Transcript Chapter 26 Powerpoint

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Coupling and Filter Circuits
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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
23456789
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
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
1
2
3
4
5
10
100
1k
10k
100k
Calculate the following in your head:
Log(1M)
Log(1G)
Log(1)
Log(.1)
6
9
0
-1
Log(.001) -3
Log(1n) -9
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
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)
Log(500,000) 5.7
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 10x.
ie: Solve for V
2.5 = log(v)
102.5 = 10log(v)
102.5 = v
316 = v
Using your calculator:
The log of what number gives 4?
The log of what number gives 5?
10,000
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
The log of what number gives -3? 10-3 = .001
The log of what number gives -1.5? 10-1.5 = .0316
The units of the log function are sometimes
referred to as “Bels”
6
9
0
-1
60 dB
90 dB
0 dB
-10 dB
Log(.001) -3
Log(1n) -9
-30 dB
-90 dB
Log(1M)
Log(1G)
Log(1)
Log(.1)
𝐺𝑎𝑖𝑛 𝑑𝐵 = 10 ∙ 𝑙𝑜𝑔 𝐺𝑎𝑖𝑛
𝑃𝑂𝑈𝑇
𝐺𝑎𝑖𝑛 𝑑𝐵 = 10 ∙ 𝑙𝑜𝑔
𝑃𝐼𝑁
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
6
9
0
-1
60 dB
90 dB
0 dB
-10 dB
Log(.001) -3
Log(1n) -9
-30 dB
-90 dB
Log(1M)
Log(1G)
Log(1)
Log(.1)
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/m2
If the sound of my clap was 1mW/m2 then what level dB
are you hearing when I clap?
𝐺𝑎𝑖𝑛 𝑑𝐵 = 10 ∙ 𝑙𝑜𝑔
𝑃𝑂𝑈𝑇
𝑃𝐼𝑁
= 10 ∙ 𝑙𝑜𝑔
.001
.000000000001
=10 ∙ 𝑙𝑜𝑔 1,000,000,000 =10∙9 = 90dB
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 Change
1dB
Barely Perceptible Change
3dB
Clearly Noticeable Change
5dB
About Twice as Loud
10dB
About Four Times as Loud
20dB
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)
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120 -
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
1W
Electronic Circuit
𝐺𝑎𝑖𝑛 𝑑𝐵 = 10 ∙ 𝑙𝑜𝑔
𝑃𝑂𝑈𝑇
𝑃𝐼𝑁
= 10 ∙ 𝑙𝑜𝑔
100 W
100
1
=10∙2 = 20dB
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
1mW
Electronic Circuit
𝐺𝑎𝑖𝑛 𝑑𝐵 = 10 ∙ 𝑙𝑜𝑔
𝑃𝑂𝑈𝑇
𝑃𝐼𝑁
= 10 ∙ 𝑙𝑜𝑔
1kW
1,000
.001
= 60dB
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
5W
Electronic Circuit
𝐺𝑎𝑖𝑛 𝑑𝐵 = 10 ∙ 𝑙𝑜𝑔
𝑃𝑂𝑈𝑇
𝑃𝐼𝑁
= 10 ∙ 𝑙𝑜𝑔
50mW
.05
5
= -20dB
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
17W
Electronic Circuit
𝐺𝑎𝑖𝑛 𝑑𝐵 = 10 ∙ 𝑙𝑜𝑔
𝑃𝑂𝑈𝑇
𝑃𝐼𝑁
= 10 ∙ 𝑙𝑜𝑔
17W
17
17
= 0dB
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.
The threshold of pain is for the human ear is 1W/m2. What
level dB is this?
𝐺𝑎𝑖𝑛 𝑑𝐵 = 10 ∙ 𝑙𝑜𝑔
𝑃𝑂𝑈𝑇
𝑃𝐼𝑁
= 10 ∙ 𝑙𝑜𝑔
1
.000000000001
=10 ∙ 𝑙𝑜𝑔 1,000,000,000,000 =10∙ 12 = 120dB
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
What is
What is
What is
the dB gain in the first stage of the following circuit:
the dB gain in the second stage:
the dB gain in the third stage:
the overall gain from the first input, to the last output:
2500
10 ∙ 𝑙𝑜𝑔
= 27dB
5
5W
Electronic
Circuit
20dB
500W
+
Electronic
Circuit
10dB
5000W
+
Electronic
Circuit
-3dB
2500W
= 27dB
Notice, this overall gain is the same gain as just adding up all the
individual dB gains along the way.
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):
𝑉𝑂𝑈𝑇 2
𝑅
𝑉𝐼𝑁 2
𝑅
𝑃𝑂𝑈𝑇
𝑑𝐵 = 10𝑙𝑜𝑔
= 10𝑙𝑜𝑔
𝑃𝐼𝑁
𝑉𝑂𝑈𝑇
= 10𝑙𝑜𝑔
𝑉𝐼𝑁
2
= 10𝑙𝑜𝑔
𝑉𝑂𝑈𝑇
= 20𝑙𝑜𝑔
𝑉𝐼𝑁
𝑉𝑂𝑈𝑇 2
𝑉𝐼𝑁 2
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
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)
BPF
LPF
BSF
What type of circuit is the following?
C1
R1
HPF
R
C
LPF
C1
R1
HPF
C1
R2
R1
BPF
C2
R
L
HPF
R
C
LPF
C
L
R
BPF
BSF or Notch or Band Reject Filter
C1
R1
HPF
L
R
LPF
R
L
HPF
R
C
LPF
C1
R1
HPF
L
R
LPF
R
L
HPF
R
C
LPF
L
R
LPF
R
L
HPF
R
C
LPF
C1
R1
HPF
L
R
LPF
R
L
HPF
R
C
LPF
C1
R1
HPF
C1
R2
R1
BPF
C2
Stopband
Passband
BPF
HPF
Passband
LPF
Stopband
Output is
equal to
input at
passband
and near 0
at stop
band
BSF
-3dB
HPF
fc
So where is the pass band
and where is the stop band?
(In other words where is the
cutoff?)
The cut off frequency is at – 3dB
fc
Recall that the -3dB point is the point where the output gets half of the input power.
For the circuit below, when R and XC are the same size, the power across R is half
the input power. Thus the cutoff frequency is as follows:
1
1
1
𝑋𝐶 =
𝑅=
𝑓𝑐 =
2𝜋𝑓𝐶
2𝜋𝑓𝐶 𝐶
2𝜋𝑅𝐶
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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 (VR angle)]
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See C1 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?
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