# System Design Tools

#### db Power Ratio

This calculation will give you the ratio, in decibels, between two power values. For example, you can calculate the difference in dB between two amplifiers with different power output specifications.

Enter any two values and press "Calculate" for the remaining value.

Equation used to calculate the data:

** dB = 10 * Log (Pout / Pin)**

#### db Voltage Ratio

This calculation will give you the ratio, in decibels, between two voltages. For example, you can calculate the gain needed to raise the output level from 0.775 volts to 1.4 volts. You can also use this to calculate how much attenuation you need if, for instance, you have a 2.0 volt input level and you need to attenuate it to 0.2 volts to prevent input overload.

Enter any two values and press "Calculate" for the remaining value.

Equation used to calculate the data:

**dB = 20 * Log (Vout / Vin)**

#### Amplifier Power Required

This calculator provides the required electrical power (power output from the amplifier) to produce a desired Sound Pressure Level (SPL) at a given distance, along with an amount of headroom to keep the amplifier(s) out of clip.

Example: You are designing a system where the farthest listening position from the loudspeaker is 100 meters, and the desired Sound Pressure Level is 85 dB SPL The loudspeaker chosen for the job has a sensitivity rating of 95 dB. With the minimum recommended amplifier headroom of 3 dB, then you need to choose an amplifier that can supply at least 1,995 watts to the loudspeaker.

Equations used to calculate the data:

**dBW = Lreq - Lsens + 20 * Log (D2/Dref) + HR**

**W = 10 to the power of (dBW / 10)**

*Where:*

**Lreq** = required SPL at listener

**Lsens** = loudspeaker sensitivity (1W/1M)

**D2** = loudspeaker-to-listener distance

**Dref** = reference distance

**HR** = desired amplifier headroom

**dBW** = ratio of power referenced to 1 watt

**W** = power required

#### Inverse Square Law

This calculation will give you the amount of attenuation, in decibels, you can expect with a change in receiver distance, in a free field (outdoors).

For example if you were standing 20 feet from a loudspeaker, and were to move to 40 feet away from that loudspeaker, you would expect to see a drop in level of 6 dB. Sound that is radiated from a point source drops in level at 6 dB per doubling of distance.

Equation used to calculate the data:

**Snew = Sref + (20 * Log (Dref / Dnew))**

*Where:*

**Dref** = Reference Distance

**Dnew** = New Distance

**Sref** = Reference Sound Level

**Snew** = New Sound Level

#### Line Loss

This calculator provides line loss with 2-conductor cable on a constant voltage line.

Equation used to calculate the data:

**Ploss = 10 * Log [1 - ((2 * RL) / (2 * RL + (Vline squared / Prated))]**

**RL = (Rref / 1000) * D**

*Where:*

**D** = length of wire used

**Ploss** = power loss in dB

**Prated** = power driven on line

**RL** = wire guage resistance

**Vline** = voltage on line

#### Ohm's Law / Watt's Law

Ohm's Law states the relationship between current, voltage and resistance. Watt's Law states the relationships of power to current, voltage and resistance.

Enter any two known values and press "Calculate" to solve for the others.

Equations used to calculate the data:

**V = IR**

**P = VI**

*Where:*

**I** = current

**P** = power

**R** = resistance

**V** = voltage

#### "Constant Voltage" Transformer Delivered Power

Many people don't realize that a transformer labeled for use with a specific voltage will work just as well at other voltages. This calculator provides power delivered from a transformer tap when driven with other than the rated voltage.

Example: You are installing a distributed system with very long lines. To overcome line loss, you select a 140 volt system. Which transformer tap will feed 10 watts to a loudspeaker with a 70V transformer?

Enter values for "Voltage Rating of Transformer", "New Voltage", and "Power Rated".

Equation used to calculate the data:

**Pactual = (Vnew squared / Vrated squared) * Prated**

*Where:*

**Prated** = transformer tap value

**Pactual** = new power from tap

**Vrated** = voltage rating of transformer

**Vnew** = new voltage