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Chapter 1: Introductory Topics Cont’

Chapter 1: Introductory Topics Cont’. Communication Systems Decibels Electrical Noise Sources Measurements Information and Bandwidth Fourier Analysis LC Circuit Review Oscillator Review Troubleshooting Electronic Systems. Noise!.

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Chapter 1: Introductory Topics Cont’

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  1. Chapter 1: Introductory Topics Cont’

  2. Communication Systems • Decibels • Electrical Noise • Sources • Measurements • Information and Bandwidth • Fourier Analysis • LC Circuit Review • Oscillator Review • Troubleshooting Electronic Systems

  3. Noise! There are two basic limitations on the performance of a communication system. We covered the first last class. What was it?

  4. Information and Bandwidth

  5. 1.4 Information and Bandwidth The second limitation is the bandwidth utilized by the system. Bandwidth - the range of frequencies within a given waveband used for a particular transmission “The greater the bandwidth, the greater the information that can be transferred from source to destination”

  6. 1.4 Information and Bandwidth The concept of utilizing bandwidth to peak efficiency is an entire area of theoretical research of its own known as Information Theory. Information Theory – the study of information to provide the most efficient use of a band of frequencies (a channel)

  7. 1.4 Information and Bandwidth The band of usable frequencies is limited, and we are living in a world that is increasingly dependant on electronic communication. Moreover, we must all share the same frequencies. Thus, regulatory agencies (such as the FCC) tightly control the usable frequency spectrum. Why is efficient channel utilization so important?

  8. www.ntia.doc.gov/files/ntia/publications/2003-allochrt.pdf

  9. A Formal relationship between bandwidth and information was provided by Hartley at Bell Laboratories in 1928. Hartley’s Law– information that can be transmitted is proportional to the product of the bandwidth times the time of transmission.

  10. Let’s take an example from the digital work. If we have a channel that allows for 128 kBytes / second, and we transmit for 10 seconds, how much information can we transmit?

  11. On an AM station, the 30 kHz bandwidth doesn’t provide enough bandwidth to allow for all of the information to be reproduced (we’ll learn more about why and how much can reproduced later). The 200 kHz of the FM signal, however, is enough to reproduce the full amount of information. Humans can hear from just above 0 Hz to about 15 kHz. The allocated bandwidth of standard AM stations is about 30 kHz. On the other hand, FM stations are allocated a larger bandwidth around 200 kHz. Which will sound better and why?

  12. Fourier Analysis

  13. 1.5 Fourier Analysis So far in your EET studies you probably have been concerned primarily with the time domain. The time domainis concerned with how a signal changes throughout time:

  14. 1.5 Fourier Analysis The time domain isn’t the only way to represent a signal. In many areas (including communications and DSP), the frequency domain is actually more useful! The frequency domainis concerned with how much of the signal lies within each given frequency band over a range of frequencies :

  15. 1.5 Fourier Analysis Fourier Analysis and the Fourier Transform are tools that allow us to switch between the Time Domain and the Frequency Domain.

  16. 1.5 Fourier Analysis Fourier Analysis is based on the principle that any complex repetitive waveform can be resolved into an infinite series of sine or cosine waves of the form: where: t is called the fundamental frequency is the third harmonic is the fifth harmonic, etc

  17. 1.5 Fourier Analysis Let’s take a square wave as an example:

  18. 1.5 Fourier Analysis We start with the fundamental frequency (first harmonic)

  19. 1.5 Fourier Analysis If we add to the first harmonic the third harmonic:

  20. 1.5 Fourier Analysis First, Third, and Fifth Harmonic:

  21. 1.5 Fourier Analysis The more harmonics, the better representation (13 Harmonics)

  22. 1.5 Fourier Analysis The more bandwidth, the closer we get to ideal (51 Harmonics)

  23. 1.5 Fourier Analysis

  24. 1.5 Fourier Analysis As will become apparent in future lectures, knowing the frequency components of a signal is vital in communications. To assist with this, most modern oscilloscopes and spectrum analyzers make use of the Fast Fourier Transform (FFT).

  25. 1.5 Fourier Analysis

  26. 1.5 Fourier Analysis

  27. 1.5 Fourier Analysis

  28. 1.5 Fourier Analysis What would happen if we tried to transmit the square wave through a bandwidth-limited channel such as a voice telephone channel which is limited to 3 kHz?

  29. LC Circuits

  30. 1.6 LC Circuits Practical Inductors • Also known as chokes or coils • Have an inductance rating in henries • Have a maximum current rating Practical Capacitors • Have an capacitance rating in farads • Have a maximum voltage rating

  31. 1.6 LC Circuits When used at Radio Frequencies (RF), a new metric must also be considered – Quality (Q) Quality (Q) - the ratio of the energy stored to that which is lost in the component. “The higher the quality factor, the better the component is at doing it’s job”

  32. 1.6 LC Circuits Quality (Q) for Practical Inductors • Inductors store energy in the surrounding magnetic field and lose (dissipate) energy in their winding resistance Quality (Q) for Practical Capacitors • Capacitors store energy in the electric field between their plates and primarily lose energy due to leakage between the plates

  33. 1.6 LC Circuits Resonance – a circuit condition whereby the inductive reactance and the capacitive reactance have been balanced (XL=XC) Note: Remember from AC Circuits that capacitive/inductive reactance describe the opposition (in Ohms) a capacitor/inductor provide at different frequencies:

  34. 1.6 LC Circuits If we take a simple RLC circuits from AC The total impedance (Z) is provided by

  35. 1.6 LC Circuits Thus, at the resonant frequency (fr) where XL=XC , the circuit is in a condition of resonance and the impedance is equal to only the value of the resistor:

  36. 1.6 LC Circuits The impedance of a series RLC circuit is at a minimum at the resonant frequency (fr) and equal to the value of R. If we plot eout / ein in this configuration we can see that voltages around fr will be brought to 0 and thus “filtered” out. This is a band-reject filter.

  37. 1.6 LC Circuits A B Determine the resonant frequency for the given circuit. Also, calculate the total impedance when f = 12 kHz.

  38. 1.6 LC Circuits Given what we know about resonant frequency, if we change the circuit configuration like so, what would the output response look like?

  39. 1.6 LC Circuits This circuit is known as a band-pass filter, because it only allows a certain band of frequencies through: flc = low frequency cut-off point (where eout < .707ein) fhc = high frequency cut-off point (where eout < .707ein) What might this circuit be used for?

  40. 1.6 LC Circuits The bandwidth (BW) that this filter provides can be given as: BW = fhc – flc The Quality (Q) factor that this filter provides can be given as: This provides an indication of how selective the filter is.

  41. 1.6 LC Circuits Determine: (A) Bandwidth (BW) (B) Quality (Q) (C) L if C = 0.001 uF BW = fhc – flc = 460 kHz – 450 kHz = 10 kHz Q = fr / BW = 455 kHz / 10 kHz = 45.5 kHz

  42. 1.6 LC Circuits Finally the following circuit is called a tank circuit.

  43. Oscillators

  44. 1.7 Oscillators The most basic building block in a communication system is an oscillator. Oscillator = a circuit capable of converting energy from a DC form to a AC.

  45. 1.7 Oscillators There are many different oscillator designs to choose from, and the choice is usually made based on: • Output frequency required • Frequency stability required • Is the frequency to be varied, and if so, over what range? • Allowable waveform distortion • Power output required These performance characteristics along with economic factors will dictate the form of oscillator to be used in a given design

  46. 1.7 Oscillators Simple LC Oscillator This circuit will oscillate at a resonant frequency, but will dampen out. To be continuous wave (CW), we need to provide some positive feedback.

  47. 1.7 Oscillators Hartley Oscillator Used for Biasing RFC open circuit at f, provides bias current Only pass f (C3 stops DC from flowing into the tank, C2 provides isolation from the base and tank)

  48. 1.7 Oscillators Colpitts Oscillator

  49. 1.7 Oscillators Clapp Oscillator • + Better temperature stability • Reduced frequency adjustment range

  50. 1.7 Oscillators LC Oscillators work well, but when greater frequency stability is required (i.e. the FCC is involved), a crystal-controlled oscillator is often used. Crystal Oscillators • Vibrates as a result of the piezoelectric effect • Available at frequencies from about 15 kHz and up • Available with Q factors of 20,000 up to 1,000,000 as compared to a typical Q of 1000 with an LC

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