If the oscillator phase is 90° away from the optimum value a null in audio output will result which is typical of detectors of this type. The actual method of phase control will be explained shortly, but for the purpose of this discussion maintenance of correct oscillator phase shall be assumed."Using a loop filter with an integrator allows a steady-state phase error of zero. See . The small phase difference implies that frequency lock has been achieved. QPSK Costas loop Classical Costas loop can be adapted to QPSK modulation for higher data rates . Classical QPSK Costas loop The input QPSK signal is as follows : m_1(t)\cos\left(\omega_\text{ref} t\right) + m_2(t)\sin\left(\omega_\text{ref} t\right), m_1(t) = \pm 1, m_2(t) = \pm 1. Inputs of low-pass filters LPF1 and LPF2 are :\begin{align} \varphi_1(t) &= \cos\left(\theta_\text{vco}\right)\left(m_1(t)\cos\left(\omega_\text{ref} t\right) + m_2(t)\sin\left(\omega_\text{ref} t\right)\right), \varphi_2(t) &= \sin\left(\theta_\text{vco}\right)\left(m_1(t)\cos\left(\omega_\text{ref} t\right) + m_2(t)\sin\left(\omega_\text{ref} t\right)\right). \end{align} After synchronization outputs of LPF1 Q(t) and LPF2 I(t) are used to get demodulated data (m_1(t) and m_2(t)). To adjust frequency of VCO to reference frequency signals Q(t) and I(t) goes through limiters and cross-multiplied: :u_d(t) = I(t)\sgn(Q(t)) - Q(t)\sgn(I(t)). After that signal u_d(t) is filtered by Loop filter and forms tuning signal for VCO u_\text{LF}(t) similar to BPSK Costas loop. Thus, QPSK Costas can be described by system of ODEs :\begin{align} \dot{x}_1 &= A_\text{LPF} x_1 + b_\text{LPF}\varphi_1(t), \dot{x}_2 &= A_\text{LPF} x_2 + b_\text{LPF}\varphi_2(t), \dot{x} &= A_\text{LF} x + b_\text{LF}\left(c_\text{LPF}^* x_1\sgn\left(c_\text{LPF}^* x_2\right) - c_\text{LPF}^* x_2\sgn\left(c_\text{LPF}^* x_1\right)\right), \dot{\theta}_\text{vco} &= \omega_\text{vco}^\text{free} + K_\text{VCO}\left(c^*_\text{LF} x + h\left(c_\text{LPF}^* x_1\sgn\left(c_\text{LPF}^* x_2\right) - c_\text{LPF}^* x_2\sgn\left(c_\text{LPF}^* x_1\right)\right)\right). \end{align} Here A_\text{LPF}, b_\text{LPF}, c_\text{LPF} \- parameters of LPF1 and LPF2 and A_\text{LF}, b_\text{LF}, c_\text{LF}, h_\text{LF} \- parameters of loop filter. References * Category:Electronic oscillators Category:Communication circuits "