MadSci Network: Physics
Query:

Re: How do the crystals in a radio determine the recieved frequency?

Date: Tue Mar 10 11:21:49 1998
Posted By: Adrian Popa, Directors Office, Hughes Research Laboratories
Area of science: Physics
ID: 889062409.Ph
Message:


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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