The relationship between pulse duration and the width of its spectrum

Sources of oscillations in the form of pulses are most often pulse generators - autonomous converters of the energy of the power source into the energy of discontinuous oscillations of the required shape. Another way to obtain pulses is to form them by changing the parameters of oscillations of a different shape, for example sinusoidal.

For this purpose, shaping devices are used - amplitude limiters, differentiation circuits and other devices that change the vibration parameters - amplitude, repetition period, shape, etc.

An electrical impulse is a voltage or current that differs from zero or a constant value only for a short period of time, which is less than or comparable to the duration of the establishment of processes in the electrical system in which they operate. Pulses can be either periodic or single (Fig. 1)

Rice. 1. Pulses of various shapes

In the case of consecutive pulses (i.e., periodic), it is usually assumed that the interval between them significantly exceeds the duration of the establishment processes. Otherwise, this signal is called a non-sinusoidal voltage or current. This definition is not strict, because transient processes, as is known, take an infinitely long time. However, it makes it possible to distinguish impulses in the generally accepted sense from voltages of complex shape.

Electrical pulse parameters

Pulses and pulse sequences are characterized by a number of parameters (pulse duration, pause duration, rise time, trailing period, etc.). The method for measuring these parameters is presented in Fig. 2.

Rice. 2. Basic parameters of pulses

Um – pulse amplitude. This is the largest voltage deviation from the initial, steady-state value Uo ;

tfr – duration of the pulse front (or front time) . This is the time interval during which the voltage increases from 0.1Um to 0.9Um. In other words, the rise time is measured not by the maximum and minimum voltage values, but by levels 0.1-0.9 from the maximum value.

tcп – pulse decay duration (or decay time) . This is the time interval during which the voltage drops from 0.9Um to 0.1Um. It is sometimes also called the pulse cutoff time.

ti – pulse duration . This is the time interval between moments at adjacent intervals tfr and tcп, for which u = 0.5Um. In other words, the pulse duration is measured at half the amplitude.

tп – pause duration . It is measured at a level of 0.5 similar to the pulse duration. In this case, the relation tп = T-tи is observed.

T – pulse repetition period. This is the time interval between moments on adjacent intervals tfr or tcп, for which u = 0.5Um. In other words, the period is measured at the level of half the amplitude between two adjacent rises or falls.

f – pulse repetition frequency . This is the reciprocal of the period f =1 / T.

Q - duty cycle of pulses . This is a value equal to the ratio of the period to the pulse duration: Q = T/ti

Kz – pulse duty cycle . This is a value equal to the ratio of the pulse duration to the period: Kз = tи/T . The duty cycle and duty cycle are reciprocal quantities.

Date added: 2016-02-27; ; ORDER A WORK WRITING

Design of a device measuring pulse duration

Currently, microprocessor technology is making great strides in its application in various industries. Nowadays, microprocessors have begun to be used not only in household appliances and cars, but even in production, controlling the most complex technological processes.

The purpose of the course project was to create a measuring device based on the AVR90S8515 microprocessor

Microprocessors from the American company ATMEL have been making significant progress in developing new areas of their application in recent years. The microprocessor core used in AVR microcontrollers is similar to most RISC processors, perhaps with the exception of 8-bit registers. Developed by two developers from Norway, in the city of Trondheim. Later, in 1995, the development was acquired by Atmel. Until now, core development has taken place in Norway, while peripherals and memory are developed at Atmel's California division.

Using the designed device it will be possible to measure the length of pulses in the range from 10 mSec to 10 Sec; the measured value will be displayed on a four-digit LED indicator

It is necessary to design a device to measure pulse duration.

Types of pulses and their parameters.

A pulse is understood as a short-term deviation of voltage or current from some constant level, in particular from zero.

There are two types of pulses: video pulses and radio pulses.

Video pulses represent a short-term change in voltage or current in a DC circuit. Video pulses have rectangular, trapezoidal, triangular, exponential and bell-shaped shapes (Fig. 15.1).

Rice. 15.1. Idealized pulse shapes of rectangular (a), trapezoidal (b), triangular (c), exponential (d) and bell-shaped (e).

It should be borne in mind that real pulses do not have a shape that strictly corresponds to the name. For example, rectangular pulses have a shape close to trapezoidal, and triangular pulses have a shape close to exponential.

There are pulses of positive and negative polarity, as well as double-sided (multipolar) pulses (“meander”).

Rice. 15.2. Bilateral (multipolar) impulses.

The most commonly used are rectangular pulses.

Radio pulses are short-term bursts of sinusoidal voltage or current. They are taken from the output of a high-frequency generator, which is controlled (modulated) by video pulses. Therefore, the shape of the radio pulse envelope corresponds to the shape of the modulating video pulses (Fig. 15.3).

Rice. 15.3. Types of radio pulses: rectangular (a), trapezoidal (b), triangular (c), exponential (d, e) shapes.

Let us introduce the concept of the basic parameters of a pulse using the example of a real rectangular pulse. As shown in Fig. 15.4 such pulses have a leading edge, a cutoff (trailing edge) and a flat top (the section of the pulse between the fronts). The figure also shows the flat top drop (∆U) and the resulting small voltage surge. The parameters of a real pulse are: the amplitude of the pulse, its duration and slope of the fronts, as well as the power in the pulse.

Rice. 15.4. Rectangular voltage pulse.

Pulse amplitude

– this is the highest value of voltage or current. The amplitude of voltage or current is expressed in volts, kilovolts, millivolts, microvolts or amperes, milliamps, microamps.

Pulse duration

. The active pulse duration is taken to be a time interval measured at a level corresponding to half the amplitude. Sometimes the pulse duration is determined at the level of 0.1 (0.1 or by the base of the pulse. In the future, unless otherwise specified, the pulse duration will be determined by the base and denoted by . The pulse duration is expressed in time units: seconds, milliseconds, microseconds and nano- seconds.

Duration and slope of the front (fall) of the pulse

. The duration of the leading edge of the pulse is determined by the rise time of the pulse, and the duration of the cutoff is determined by the decay time of the pulse. The most often used is the concept of active front duration, which is taken to be the pulse rise time from 0.1 to 0.9. Similarly, the cutoff duration is the decay time of the pulse from 0.9 to 0.1.

Usually the duration is a few percent of . The smaller and compared to the pulse duration, the more the pulse shape approaches rectangular. Sometimes, instead of and, the pulse fronts are characterized by the rate of rise (fall). This value is called the slope of the front (decay) S

and is expressed in volts per second. For a rectangular pulse approximately:

S = (15.1)

Pulse power

. The energy W of the pulse relative to its duration determines the power in the pulse:

= (15.2)

This power is expressed in watts, kilowatts, megawatts.

2. Pulse sequence parameters.

Pulses repeated at regular intervals form a periodic sequence. Such a sequence, the parameters of which change in accordance with the transmitted information, is a signal.

In addition to the parameters inherent to a single pulse, the pulse sequence is characterized by additional parameters: pulse repetition period, pulse repetition frequency, duty cycle, pulse duty cycle, as well as the average value of pulse oscillation power.

Pulse period and frequency

. The time interval between the beginning of two adjacent unipolar pulses is called the pulse repetition period. It is expressed in time units: seconds, milliseconds, microseconds. The reciprocal of the repetition period is called the pulse repetition rate. The pulse repetition rate determines the number of periods within one second and is expressed in hertz, kilohertz, megahertz (Fig. 15.5).

Rice. 15.5. Sequence of triangular pulses.

Duty factor and duty cycle

. Part of the period T is occupied by a pause - this is the period of time between the end and the beginning of two adjacent pulses, i.e.:

= — (15.3)

The ratio of the pulse duration to the repetition period is called the duty cycle:

γ = (15.4)

Fill factor is a dimensionless quantity less than unity.

The reciprocal of the duty cycle is called the duty cycle:

q = = (15.5)

The duty cycle is a dimensionless value greater than unity.

Average value of voltage (current) of pulse oscillation

. When determining the average value of the voltage (current) of a pulse oscillation over a period ( ), the voltage or current is distributed evenly over the entire period so that the area of ​​the rectangle is equal to the area of ​​the pulse.

Since for a rectangular pulse:

= (15.6)

and = = γ = (15.7)

those. the average value of voltage (current) of a rectangular pulse oscillation is q times less than the amplitude.

Average power

. The pulse energy W related to the pulse period determines the average pulse power:

= (15.8)

Comparing the expressions and , we get:

= (15.9)

= = q (15.10)

= = (15.11)

Those. the average power and the power per pulse differ by q times. It follows that the pulse power provided by the generator can be q times greater than the average power of the generator.

On-camera flashes

Installed in the camera's hot shoe. They can have different powers, but the most powerful ones, as a rule, do not exceed 80 J. Very flexible in operation, they work autonomously from the camera.

Reviews of on-camera flashes

Review and test of the Godox Witstro AD360II-C flash Review and test of the Profoto A1 flash Review of Falcon Eyes X-Flash flashes

Monoblocks

A monoblock is a flash with a built-in power adapter. As a rule, it runs on mains power, although now there are all-in-one computers with a battery and all-in-one computers that can operate on both mains and battery power.

Monoblocks are much larger than on-camera flashes, but allow you to use all studio light modifiers, which is very important. After all, you can’t do much with a “naked” flash. Monoblocks also come in much higher power than on-camera flashes (up to 1500 J). Operating the monoblock from a diesel generator is not recommended - you can burn the monoblock.

All-in-One PC Reviews

Review and test of the Profoto D2 Air TTL monoblock Review and test of the Profoto B10 cordless flash Review and test of the Profoto B1 cordless flash Review of the Broncolor Siros L 800 cordless monoblock Review of the Bowens XMS 500 BW5300 monoblock

Pulse generators

A pulse generator is essentially a minicomputer (since it has a processor, memory, screen, etc.), a power supply, capacitors and complex discharge pulse control boards. Simply put, this is the “crown of creation” of pulsed light sources.

There are studio generators, i.e. powered from an outlet and rechargeable, powered from a battery.

In the photo - Profoto B2 battery generator

Pictured is the Profoto Profoto Pro-8a Air studio generator

Studio generators are usually more powerful because... there is no task to save battery. Some studio generators can be powered by a diesel generator and thus become mobile. The power of a studio generator can reach 6400 J, but the most commonly used studio generators are 1600 J, 2400 J and 3200 J (and battery generators are usually from 250 J to 1200 J).

Transition amplitude envelopes

The steady state amplitude remains constant over time and is therefore represented by a scalar. Otherwise, the amplitude is nonstationary and must be represented either as a continuous function or as a discrete vector. In audio, transient amplitude envelopes model signals better because many common sounds have transient volume attack, decay, sustain, and decay.

Other parameters can be assigned steady-state or transient amplitude envelopes: high-frequency/low-frequency/amplitude modulation, Gaussian noise, overtones, etc. [8]

Amplitude normalization

With waveforms containing many overtones, complex transient timbres can be achieved by assigning each overtone its own separate transient amplitude envelope. Unfortunately, this also affects the modulation of audio volume. It makes more sense to separate volume and harmonic quality so that the parameters can be adjusted independently of each other.

To do this, the amplitude envelopes of the harmonics are normalized frame by frame to obtain the amplitude. proportion

envelopes, where at each time interval all harmonic amplitudes will add up to 100% (or 1). This way you can cleanly control the main envelope that controls the volume. [8]

In sound recognition, maximum amplitude normalization can be used to equalize the fundamental harmonic characteristics of two similar sounds, allowing similar timbres to be recognized regardless of loudness. [9][10]

Formal representation

In this simple wave equation

X = A sin ⁡ ( ω [ t − K ] ) + b , {displaystyle x = Asin (omega [tK]) + b,}

• A {displaystyle A} is the amplitude (or peak amplitude),
• X {displaystyle x} is an oscillating variable,
• ω {displaystyle omega} is the angular frequency,
• t {displaystyle t} time,
• K {displaystyle K} and b {displaystyle b} are arbitrary constants representing time offsets and offsets, respectively.

Units

The units of amplitude depend on the type of wave, but are always in the same units as the oscillatory variable. The more general representation of the wave equation is more complex, but the role of amplitude remains similar to this simple case.

For waves on a thread, or in a medium such as water, the amplitude is offset.

The amplitude of sound waves and sound signals (which refers to loudness) conventionally refers to the amplitude of the air pressure in the wave, but sometimes the amplitude of the displacement (of air movement or the speaker's diaphragm) is described. The logarithm of the squared amplitude is usually specified in , so zero amplitude corresponds to - dB. Loudness is related to amplitude and intensity and is one of the most noticeable qualities of sound, although in general sounds it can be recognized regardless of amplitude. The square of the amplitude is proportional to the intensity of the wave.

For electromagnetic radiation, the amplitude of the photon corresponds to changes in the electric field of the wave. However, radio signals can be carried by electromagnetic radiation; the intensity of the radiation (amplitude modulation) or the frequency of the radiation (frequency modulation) oscillates, and then the individual oscillations are changed (modulated) to produce a signal.