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Oscillators Electronic Engineering © University of Wales Newport 2009 This work is licensed under a  Creative Commons Attr...
<ul><li>The following presentation is a part of the level 5 module  -- Electronic Engineering. This resources is a part of...
Oscillator Circuits <ul><li>An amplifier will become unstable if it has positive feedback applied to it </li></ul><ul><li>...
<ul><li>A will amplify a signal on the input and then a proportion of the amplified signal will be fed back. If this is la...
Wien Bridge Oscillator This uses a feedback network of the following form: Note the resistors have the same value as do th...
Oscillators
Oscillators
Example R = 10k   and C = 10nF Frequency Gain Phase 900 0.3093889 2.34789 1000 0.3173753 2.864766 1100 0.3232355 3.289809...
Gain curve Phase curve 1.59kHz 0.333 Oscillators
From the graph: Zero degrees phase shift occurs at 1.59kHz The gain at this point equals approximately 0.333 Can we determ...
<ul><li>Gain at this frequency: </li></ul><ul><li>But –  </li></ul><ul><li>Which leaves us with: </li></ul><ul><li>To use ...
R 2 R 1 R R C C Vout Feedback Amplifier If the gain is too large the sine wave will clip at the supply rails and if it is ...
R. C. Phase Shift Oscillator. <ul><li>As we are aware, an R C network will alter the amount of signal it passes as the fre...
V OUT To derive a relationship between input and output use Nodal Analysis. @ V OUT   R C R C R C V IN V 1 V 2
@ V 2 but Oscillators
@V 1 but
As the frequency is varied the gain magnitude and phase will vary. Oscillators
Oscillators
C= 10 nF and R = 10k  Range 100 Hz to 1600 Hz Frequency Gain Phase 100 0.00024187 -107.824 200 0.00180268 -124.679 300 0....
~650Hz Gain curve Phase curve Gain = ~0.035
From the graph: -180 degrees phase shift occurs at 650Hz The gain at this point equals approximately 0.035 Can we determin...
Now the gain – use: <ul><li>To use this to produce an oscillator we need an amplifier with the following characteristics: ...
R R R C C C Rin Rf Vout Amplifier Feedback R. C. Phase shift Oscillator The values of Rin and Rf must be selected so that ...
Tuned Collector L C Oscillator.   <ul><li>This is a development of the four-resistor biased single stage transistor amplif...
C L R The impedance of this network can be determined in the following way:
Example L = 10 mH, R = 10   , C = 10 nF. Plot the value of Z over the range: Oscillators
Frequency Impendance Phase 12000 1747.19495 88.2391 12500 2049.5822 88.09622 13000 2453.70559 87.89268 13500 3022.7584 87....
15.9 kHz Oscillators
Zero phase shift occurs at about 15.9 kHz and this approximately coincides with the peak in the gain (within the limits of...
Note: so If we use this parallel network instead of the collector resistor we will have an amplifier whose gain is frequen...
G MAX F R
The peak gain G MAX  occurs at the resonant frequency F R . We now need to introduce feedback and this is done by converti...
When the dc bias is set up the new capacitor has no effect and the new inductor acts like a short circuit. When operating ...
Generalised Oscillator Circuit The circuit shows an inverting amplifier with three complex components connected to it. (Th...
This can be redrawn in the following way – Note  Z 1  = jX 1  etc. R OUT  is the output resistance of the amplifier Oscill...
The load on the output Z LOAD  of the amplifier is given by This allows us to determine the gain of the amplifier. Oscilla...
Using j x j = -1  The feedback ratio for the network involves X1 and X2. The Loop Gain LG for the circuit is equal to Gain...
For this to be an oscillator the equation must have no j component and therefore: This means that for the above equation t...
As this value must be positive it means that X2 and X3 must be of the same sign – they must be either capacitors or induct...
Colpitts Oscillator Oscillation Frequency. Oscillators C 2 C 3 L 1 -A
Amplifier Gain Example If we need a 25kHz oscillator, What value of L 1  do we require and what should the gain of the amp...
Hartley Oscillator Oscillation Frequency. Oscillators L 2 L 3 C 1 -A
Amplifier Gain Example Determine the values of L 2  and L 3  if the oscillator is to operate at 10kHz Oscillators L 2 L 3 ...
Crystal Oscillator <ul><li>A  crystal oscillator  is an electronic circuit that uses the mechanical resonance of a vibrati...
Crystal Modelling   <ul><li>*A quartz crystal can be modelled as an electrical network with a low impedance (series) and a...
<ul><li>Adding additional capacitance across a crystal will cause the parallel resonance to shift downward. This can be us...
Oscillators This resource was created by the University of Wales Newport and released as an open educational resource thro...
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Oscillators

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The following presentation is a part of the level 5 module -- Electronic Engineering. This resources is a part of the 2009/2010 Engineering (foundation degree, BEng and HN) courses from University of Wales Newport (course codes H101, H691, H620, HH37 and 001H). This resource is a part of the core modules for the full time 1st year undergraduate programme.
The BEng & Foundation Degrees and HNC/D in Engineering are designed to meet the needs of employers by placing the emphasis on the theoretical, practical and vocational aspects of engineering within the workplace and beyond. Engineering is becoming more high profile, and therefore more in demand as a skill set, in today’s high-tech world. This course has been designed to provide you with knowledge, skills and practical experience encountered in everyday engineering environments.

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  1. 1. Oscillators Electronic Engineering © University of Wales Newport 2009 This work is licensed under a Creative Commons Attribution 2.0 License .
  2. 2. <ul><li>The following presentation is a part of the level 5 module -- Electronic Engineering. This resources is a part of the 2009/2010 Engineering (foundation degree, BEng and HN) courses from University of Wales Newport (course codes H101, H691, H620, HH37 and 001H). This resource is a part of the core modules for the full time 1 st year undergraduate programme. </li></ul><ul><li>The BEng & Foundation Degrees and HNC/D in Engineering are designed to meet the needs of employers by placing the emphasis on the theoretical, practical and vocational aspects of engineering within the workplace and beyond. Engineering is becoming more high profile, and therefore more in demand as a skill set, in today’s high-tech world. This course has been designed to provide you with knowledge, skills and practical experience encountered in everyday engineering environments. </li></ul><ul><li>Contents </li></ul><ul><li>Oscillator Circuits </li></ul><ul><li>Wien Bridge Oscillator </li></ul><ul><li>R. C. Phase Shift Oscillator. </li></ul><ul><li>Tuned Collector L C Oscillator. </li></ul><ul><li>Generalised Oscillator Circuit </li></ul><ul><li>Colpitts Oscillator </li></ul><ul><li>Hartley Oscillator </li></ul><ul><li>Crystal Oscillator </li></ul><ul><li>Crystal Modelling </li></ul><ul><li>Credits </li></ul><ul><li>In addition to the resource below, there are supporting documents which should be used in combination with this resource. Please see: </li></ul><ul><li>Clayton G, 2000, Operational Amplifiers 4th Ed, Newnes  </li></ul><ul><li>James M, 2004, Higher Electronics, Newnes </li></ul>Oscillators
  3. 3. Oscillator Circuits <ul><li>An amplifier will become unstable if it has positive feedback applied to it </li></ul><ul><li>See below </li></ul>A is the gain of the amplifier and B is the proportion of the output fed back to the input. Oscillators Vout A B
  4. 4. <ul><li>A will amplify a signal on the input and then a proportion of the amplified signal will be fed back. If this is large enough to replace the original signal the system keeps generating an output. There are a few rules that determine the nature of the output. </li></ul><ul><li>These are stated in the Barkhausen Criterion. </li></ul><ul><li>It states: </li></ul><ul><li>For Sinusoidal Oscillation to occur at a single frequency we must have: </li></ul><ul><li>A loop gain of unity (A x B = 1) </li></ul><ul><li>A loop phase shift of zero (A  + B  = 0  or 360  ) </li></ul><ul><li>Condition 1 or 2 to be true only at a single frequency. </li></ul><ul><li>We will examine a range of sinusoidal oscillators. </li></ul>Oscillators
  5. 5. Wien Bridge Oscillator This uses a feedback network of the following form: Note the resistors have the same value as do the capacitors. As the input frequency is varied the output will have a different gain and phase relationship with the input. At one frequency the input and output will be in phase. R R C C Z S Z P Vout Vin
  6. 6. Oscillators
  7. 7. Oscillators
  8. 8. Example R = 10k  and C = 10nF Frequency Gain Phase 900 0.3093889 2.34789 1000 0.3173753 2.864766 1100 0.3232355 3.289809 1200 0.3274285 3.527987 1300 0.3303008 3.459755 1400 0.3321152 2.938197 1500 0.3330734 1.785935 1600 0.3333313 -0.20661 1700 0.3330114 -3.27647 1800 0.3322112 -7.6651 1900 0.331009 -13.5567 2000 0.3294684 -20.9608
  9. 9. Gain curve Phase curve 1.59kHz 0.333 Oscillators
  10. 10. From the graph: Zero degrees phase shift occurs at 1.59kHz The gain at this point equals approximately 0.333 Can we determine this from the equations? For this to equal 0 then:
  11. 11. <ul><li>Gain at this frequency: </li></ul><ul><li>But – </li></ul><ul><li>Which leaves us with: </li></ul><ul><li>To use this to produce an oscillator we need an amplifier with the following characteristics: </li></ul><ul><li>Gain = 3 (to give loop gain of unity) </li></ul><ul><li>Phase shift of 0  (to give a loop phase shift of zero) </li></ul>Oscillators
  12. 12. R 2 R 1 R R C C Vout Feedback Amplifier If the gain is too large the sine wave will clip at the supply rails and if it is too small it will not oscillate at all. Wien Bridge Oscillator Oscillators
  13. 13. R. C. Phase Shift Oscillator. <ul><li>As we are aware, an R C network will alter the amount of signal it passes as the frequency varies. It also introduces different amounts of phase shift. </li></ul>R C V IN V OUT The maximum amount of phase shift available from a single R C combination is 90  . If we have three such combinations with the same resistors and capacitors we will have up to 270  of phase shift. Oscillators
  14. 14. V OUT To derive a relationship between input and output use Nodal Analysis. @ V OUT R C R C R C V IN V 1 V 2
  15. 15. @ V 2 but Oscillators
  16. 16. @V 1 but
  17. 17. As the frequency is varied the gain magnitude and phase will vary. Oscillators
  18. 18. Oscillators
  19. 19. C= 10 nF and R = 10k  Range 100 Hz to 1600 Hz Frequency Gain Phase 100 0.00024187 -107.824 200 0.00180268 -124.679 300 0.00547793 -139.942 400 0.01144164 -153.412 500 0.01946552 -165.165 600 0.02916192 -175.403 700 0.04013019 -184.346 800 0.05201965 -192.201 900 0.06454692 -199.142 1000 0.07749321 -205.315 1100 0.09069431 -210.839 1200 0.10402935 -215.813 1300 0.11741055 -220.316 1400 0.13077482 -224.417 1500 0.14407717 -228.17 1600 0.15728573 -231.621
  20. 20. ~650Hz Gain curve Phase curve Gain = ~0.035
  21. 21. From the graph: -180 degrees phase shift occurs at 650Hz The gain at this point equals approximately 0.035 Can we determine this from the equations? For this to equal 0 (-180 °) Oscillators
  22. 22. Now the gain – use: <ul><li>To use this to produce an oscillator we need an amplifier with the following characteristics: </li></ul><ul><li>Gain = 29 (to give loop gain of unity) </li></ul><ul><li>Phase shift of 180  (to give a loop phase shift of zero (360)) </li></ul>Oscillators
  23. 23. R R R C C C Rin Rf Vout Amplifier Feedback R. C. Phase shift Oscillator The values of Rin and Rf must be selected so that the gain of the amplifier equals twenty nine. Oscillators
  24. 24. Tuned Collector L C Oscillator. <ul><li>This is a development of the four-resistor biased single stage transistor amplifier: </li></ul>From equivalent circuit analysis it can be shown that the gain of the amplifier depends (for a limited range) on the value of the collector resistor. If this is replaced by a tuned L C parallel network then we will have a gain which is dependent on frequency.
  25. 25. C L R The impedance of this network can be determined in the following way:
  26. 26. Example L = 10 mH, R = 10  , C = 10 nF. Plot the value of Z over the range: Oscillators
  27. 27. Frequency Impendance Phase 12000 1747.19495 88.2391 12500 2049.5822 88.09622 13000 2453.70559 87.89268 13500 3022.7584 87.5925 14000 3885.71647 87.12191 14500 5352.88937 86.30287 15000 8405.51864 84.57067 15500 18571.4156 78.7095 16000 68655.401 -47.2146 16500 13729.3845 -82.6617 17000 7558.08851 -86.202 17500 5253.32655 -87.5099 18000 4049.04035 -88.1861 18500 3308.55693 -88.597 19000 2806.81681 -88.8716 19500 2444.08824 -89.0672 20000 2169.40337 -89.2129
  28. 28. 15.9 kHz Oscillators
  29. 29. Zero phase shift occurs at about 15.9 kHz and this approximately coincides with the peak in the gain (within the limits of our results) Can we determine this from the equations? This must equal 0 so: Impedance at this frequency: Oscillators
  30. 30. Note: so If we use this parallel network instead of the collector resistor we will have an amplifier whose gain is frequency dependent. Oscillators
  31. 31. G MAX F R
  32. 32. The peak gain G MAX occurs at the resonant frequency F R . We now need to introduce feedback and this is done by converting the inductor of the parallel L C combination into a transformer and applying the feedback signal to the base. An extra capacitor is required to connect the other side of the transformer to ground for ac signals. Amplifier Feedback Oscillators
  33. 33. When the dc bias is set up the new capacitor has no effect and the new inductor acts like a short circuit. When operating a fraction of the output is generated across the new inductor and this is effectively between the base and ground. The amount of feedback is determined by the turns ratio TR of the transformer. If we arrange for the turns ratio of the transformer to have a value given by: Then we will have a Loop Gain of unity only at the peak gain and therefore this part of the criterion is met only at a single frequency. The Loop Phase Shift can be kept at 0  for all frequencies. Oscillation frequency is given by: Oscillators
  34. 34. Generalised Oscillator Circuit The circuit shows an inverting amplifier with three complex components connected to it. (These components could be inductors or capacitors) Oscillators Z 2 Z 3 Z 1 -A
  35. 35. This can be redrawn in the following way – Note Z 1 = jX 1 etc. R OUT is the output resistance of the amplifier Oscillators jX 1 jX 2 jX 3 R OUT Vin AVin - + ~
  36. 36. The load on the output Z LOAD of the amplifier is given by This allows us to determine the gain of the amplifier. Oscillators
  37. 37. Using j x j = -1 The feedback ratio for the network involves X1 and X2. The Loop Gain LG for the circuit is equal to Gain x Feedback
  38. 38. For this to be an oscillator the equation must have no j component and therefore: This means that for the above equation to be true the three components cannot be the same type (e.g. three capacitors) as this will produce a positive or negative result – there must be a mix e.g. two inductors and one capacitor. The Loop Gain equation is therefore: Oscillators
  39. 39. As this value must be positive it means that X2 and X3 must be of the same sign – they must be either capacitors or inductors. <ul><li>From this general design we can generate two oscillators: </li></ul><ul><li>X1 = Inductor X2 = Capacitor X3 = Capacitor </li></ul><ul><li>X1 = Capacitor X2 = Inductor X3 = Inductor </li></ul>Oscillators
  40. 40. Colpitts Oscillator Oscillation Frequency. Oscillators C 2 C 3 L 1 -A
  41. 41. Amplifier Gain Example If we need a 25kHz oscillator, What value of L 1 do we require and what should the gain of the amplifier equal? Oscillators 100pF 470pF L 1 -A
  42. 42. Hartley Oscillator Oscillation Frequency. Oscillators L 2 L 3 C 1 -A
  43. 43. Amplifier Gain Example Determine the values of L 2 and L 3 if the oscillator is to operate at 10kHz Oscillators L 2 L 3 1nF -10
  44. 44. Crystal Oscillator <ul><li>A crystal oscillator is an electronic circuit that uses the mechanical resonance of a vibrating crystal of piezoelectric material to create an electrical signal with a very precise frequency. This frequency is commonly used to keep track of time (as in quartz wristwatches), to provide a stable clock signal for digital integrated circuits, and to stabilize frequencies for radio transmitters. </li></ul><ul><li>Using an amplifier and feedback, it is an especially accurate form of an electronic oscillator. The crystal used therein is sometimes called a &quot;timing crystal&quot;. On schematic diagrams a crystal is sometimes labelled with the abbreviation XTAL . </li></ul>Oscillators
  45. 45. Crystal Modelling <ul><li>*A quartz crystal can be modelled as an electrical network with a low impedance (series) and a high impedance (parallel) resonance point spaced closely together. </li></ul>* The above text is taken from http://en.wikipedia.org/wiki/Crystal_oscillator and is available under the Creative Commons Attribution-ShareAlike License . Oscillators C 0 C 1 L 1 R 1
  46. 46. <ul><li>Adding additional capacitance across a crystal will cause the parallel resonance to shift downward. This can be used to adjust the frequency that a crystal oscillator oscillates at. Crystal manufacturers normally cut and trim their crystals to have a specified resonant frequency with a known 'load' capacitance added to the crystal. For example, a 6pF 32kHz crystal has a parallel resonance frequency of 32,768 Hz when a 6.0pF capacitor is placed across the crystal. Without this capacitance, the resonance frequency is higher than 32,768. </li></ul><ul><li>* The above text is taken from http://en.wikipedia.org/wiki/Crystal_oscillator and is available under the Creative Commons Attribution-ShareAlike License . </li></ul>Oscillators
  47. 47. Oscillators This resource was created by the University of Wales Newport and released as an open educational resource through the Open Engineering Resources project of the HE Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCE and part of the JISC/HE Academy UKOER programme. © 2009 University of Wales Newport This work is licensed under a Creative Commons Attribution 2.0 License . The JISC logo is licensed under the terms of the Creative Commons Attribution-Non-Commercial-No Derivative Works 2.0 UK: England & Wales Licence.  All reproductions must comply with the terms of that licence. The HEA logo is owned by the Higher Education Academy Limited may be freely distributed and copied for educational purposes only, provided that appropriate acknowledgement is given to the Higher Education Academy as the copyright holder and original publisher. The name and logo of University of Wales Newport is a trade mark and all rights in it are reserved. The name and logo should not be reproduced without the express authorisation of the University.
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