| MadSci Network: Physics |
Greetings: References: 1. Many drawings and diagrams are on the Oscillatek Inc - Introduction to Quartz Frequency Standards web pages at: http://www1.otek.com/vig/vigqrtz.html 2. Virgil E. Bottom, “A HISTORY OF THE QUARTZ CRYSTAL INDUSTRY IN THE USA”, Proceedings of the 35th Annual Frequency Control Symposium, pp. 3-12, 1981 I'll start to answer your questions by first discussing tuned circuits and oscillators. Next I'll discuss the piezoelectric effect and quartz crystal oscillators. Finally I'll discus frequency synthesizers and future developments. TUNED CIRCUITS (coils an capacitors) and Oscillators When an electronic amplifier circuit has a sample of its output signal connected back to it’s input circuit (e.g. feedback) in the proper phase as determined by the feedback circuit, the amplifier circuit generates an AC signal and we call the circuit an oscillator. In public address sound systems we hear this feedback effect as an uncontrolled squealing sound caused by the loudspeaker output signal from an amplifier feeding back into the microphone input circuit of the amplifier. The frequency at which the amplifier circuit oscillates is not controlled unless special circuits are used in conjunction with the feedback circuit. At audio, radio, microwave and laser frequencies these oscillator frequency control circuits have different forms. At radio frequencies between about 300 kHz (300 thousand oscillations per second) and 300 MHz (300 million oscillations per second) frequency control circuits are usually made from inductors (wire coils) and capacitors (metal plates separated by a nonconducting dielectric material). If the inductor and the capacitor are connected in series the control circuit is called a SERIES RESONANT CIRCUIT and the circuit has a minimum resistance, minimum voltage and maximum current at the resonant frequency. If the control circuit has an inductor and capacitor connected in parallel the control circuit is called a PARALLEL RESONANT CIRCUIT and the circuit has a maximum resistance, maximum voltage and minimum current at the resonant frequency. When placed in the proper location in an oscillator circuit the oscillator frequency is determined by a resonant circuit. In most receivers the local oscillator can be “tuned” in frequency by changing the value of the capacitor or the inductor or both with control knobs and switches. A measure of how accurately a resonant circuit can set the frequency of an oscillator is called the circuit’s QUALITY FACTOR or "Q". The circuit Q is a measure of the frequency width of the control circuit resonance between the one half power frequencies divided by the center frequency of the resonance (the sharpness of the resonance). Q = delta frequency(-3dB power points)/center frequency Theoretically a resonant circuit should be infinitely sharp ( a single frequency); however, in the real world resistance in the coils of the inductor wire and dielectric losses in the capacitor broaden the resonance frequency. At radio frequencies resonant circuits have Q values ranging from about 30 to 100. At a Q of 100 ( Q= 1000 kHz/10 kHz = 100) the circuit is accurate to 1% of the center frequency. At 1 MHz in middle of the AM radio band a Q of 100 means that the frequency can range more than 10 kHz or about one station width. This is why AM radios often drift with time because of temperature changing the value in the resonant circuit’s components including the oscillator transistor or tube. While frequency drift is only a nuisance in radio receivers used for entertainment purposes, drift is a major problem in public safety and navigation receivers and to have transmitters drifting all over the frequency spectrum would have serious safety consequences. Thus control circuits with better quality were needed as the number of radio transmitters rapidly grew during the 1920s. The solution to the frequency control problem came from the discovery of PIEZOELECTRIC effect. QUARTZ CRYSTAL OSCILLATORS and the PIEZOELECTRIC EFFECT The first experimental demonstration of a connection between macroscopic piezoelectric phenomena and crystallographic structure was published in 1880 by Pierre and Jacques Curie. Their experiment consisted of a conclusive measurement of surface charges appearing on specially prepared crystals (tourmaline, quartz, topaz, cane sugar and Rochelle salt among them) which were subjected to mechanical stress. The Curie brothers did not, however, predict that crystals exhibiting the direct piezoelectric effect (electricity from applied stress) would also exhibit the converse piezoelectric effect (stress in response to applied electric field). This property was mathematically deduced from fundamental thermodynamic principles by Lippmann in 1881. In summary a material that exhibits the piezoelectric effect generates a voltage across the material when under mechanical stress and if an external voltage is applied to the material the molecules elongate in some directions and compress in other directions producing internal mechanical stress in the material. This is shown graphically in the first reference. With the proper design piezoelectric crystals mechanically vibrate somewhat like tuning forks at KHz and MHz frequencies The vibration frequency is determined by the crystal's dimensions and shape. After the Curies the first application of the piezoelectric effect was made by Prof. P. Langevin in France in 1917 during World War I and he used X-cut plates of quartz to generate and detect sound waves in water. His object was to provide a means for detecting submarines and his work led to the development of SONAR and to the science of ultrasonics. Langevin's work stimulated others to investigate the phenomenon of resonance in piezoelectric crystals. Among those who became interested in the piezoelectric effect were A.M. Nicholson of the Bell Telephone Laboratories and Prof. W. G. Cady at Wesleyan University. Both men, working with Rochelle salt, observed the reaction of the resonant piezoelectric material on the driving circuit of an oscillator and both applied for patents based upon their observations. Subsequent litigation resulted in a legal decision in favor of Nicholson who is therefore considered to be the inventor. In 1919 Cady used a quartz crystal to control the frequency of an oscillator and developed the first frequency standard. Prof. K. S. Van Dyke, a student and colleague of Cady, showed in 1925 that the two electrode piezoelectric resonator is the electrical equivalent of a SERIES RESONANT CIRCUIT shunted by a capacitor. In 1923 the Bell Telephone Laboratories established a quartz laboratory and the General Electric Company did likewise the following year. In 1926 the A. T. & T. radio station WEAF in New York City became the first radio station in the United States to control its frequency with a quartz crystal unit. Within a few years all radio stations went to crystal control. MegaHertz quartz resonators were developed as frequency stabilizers for vacuum-tube oscillators, resulting in Q values of several million and controlling AM radio stations to less the one Hertz of drift! Some cuts of the quartz crystal have a negative temperature coefficient. That means that as the temperature of the crystal increases the vibration frequency decreases. Other cuts of quartz crystals have a positive temperature coefficient and the vibration frequency increases with temperature. Over the past 50 years many refinements in the cutting and polishing of quartz crystals have developed cuts at angles where the positive and negative temperature coefficients cancel each other near room temperature leading to frequency control to one part in a billion in frequency standards. (See references). Above 100 MHz the quartz crystals become too thin the fabricate and overtone crystals are used. These crystals vibrate in modes that generate harmonic content at many times the fundamental vibration frequency. Electronic multiplier chains starting with 100 MHz crystal oscillators are now commomly used to control radars and microwave transmitters and receivers operating up to 100 000 MHz (100 Giga Hertz or GHz). At the National Institute for Standards and Technology (NIST) crystal oscillators are controlled by atomic clocks providing stabilitys of one part in one trillion and NIST has used frequency multiplier chains clear up to light wavelengths to stabilize laser transmitters with 100 MHz crystal oscillators! One major problem with frequency multiplier chains is that each multiplication by a factor of two also doubles the frequency instability and oscillator noise. It would be better if dividers could be used. In this case the instability of the crystal oscillator is halfed in a division by two. and is 1/10 in a division by 10. This is the trend of the future! FREQUENCY SYNTHESIZERS and the FUTURE While quartz crystal controlled transmitters and receivers provide great frequency precision and stability a different set of fairly expensive quartz crystals are required for each frequency to be transmitted or received. Up to the 1980s this problem limited precise frequency control to expensive aircraft and public safety radios, radars and navigation aids. The development of inexpensive transistor integrated circuitry in the radio and microwave frequency range has lead to the development of crystal controlled frequency synthesizers that can be precisely set to a large number of frequencies while using only one crystal controlled standard frequency oscillator usually operating at 100 MHz. Today 100 MHz quartz crystal oscillators with great stability are mass produced for only a few dollars each. Using digital divider chains the 100 MHz signal can be divided by 10, by 100 by 1000, by 10000 etc. providing precise, stable frequencies at 10 MHz, 1 MHz, 100 kHz, 10 kHz etc each with lower frequency having better precision and stability than the 100 MHz reference oscillator. Then by adding and subtracting these divided signals sum and difference frequencies can be obtained at thousands of frequencies. For example subtract the 10 MHz frequency and the 1 MHz frequency and you get 9 MHz. Subtract 9 MHz and 100 kHz and you get 8.9 MHz. Add 8.9 MHz and 10 kHz and you get 8.91 MHz etc. Using frequency synthesizers of this type my $250 Sony transistor radio can be precisely tuned in 10 kHz steps from 100 kHz to 30 MHz! Other radios use frequency multiplication and division to operate at cellular telephone frequencies near 1 GHz or to control satellite TV systems near 10 GHz. Your final question was: Do crystal controlled circuits still use coils? Yes some coils are still used in today’s radio frequency circuits ; however, digital techniques are replacing more and more of the radio set. In my laboratory all digital receivers for automotive applications are in development. In these circuits the antenna signal is digitally divided down to analog to digital converter (ADC) frequencies without using any amplifiers, mixers or detectors. Digital circuits do not need humans to tune them as rf circuits still do. Therefore, digital radios will have better performance at lower cost by eliminating expensive human touch labor that is still used on today's radio assembly lines. Best regards, your Mad Scientist Adrian Popa
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