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Chapter 26

Chapter 26. Coupling and Filter Circuits. Filter – a device that removes or “filters” or attenuates unwanted signals, and keeps (and sometimes magnifies) the desired frequencies. Attenuation – opposite of gain and magnification. To shrink or remove. A couple definitions.

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Chapter 26

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  1. Chapter 26 Coupling and Filter Circuits

  2. Filter – a device that removes or “filters” or attenuates unwanted signals, and keeps (and sometimes magnifies) the desired frequencies Attenuation – opposite of gain and magnification. To shrink or remove. A couple definitions

  3. In order to know how something is magnified or attenuated, we need to understand the decibel. I need a volunteer from the audience! On the white board, please graph the point: (10, 1) (10, 10) (10, ?)

  4. In order to shrink down the scale of the graph to fit all the points on one graph, we can use the log scale Graphs using the Log scale

  5. 2 3 4 5 6 7 8 9 20 30 40 50 60 70 80 90 1 decade (Ten times the frequency) 1 octave (double the frequency) 1 10 100 1k 10k 100k

  6. Using your calculators, what is log(10)? log(100)? log(1000)? log(10,000)? log(100,000)? This is how it is possible to shrink very large numbers down to fit on one scale 1 2 3 4 5 1 10 100 1k 10k 100k

  7. Calculate the following in your head: It turns out that the exponents for our prefixes is the log of that number. 6 Log(1M) 9 Log(1G) 0 Log(1) Log of a number represents how many zeros are in that number. So Log 1 million is 6 because there are 6 zeros in 1 million -1 Log(.1) -3 Log(.001) -9 Log(1n) More logarithms

  8. If Log(100) = 2 and Log(1000) = 3, what is Log(550)? (since 550 is half way between the two) Log(550) = 2.74 [The log scale is not linear] Calculate the following using your calculator: 2.3 Log(200) 3.94 Log(8742) 4.25 Log(17782) 5.7 Log(500,000) More logarithms What number would result in a log of 2.5? This is called the “antilog.”

  9. The opposite of the log function is the antilog. The opposite log(x) is 10x. ie: Solve for V 2.5 = log(v) 102.5 = 10log(v) 102.5 = v 316 = v Antilog

  10. Using your calculator: The log of what number gives 4? 10,000 The log of what number gives 5? 100,000 The log of what number gives 4.5? 104.5 = 31,623 The log of what number gives 2.1? 102.1 = 125.9 The log of what number gives 0? 100 = 1 Antilog Problems The log of what number gives -3? 10-3 = .001 The log of what number gives -1.5? 10-1.5 = .0316

  11. The units of the log function are sometimes referred to as “Bels” However, in electronics the unit of gain is the deciBel (decibel) [dB]. 6 60 dB Log(1M) 9 90 dB Log(1G) We can convert Bels to decibels by multiplying by 10. 0 0 dB Log(1) -1 -10 dB Log(.1) What is bigger, a Bel or a deciBel? -3 -30 dB Log(.001) “deci” stands for 1 tenth of a Bel This is similar to how “milli” stands for 1 thousandth -9 -90 dB Log(1n) From the previous slide:

  12. 6 60 dB Log(1M) If there is a gain or magnification in a circuit, the dB is positive 9 90 dB Log(1G) If there is neither gain nor loss, this is called “Unity gain” and the dB is 0. 0 0 dB Log(1) -1 -10 dB Log(.1) If there is a loss or attenuation in a circuit, the dB is negative -3 -30 dB Log(.001) -9 -90 dB Log(1n) The deciBel is really a unit of gain/attenuation

  13. What is the decibel level of my clap? This question only makes sense if we are comparing it to something else. The thing we are comparing sound to is the smallest audible sound possible: 1pW/m2 If the sound of my clap was 1mW/m2 then what level dB are you hearing when I clap? The decibel is NOT a unit of power(It is a ratio of power) = 10 =10 =109 = 90dB The dB level for sound is always compared to or in reference to 1pW

  14. 30 db change – 8 times louder This is 1000 times more than 1 but sounds 8x louder (see red bottom pg 297) 40 db change – 16 times louder 50 db change – 32 times louder (this is the whale vs. the jet engine) FYI info

  15. Other FYI 120 -

  16. What do you think is louder, a blue whale’s mating call or the sound of a 747 jet at max power cruising speed? 747 jet is 140dB (100W) Blue Whale is 188dB (6.3MW) The human ear detects every 10dB gain to sound twice as loud. Since the blue whale is about 50dB louder than the jet engine, it sounds 2x2x2x2x2 = 32 times louder. Sound Comparison (Just for fun) The loudest possible sound that can be made is 194dB within the atmosphere of earth. (This is due to atmospheric pressures)

  17. Suppose in the circuit below 1 Watt of power was put in and 10 Watts of power came out. How much magnification was there? 100 What is the decibel gain of the circuit? dB = 10·log(100) = 20dB Electronic Circuit 1 W 100 W Decibel level in a circuit = 10 =102 = 20dB

  18. Suppose in the circuit below 1mW of power was put in and 1kW of power came out. How much magnification was there? 1,000,000 What is the decibel gain of the circuit? dB = 10·log(1,000,000) = 60dB Electronic Circuit 1mW 1kW Decibel level in a circuit = = 60dB

  19. Suppose in the circuit below 5W of power was put in and 50mW of power came out. What is the decibel gain of the circuit? dB = 10·log(.01) = -20dB Electronic Circuit 5W 50mW Decibel level in a circuit = = -20dB

  20. Suppose in the circuit below 17W of power was put in and 17W of power came out. How much magnification was there? x1 (unity gain) What is the decibel gain of the circuit? dB = 10·log(1) = 0dB Electronic Circuit 17W 17W Decibel level in a circuit = = 0dB

  21. 2mW input 4W output 33dB 14W input .03W output -26.7dB 50W input 25W output -3dB This last example is very important!! Half power occurs at -3dB. This level of gain is used everywhere. What is the dB gain for the following:

  22. The threshold of pain is for the human ear is 1W/m2. What level dB is this? = 10 =10 =10 = 120dB Other dB ideas

  23. 1pW is the reference for sound power when calculating dB Another reference in electronics is the dBm which represents the power level relative to 1mW. (If you notice on the VOM, the was a dB scale which was referencing this dBm level. You will you this in the communications class References for other applications(aka PIN)

  24. What is the dB gain in the first stage of the following circuit: What is the dB gain in the second stage: What is the dB gain in the third stage: What is the overall gain from the first input, to the last output: 10 = 27dB Electronic Circuit Electronic Circuit Electronic Circuit 5000W 2500W 500W 5W Multi-stage gains + + = 27dB 20dB 10dB -3dB Notice, this overall gain is the same gain as just adding up all the individual dB gains along the way.

  25. Another multi-stager

  26. Each individual stage gas a dB gain of 3 Yet another multistage gain circuit

  27. Example

  28. So far we have talked about the gain equation when using power. It turns out if voltage is the unit being measured for gain the equation is slightly different: This should make sense because (for you math people): Gains for VOLTAGE

  29. Voltage gain

  30. Random Video of the Day 1 Random Video of the Day 2 RVOTD

  31. Coupling - the association of two circuits or systems in such a way that power may be transferred from one to the other; a linkage of circuits Filters As frequency changes on resistive circuit, nothing happens to output What happens to the output as frequency goes up in the other 2 circuits

  32. Low Pass Filter (LPF) Handout Note to instructor: INTRODUCE THIS SECTION DRAW 5 RC LOW PASS FILTERS ON THE BOARD WHERE THE ONLY THING CHANGING IS THE FREQUENCY. FIND Vc FOR EACH CIRCUIT AND AFTERWARDS GRAPH VOLTAGE VS. FREQUENCY. Vs= 1000V, R = 15915Ohm, C = 10nF F=10Hz, 100Hz, 1kHz 10kHz, 100kHz

  33. HPF Filters are used to pass or block a specific range of frequencies. (Voltage or current doesn’t get through at those specific frequencies) • There are 4 main types of filters: • High Pass Filter (HPF) • Low Pass Filter (LPF) • Band Pass Filter (BPF) • Band Stop Filter (BSF) LPF Types of Filters BSF BPF

  34. What type of circuit is the following? C1 R1 HPF

  35. R C LPF

  36. C1 R1 HPF

  37. C1 R2 R1 C2 BPF

  38. R L HPF

  39. R C LPF

  40. C L R BPF

  41. BSF or Notch or Band Reject Filter

  42. C1 R1 HPF

  43. L R LPF

  44. R L HPF

  45. R C LPF

  46. C1 R1 HPF

  47. L R LPF

  48. R L HPF

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