Voltage Ratio to dB

This tool converts from Voltage Ratio to dB or deciBel.

Enter the Voltage Ratio (a positive real number) to get the equivalent dB value.

???? dB to Voltage Ratio

Formula

P_dB = 20*Log₁₀(V_ratio)

V_ratio = 10^(P_dB/20)

Notes

• These formulas assume the input and output impedances are the same.
• V_ratio is the ratio of two Root-mean-square voltage values (not the peak or average)
• V_ratio is always a positive number

Example Calculations

A voltage ratio of 10 is equivalent to 20 dB. A voltage ratio of 0.1 is equivalent to -20 dB.

Background

A Ratio is a measure of how many times one number contains another. In this case, if the output voltage is 25 times the input power, then Vout:Vin = 25:1. Alternatively Vin:Vout is 1:25 and it can also be expressed as a fraction 1/25 or as a number 0.04.

A ratio has no units as the input and the output are expressed in the same units. For instance, in this case it’s Volt.

The dB scale is a convenient way to represent both large and small numbers. For instance, the voltage ratio 10000000000:1 = 200 dB while 0.0000000001:1 = -200 dB.

The dB value does not have units. If a number A is 100 times greater than another number B, then on the log scale we can say that A is 20*Log₁₀(100) = 40 dB greater than B.

Example calculation

Let’s say an operational amplifier increases the input signal voltage by a factor of 100. The ratio of output to input is 100:1. Using the calculator, we can say that it is a 40 dB amplifier.

Why Convert to dB?

There are a few reasons for this. Here are a couple of main ones:

• the dB scale makes it easy to represent large and small ratios in fewer digits. For example a voltage ratio of 10000000 = 140 dB
• When making calculations in Radio Frequency systems such as calculating the gain in a transmitter chain, it’s easy to add and subtract gain and attenuation expressed in dB. For example, consider a signal chain consisting of two amplifiers with gain levels 10 and 15 dB and a 3 dB insertion loss equates to a total gain of 22 dB. RF component vendors specify gain and attenuation in dB so it’s easy to get these numbers from a data sheet and even do the arithmetic mentally (if there are a small number of components). Operating in the linear regime means you have to multiply and divide. It’s much more difficult to do this in your head, unless you’re a super math nerd ????.