Experimental Methods Course in Physics (PCF, UNAM)

Curso de Métodos experimentales • En la Física PCF UNAM • Cuernavaca, Agosto 2008 • Tercera semana • Dr. Antonio M. Juárez Reyes, ICF UNAM • Física Atómica, Molecular y óptica.

Cuernavaca, Agosto 2008 • TEMARIO PARTE 1 • I.- Instrumentos y conceptos básicos (Toño, 5 semanas) • I.1.- Conceptos básicos de instrumentación • Conceptos generales de seguridad en el laboratorio (eléctrica, de gases comprimidos, láseres y químicos. • -El proceso de medida y asignación de incertidumbres. • I.2.- Instrumentos básicos • 2.1 sistemas de vacío. • -Conductancia, velocidad de bombeo, viscosidad, • -bombas: Rotatorias, de diafragma, difusoras, turbo, de sublimación, ionicas. razón de compresión en bombas, • - transductores de presión, pirani, Bayer Alpert, Baratrón, análisis de gases residuales. • 2.2 Instrumentos básicos de electrónica: • -osciloscopios, generadores de señales, electrómetros, • 2.3 Instrumentos avanzados • -Amplificador Lock In • -Integrador Boxcar • -Monocromadores

Cuernavaca, Agosto 2008 I.3.- Conceptos generales de láseres y fuentes de luz: - Cavidades, ganancia y finesa - Etalones de Fabri Perot,elementos ópticos - Láseres pulsados de nitróngeno, Nd:YAG, pulsadores del tipo Q-Switch, láseres de diodo de cavidad extendida, -Otras fuentes de luz: sincrotrónesy Free electron Lasers, I.4.-Conceptos generales de diseño: herramientas de dibujo, herramientas de simulación de circuitos, criterios generales de diseño de piezas asociadas a instrumentación científica. El taller de electrónica y el taller de mecánica del ICF 1.5 Elección del proyectos semestrales de instrumentación

Osciloscopios

Cuernavaca, Agosto 2008

Cuernavaca, Agosto 2008 The higher the bandwidth, the more accurate the reproduction of your signal, as illustrated with a signal captured at 250 MHz, 1 GHz and 4 GHz bandwidth levels.

Cuernavaca, Agosto 2008 Record length, expressed as the number of points that comprise a complete waveform record, determines the amount of data that can be captured with each channel. Since an oscilloscope can store only a limited number of samples, the waveform duration (time) will be inversely proportional to the oscilloscope's sample rate. Capturing the high frequency detail of this modulated 85 MHz carrier requires high resolution sampling (100 ps). Seeing the signal's complete modulation envelope requires a long time duration (1 ms). Using long record length (10 MB), the oscilloscope can display both.

Sample Rate Equals Resolution • Cuernavaca, Agosto 2008 Peak detect mode enables the TDS7000 Series oscilloscope to capture transient anomalies as narrow as 100 ps.

Sample Rate Equals Resolution • Cuernavaca, Agosto 2008 How do you calculate your sample rate requirements? The method differs based on the type of waveform you are measuring, and the method of signal reconstruction used by the oscilloscope. Most Tektronix oscilloscopes let you select either sin(x)/x interpolation for measuring sinusoidal signals, or linear interpolation for square waves, pulses and other signal types. Sample rate varies with time base settings - the slower the time base setting, the slower the sample rate. Some digital oscilloscopes provide peak detect mode to capture fast transients at slow sweep speeds.

Cuernavaca, Agosto 2008 In electronics, when describing a voltage or currentstep function, rise time (also risetime) refers to the time required for a signal to change from a specified low value to a specified high value. Typically, these values are 10% and 90% of the step height. The output signal of a system is characterized also by fall time: both parameters depend on rise and fall times of input signal and on the characteristics of the system. To calculate the oscilloscope rise time required for your signal type, use the following equation:

Sample Rate Equals Resolution To calculate the oscilloscope rise time required for your signal type, use the following equation:

Sample Rate Equals Resolution • Cuernavaca, Agosto 2008 An oscilloscope's trigger function is crucial for clear signal characterization because it is what synchronizes the horizontal sweep at the correct point of the signal. Trigger controls allow you to stabilize repetitive waveforms and capture single-shot waveforms. Edge triggering is the basic and most common type. Advanced trigger controls enable you to isolate specific events of interest to optimize the oscilloscope's sample rate and record length.

Cuernavaca, Agosto 2008 Advanced triggering capabilities on Tektronix oscilloscopes give you highly selective control. You can trigger on pulses defined by amplitude (such as runt pulses), qualified by time (pulse width, glitch, slew rate, setup-and-hold and time-out), and delineated by logic state or pattern (logic triggering). Optional trigger controls are designed specifically to examine communications signals.

Cuernavaca, Agosto 2008 Runt Pulse Triggering. Runt triggering allows you to capture and examine pulses that cross one logic threshold, but not both. Pulse Width Triggering. Using pulse width triggering, you can monitor a signal indefinitely and trigger on the first occurence of a pulse whose duration (pulse width) is outside the allowable limits.

Cuernavaca, Agosto 2008 generadores de señales, Almost self explanatory … (revise this with the class “in vivo”

Cuernavaca, Agosto 2008 generadores de señales,

Cuernavaca, Agosto 2008 electrómetros,

Cuernavaca, Agosto 2008 electrómetros, An electrometer is a highly sensitive electronic voltmeter whose input impedance is so high that the current flowing into it can be considered, for practical purposes, to be zero. The most modern electrometers consist of a solid stateamplifier circuit using FETs, connections for external measurement devices, and also possibly a display, data-logging connections, and/or a high-voltage supply. The amplifier magnifies small currents so that they are more easily measured.

Cuernavaca, Agosto 2008 In numbers: • Measures resistances up to 1016Ω • 1fA to 20mA current measurement range • 200TΩ input impedance • <3fA bias current • 0.75fA p-p noise

Cuernavaca, Agosto 2008 If you wanna make your own: This simple electrometer is very sensitive, regardless Of its simplicity. A plastic pen rubbed against your hair slams the needle at more than 2 feet away (60 cm). http://www.vk2zay.net/article.php/9

Cuernavaca, Agosto 2008 Digital volt-meters Simple, eh! Well, not so much if you consider that digital volt-meters are one of the many examples of a analog to digital Converter ( a converter that translates “reality” into Numbers).

Cuernavaca, Agosto 2008 For those of you that are not familiar with DAC or ADC, here Is a simple definition: An analog-to-digital converter (abbreviated ADC, A/D or A to D) is an electronic circuit, which converts continuous signals to discretedigital numbers. The reverse operation is performed by a digital-to-analog converter (DAC). . They sound weird, but you use them all the time ( in your Cell phone, watching cable T.V. playing MP3 files, etc..

Cuernavaca, Agosto 2008 The resolution of the converter indicates the number of discrete values it can produce over the range of analog values. The values are usually stored electronically in binary form, so the resolution is usually expressed in bits. In consequence, the number of discrete values available, or "levels", is usually a power of two. For example, an ADC with a resolution of 8 bits can encode an analog input to one in 256 different levels, since 28 = 256 (what about a 16 bit? ADC ?)

Cuernavaca, Agosto 2008 Coming back to voltmeters, since they use ADC, The resolution of the voltmeters is related to the number of bits of the ADC used in it. This is reflected inb the number of “digits” that the voltmeter can represent. Whenever you need a voltmeter, you specify it by the number of digits. More digits means a more resolved ADC and more money $$$

Cuernavaca, Agosto 2008 • How do you determine the number of digits needed for your application • Determine the range • Determine the resolution you need It looks reasonable to call a 0-30v meter with 30,000 steps a 4.5 digit meter, and that's the way they are sold.

Cuernavaca, Agosto 2008 2.3 Instrumentos avanzados -Amplificador Lock In -Integrador Boxcar -Monocromadores

Amplificador Lock In A lock-in amplifier (also known as a phase sensitive detector) is a type of amplifier that can extract a signal with a known carrier wave from extremely noisy environment The lock-in amplifier was invented by Princeton University physicist Robert H. Dicke who founded the company Princeton Applied Research (PAR) to market the product.

Amplificador Lock In Operation of a lock-in amplifier relies on the orthogonality of sinusoidal functions. Specifically, when a sinusoidal function of frequency ν is multiplied by another sinusoidal function of frequency μ not equal to ν and integrated over a time much longer than the period of the two functions, the result is zero. In the case when μ is equal to ν, and the two functions are in phase, the average value is equal to half of the product of the amplitudes

Amplificador Lock In Lock-in amplifiers are used to measure the amplitude and phase of signals buried in noise. They achieve this by acting as a narrow bandpass filter which removes much of the unwanted noise while allowing through the signal which is to be measured. (think fourier transform, and consider the lock in amplifier As a filter that only passes one frequency component of The whole signal . That frequency component corresponds To the signal you want to hear.

Amplificador Lock In The frequency of the signal to be measured and hence the passband region of the filter is set by a reference signal, which has to be supplied to the lock-in amplifier along with the unknown signal. The reference signal must be at the same frequency as the modulation of the signal to be measured.

Amplificador Lock In A basic lock-in amplifier can be split into 4 stages: an input gain stage, the reference circuit, a demodulator and a low pass filter. Input Gain Stage: The variable gain input stage pre-processes the signal by amplifying it to a level suitable for the demodulator. Nothing complicated here, but high performance amplifiers are required. Reference Circuit: The reference circuit allows the reference signal to be phase shifted.

Amplificador Lock In A basic lock-in amplifier can be split into 4 stages: an input gain stage, the reference circuit, a demodulator and a low pass filter. Reference Circuit: The reference circuit allows the reference signal to be phase shifted.

Amplificador Lock In A basic lock-in amplifier can be split into 4 stages: an input gain stage, the reference circuit, a demodulator and a low pass filter. Reference Circuit: The reference circuit allows the reference signal to be phase shifted. Demodulator: The demodulator is a multiplier. It takes the input signal and the reference and multiplies them together. When you multiply two waveforms together you get the sum and difference frequencies as the result. As the input signal to be measured and the reference signal are of the same frequency, the difference frequency is zero and you get a DC output which is proportional to the amplitude of the input signal and the cosine of the phase difference between the signals.

Amplificador Lock In A basic lock-in amplifier can be split into 4 stages: an input gain stage, the reference circuit, a demodulator and a low pass filter. Demodulator: The demodulator is a multiplier. It takes the input signal and the reference and multiplies them together. When you multiply two waveforms together you get the sum and difference frequencies as the result. As the input signal to be measured and the reference signal are of the same frequency, the difference frequency is zero and you get a DC output which is proportional to the amplitude of the input signal and the cosine of the phase difference between the signals. By adjusting the phase of the reference signal using the reference circuit, the phase difference between the input signal and the reference can be brought to zero and hence the DC output level from the multiplier is proportional to the input signal.

Amplificador Lock In A basic lock-in amplifier can be split into 4 stages: an input gain stage, the reference circuit, a demodulator and a low pass filter. Low Pass Filter: As the various noise components on the input signal are at different frequencies to the reference signal, the sum and difference frequencies will be non zero and will not contribute to the DC level of the output signal. This DC level (which is proportional to the input signal) can now be recovered by passing the output from the demodulator through a low pass filter.

Amplificador Lock In Application to signal measurements in a noisy environment The essential idea in signal recovery is that noise tends to be spread over a wider spectrum, often much wider than the signal. In the simplest case of white noise, even if the root-mean-square of noise is 106 times as large as the signal to be recovered, if the bandwidth of the measurement instrument can be reduced by a factor much greater than 106 around the signal frequency, then the equipment can be relatively insensitive to the noise. In a typical 100-MHz bandwidth (e.g. an oscilloscope), a bandpass filter with width much narrower than 100 Hz would accomplish this.

Amplificador Lock In In the simplest case of white noise, even if the root-mean-square of noise is 106 times as large as the signal to be recovered, if the bandwidth of the measurement instrument can be reduced by a factor much greater than 106 around the signal frequency More info, check the document: Note on lock in.pdf Included in this folder

Cuernavaca, Agosto 2008 Gated integrators and boxcar averagers are designed to recover fast, repetitive, analog signals. In a typical application, a time "gate" of predetermined width is precisely positioned relative to an internal or external trigger to coincide with your signal. A gated integrator amplifies and integrates the signal that is present during the time the gate is open, ignoring noise and interference that may be present at other times.

Cuernavaca, Agosto 2008 To see quantitatively whay averaging improves The signal to noise ratio, see the document Boxcar intecgrator.PDF in this folder.

Cuernavaca, Agosto 2008 A monochromator is an optical device that transmits a mechanically selectable narrow band of wavelengths of light or other radiation chosen from a wider range of wavelengths available at the input. The name is from the Greek roots mono-, single, and chroma, colour, and the Latin suffix -ator, denoting an agent.

Cuernavaca, Agosto 2008 • The main parameters of a monocromator are: • The slit aperture width (entrance and exit) d1 and d2 • The number of lines of the diffraction grating • The spectral bandwidth

Experimental Methods Course in Physics (PCF, UNAM)

Experimental Methods Course in Physics (PCF, UNAM)

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Campus Cuernavaca

Curso de Métodos experimentales En la Física PCF UNAM Cuernavaca, Agosto 2008 cuarta semana Dr. Antonio M.