Interpretation of electroacoustic calculation formulas commonly used in sound reinforcement systems

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(1 ) Calculation of maximum power capacity and maximum voltage capacity

Formula 1: Maximum voltage capacity V = √ maximum power W × load impedance Ω

Formula 2: Maximum power capacity W = maximum voltage V2 × load impedance Ω

If you know the maximum continuous power (AES/ANSI) of a speaker and the indicated load impedance, you can calculate the maximum voltage of the speaker. For example, the maximum power of the A speaker is 600WRMS (ES/ANSI) and the impedance is 8Ω. The system's compressor or speaker controller sets the maximum output voltage value of the amplifier, protects the A speaker, and puts the relevant data into the formula one:

Maximum voltage capacity V=√600W×8Ω

=√4800

=69.28V

It is concluded that the voltage of 69.28V plus the load impedance of 8Ω can generate a maximum of 600WRMS, so we must set the maximum output voltage of the amplifier to not exceed 69.28V on the compressor or the speaker controller to effectively protect A. The speakers will not burn out.

(2 ) Calculation of power amplifier voltage gain

Equation 3: Voltage gain = output voltage V / input voltage V

The gain is determined by the relationship between the input and output of the audio circuit. The gain is expressed as a multiple (×) or in dB. If we want to know the gain of a power amplifier (called voltage gain), we must know the input signal. Ping its corresponding output signal level. For example, it is known that the signal level input from the preamplifier of the system to the A power amplifier is 0.775V, and the output signal is 31V. The relevant data can be put into the formula 3 to know the voltage gain of the A power amplifier:

Voltage gain = output voltage V / input voltage V

=31V/0.775V

=40×(times)

For example, it is known that the signal level input from the front stage of the system to the B power amplifier is 0.5V, and the output signal is 20V. The voltage of the B power amplifier can also be known by putting the relevant data into the formula 3.

Voltage gain = output voltage V / input voltage V

=20V/0.5V

=40×(times)

Note that from the above two examples, it can be seen that the voltage gains of the two amplifiers A and B are 40×, so the voltage gain is independent of the input signal.

(3 ) Input sensitivity and voltage gain

Formula 4: Input sensitivity V = maximum voltage capacity V / voltage gain ×

Contrary to customary beliefs, amplifiers cannot generate power by themselves. The power amplifier amplifies the input signal level by a certain multiple output. The level of the output is determined by the amplification factor. The standard statement should be: the output voltage of the power amplifier drives the load impedance of the speaker and thus converts it into electro-acoustic power. Professional Audio. The maximum input voltage that a power amplifier can accept is also called input sensitivity. If the input voltage exceeds the maximum input voltage, the output capacity of the amplifier will exceed the maximum range and generate large frequency response distortion. So if you divide the maximum voltage capacity by the voltage gain, you can get the maximum input voltage (input sensitivity). For example, the A power amplifier is connected to the A speaker, and the related parameters of the two are as follows:

A power amplifier: FTC power 550W@8Ω, voltage gain 40 times; A speaker: 600WRMS (AES/ANSI), impedance 8Ω (the power of the speaker is 50W higher than the power amplifier).

Calculation Step 1: Calculation of the maximum voltage capacity of the A power amplifier

A power amplifier maximum voltage capacity V = √ 550W × 8Ω

=√4400

=66.33V

Calculation Step 2: Input Sensitivity Calculation of A Power Amplifier

A power amplifier input sensitivity V = maximum voltage capacity V / voltage gain

=66.33V/40×

=1.65V (maximum input limit threshold)

Calculation result: When the A is placed at 1.65V, the output voltage is 66.33V. When the impedance is 8Ω, it is equivalent to 550W, which means that if we want to avoid over-driving the A, we should avoid the input voltage. Reach 1.65V (the maximum input limit threshold for this system). Professional Audio. We can be sure that after the A amplifier has a limit circuit with a limit of 1.65V (speaker processor or digital divider), the input of the A amplifier will not exceed 1.65V. Therefore, when the speaker processor or digital crossover outputs 1.65V to A power amplifier, A power amplifier will output 66.33V to the speaker (66.33V=550W@8Ω), if the speaker processor or digital divider output is greater than 1.65V Voltage to the amplifier will cause the amplifier to be distorted and output a larger voltage, and will be converted into greater power and coil heat, which is likely to cause damage to the speaker. In order to protect the speaker, the limit threshold of the speaker processor or digital divider needs to be set at 1.65V (6.5dBu).

Another example is the connection between the A power amplifier and the B speaker. The relevant parameters of the two are as follows:

A power amplifier: FTC power 550W@8Ω, voltage gain 40 times; A speaker: 400WRMS (AES/ANSI), impedance 8Ω (the power of the speaker is 150W lower than the power amplifier).

Calculation Step 1: Calculation of the maximum voltage capacity of the B speaker

B speaker maximum voltage capacity V = √ 400W × 8Ω

=√3200

=56.56V professional audio.

Calculation Step 2: Input Sensitivity Calculation of A Power Amplifier

A power amplifier input sensitivity V = maximum voltage capacity V / voltage gain

=56.56V/40×

=1.41V (maximum input limit threshold)

Calculation result: When the input power is 1.41V, the output voltage is 56.56V. When the impedance is 8Ω, it is equivalent to generating 400W, which means that if we want to avoid exceeding the maximum power of the speaker, we should avoid it. The amplifier input voltage reaches 1.41V (the maximum input limit threshold for this system). Professional Audio. We can be sure that after the A amplifier has a limit circuit with a limit of 1.41V (speaker processor or digital divider), the input of the A amplifier will not exceed 1.41V. Therefore, when the speaker processor or digital divider outputs 1.41V to A power amplifier, the A power amplifier will output 56.56V to the speaker (56.56V=400W@8Ω), if the speaker processor or digital divider output is greater than 1.41V Voltage to the amplifier will cause the amplifier to output a larger voltage to the speaker, and will translate into a larger distortion of the speaker and coil heat, which is likely to cause damage to the speaker. In order to protect the speakers, the limit threshold of the speaker processor or digital divider needs to be set at 1.41V (5.19dBu).

(4 ) Level control of the power amplifier

In the above example, the level control volume of all amplifiers is assumed to be at the maximum position (0dB attenuation). When the power discharge level adjustment knob changes, the input sensitivity and voltage gain of the power amplifier will also change. When the level control of the amplifier is reduced, the voltage gain is reduced and the input sensitivity is increased.

(5 ) Matching of power capacity

The AES/ANSI short-term peak power capacity of a speaker allows for more than 6dB of continuous power capacity, which means that the peak power is four times the continuous power. For example, if a speaker has a continuous power of 100W, its peak power is 400W.

Similarly, the continuous FTC power capacity of a power amplifier allows its peak to exceed 3dB of continuous power, which means that one amplifier allows its peak power to be twice the continuous power. For example, if the continuous power is 100W, its peak power is 200W.

Therefore, if a power amplifier can provide 400W peak power, its continuous FTC power is required to be 200W. In other words, if the amplifier is to reach the peak power capacity of the speaker, the continuous FTC power of the amplifier is required to be twice the continuous power of the speaker.

For example, if the ASE/ANSI continuous power of the C speaker is 300W, its peak power is 1200W (300W×4). If the power amplifier requires 1200W peak power, the power amplifier requires 600W (600W×2) continuous FTC power. ), from this: ASE / ANSI continuous power capacity of 300W speakers, the need for FTC continuous power 600W amplifier to drive.

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