Decibel | Dokumen 471 DECIBEL

Pengertian Gain, Attenuasi dan
Decibels
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Gain, attenuation, dan
Decibel
• Gain = penguatan, atau dikatakan
sebagai perbandingan output dan input
dimana output lebih besar daripada input.
• Attenuation = redaman, dikatakan
sebagai perbandingan output dan input
dimana output lebih kecil daripada input.
• Decibel (dB): satuan ukuran yang dipakai
untuk menyatakan Gain dan Attenuation.

Gain = amplification
output Vout
Av 


input
Vin

Vout
A  gain 
Vin

output Pout
Ap 

input
Pin

Contoh soal
1. Berapa penguatan tegangan sebuah penguat yang menghasilkan
tegangan keluaran 750 mV dari sumber masukan 30 V ?

Vout 750 10 3
Av 


25.000
6
Vin
30 10
2. The power output of an amplifier is 6 watts (W). The power gain is 80.
What is the input power?

Pout
Ap 
Pin

therefore

Pout
Pin 
Ap

6
Pin  0.075 W 75 mW

80

Contoh soal
3. Three cascaded amplifiers have power gain of 5, 2, and 17.
The input power is 40 mW. What is the output power?

Ap  A1 A2 A3 5 2 17 170
Pout
Ap 
Pin

therefore

Pout  Ap Pin

Pout 170(40 10  3 ) 6.8 W
4. A two stage amplifier has an input power of 25 W and an output
power of 1.5 mW. One stage has a gain of 3. What is the gain of
the second stage?

Pout 1.5 10  3
Ap 

60
6
Pin 25 10
Ap  A1 A2
if A1 3, then 60 3 A2 and A2 60 / 3 20

Attenuation = redaman
Vin

output Vout
attenuation A 

input
Vin
R1=200

R2=100

Vin

Vout

 R2 

Vin 
 R1  R2 

 R2  100
 
A 
0.3333
 R1  R2  300
Loss
stage

Loss
circuit

Loss
component

A1=0,2

A2=0,9

A3=0,06

AT= A1 x A2 x A3 = 0.2 X 0.9 x 0.06 = 0.0108
Vout = AT Vin= 0.0324 = 32.4 mV

Vout

Redaman
Vin
R1=750

Vout = Vin

R2=250

Vin = 1.5 V

250
(750  250)
250
A1 
0,25
1000
A1 

A2 = 4

Loss 0.15V
stage
A1= 0.1

A2= 10

1.5V

AT  A1 A2 0,25(4) 1

Vout = 6.75 V

Loss 0.45V
stage
A3= 0.3

A4= 15

AT = A1 A2 A3 A4 = (0.1)(10)(0.3)(15) = 4.5

Contoh soal
A voltage divider like that shown in Fig. 2-5 has values of R1 = 10 k and
R2 = 470 .
a. What is the attenuation?

A1 

R2
470

R1  R2 10,470

A1 0.045

b. What amplifier gain would you need to offset the loss for an overall
gain of 1 ?
AT = A1A2
where A1 is attenuation and A2 is the amplifier gain

1 0.045 A2

1
A2 
22.3
0.045

Note:
To find the gain that will offset the loss for unity gain, just take
the reciprocal of attenuation: A2 = 1/A1

Contoh soal
An amplifier has a gain of 45,000, which is too
much for the application. With an input voltage of
20V, what attenuation factor is needed to keep
the output voltage from exceeding 100 mV?
Let A1 = amplifier gain = 45,000; A2 =
attenuation factor; AT = total gain.

Vout 100 10  3
AT 

5,000
6
Vin
20 10
AT  A1 A2

therefore

AT
5,000
A2  
0.1111
A1 45,000

Decibel (dB)
Vout
dB 20 log
Vin

(1)

I out
dB 20 log
I in

( 2)

Pout
dB 10 log
Pin

(3)

It is common for electronic circuits
and systems to have extremely
high gains or attenuations, often
in excess of 1 million.
Dengan mengubah angka di atas
menjadi decibel (dB) akan
membuatnya terkesan menjadi
lebih kecil dan mudah digunakan.

Formula (1) untuk menyatakan penguatan (gain) atau
redaman (attenuation) tegangan dari suatu rangkaian.
Formula (2) untuk penguatan atau redaman arus
Formula (3) untuk penguatan atau redaman daya

Contoh
a. An amplifier has an input of 3 mV and an output of 5 V. What is
the gain in decibels?

dB 20 log

5
20 log 1666.67 20(3.22) 64.4
0.003

b. A filter has a power input of 50 mW and an output of 2 mW.
What is the gain or attenuation?

 2
dB 10 log  10 log 0.04 10( 1.398)  13.98
 50 
Note that when the circuit has gain, the decibel figure
is positive. If the gain is less than 1, which means that
there is an attenuation, the decibel figure is negative.

dB (decibel)
Adalah satuan factor penguatan jika nilainya positif, dan
pelemahan/redaman/loss jika nilainya negative.
Jika input = 1 watt, output = 100 watt maka terjadi
penguatan (G) 100 kali, maka G = 10 log 100/1 = 20 dB
Jika input = 100 watt, output = 50 watt maka terjadi
redaman/loss daya (G), maka G = 10 log 50/100 = -3 dB
( maka disebut redaman / loss 3 dB)

• dBW (Decibel Watt ) dan dBm adalah satuan level
daya
• dBW :adalah satuan level daya dengan
referensi daya 1 watt P(dBW) = 10 Log P(watt)/1
watt
dBm:adalah satuan level daya dengan referensi
daya 1 mW = 10-3 watt
• P (dBm) = 10 Log P(watt)/10-3 watt
• 10 Watt = P (dBW) = 10 Log 10 Watt/1 Watt (= 10 Log
10 = 10 dBW)
• 1000 Watt = P (dBW) = 10 Log 1000 Watt /1 Watt (=
10 Log 1000 = 30 dBW)
• 10 Watt = P(dBm) = 10 Log 10/10-3 = 10 Log 104 =
10*4 = 40 dBm
• 100 Watt = P(dBm) = 10 Log 100/10-3 = 10 Log 105
= 10*5 = 50 dBm
• 1000 Watt = P(dBm) = 10 Log 1000/10-3 = 10 Log
106 = 10*6 = 60 dBm

• Terlihat bahwa dari dBw ke dBm terdapat selisih 30 dB
sehingga dapat dirumuskan :
P (dBm) = P (dBW) + 30 atau, P (dBW) = P (dBm) – 30
Contoh :
1. Sebuah Amplifier mempunyai gain = 20 dB, jika
diberi input 10 dBm berapa output amplifier
tersebut? Jawab : Pout (dBm) = Pin(dBm) + G =
10 + 20 = 30 dBm.
2. Sebuah Amplifier dengan gain 30 dB, jika
outputnya sebesar 45 dBm berapa level
inputnya? Jawab : Pout(dBm) = Pin (dBm) + G =?
Pin = Pout G = 45 - 30 = 15 dBm
3. Output amplifier sebesar 30 dBm akan dilewatkan
kabel dengan redaman / loss 2 dB. Berapa level
sinyal setelah melewati kabel?
Jawab : Pout = Pin L = 30 - 2 = 28 dBm

gain (redaman) total:
A1=15dB

A2= - 20dB

A3= 35dB

Loss
stage

AT = A1 + A2 + A3
AT = 15 – 20 + 35 = 30 dB

Antilog:

Contoh soal
1. A power amplifier with a 40 dB gain has an output power of 100 W.
What is the input power?

Pout
dB 10 log
Pin
Pout
40
log
10
Pin
Pout
10 4
Pin



Pout
anti log 4
Pin





Pout
dB
log
10
Pin

P
100
Pin  out 
10 mW
10,000 10,000

2. A power amplifier has a gain of 60 dB. If the input voltage is 50V,
what is the output voltage?

dB 20 log
Vout
3 log
Vin

Vout
Vin


Vout 1000 Vin



V
dB
log out
20
Vin

Vout
103 1000
Vin


Vout 1000(5 10  6 ) 50 mV

dBm dan dB
dBm adalah ratio logaritmik dengan acuan 1 mW  untuk daya
dB adalah ratio logaritmik dengan acuan 1 Volt  untuk
tegangan

Px
dBm 10 log
1 mW

Vx
dan dB 20 log
1 V

Contoh:
1. Nyatakan 20 dBm dalam watt.

Daya = 100 mW

2. Nyatakan 40 dB dalam volt.

Tegangan = 100 V

Contoh:

A1= 30dB

1mW

A2= - 10dB

Loss
stage

A3= 3dB

???