To convert a voltage ratio to decibels (dB), you can use the following formula:
dB
=
20
×
log
10
(
out
in
)
dB=20×log
10
(
V
in
V
out
)
Where:
out
V
out
is the output voltage.
in
V
in
is the input voltage.
Here's a step-by-step guide on how to convert a voltage ratio to decibels:
Determine the input and output voltages: Identify the values for
in
V
in
(input voltage) and
out
V
out
(output voltage) in the voltage ratio you want to convert.
Calculate the voltage ratio: Divide the output voltage by the input voltage to find the voltage ratio:
Voltage Ratio
=
out
in
Voltage Ratio=
V
in
V
out
Apply the formula: Use the formula mentioned above to convert the voltage ratio to decibels:
dB
=
20
×
log
10
(
out
in
)
dB=20×log
10
(
V
in
V
out
)
Calculate the value: Use a calculator to find the logarithm and then multiply it by 20 to get the value in decibels.
Keep in mind that this formula is applicable for voltage ratios. If you have power ratios, the formula will be slightly different. For power ratios, the formula is:
dB
=
10
×
log
10
(
out
in
)
dB=10×log
10
(
P
in
P
out
)
Where:
out
P
out
is the output power.
in
P
in
is the input power.
But when dealing with simple voltage ratios, the first formula with a factor of 20 is the one to use.