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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

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

Calculate the following in your head:
Log(1M)
Log(1G)
Log(1)
Log(.1)
Log(.001)
Log(1n)
6
9
0
-1
-3
-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:
Log(200)
Log(8742)
2.3
3.94
Log(17782)
Log(500,000)
4.25
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 10 x .
ie: Solve for V 2.5 = log(v)
10 2.5
= 10 log(v)
10 2.5
= 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?
10,000
100,000
10 4.5
= 31,623
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 2.1
= 125.9
10 0 = 1
10 -3 = .001
10 -1.5
= .0316

The units of the log function are sometimes referred to as “Bels”
Log(1M)
Log(1G)
Log(1)
Log(.1)
Log(.001)
Log(1n)
6
9
0
-1
-3
-9
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
𝑂𝑈𝑇
𝐼𝑁
This is similar to how “milli” stands for 1 thousandth

Log(1M)
Log(1G)
Log(1)
Log(.1)
Log(.001)
Log(1n)
6
9
0
-1
-3
-9
60 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?
𝑃
𝑂𝑈𝑇
𝑃
𝐼𝑁
= 10
.001
.000000000001
=10
=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
Clearly Noticeable Change
About Twice as Loud
About Four Times as Loud
3dB
5dB
10dB
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
1 W
Electronic Circuit 100 W
𝑃
𝑂𝑈𝑇
𝑃
𝐼𝑁
= 10
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?
1mW
Electronic Circuit dB =
10·log(1,000,000)
= 60dB
1kW
𝑃
𝑂𝑈𝑇
𝑃
𝐼𝑁
=
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 50mW
𝑃
𝑂𝑈𝑇
𝑃
𝐼𝑁
=
.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 17W
𝑃
𝑂𝑈𝑇
𝑃
𝐼𝑁
=
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/m 2 . What level dB is this?
𝑃
𝑂𝑈𝑇
𝑃
𝐼𝑁
= 10
1
.000000000001
=10
=10
= 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 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 ∙ 𝑙𝑜𝑔
2500
5
= 27dB
5W Electronic
Circuit
500W
Electronic
Circuit
5000W
Electronic
Circuit
2500W
20dB -3dB
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): 𝑑𝐵 = 10𝑙𝑜𝑔
𝑃
𝑂𝑈𝑇
𝑃
𝐼𝑁
= 10𝑙𝑜𝑔
𝑉
𝑂𝑈𝑇
𝑅
2
𝑉
𝐼𝑁
𝑅
2
= 10𝑙𝑜𝑔
𝑉
𝑂𝑈𝑇
𝑉
𝐼𝑁
2
2
2
𝑂𝑈𝑇
𝐼𝑁
𝑂𝑈𝑇
𝐼𝑁

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)
LPF
BSF
BPF

C1
R1
HPF

R
LPF
C

C1
R1
HPF

C1
R1
R2
C2
BPF

R
HPF
L

R
LPF
C

C
L
BPF
R

C1
R1
HPF

L
R
LPF

R
HPF
L

R
LPF
C

C1
R1
HPF

L
R
LPF

R
HPF
L

R
LPF
C

L
R
LPF

R
HPF
L

R
LPF
C

C1
R1
HPF

L
R
LPF

R
HPF
L

R
LPF
C

C1
R1
HPF

C1
R1
R2
C2
BPF

Stopband Passband
HPF
Passband Stopband
LPF
BSF
BPF

HPF
-3dB
c
f
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:
𝑋
𝐶
=
1
2𝜋𝑓𝐶
𝑅 =
1
2𝜋𝑓
𝐶
𝐶
𝑐

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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 (V
R 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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