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Most frequency counters work by using a digital counter which counts the number of events occurring within a specific precise period of time, the gate time or gate period. During the gate period, the counter is incremented by each oscillation of the input signal. At the end of the gate period, the number in the counter is transferred to a digital display and the counter is reset to zero in preparation for the next counting cycle. The gate timing signal is generated by an internal electronic oscillator called the timebase, divided down by decade counters. For example, if the gate time is one second, the count represents the average frequency of the input signal in hertz.
The timebase must be calibrated very accurately, for it determines the accuracy of the frequency measurement. Precision crystal oscillators are used. Oven controlled crystal oscillators (OXCOs) can achieve accuracy of around 10-11.
If the signal to be counted is already in electronic form, simple interfacing to the instrument is all that is required. Cyclic processes that are not inherently electronic, such as sound waves, mechanical vibrations or the rotation rate of a shaft, can be converted to a repetitive electronic signal by a transducer and the frequency measured by the counter. In the instrument, the input signal is put through a comparator before applying it to the counter, which converts it to a square wave with fast transitions to improve the accuracy of the counting process. More complex signals may need additional conditioning to make them suitable for counting. Most general purpose frequency counters will include some form of amplifier, noise filtering and shaping circuitry at the input. DSP technology, sensitivity control and hysteresis are other input processing techniques used to improve performance.
When the frequency of the input signal is low compared to the gating interval, so only a small number cycles are counted, the resolution of the measurement will be low, and the quantization error (described below) will be significant. In this case it is usually more accurate to measure the period of the signal rather than the frequency. Frequency counters accomplish this by exchanging the roles of the input signal and the gating signal in the counting process, so the number of cycles of the gating signal in a single cycle of the input are counted. A higher frequency gating signal is used in this case.
Frequency counters can measure frequencies up through the radio frequency range and even into the microwave range. In microwave frequency counters the input signal is often put through a prescaler, a digital divider which reduces the frequency to . The maximum frequency that can be measured is limited by the maximum speed that digital counters can work. Frequency counters currently can cover the range up to about 150 - 200 MHz. Frequencies above this must be measured by indirect techniques.
It can be seen from the description above that the frequency count will be:
If Ti is the period for one cycle of the input signal, and Tg is the gate time, fi = 1/Ti is the input frequency, and fg = 1/Tg is the frequency of the gate signal. So the frequency of the input signal is given by:
The uncertainty of ± ½, or one count, shown above is called quantization error or gating error and is due to the fact that the input signal is asynchronous to the gating signal. Depending on where the gate window falls in the input stream during each counting interval, it may randomly include one more transition of the input waveform, or not. The fractional quantization error is:
It can be seen that the quantization error is o
Most frequency counters work by using a counter which accumulates the number of events occurring within a specific period of time. After a preset period (1 second, for example), the value in the counter is transferred to a display and the counter is reset to zero. If the event being measured repeats itself with sufficient stability and the frequency is considerably lower than that of the clock oscillator being used, the resolution of the measurement can be greatly improved by measuring the time required for an entire number of cycles, rather than counting the number of entire cycles observed for a pre-set duration (often referred to as the reciprocal technique). The internal oscillator which provides the time signals is called the timebase, and must be calibrated very accurately.
If the thing to be counted is already in electronic form, simple interfacing to the instrument is all that is required. More complex signals may need some conditioning to make them suitable for counting. Most general purpose frequency counters will include some form of amplifier, filtering and shaping circuitry at the input. DSP technology, sensitivity control and hysteresis are other techniques to improve performance. Other types of periodic events that are not inherently electronic in nature will need to be converted using some form of transducer. For example, a mechanical event could be arranged to interrupt a light beam, and the counter made to count the resulting pulses.
Frequency counters designed for radio frequencies (RF) are also common and operate on the same principles as lower frequency counters. Often, they have more range before they overflow. For very high (microwave) frequencies, many designs use a high-speed prescaler to bring the signal frequency down to a point where normal digital circuitry can operate. The displays on such instruments take this into account so they still read true. Microwave frequency counters can currently measure frequencies up to almost 100 GHz. Above these frequencies the signal to be measured is combined in a mixer with the signal from a local oscillator, producing a signal at the difference frequency, which is low enough to be measured directly.
In physics and mathematics, simple harmonic motion (SHM) is the motion described by a point that is the projection on the x-axis of a point moving at a constant speed in a circle about the origin. The motion is periodic; the point oscillates back and forth about a central equilibrium position (the origin) with a smooth sinusoidal motion, that is, given by a mathematical sine or cosine function. The time taken by a single cycle of the motion, that is a single rotation of the generating point about the origin, is called the period, T.
Since the motion is defined by a point on a circle, the position of the point at any particular time in its cycle can be described by its phase angle, the angle a line through the point makes with the x-axis. As point rotates, the phase angle increases steadily from 0 to 2π (360°), then starts over again at 0.
An example of an object that moves with SHM is a piston in an automobile engine, or a weight bobbing up and down on a spring. Simple harmonic motion describes the motion of many oscillating and vibrating objects in physics, known as harmonic oscillators.
The position of a point in simple harmonic motion is given at any time by the equation:
The motion is described by the three constants , , and :
The frequency can alternately be replaced by the radian frequency:
in radians per second, which is the angle in radians that the generating point turns in one second instead of the number of cycles.
simple harmonic oscillator, a motion that is neither driven nor damped. A body in simple harmonic motion experiences a single force which is given by Hooke's law; that is, the force is directly proportional to the displacement x and points in the opposite direction.
The motion is periodic: the body oscillates about an equilibrium position in a sinusoidal pattern. Each oscillation is identical, and thus the period, frequency, and amplitude of the motion are constant. If the equilibrium position is taken to be zero, the displacement x of the body at any time t is given by
where A is the amplitude, f is the frequency, and φ is the phase.
The frequency of the motion is determined by the intrinsic properties of the system (often the mass of the body and a force constant), while the amplitude and phase are determined by the initial conditions (displacement and velocity) of the system. The kinetic and potential energies of the system are also determined by these properties and conditions.
Simple harmonic motion can serve as a mathematical model of a variety of motions, such as the oscillation of a spring. Other phenomena can be approximated by simple harmonic motion, including the motion of a pendulum and molecular vibration.
Simple harmonic motion provides the basis of the characterization of more complicated motions through the techniques of Fourier analysis.
The magnetic field of permanent magnets is generated by the orbital electrons in their atoms. The electrons behave as if they spin about an axis like tops. This creates a tiny magnetic field.
In most materials, the electrons come in pairs. The electrons in these pairs are oriented with their magnetic fields in opposite directions, N to S, so their magnetic fields oppose one another and cancel. Permanent magnetism occurs only in substances that have atoms with unpaired electrons. In a few of these substances, iron and the other ferromagnetic materials, the unpaired electrons spontaneously align so their axes of spin are parallel, and their tiny magnetic fields reinforce each other and add together to make a strong magnetic field.
Considering the above, why isn't every piece of iron a magnet? Iron and other ferromagnetic materials are divided into millions of microscopic regions called magnetic domains that act like tiny bar magnets. Their size is of the order of 10-5 m.[1] In a piece of unmagnetized iron the magnetic domains point in different random directions, so their tiny magnetic fields cancel each other out and the iron has no net magnetic field. In a magnet, most of the domains are aligned with their North poles pointing in the same direction. So their tiny magnetic fields add to each other, creating a large magnetic field that extends out from the magnet into the space around it.
When another piece of iron or other ferromagnetic material comes near a magnet, the magnetic field of the magnet aligns the magnetic domains in the iron. The iron object becomes a magnet itself for as long as it is in the field of the other magnet. Unlike poles of the magnet and the iron are closest to each other, North to South, so they attract. <improve>
In 'soft' magnetic materials like ordinary iron, the magnetic domains can easily turn their direction of magnetization, so once the external magnetic field is removed the domains tend to attract one another and lose alignment, pointing in random directions again, so the material doesn't stay magnetized. In contrast, in 'hard' magnetic materials used to make permanent magnets, the domains are 'pinned down' by the crystal structure and can't turn their direction of magnetization easily. Once the domains are aligned they tend to stay aligned, and the material stays magnetized.
I agree with your point that the "threshold" of a diode is an optical illusion, depending on the scale of the vertical (current) axis. Nevertheless the forward "voltage drop" of a detector diode is still an important factor in crystal set design. The lower the "voltage drop" across the diode at any given voltage, the higher the "detection efficiency", the ratio of DC current to applied AC voltage.
"naive" crystal radio circuit:
Full wave crystal circuits:
Direct coupled impedance matched circuits:
Untuned crystal radio circuit:
Inductively coupled set with buzzer attached to ground wire"
Mach's principle is an imprecise conjecture in physics and cosmology, first advanced by Austrian physicist Ernst Mach in 1910 and named and popularized by Albert Einstein, that is variously said to consist of two related ideas: (1) that accelerated motions are relative; meaning that acceleration or rotation of an object can only be defined by comparing its motion relative to other objects, so there is no way to define "absolute" acceleration or rotation, and (2) that inertial forces on an object, such as centrifugal force, are caused by other matter in the universe.
This principle was a guiding force for Einstein in his development of the General Theory of Relativity in 1916. As indicated by the name he gave it, Einstein initially believed his General Theory of Relativity established that all motion is relative, and so proved Mach's principle, but later he gave up this view. The General Theory does predict, in conformity with idea (2) of Mach's principle above, that inertial forces on an object are caused by the distribution and motion of other matter in the universe. For centrifugal forces this is called the Lense-Thirring effect, and recent experiments, such as Stanford's Gravity Probe B, have begun to confirm its existence. However the statement of Mach's principle is somewhat imprecise, and there has been debate ever since about idea (1) above, that accelerated motion is relative, and whether modern relativistic physics and cosmology supports it or not.
An example will show the relation between the two ideas introduced above. If an ice skater is spinning, it appears to her as if she is stationary and the surrounding skating rink, buildings, the Earth, Sun and the stars, and the entire universe, are spinning around her in the opposite direction. Mach's principle says that this is an equally valid way of looking at the situation, and there is no way of determining which is "actually" rotating. However, the skater feels a force pulling her arms away from her body. According to classical Newtonian physics this force, actually a pseudoforce called centrifugal force caused by the inertia of her body, indicates that she is actually the one rotating, not the universe. In fact, if she was unable to see other objects, with no other objects in the universe to refer her motion to, this centrifugal force would be the only way she could tell if she was rotating or not. Newtonian physics says that there is a distinction between rotating and nonrotating or inertial reference frames, that if she was not rotating but the universe was rotating around her, there wouldn't be a force pulling her arms outward.
Mach's view was that, if the universe was rotating, she would still feel her arms pulled outward. In the Machian view, centrifugal force is an effect caused by the relative motion of all the other mass in the universe; and a circulation of mass around an object would cause an outward force identical to centrifugal force. The only thing the centrifugal force on the skater indicates is a relative rotation between the skater and the other masses in the universe, so it can't distinguish which is "actually" rotating, or whether perhaps both are rotating at different rates. So in the Machian view, the concept of absolute rotation has no meaning.
Similarly, the Machian view is that linear acceleration is also relative. A person in an accelerating car is pressed into his seat by a force caused by his body's inertia. In Mach's view if the car was stationary and the universe was accelerating backward instead, this inertial force would still be present.
The idea that unaccelerated motions are relative is a cornerstone of both Newtonian and modern relativistic physics, accepted since the time of Galileo. It is expressed by the concept of an inertial reference frame. A person moving at a constant speed in a straight line can only determine whether he is moving, and in which direction, by reference to other objects. Because the laws of physics work the same in any inertial reference frame, there is no experiment that can determine whether he is "actually" moving or stationary. Therefore there is no way to define a preferred "stationary" reference frame; all inertial frames are equivalent. Mach's principle would extend this idea to all motion, including accelerated motion (noninertial reference frames).
A diplomatic mission is a group of official representatives of one country present in another country. Most countries keep permanent diplomatic missions, called embassies and consulates, in many other countries. International law has long recognised that to do their jobs effectively, diplomatic missions need to be able to communicate freely and confidentially with their home governments. During the 16th and 17th centuries, waylaying and bribing couriers in order to read governmental communications was a common method of espionage between nations. In order to prevent these abuses, the ______ in ___ provided a legally protected channel for missions to communicate; the diplomatic courier and diplomatic bag. During the 20th century, in order to allow secure transport of larger items needed by missions, such as cipher machines and radio transmitters, the definition of a diplomatic bag was expanded to cover arbitrary sized containers.
International law protects diplomatic bags from search or detention, not just by the country hosting the mission, but by any other countries the bag must travel through. A diplomatic bag must be accompanied by a diplomatic courier with one exception: in order to allow air freight shipment, a diplomatic bag may be transported unaccompanied on an aircraft, with the pilot assuming legal custody of it during the trip.
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