How do you convert a voltage ratio to decibels?

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.