Introduction: Introduction: Analyzing a Crystal Filter
The crystal Filter is critical circuit used in most areas of the telecommunications industry. It finds itself used in areas as different as smartphones and television transmitters and receivers. Wherever you want to pass a very narrow bandwidth of signal and reject everything else, you will need a crystal filter. A useful crystal filter can be easily made from a standard computer crystal and a couple of resistors and capacitors. Since the subject of filters is a complex science in itself and engineering texts have been written on that subject alone, with pages and pages of calculations, I will simply touch on the subject here.
Most electronic design today is done with the use of computer software that simulates mathematically the "ideal" device. The purpose of this instructable is to make a comparison between the mathematical model for a 10MHz crystal filter and actually build one using a breadboard and "off the shelf" components including a standard 10MHz computer crystal. The electronics design program that I used is Circuitmaker 2000, which can be downloaded free from a number of sources. Different programs might have different results due to the mathematical model used.
Step 1: The Simulated Response Curve Predicted by the Circuitmaker Program.
This frequency plotted against amplitude in dB shows the predicted response curve using the mathematical model for an ideal crystal. The frequency sweep starts at 8.750 MHz and stops at 11 MHz. I measured the bandwidth at the -15dB points and the bandwidth was 439.41 KHz! Surprisingly wide for this type of circuit. In the following pages, I will make a comparison with the actual "built" model and measurements made with a tracking generator.
Step 2: Measurements Made With a "built" or "real World" Model
The frequency sweep on the left shows the full frequency sweep from 8.750 to 11 MHz. The area around 10MHz shows a much sharper response than the predicted one plus two other lesser responses higher up in frequency. This is due to the imperfections in the real world circuit. For a better look at the main response, a smaller frequency sweep was done as can be seen in the second picture. The frequency range was the much smaller 9.950 to 10.050 MHz or a 100 KHz sweep. The three additional frames show the frequencies at different points in the response. The -15 dB bandwidth calculated was the much narrower 5625 Hz or almost 100th of the bandwidth of that predicted by Circuitmaker!
Step 3: Conclusion
The comparison of the predicted and actual behavior of the circuit was very interesting. In this circuit, the built circuit actually performed better than the mathematical model provided by Circuitmaker. The other way around is usually the case. While I have found Circuitmaker 2000 to be a useful program in many ways and to be able to predict accurately the behavior of transistors and IC's, it does have it's limitations. This is not to say that it's models for crystal filters are useless. It just shows that design programs are not perfect and the more knowledge one has of the behavior of components, will allow them to spot results which are not realistic, such as the excessively wide bandwidth of the simulated model. The design program is just one of the tools at one's disposal and an actual working circuit should be built and tested.