www.paformusic.info Calculations |
This page provides some formulae for general audio-related calculations, however for all calculations involving decibels see the Decibels page.
Below the general formulae on this page are calculators for these electrical calculations useful in audio work:
- Parallel resistors
- Resistive dividers
- Series capacitor low-cut filters
- Parallel capacitor hi-cut filters
The symbols and units used in the formulae below are:
- I for DC or RMS current in amps
- V for DC or RMS voltage in volts (the symbol U may elsewhere be used in place of V)
- R for resistance in ohms
- P for power in watts
- p for pressure in Pascals
- VA for apparent power in volt-amps
- dB for decibels
- f for frequency in Hz
- Z for impedance in ohms
- X for reactance in ohms
- C for capacitance in farads
- L for inductance in henrys
- v for velocity in metres per second
- T for temperature in degrees Celsius
- t for time in seconds
- d for distance in metres
- λ for wavelength in metres
- The subscript '_{ref}' indicates a reference value.
Ohm's Law | ||
V = IR | I = V / R | R = V / I |
Series resistance | ||
R_{total} = R1 + R2 + R3 ... | ||
Parallel resistance − calculators are available here | ||
R_{total} = 1 / [(1 / R1) + (1 / R2) + (1 / R3) + ...] | ||
Overall impedance of identical items (e.g. speakers) wired in parallel (typically, by daisy-chaining) | ||
Z_{overall} = Z_{one item} / number of items | ||
Resistive divider
(unbalanced
attenuator)
− a calculator is available
here R_{upper} is the resistance connecting the input to the output. R_{lower} is the resistance connecting the output to signal earth. Zero source impedance and infinite load impedance are assumed. |
||
V_{out} = V_{in} R_{lower} / (R_{lower} + R_{upper}) | ||
Reactance of capacitors and inductors | ||
X_{C} = 1 / (2 π f C) | X_{L} = 2 π f L | |
3 dB cut-off frequency of simple RC filters − see these calculators | ||
f = 1 / (2 π R C) | ||
Power (when voltage and current are DC or are in phase) | ||
P = IV | I = P / V | V = P / I |
P = V^{2} / R | V = sqrt(PR) | R = V^{2} / P |
P = I^{2}R | I = sqrt(P / R) | R = P / I^{2} |
Apparent power | ||
VA = IV | I = VA / V | V = VA / I |
Decibels (power ratios) − click here for value converters | ||
dB = 10 log_{10} (P / P_{ref}) | P = P_{ref} 10^{(dB / 10)} | |
Decibels (voltage ratios) − click here for value converters | ||
dB = 20 log_{10} (V / V_{ref}) | V = V_{ref} 10^{(dB / 20)} | |
Decibels (pressure ratios) − click here for value converters | ||
dB = 20 log_{10} (p / p_{ref}) | p = V_{ref} 10^{(dB / 20)} | |
dBV & dBu − follow the links for information & value converters | ||
dBV = 20 log_{10} V | dBV = dBu − 2.2 | V = 10^{(dBV / 20)} |
dBu = 20 log_{10} (V / 0.775) | dBu = dBV + 2.2 | V = 0.775 x 10^{(dBu / 20)} |
dB SPL − follow the link for information & value converter | ||
dB SPL = 20 log_{10} (p / 20E−6) | p = 20E−6 x 10^{(dB SPL / 20)} | [20E−6 means 20 x 10^{−6}] |
Dynamic range (DR),
signal-to-noise
ratio (SNR) &
headroom of equipment (all in dB) |
||
DR = SNR + headroom | SNR = DR − headroom | headroom = DR − SNR |
For microphone noise levels see
Types of
Noise Specification on the Microphones page |
||
Octaves | ||
number of octaves = 3.322 log_{10} (f / f_{ref}) | ||
Velocity (speed) of sound in air | ||
v
≅ 331 + 0.6T (≅ 343 at 20ºC) |
||
Propagation time | ||
t
= d / v |
||
Wavelength | ||
λ
= v / f |
f
= v / λ |
v = fλ |
UK UHF channel number (N) and frequency | ||
N.B. f here is in MHz. | ||
channel N starts at f = 8N + 302 |
channel N ends at f = 8N + 310 |
N
= (f − 302) / 8 ignore decimal part |
When calculating N, if (f − 302) / 8 has
no decimal part then f lies exactly on the boundary between channels (N − 1) and N. |
Parallel resistance calculator:
Use the first line for 2 resistances in parallel, OR the
second line for 3 resistances in parallel.
Enter the known values in the relevant R1 / R2 / R3 boxes
and click '=' to get the calculated value.
Use consistent units for each calculation − e.g.
all ohms, all kilohms or all megohms.
Use the following calculator in the case where a second resistor will be connected in parallel with a known existing one, and it is required to determine what value this second resistor needs to be in order to give a required total resistance. In practice, as resistors come in standard values (see Tolerance), after using the calculator below the second resistor will need to be selected as being the closest available value. The calculator above can then be used to determine the actual total value that would be obtained using that value.
Enter the required total value and the known resistor's value in the Total and R1 boxes respectively, and click '=' to get the calculated second resistor value.
The Total value entered must be less than the R1 value. Use consistent units for each calculation − e.g. all ohms, all kilohms or all megohms.
Resistive divider calculator:
This gives the output voltage of
a simple unbalanced resistive
divider (attenuator),
for a given input
voltage.
The change of level in dB
(see Loss) is also calculated.
This type of attenuator is appropriate for
voltage-matched
interconnections; it is not suitable for
impedance-matched
interconnections. Note that the
power rating of the
resistors used must be adequate
for the actual voltages involved.
Enter the known values in the three
left-most boxes and click '=' to get the
calculated values. (If you are only interested in the
dB loss then enter any random value for V in.)
'Upper R' is the resistance connecting the input to
the output. 'Lower R' is the resistance connecting the
output to signal earth.
This calculator assumes a zero
source impedance and
infinite load impedance.
In the case of a resistive source impedance, first add its value
to the upper resistor value. In the case of a resistive load
impedance, first calculate the parallel value of that impedance
and the lower resistor value (see the previous calculator).
Use consistent resistance units for each calculation −
e.g. both ohms, both kilohms or both megohms.
Balanced attenuators employ identical-value series resistors in each leg, followed by a parallel resistor between the two legs. For these attenuators, enter twice the value of each single series resistor in 'Upper R' and the actual value of the parallel resistor in 'Lower R'.
Series capacitor low-cut calculators:
These are calculators for simple series-capacitor
low-cut
filters, such as are formed
by a coupling capacitor at the input or output of an
amplifier, or between an amplifier's internal
stages. They are accurate
only when both the source impedance and the load impedance
are purely resistive.
Enter the known values in the left-most boxes
and click '=' to get the calculated value(s).
'Source R' is the resistive
source impedance
feeding the filter, including any intentional series
resistance, in ohms.
'Load R' is the resistive
load impedance
being fed from the filter, including any intentional
parallel resistance, in ohms.
'C' is the value of the capacitor in µF (microfarads).
'f' is the frequency in Hz.
This calculates the
cut-off frequency.
The frequency calculated is that at which the level
into the specified load has fallen by 3 dB from
the level obtained at frequencies well above the
cut-off frequency.
This calculates the loss in dB at a given frequency. Two values are calculated. The 'relative loss' is the loss provided by the filtering action alone − i.e. the additional loss relative to that obtained at frequencies well above the cut-off frequency. The 'total loss' figure includes the basic loss introduced by the attenuating effect of the resistive source and load impedances. (Remember that units are ohms, µF and Hz.)
Parallel capacitor high-cut calculators:
These are calculators for simple parallel-capacitor
high-cut
filters, such as are often used to form
a basic RF filter at the input of an
amplifier, or by unintentional cable capacitances. They are accurate
only when both the source impedance and the load impedance
are purely resistive.
Enter the known values in the left-most boxes
and click '=' to get the calculated value(s).
'Source R' is the resistive
source impedance
feeding the filter, including any intentional series
resistance, in ohms.
'Load R' is the resistive
load impedance
being fed from the filter, including any intentional
parallel resistance, in ohms.
'C' is the value of the capacitor in µF (microfarads).
'f' is the frequency in Hz.
This calculates the
cut-off frequency.
The frequency calculated is that at which the level
into the specified load has fallen by 3 dB from
the level obtained at frequencies well below the
cut-off frequency.
This calculates the loss in dB at a given frequency. Two values are calculated. The 'relative loss' is the loss provided by the filtering action alone − i.e. the additional loss relative to that obtained at frequencies well below the cut-off frequency. The 'total loss' figure includes the basic loss introduced by the attenuating effect of the resistive source and load impedances. (Remember that units are ohms, µF and Hz.)
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This page last updated 14-Jul-2020.