# DB OR NOT DB

#### DB OR NOT DB

#### by Bruce Bartlett

In the studio, we need to set and measure signal levels, andmatch equipment levels. We also need to evalute microphones by their sensitivity specs. To learn these skills, it helps to understand the decibel, the unit of measurement of audio level.

**DEFINITIONS**

In a recording studio, "level" originally meant power, andamplitude referred to voltage. Nowadays, many audio people alsodefine "level" in terms of voltage or sound pressure, even though this terminology is not strictly correct. You should know bothdefinitions in order to communicate.Audio level is measured in decibels (dB). One dB is the smallestchange in level that most people can hear--the just-noticeabledifference. Actually, the just- noticeable-difference varies from0.1 dB to about 5 dB, depending on bandwidth, frequency, programmaterial, and the individual. But 1 dB is generally accepted asthe smallest change in level that most people can detect. A 6 to10 dB increase in level is considered by most listeners to be"twice as loud."Sound pressure level, signal level, and change in signal levelall are measured in dB.

**SOUND PRESSURE LEVEL**

Sound pressure level (SPL) is the pressure of sound vibrationmeasured at a point. It's usually measured with a sound levelmeter in dB SPL (decibels of sound pressure level).The higher the sound pressure level, the louder the sound. Thequietest sound you can hear, the threshold of hearing, is 0 dBSPL. Average conversation at one foot is 70 dB SPL. Averagehome-stereo listening level is around 85 dB SPL. The threshold ofpain--so loud that the ears hurt and can be damaged -- is 125 to130 dB SPL.Sound pressure level in decibels is 20 times the logarithm of theratio of two sound pressures:dB SPL = 20 log (P/P ref)where P is the measured sound pressure in dynes/cm^2, and P refis a reference sound pressure: 0.0002 dyne/cm^2 (the thresholdof hearing).(In the equations in this article, ^ means exponent, or "raisedto the power of.")

**SIGNAL LEVEL**

Signal level also is measured in dB. The level in decibels is 10times the logarithm of the ratio of two power levels:dB = 10 log (P/P ref)where P is the measured power in watts, and P ref is a referencepower in watts.Recently it's become common to use the decibel to refer tovoltage ratios as well:dB = 20 log (V/V ref)where V is the measured voltage, and V ref is a reference voltage.This expression is mathematically equivalent to the previous one,because power equals the square of the voltage divided by thecircuit resistance:dB = 10 log (P1/P2)= 10 log [(V1^2/R)/(V2^2/R)]= 10 log (V1^2/V2^2)= 20 log V1/V2The resistance R (or impedance) in this equation is assumed tobe the same for both measurements, and thus divides out.Signal level in decibels can be expressed in various ways, usingvarious units of measurement:*dBm: decibels referenced to 1 milliwatt*dBu or dBv: decibels referenced to 0.775 volt (dBu is preferred)*dBV: decibels referenced to 1 volt

**dBm**

If you're measuring signal power, the decibel unit to use is dBm,expressed in the equationdBm = 10 log (P/P ref)where P is the measured power, and P ref is the reference power(1 millwatt).For an example of signal power, use this equation to convert 0.01watt to dBm:dBm = 10 log (P/P ref)= 10 log (0.01/0.001)= 10So, 0.01 watt is 10 dBm (10 decibels above 1 milliwatt).Now convert 0.001 watt (1 milliwatt) into dBm:dBm = 10 log (P/P ref)= 10 log (0.001/0.001)= 0So, 0 dBm = 1 milliwatt. This has a bearing on voltagemeasurement as well.Any voltage across any resistance that results in 1 milliwatt is0 dBm. This relationship can be expressed in the equation0 dBm = V^2/R = 1 milliwattwhere V = the voltage in volts, and R is the circuit resistancein ohms.For example, 0.775 volt across 600 ohms is 0 dBm. One volt across1000 ohms is 0 dBm. Each results in 1 milliwatt.Some voltmeters are calibrated in dBm. The meter reading in dBmis accurate only when you're measuring across 600 ohms. For anaccurate dBm measurement, measure the voltage and circuitresistance, then calculate:dBm = 10 log [(V^2/R)/0.001]

**dBv or dBu**

Another unit of measurement expressing the relationship ofdecibels to voltage is dBv or dBu. This means decibels referencedto 0.775 volt. This figure comes from 0 dBm, which equals 0.775volt across 600 ohms (because 600 ohms used to be a standardimpedance for audio connections):dBu = 20 log (V/V ref)where V ref is 0.775 volt.

**dBV**

Signal level also is measured in dBV (with a capital V), ordecibels referenced to 1 volt:dBV = 20 log (V/V ref)where V ref is 1 volt.For example, use this equation to convert 1 millivolt (0.001volt) to dBV:dBV = 20 log (V/V ref)= 20 log (0.001/1)= -60So, 1 millivolt = -60 dBV (60 decibels below 1 volt).Now convert 1 volt to dBV:dBV = 20 log (1/1)= 0So, 1 volt = 0 dBV.To convert dBV to voltage, use the formulaVolts = 10^(dBV/20)

**CHANGE IN SIGNAL LEVEL**

Decibels also are used to measure the change in power or voltageacross a fixed resistance. The formula isdB = 10 log (P1/P2)ordB = 20 log (V1/V2)where P1 is the new power level, P2 is the old power level, V1 isthe new voltage level, and V2 is the old voltage level.For example, if the voltage across a resistor is 0.01 volt, andit changes to 1 volt, the change in dB isdB = 20 log (V1/V2)= 20 log (1/0.01)= 40 dBDoubling the power results in an increase of 3 dB; doubling thevoltage results in an increase of 6 dB.

**THE VU METER, ZERO VU, AND PEAK INDICATORS**

A VU meter is a voltmeter of specified transient response,calibrated in volume units or VU. It shows approximately therelative volume or loudness of the measured audio signal.The VU-meter scale is divided into volume units, which are notnecessarily the same as dB. The volume unit corresponds to thedecibel only when measuring a steady sine wave tone. In otherwords, a change of 1 VU is the same as a change of 1 dB only whena steady tone is applied.Most recording engineers use 0 VU to define a convenient "zeroreference level" on the VU meter. When the meter on your mixer orrecorder reads "0" on a steady tone, your equipment is producinga certain level at its output. Different types of equipmentproduce different levels when the meter reads 0. 0 VU correspondsto:*+8 dBm in older broadcast and telephone equipment*+4 dBm in balanced recording equipment*-10 dBV in unbalanced recording equipmentWhen a tape operator says to a mixing engineer, "Send me a 0 VUtone," it means, "Send me a tone that reads 0 on your VU meter."The signal level itself isn't too important because the tapeoperator receiving the tone just wants to match the tape-deckmeters to those on the console.A 0 VU recording level (0 on the record level meter) is thenormal operating level of an analog tape recorder; it producesthe desired recorded flux on tape. A "0 VU recording level" doesnot mean a "0 VU signal level."With a VU meter, 0 VU corresponds to a recording level 8 dB belowthe level that produces 3 percent third-harmonic distortion onanalog tape at 400 Hz. Distortion at 0 VU typically is below 1percent.The response of a VU meter is not fast enough to track rapidtransients accurately. In addition, when a complex waveform isapplied to a VU meter, the meter reads less than the peak voltageof the waveform. (This means you must allow for undisplayed peaksabove 0 VU that use up headroom.)In contrast, a peak indicator responds quickly to peak programlevels, making it a more accurate indicator of recording levels.One type of peak indicator is an LED that flashes on peakoverloads. Another is the LED bargraph meter commonly seen oncassette decks. Yet another peak indicator is the PPM (peakprogram meter). It is calibrated in dB, rather than VU. Unlikethe VU meter reading, the PPM reading does not correlate withperceived volume.In a digital recorder, the meter is an LED or LCD bargraph meterthat reads up to 0 dBFS (FS means Full Scale). In theory, 0 dBFSmeans all 16 or 24 bits are ON. The OVER indication means thatthe input level exceeded the voltage needed to produce 0 dBFS,and there is some short-duration clipping of the output analogwaveform. Some manufacturers calibrate their meters so that 0dBFS is less than 16 or 24 bits ON; this allows a little headroom.

**BALANCED VERSUS UNBALANCED EQUIPMENT LEVELS**

Generally, audio equipment with balanced (3-pin) connectors worksat a higher nominal line level than equipment with unbalanced(phono) connectors. There's nothing inherent in balanced orunbalanced connections that makes them operate at differentlevels; they're just standardized at different levels.These are the nominal (normal) input and output levels for thetwo types of equipment:*Balanced: +4 dBm (1.23 volts)*Unbalanced: -10 dBV (0.316 volt)In other words, when a balanced-output recorder reads 0 VU on itsmeter with a steady tone, it is producing 1.23 volts at itsoutput connector. This voltage is called +4 dBm when referencedto 1 milliwatt. When an unbalanced-output recorder reads 0 on itsmeter with a steady tone, it is usually producing 0.316 volt atits output connector. This voltage is called -10 dBV whenreferenced to 1 volt.

**INTERFACING BALANCED AND UNBALANCED EQUIPMENT**

There's a difference of 11.8 dB between +4 dBm and -10 dBV. Tofind this, convert both levels to voltages:dB = 20 log (1.23/0.316) = 11.8So, +4 dBm is 11.8 dB higher in voltage than -10 dBV (assumingthe resistances are the same).A cable carrying a nominal +4 dBm signal has a signal-to-noiseratio (S/N) 11.8 dB better than the same cable carrying a -10 dBVsignal. This is an advantage in environments with strong radiofrequency or hum fields. But in most studios with short cables,the difference is negligible.Connecting a +4 dBm output to a -10 dBV input might causedistortion if the signal peaks of the +4 equipment exceed theheadroom of the -10 equipment. If this happens, use a pad toattenuate the level 12 dB (Fig. 1). The pad converts frombalanced to unbalanced as well as reducing the level 12 dB. Youmay have to substitute a stereo phone plug for the 3-pinconnector.

*FIGURE 1. Use a pad of 12 dB to match a balanced +4dBm output to **an unbalanced -10dBV input.*

You don't always need that pad. Many pieces of equipment have a+4/-10 level switch. Set the switch to the nominal level of theconnected equipment.

**MICROPHONE SENSITIVITY**

Decibels are an important concern in another area: microphonesensitivity. A high-sensitivity mic puts out a stronger signal(higher voltage) than a low-sensitivity mic when both are exposedto the same sound pressure level.A mic-sensitivity spec tells how much output (in volts) amicrophone produces for a certain input (in SPL). The standard ismillivolts per pascal, where one pascal (Pa) is 94 dB SPL.A typical "open-circuit sensitivity" spec is 5.5 mV/Pa for acondenser mic and 1.8 mV/Pa for a dynamic mic. "Open-circuit"means that the mic is unloaded (not connected to a load, orconnected to a mic preamp with a very high input impedance).If the spec is 5.5 mV/Pa, that means the mic produces 5.5 mV whenthe SPL at the mic is 94 dB SPL.If you put a microphone in a 20 dB louder sound field, itproduces 20 dB more signal voltage. For example, if 74 dB SPL ingives 0.18 mV out (-75 dBV), then 94 dB SPL in gives 1.8 mV out(-55 dBV.) 150 dB SPL in gives 1.1 volt out (+1 dBV), which isapproximately line level! That's why you need so much inputpadding when you record a kick drum or other loud source.

Copyrighted 1999 by Deltamedia. May not be reproduced in whole or part without permission.