This tool is designed to convert power ratios to decibel

### Output

### Overview

Power ratios are presented in decibels to avoid handling very small or very large values. This calculator will help you convert power ratios to decibels. Take note that you can choose between milliwatts or watts for both the input and output power.

### Equation

$$Ratio_{dB} = 10 log(\frac{P_{out}}{P_{in}})$$

Where:

$$P_{out}$$ = output power in watts or milliwatts

$$P_{in}$$ = input power in watts or milliwatts

### Applications

Power ratios are common in electronics engineering, especially when handling amplifiers and other active devices. An amplifier's gain is the ratio of the power at its output to the power at its input. Naturally in an amplifier, the output power is higher than the input power so the ratio is greater than one. In decibels, this would be a positive number. If the ratio is less than one, it is considered a loss. A loss in decibels is a negative value. Losses are generally undesirable in RF technology but there are instances where a loss is inserted in the circuit to "attenuate" power.

Decibels are handy in presenting very small or very large ratios. For example, the ratio 100000000/100 would be presented as 1000000. In decibels, this would be just 60 dB. Another example is the ratio 0.0001 which is equal to -4 dB.

If there are two or more amplifiers connected in cascade, you can compute their overall gain. If the gains are presented in ratio, the overall gain can be calculated by multiplying the individual gains of the amplifiers. If the gains are presented in decibels, the overall gain is the sum of the individual gains. This is true for calculating the total losses in a circuit. This makes calculations easier and is one of the reason why ratios are often presented in decibels in electronics engineering.

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