# dBm to RMS Voltage Calculator, Formula, dBm to RMS Voltage Calculation

## dBm to RMS Voltage Calculator:

Enter the values of impedance, Z(Ω) and power level of dBm to determine the value of RMS voltage, Vrms(V).

 Enter Impedance: Ω Enter Power Level: dBm Result – RMS Voltage: V

## dBm to RMS Voltage Formula:

dBm to RMS voltage conversion is an essential concept in electrical engineering, especially in fields like telecommunications and audio engineering.

This conversion allows you to understand the root mean square (RMS) voltage corresponding to a power level expressed in dBm, a logarithmic unit that represents power relative to 1 milliwatt.

The formula involves the impedance (Z) of the circuit and the dBm value. Understanding this conversion is crucial for accurate signal processing and circuit design.

RMS voltage, Vrms(V) in volts equals the multiplication of square root of ratio of impedance, Z(Ω) in ohms and 1000 by ten raise to the power of dBm divided by 20.

RMS voltage, Vrms(V) = √(Z(Ω) / 1000) * 10(dBm/20)

Vrms(V) = rms voltage in volts, V.

Z(Ω) = impedance in ohms, Ω.

dBm = power level in dBm.

### dBm to RMS Voltage Calculation:

1. Calculate the RMS voltage for a signal with a power level of 30 dBm and an impedance of 50 ohms:

Given: Z(Ω) = 50 Ω, dBm = 30.

RMS voltage, Vrms(V) = √(Z(Ω) / 1000) * 10(dBm/20)

Vrms(V) =√( 50 / 1000) * 10(30/20)

Vrms(V) = √0.05 * 101.5

Vrms(V) = 0.224 * 31.62

Vrms(V) = 7.08V.

1. Suppose the RMS voltage is 0.867V for a signal is needed for a power level of 10dBm. Calculate the impedance.

Given: Vrms(V) = 0.867V, dBm = 10.

RMS voltage, Vrms(V) = √(Z(Ω) / 1000) * 10(dBm/20)

Z(Ω) = 1000 * (Vrms(V) / 10(dBm/20))2

Z(Ω) = 1000 * (0.867 / 10(10/20))2

Z(Ω) = 1000 * (0.867 / 100.5)2

Z(Ω) = 1000 * (0.867 / 3.162)2

Z(Ω) = 1000 * 0.075

Z(Ω) = 75 Ω.

### Applications and Considerations:

• Telecommunications: Converting dBm to RMS voltage is critical for signal strength analysis and transmission line design.
• Audio Engineering: Understanding RMS voltage from dBm helps in designing and calibrating audio equipment.
• Instrumentation: Accurate dBm to RMS voltage conversion is essential for measurement and instrumentation accuracy.