Technology Brief Understanding Relationships Voltage-Current-Impedance

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Technology Brief: Designing for Great Performances
Appendix
1: To nd the maximum speaker power use the equation:
DB
SPL
= dB
SPL
/W/M + 10log(P
NOM
/ 1W) - 20log(d
METERS
/ 1M)
To nd the required nominal speaker power PNOM use the equation:
P
dB-NOM
= DB
SPL
+ 20log(d
METERS
/ 1M) - dB
SPL
/W/M.
P
NOM
= 10^(P
dB-NOM
/10)
2: Ohm’s law is a denition based on observations made by German
physicist Georg Ohm in the early 1800s. He measured current ow
(I) through various conductors as different voltages V, were applied.
Ohm found that the ratio of voltage to current (V/I) was always the
same for the same material. Today we call that ratio resistance,
measured in ohms and expressed as R = V / I. With a little algebra we
can rewrite the equation as V = I R or I = V / R. A second denition
concerns the power dissipated in a resistance. Power in watts is
dened as P = V I, the product of voltage times current. We can
use the Ohm’s law forms of V = I R or I = V / R to substitute into
the power denition for alternate power expressions P = I2 R and
P = E2 / R, or rearranging, I = SQRT (P / R) or E = SQRT (P R)
3: For a sinewave, V
PEAK
= 1.414 V
RMS
. For music, V
PEAK
is typically 3
to 10 times V
RMS
corresponding to +10 to +20 dB of headroom.
Voltage ratios and Gain ratios are often described in decibels. Most
often the voltage ratio, dBu, is given by the following denition:
dBu = 20log(V
RMS
/ 0. 775v).
Gain ratios are usually expressed as: dB = 20log(V
OUT
/ V
IN
)
4: We use I = SQRT (P / R) or E = SQRT (P R) to calculate RMS
voltage and current. Peak values are (1.414 x RMS).
5: If you want to limit the power to the speaker or ‘P
MAX
’ use the
equation:
V
RMS
= SQRT (P
MAX
R
LOAD
) to set the amplier output VPL voltage
protection limiter control or V
LIMIT
to V
RMS
(or VPK = 1.414 V
RMS
) to
protect the speakers.
The output voltage V
RMS
value corresponds to a dBu value of
dBu
OUT
=20log(V
RMS
/ 0.775). Set the amplier Gain control to
produce this level for 10 dBu input as given by GdB= dBu
OUT
– dBu
IN
.
Alternately, we can map 0 dBu input to V
NOM
to exchange V
NOM
for
V
RMS
, now using the voltage limiter to control nominal output instead
of maximum output.
Item no. DPA-CS_v3 - 25.04.16