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.

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, 1,000,000)

In order to shrink down the scale of the graph to fit all the points on one graph, we can use the log scale

k 10k 100k octave (double the frequency) 1 decade (Ten times the frequency)

k 10k 100k 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

Calculate the following in your head: Log(1M) Log(1G) Log(1) Log(.1) Log(.001) Log(1n) It turns out that the exponents for our prefixes is the log of that number. 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

Calculate the following using your calculator: Log(200) Log(8742) Log(17782) Log(500,000) 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] What number would result in a log of 2.5? This is called the “antilog.”

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

Using your calculator: The log of what number gives 4? The log of what number gives 5? The log of what number gives 4.5? The log of what number gives 2.1? The log of what number gives 0? The log of what number gives -3? The log of what number gives -1.5? 10, , = 31, = = = =.0316

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

Log(1M) Log(1G) Log(1) Log(.1) Log(.001) Log(1n) dB 90 dB 0 dB -10 dB -30 dB -90 dB If there is a gain or magnification in a circuit, the dB is positive If there is neither gain nor loss, this is called “Unity gain” and the dB is 0. If there is a loss or attenuation in a circuit, the dB is negative

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/m 2 If the sound of my clap was 1mW/m 2 then what level dB are you hearing when I clap? The dB level for sound is always compared to or in reference to 1pW

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. The loudest possible sound that can be made is 194dB within the atmosphere of earth. (This is due to atmospheric pressures)

Perceptions of Increases in Decibel Level Imperceptible Change1dB Barely Perceptible Change3dB Clearly Noticeable Change5dB About Twice as Loud10dB About Four Times as Loud20dB 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)

120 -

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

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

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

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

2mW input4W output 33dB 14W input.03W output -26.7dB 50W input25W output -3dB This last example is very important!! Half power occurs at -3dB. This level of gain is used everywhere.

The threshold of pain is for the human ear is 1W/m 2. What level dB is this?

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

What is the dB gain in the first stage of the following circuit: Electronic Circuit 5W 500W Electronic Circuit 5000W Electronic Circuit 2500W 20dB10dB-3dB 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: Notice, this overall gain is the same gain as just adding up all the individual dB gains along the way. + + = 27dB

Each individual stage has a dB gain of 3

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):

Random Video of the Day 1 Random Video of the Day 2

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 As frequency changes on resistive circuit, nothing happens to output What happens to the output as frequency goes up in the other 2 circuits

Note to instructor: (In student packet as well as log paper) 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

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) HPF LPF BPF BSF

R1 C1 HPF What type of circuit is the following?

C R LPF

R1 C1 HPF

C2 R2 R1 C1 BPF

L R HPF

C R LPF

L C BPF R

BSF or Notch or Band Reject Filter

R1 C1 HPF

R L LPF

L R HPF

C R LPF

R1 C1 HPF

R L LPF

L R HPF

C R LPF

R L

L R HPF

C R LPF

R1 C1 HPF

R L LPF

L R HPF

C R LPF

R1 C1 HPF

C2 R2 R1 C1 BPF

HPF LPF BPF BSF Output is equal to input at passband and near 0 at stop band Stopband Passband Passband Stopband

HPF So where is the pass band and where is the stop band? (In other words where is the cutoff?) -3dB The cut off frequency is at – 3dB fcfc fcfc Recall that the -3dB point is the point where the output gets half of the input power. For the circuit below, when R and X C are the same size, the power across R is half the input power. Thus the cutoff frequency is as follows:

This is also known as a BODE plot

Determine the cutoff frequency for the HPF on the right: Determine the cutoff frequency for the LPF on the right: Draw on board what this means graphically

Not only is there an attenuation curve but there is a phase shift curve at the output at varying frequencies. [Show Multisim example of how varying the frequency varies the phase angle of the circuit (V R angle)]Multisim example

See C1 of sheet 3C1 of sheet 3 What is the cutoff frequency in the following circuit? Show what the signal looks like before and after the filter. What would happen if I put another 1uF Capacitor in parallel?