How to Convert Vpp to dBm

Audio volume levels are sometimes referenced to the decibel (dB).

The conversion of Vpp (volts peak-to-peak) to dBm (decibels milliwatt) is a common practice in electronics, especially in communication technology. Vpp is a measurement of the size (amplitude or volume) of an electronic signal's sine wave, from the highest point of the wave to the lowest point. The decibel is a logarithmic measurement of the power (strength) of an electronic signal, and it is scaled to the milliwatt (dBm) when the signal is small, or low in power. Converting from Vpp to dBm is a way of determining how much power a certain signal voltage can produce. The conversion can be done with a reference table or through calculation, with a few mathematical formulas.

Things You'll Need

• Scientific calculator
• Electronic device specs
• dBm-to-voltage conversion chart

Instructions

Finding Reference Voltage

1. Obtain the impedance value of the electronic device. Standard values are 50 ohms, 75 ohms and 600 ohms. The number may be listed in the specifications or directly on the device, as "impedance."

2. Locate the zero-dBm reference voltage that matches the impedance of the device. If you are using a conversion chart, the number is listed next to "0 dBm" in the column for 50 ohms, 75 ohms or 600 ohms.

3. Calculate the reference voltage with the dBm power formula (V = square root of P*R), if you don't have a chart or if the impedance is not a standard value. For a 50 ohm device, use a value of 50 for R and .001 for P (milliwatt reference). Solve for V (V = sqrt .001 * 50, V = sqrt .05, Vrms = .224). Note that the resultant voltage is in Vrms (volts root-mean-square).

Calculating dBm

1. Convert Vpp to Vp (volts peak). Divide Vpp by 2 to get Vp (Vpp/2 = Vp). Use a value of .800 for Vpp, as an example (.800/2 = .4, Vpp = .4).

2. Convert Vp to Vrms. Multiply Vp by .707 to get Vrms (Vrms = Vp * .707, Vrms = .4 * .707, Vrms = .283).

3. Locate the dBm level for the calculated Vrms voltage, on the conversion chart, if the specific Vrms value is listed.

4. Calculate dBm, if Vrms is not listed, by using the dBm voltage formula (dBm = 20 * log10 * V2/V1). Use the converted Vrms number (.283) for V2 and use the zero-dBm reference (.224) for V1. Solve for dBm (dBm = 20 * log10 *.283/.224, dBm = 20 * log10 * 1.263, dBm = 20 * .1014, dBm = 2.028).

5. Compare the dBm figure to the listings on the conversion chart. For the impedance value, it should fall within the range of the listed dBm levels.

Tips & Warnings

• Make sure that the zero-dBm value matches the impedance value (50, 75, 600 or other).

• Make sure that both voltages (V2 & V1) are in Vrms.

• In the equations, perform multiplication and division first, before performing log or square root calculations.

• The '10' next to Log means that it is a base-10 logarithm. Generally, it is the "LOG" key on the calculator (consult the calculator manual).

• A conversion chart is recommended, as a guideline for these conversions. For instance, the chart provided by Tecmag Inc, "dBm -- Voltage Chart," lists specific Vpp to dBm values for a 50 ohm impedance.

References

• InfoComm IQ: Understanding and Measuring Digital Audio Levels
• Mini-Circuits: dBm - Volts - Watts Conversion
• "Modern Electronic Communication"; Jeffrey S. Beasley and Gary M. Miller; 2006

Resources

• Tecmag: dBm - Voltage Chart
• University of North Carolina: How Many? A Dictionary of Units of Measurement