V. Bande, Applied Electronics Department (English version)-> Information for students Lecture 12 1 Passive Electronic Components and Circuits (PECC) Quartz resonators. Non-linear passive electronic components

Quartz resonators Structure Short history Piezoelectric effect Equivalent circuit Quartz resonators parameters Quartz oscillators Non-linear passive electronic components Non-linear resistors – thermistors Nonlinearity phenomena Quartz resonators. Non-linear passive electronic components

Quartz resonators  Structure Casing Socket Silver electrodes (on both sides) Silver contacts Quartz crystal Dry inert gas

Quartz resonators Structure Short history Piezoelectric effect Equivalent circuit Quartz resonators parameters Quartz oscillators Non-linear passive electronic components Non-linear resistors – thermistors Nonlinearity phenomena Quartz resonators. Non-linear passive electronic components

Quartz resonators  Short history Coulomb is the first that scratches the surface in respect with the piezoelectric effect. Currie brothers are the first scientists that reveal the phenomenon - in During first World War, quartzes are being for submarines detection – SONAR sensors – Walter Cady – discovers how to control frequency with the help of a quartz – the first radio station (NY) is broadcasting on a quartz controlled frequency. During World War II, the US Army modifies all its communication equipment in order to generate quartz controlled frequencies.

Quartz resonators Structure Short history Piezoelectric effect Equivalent circuit Quartz resonators parameters Quartz oscillators Non-linear passive electronic components Non-linear resistors – thermistors Nonlinearity phenomena Quartz resonators. Non-linear passive electronic components

Quartz resonators  Piezoelectric effect Under the effect of a variable electrical field, the quartz crystal is mechanically vibrating on the same frequency as the electrical field. If the oscillating frequency has a certain value, the mechanical vibration maintain as well the electrical field. The frequency at which this phenomenon occurs is called piezoelectric resonance and is strongly dependent by the quartz crystal’s dimensions. The piezoelectric effect can be used to generate very stable electrical frequencies (quartz controlled oscillators), force measurement (piezoelectric sensors) by acting on the quartz dimensions and modifying its resonance frequency.

Quartz resonators Structure Short history Piezoelectric effect Equivalent circuit Quartz resonators parameters Quartz oscillators Non-linear passive electronic components Non-linear resistors – thermistors Nonlinearity phenomena Quartz resonators. Non-linear passive electronic components

Equivalent circuit LmLm CmCm RsRs C0C0  Mechanical – Electrical Analogy Mechanical energy Electrical energy Pressure and displacement Voltage and current (L m,C m ) R s – ESR – E quivalent S eries R esistance – models the quartz energy losses C 0 – Shunt Capacitance – the electrodes parasitic capacitance C m, L m – the LC circuit that models the movement (displacement)

Equivalent circuit  The equivalent electrical impedance The equivalent electrical circuit is basically a series RLC circuit connected in parallel with a C 0 capacitance:

Equivalent circuit  The variation of the impedance module In the adjacent picture, the reactance (imaginary part) variation is presented. There are two frequencies at which the reactance becomes zero: F s and F a. Thus, in this situation, the quartz impedance has only real part.

Equivalent circuit  The electrical meaning of the resonance frequencies At this two resonance frequencies, the equivalent impedance has a purely resistive behavior  the phase-shift between voltage and current is zero. The series resonance frequency – F s – is the series LC circuit resonance frequency. At this value, the impedance has minimum value. The parallel resonance frequency – F a – is the frequency at which the real part can be neglected. At this value, the impedance has maximum value.

Equivalent circuit  F s and F a determination If we impose the condition that the imaginary part to be zero (purely resistive impedance: In the parenthesis, the term that contains the R s can be neglected – very low value, almost zero:

Equivalent circuit  F s and F a determination The solutions are:

Equivalent circuit  The impedance value at both resonance frequencies:

Equivalent circuit  Conclusions: The series resonance frequency is dependent by the L1 and C1 parameters, thus is dependent by the quartz geometrical parameters. This frequency can be adjusted only through mechanical actions ! The parallel resonance frequency can be adjusted in a small domain by connecting a C p capacitance in parallel with the quartz crystal. This capacitance will be connected in parallel with the C 0 – electrodes capacitance, resulting an equivalent capacitance: C ech = C o + C p. The boundaries between which the adjustment can be made are very close, because growing the C ech, you can reach the series resonance frequency value.

Quartz resonators Structure Short history Piezoelectric effect Equivalent circuit Quartz resonators parameters Quartz oscillators Non-linear passive electronic components Non-linear resistors – thermistors Nonlinearity phenomena Quartz resonators. Non-linear passive electronic components

Quartz resonators parameters The nominal frequency – is the resonator’s assigned frequency during fabrication and its being printed on the resonator’s casing. The load resonance frequency – is the oscillating frequency for the case in which a certain specified capacitance is connected in parallel. The adjustment tolerance – is the maximum possible deviation of the oscillating frequency in respect with the nominal frequency. The temperature domain tolerance – is the maximum possible deviation of the oscillating frequency when the temperature varies between minimum and maximum admitted values. The quality factor – values between 10 4 and 10 6 : The resonance equivalent series resistance – is the resistance measured at the series resonance frequency (between 25 and 100 ohms for the most common crystals).

Quartz resonators Structure Short history Piezoelectric effect Equivalent circuit Quartz resonators parameters Quartz oscillators Non-linear passive electronic components Non-linear resistors – thermistors Nonlinearity phenomena Quartz resonators. Non-linear passive electronic components

Quartz oscillators Inside electronic circuits that contain quartzes, the load connected at its terminals can be viewed as a R l impedance. Depending on the relationship between R l and R s, there can be three different regimes:  Damped regime – oscillation attenuation  Amplified regime – oscillation amplification  Auto-oscillating regime – oscillation sustaining

Quartz oscillators  Damped regime

Quartz oscillators  Amplified regime

Quartz oscillators  Auto-oscillating regime

Quartz resonators Structure Short history Piezoelectric effect Equivalent circuit Quartz resonators parameters Quartz oscillators Non-linear passive electronic components Non-linear resistors – thermistors Nonlinearity phenomena Quartz resonators. Non-linear passive electronic components

Thermistors The thermistors are variable resistors that have a very fast resistance variation when the temperature is changing. The temperature variation coefficient can be negative – NTC (negative temperature coefficient – components fabricated since 1930) or positive – PTC (positive temperature coefficient – components fabricated since 1950). Both thermistor types are non-linear, the resistance variation law with the temperature being:

Thermistors  NTC’s and PTC’s thermistors The temperature variation coefficient is defined as follows: If the material constant “B” is positive, then we will have an NTC thermistor, if “B” is positive we will have a PTC thermistor.

Thermistors  Non-linear circuits analysis

Thermistors  Using thermistors as transducers The thermistors dissipated power must be lower enough in order that the supplementary heating produced inside the thermistor body to be negligible. This condition can be assured by connecting high value resistances in series with the thermistor which will lead to a smaller current that passes through the thermistor.

Thermistors  Example: A voltage divider with a NTC thermistor

Quartz resonators Structure Short history Piezoelectric effect Equivalent circuit Quartz resonators parameters Quartz oscillators Non-linear passive electronic components Non-linear resistors – thermistors Nonlinearity phenomena Quartz resonators. Non-linear passive electronic components

Nonlinearity phenomena Almost al physical quantities variation laws are non-linear! As a consequence, the electronic components characteristics which are based on those laws are also non-linear. The non-linear systems analysis using linear methods, specific to linear systems introduces errors. Those methods can be applied only on restrictive small intervals of quantities variations. In this way, the errors are being kept under the maximum allowed errors.

Nonlinearity phenomena  Linearization – Piece by piece linearization Tangent method Chord ( ro. Coarda) method Secant method

Nonlinearity phenomena  Linearization – Piece by piece linearization You can either impose the number of the intervals on which the linearization is being made and different errors will occur from an interval to another. Or you can impose the maximum acceptable error during the linearization procedure, thus resulting the number on the interval on which the linearization can be made and also the interval maximum length. For both condition, at the end of each interval, respectively at the beginning of the following interval, the continuity condition must be assured.

Nonlinearity phenomena  Linearization – nonlinearities elimination procedure

Nonlinearity phenomena  Linearization – nonlinearities elimination procedure

Nonlinearity phenomena  Linearization – an example: Please determine the voltage- current characteristic for the situations in which the components with the two characteristics revealed in the picture are connected in series, respectively in parallel.