Class #2 DECIBELS
The Decibel The db is a logarithmic unit used to describe a ratio (between two sound pressure levels, power levels, voltages, currents, and many others). We use the terms gain or loss. it is not an absolute value measurement!
Basic Math of the decibel Exponents N e a symbol to denote the power to which a number is raised ú N e = N x N (e- 1 times) Logarithm the exponent to which a base number has to be raised in order to equal a given number ú Log 10 N = the exponent to which 10 (the base number) has to be raised to equal N ú Example: Log 10 1000 (or sometimes just Log 1000) = 3, because 10 3 (10x10x10)= 1000
A Logarithmic Scale db values are on a logarithmic scale. A logarithmic scale is a scale of measurement that uses the logarithm of a physical quantity instead of the quantity itself. ú The green line linear scale ú Blue - logarithmic scales ú Red exponential scale Why use a db scale? It allows reducing the scale of values Ex. The two extremes of sound level (barely audible and permanent ear damage) could be described as: SPL difference: 100,000,000 20 mp = 99,999,980 mp (meaningless) SPL ratio: 100,000,000 /20 mp = 5,000,000 (too large a scale) db: 134 db (manageable and better represents the human perception of loudness)
Power Ratios The Bel was devised in the 1920s by the Bell laboratories to quantify the reduction in audio power over the phone lines. As the Bel turned out to be too large a unit its tenth (the decibel) has been more commonly used: Therefore, the formula used to quantify power ratios is db = 10Log (P2/P1) Ex. ú A power ratio of 2:1 is only 0.3 Bel: Log (P2/P1) ú The same ratio is 3 db: 10Log (P2/P1)
Voltage and Current Ratios When quantifying EMF (voltage) or current with db, the formula must be modified to maintain other basic relations between power, voltage, and current (P=EI and I=ER) Therefore the correct formula is: db = 20Log(E 2 /E 1 ) for voltage ratios db = 20Log (I 2 /I 1 ) for current ratios Voltage and current ratios of 2:1 are 6dB
Basic electricity terminology Charge (Coulombs) Conductor/insulator Current (Amperes) Resistance (Ohms) Potential (Volts) also called EMF, tension or voltage Power (Watts) DC and AC
Exercise A 2V signal goes into the input of an amplifier and comes out as 50V at the output. What is the gain in decibels? 20Log(50/2)= 20 x log 25 = 28 db The amplifier is said to have a voltage gain of 28 db
Power & tension ratios
db for absolute measurements When describing an absolute value (not a ratio between two), then an absolute reference value must be given. Ex. dbm a power measurement with 1 mw as reference: ú dbm = 10Log (P / 1mW) Exercise: what is the dbm value of a 100W radio transmitter? 10Log(100/0.001) or 10Log 100000 = 50 dbm What is the dbm value of a 50W transmitter? ú Remember how many dbs denote power ratio 2:1?
Other Absolute db References VU (Volume Unit) also a power ratio scale but with machine- specific reference point; it may as well be 1 mw (like dbm) but could also be measured in magnetic flux in tape recorders for example (0 VU in one example is 250 nanowebbers/meter) ú 0VU needs to be calibrated to the nominal signal level (+4 dbu) dbu (previously called dbv) = 20Log(E/ 0.775 Volts) dbv = 20Log(E/ 1Volt) dbfs (Full Scale) a voltage scale converted from the digital domain relative to the maximum amplitude possible (FS represented with 0 dbfs) ú the highest voltage level (when converted to an analog signal) therefore is represented with 0 db, ú Its half would be - 6dB
Standard Nominal Levels (0 VU) Broadcasting: + 8 dbu (1.95 V) Pro Studio: + 4 dbu ( 1.23 V) Semi- pro Studio : - 10 dbv (0.316 V) ú Let s convert it to dbu for comparison: ú - 10dBV = 20xLog(X/1V) ú - 0.5=log X ú X= 0.316V ú In a dbu scale, the reference is 0.775 volts ú X (dbu) = 20Xlog (0.316/0.775) ú - 10dBV = - 7.8 dbu (which is around 12 db lower than +4dBu)
db SPL (Sound Pressure Level) The measure of acoustic pressure. An absolute db measurement with the reference of 20 µp (air pressure) the quietest audible sound (like a mosquito buzz about 3 meters away) db SPL = 20Log (SPL/ 20 µp) 0 db SPL: threshold of hearing: just audible (it is not silence) 130 db SPL: The threshold of pain (approx. 100 Pascal)
Sound Level Meter
db SPL (sound pressure level) A 10 db increase in SPL is somtimes considered by listeners to be about twice as loud. This is different from one listener to another and in differnet areas of the spectrum (see next slide)
Fletcher- Munson curve The human hearing is not flat (responsive to all frequencies equally): This responsiveness is also dependant on levels At about 100 db the human hearing is closest to being flat 1 phon is equal to 1 dbspl at a frequency of 1 khz
Weighting For each frequency range the type of ratio is different (each frequency would theoretically need a different db scale) dba a weighted db scale less sensitive to low and high frequencies (like the human hearing) dbc Like the A weighting, but optimized for higher levels (weighted in the midrange with somewhat better response to highs and lows than dba)
Weighted curves
BASIC ELECTRICITY
Charge (Coulombs) Charge is the basic property possessed by electrons and protons Charge can be negative or positive In general atoms have the same amount of protons and electrons and are therefore neutral in their natural state Only when electrons are added or taken out, does an object become electrically charged. Charge is measured in Coulombs 1 coulomb = the charge of 1 ampere that happens in one second (6.241 10 18 electrons)
Conductance Conductor a substance with low resistance to electron movement, allowing its outer electrons (normally 1 or 2) to move to the next atom (metals, mineral water) Insulator a substance with very high resistance to electron movement, due to its tightly bound atomic structure (ceramics, rubber, plastic, pure water)
Current (Amperes) Current - a flow of charge (the movement of electrons) through a conductor The current is measured in rate of electronflow per time interval (I=charge/time); the units used are Amps (Ampere) 1 Ampere = 1 Coulomb per second (6.241506 x 10 18 electrons - approx. 6 quintillion electrons) 1 Amp is roughly the current that a 100W standard home-use light bulb uses. Current is dependent on EMF (voltage) and resistance (the opposition to conductance); I = V/R
Resistance (Ohms) For a given potential, low resistance will result in a higher current Material - good conductors have low resistance; insulators have high resistance Size thicker wire has less resistance Temperature lower temperatures allow better conductance (lower resistance) Resistance is measured in Ohms = volts/amps The resistance results from a collision of moving electrons with atoms and it generates heat (this is used in light bulbs, toasters, and other resistive devices.)
Potential (Volts) Voltage an electromotive force (EMF); electrical current happens only if there is an electrical (potential) force of some form A 1.5 battery has a potential of 1.5 Volts between its two terminals (+ and -) The water tank and water pipe analogy (water level in the tank is analogous to the voltage and the flow rate of water in the pipe to the current); higher voltage will yield a stronger current. In electricity, however, the circuit must be complete to create a flow The potential difference (voltage) will determine the electron velocity of the current (more pressure, the quicker the flow; in fact electron velocity is often measured in voltage). 1 volt = the potential difference across a conductor when a 1A current provides 1W of power (V=W/A)
Power (Watts) Power consumption of a device is the rate at which it consumes electric energy Power is energy per time (what is the actual work that can be obtained from the electrical circuit) Watt (W) = the rate of 1 Joule per second One watt equals 1/746 horsepower A 100W light bulb will consume about 100 Joule of energy every second As seen in the equation of Volts, power is a measure combined from potential and current (W=I V)
Magnetism Electrical current creates a magnetic field around it; a steady current creates a steady magnetic field Coil allowing to contain a large area of wire within a small space; therefore enhancing the magnetic field (creating an electromagnet); controlling the current will control the magnetism strength The two ends of the coil are the magnet's poles (north being the one attracted to the earth s north pole which is a magnetic south-pole) The strength of the magnet is proportional to the current and to the number of turns in the coil (twice the amount of turns, twice the magnetic strength)
AC DC Direct Current an electrical current that flows in one direction in an electrical circuit Alternating Current a current that constantly reverses its direction (at a certain frequency); in North-America, the power outlet provides an AC that reverses direction 60 times a second. Its voltage moves from negative to positive values at a frequency of 60 Hz (sometimes in broken flourescent bulbs one can sense the resulting flicker) AC is useful because it is cheaper to produce in large quantities and also easier and cheaper to transform into lower/higher potentials.
Adding dbs When Adding two dbs of sound intensity or sound pressure we have to decide whether the two signals are correlated or not We convert back to pressure or intensity values and add: Correlated: Ptotal(t) = P1(t)+P2(t)+P3(t) +Pn(t) Uncorrelated: Ptotal=root of (P1 2 + P2 2 + P3 2 + Pn 2)
SIL The flow of energy through a unit area Watts per unit area Sound Power Level / radiating area Reference = actual power density of 1 picowatt per square meter SIL = 10Log (I / I-reference) An integer change is approx. what the ear can tell
SWL Sound Power Level Measure of the total power radiating from a source Reference = power level of 1 picowatt (10-12 Watt) Sound Power = Sound energy by a source per unit of time (Watt)
Joule Joule = A unit of electrical energy equal to the work done when a current of one ampere passes through a resistance of one ohm for one second (synonymous with watt-second). 1 amper x 1 volt x 1 second 1 amper x 1 ohm x 1 second 0.0002390 Calories
Watt The rate of energy transfer equivalent to one ampere under an electrical pressure of one volt One watt equals 1/746 horsepower 1 Joule of energy per second