Db Per Decade Calculator

The dB Per Decade Calculator helps engineers, scientists, and technicians calculate the gain or loss of a system over a 10× change in frequency. This measurement is crucial in electronics, signal processing, and control systems, where understanding how power or amplitude changes over frequency is essential.

This calculator is widely used for:

• Filter design (low-pass, high-pass, and band-pass filters)
• Frequency response analysis in circuits and systems
• Bode plot interpretation for gain and attenuation calculations
• Understanding amplifier and signal behavior over a range of frequencies

Formula for Db Per Decade Calculator

The formula used for calculating decibel change per decade depends on whether the calculation involves voltage, current, or power.

1. dB Per Decade for Voltage or Current Gain

When dealing with voltage gain, current gain, or amplitude, use:

dB per Decade = 20 × log10(Gain Ratio per Decade)

Where:

• Gain Ratio per Decade = Output/Input ratio over a 10× frequency change
• log10 = Base-10 logarithm

2. dB Per Decade for Power Gain

For power calculations, use:

dB per Decade = 10 × log10(Power Ratio per Decade)

Where:

• Power Ratio per Decade = Output/Input power ratio over a 10× frequency change

These formulas allow users to accurately determine gain or loss trends in electronic systems, making them essential for circuit design and signal processing applications.

Reference Table – Common dB Per Decade Values

To simplify dB per decade estimations, here is a reference table for commonly used gain ratios:

Gain Ratio Per Decade	dB Per Decade (Voltage/Current)	dB Per Decade (Power)
0.1 (10% reduction)	-20 dB	-10 dB
0.5 (50% reduction)	-6.02 dB	-3.01 dB
1.0 (No change)	0 dB	0 dB
2.0 (2× increase)	+6.02 dB	+3.01 dB
10.0 (10× increase)	+20 dB	+10 dB

This table allows engineers, signal processors, and system designers to quickly estimate dB per decade values without manual logarithmic calculations.

Example of Db Per Decade Calculator

1. Calculate dB Per Decade for a Voltage Gain of 5×

Using the voltage formula:

dB per Decade = 20 × log10(5)
dB per Decade ≈ 20 × 0.699 ≈ 14 dB

This means the voltage gain increases by 14 dB per decade.

2. Calculate dB Per Decade for a Power Gain of 2×

Using the power formula:

dB per Decade = 10 × log10(2)
dB per Decade ≈ 10 × 0.301 ≈ 3.01 dB

This means the power gain increases by 3.01 dB per decade.

Most Common FAQs