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X-Y-Z

zenith:  Another word for tangency.

zero-crossing:  The point in a sample where the waveform reaches zero amplitude.  When editing

loop, it is usual that both the beginning and end points of a loop are at a zero crossing.  How-
ever, zero crossings are not important if the beginning and end points of the loop are at the
same signal level and have about the same waveform slope.  The harmonic content of the wave
in the region around the loop point has much more effect on the quality of the loop than
whether the loop point is at a zero-crossing.

zero frame:  The first frame of a roll of film or video tape, appropriately numbered 00:00:00:00.

zero-level:  A level of 0dBV.  All measurements are made relative to this level as it represents

(in properly calibrated equipment) the optimal recording or broadcast level.  Higher signal
levels than this indicate the possibility of overmodulation.  Significantly lower levels than this in-
dicate the possibility of undermodulation.  See decibel, operating level.

zero-locate:  See auto locator.

zero return:  A control on a tape recorder which will automatically stop the tape on rewind

when the tape counter reaches zero.

zone:  See split point.


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Appendix A

Logarithms

Exponents

A logarithm (log) is the exponent to which a
given base must be raised to equal the quan-
tity.  For example:

Since   Log

2

=

100 , then the log of 100 to

the base 10 is equal to 2, or,   Log

10

100

=

2

Bases

There are three popular bases in use: 10, 2,
and   e .  Logarithms to the base 10 are called

common logarithms (log).  Logarithms in
base   e  are called natural logarithms, where
    e

2.71828 , abbreviated

 

Ln:

Base 10

  

Log

10

2 0.301 is 10

0.301

2

Log

10

200 2.301 is 10

2.301

200

Base 2

  

Log

2

8 3 is 2

3

8

Log

2

256 8 is 2

8

256

Base e

    

Ln

e

2.71828=1 is e

1

=

2.71828

Ln

e

7.38905= 2 is e

2

=

7.38905

Rules of Exponents

Since a logarithm is an exponent, the rules of
exponents apply to logarithms:

log (M   N) = (log M) + (log N)
log (M/N) = (log M) - (log N)

log 

  M

N

= N log M

Decibels

The bel is a logarithmic unit used to indicate a
ratio of two power levels (sound, noise, or sig-
nal voltage, or microwaves).  It is named in
honor of Alexander Graham Bell (1847-1922)
whose research accomplishments in sound
were fundamental.  A 1-bel change in
strength represents a change of ten times the
power ratio.  In normal practice, the bel is a
rather large unit, so the decibel (dB), which is

  

1

10

 of a bel, is commonly used.

Number ofdB = 10 log P2/P1

A 1dB increase is an increase of 1.258 times
the power ratio: 1dB = 10 log 1.258.  A 10dB
increase is an increase of 10 times the power
ratio, or 10dB = 10 log 10.
Other examples are:

3dB = 2 times the power ratio

20dB = 100 times the power ratio

-30dB = 0.001 times the power ratio

Note that the decibel is not an absolute
quantity.  It merely represents a change in
power level relative to the level at some
different time or place.  It is meaningless to
say that a given amplifier has an output of
xdB unless that output is referenced to a
specific power level.  If we know the value of
the input power, then the ratio of the output
power to the specific input power (the power
gain) may be expressed in dB.
If a standard reference level is used, then
absolute power may be expressed in dB
relative to that standard reference,
commonly 1mW.  Power refrenced to this
level is expressed in dBm.  Here are a few
power ratios and associated dBms:

Power Ratio

dBm

1.258

1

2

3

10

10

100

20

0.001

-30


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Appendix B

Alternating Current

To calculate power requirements:

The power required by an electrical device will be
expressed in either watts (W), amperes (A), or as
VA (Volt Amperes).  For these purposes, VA=W.
To convert from A or VA to W:

P = E   I   or,  P/E = I

Where P=power in Watts, E is the voltage (in
Volts, either 120 or 240), and I is amps.  Ulti-
mately, the total power should be expressed in
amperes because electrical circuits are rated in
amperes.  A standard outlet is 15A.  For example,
if a mixer is 120V and 70W, the formula is 70/120
= .58A.  If a limiter is 120V, 30VA, the power re-
quired is 30/120 = .25A.

Wiring practice:  220VAC One-Phase
For single-phase, 220VAC split into two 110VAC
halves, at the transformer, the high-voltage inputs
come in via three wires:  the 220VAC output
winding is divided into two equal parts and the
third wire is the center tap.  If the center tap is used
as a reference, the voltage between it and either of
the other two wires will be equal, or about
110VAC; these wires are called legs.

The three wires from the transformer are twisted
together and run as a bundle to the service en-
trance.  The non-insulated wire is the center tap
and the electrical code requires that this wire be
connected to ground at the service entrance.

Inside the main circuit breaker box are two large,
insulated (usually black) wires that go to the two
large screw terminals at the top of the banks of the
circuit breakers.  A volt meter will read 220VAC
across the two wires, and 110VAC between either
of the wires and the metal case of the box.  Circuit
breaker boxes are set up so that the breakers in a
column alternate legs so as to load-share the cur-
rent draw from the transformer.

The third wire, color-coded white, goes to a sepa-
rate terminal block away from the circuit breakers.
This is the neutral, the center tap of the trans-
former.  This wire is connected to ground at this
point.  The terminal block has both the white neu-
tral wires from all the circuits and all the ground
wires from these circuits.  This is the only place
where ground and neutral should be connected.
Ground wire is green.

Wiring practice:  3-Phase Wye 120/208
There are four wires used in this connection.  A, B,
and C are the three hot leads and the fourth wire
is neutral.  If you measure the voltage between
each of the leads and neutral, you will find
120VAC.  If you measure between any two of the
hot leads, you will find 208VAC (because the two
120VAC circuits are 120˚ apart in phase.)  There
is no ground connection because the ground is
made at the service entrance.

Because of Ohm’s law and the resistance in the
neutral wire, long runs will develop a voltage in
the neutral wire.  It can get upwards of 80VAC
between neutral and ground in a long power run;

Wiring practice:  3-Phase Delta 120/208

Delta wiring has three wires, the main configura-
tion used in major high-tension lines because there
is no need for a fourth wire.  Four-wire Delta has
the fourth wire coming form the center tap of only
one of three transformer windings, requiring a
more complicated transformer.  Because of this,
you only have two connections that yield 120V;
connecting to the third hot lead will give you
208V, between the wild leg* and neutral.  If you
measure between any two of the hot leads, you
will find 240V.  Note that Wye and Delta look the
same; it takes a volt meter to tell the difference.
(Ø = phase)

Wires

Wye

Delta

ØA to Neutral

120VAC

120VAC

ØB to Neutral

120VAC

208VAC*

ØB to Neutral

120VAC

120VAC

ØA to ØB

208VAC

208VAC

ØB to ØC

208VAC

208VAC

ØC to ØA

208VAC

 

208VAC


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Appendix B

Troubleshooting

First, find the main circuit breaker box.  This will
yield the power available and its type.  Opti-
mally, there should be a master label which tells
you if the panel is one-phase or three-phase.  If
there is a large master breaker at the top of the
box, look at the number of sections operated:  if
there are two, there is most likely single-phase.  If
there are three, then it is probably three-phase.

Underneath the master breaker (if there is one),
there will usually be two columns of breakers.  In
the case of a single-phase box, every other
breaker in a column is connected to the same leg,
and so also for rows.  With three-phase, it is
every third breaker in each column.  To connect to
power on the same leg, look for outlets with cir-
cuit breakers that are separated.  Adjacent
breakers are on different legs.

Next, look for grounded outlets close to where
you need power.  Make a visual inspection,
looking for any damage to outlets or covers, and
for evidence of major wear, such as a loose fit
when a plug is inserted.  If possible, check to
make sure that the circuit breaker in question ac-
tually controls the outlet in question.

Use a voltmeter to check the outlets.  There
should be 120VAC between hot and neutral and
also between hot and ground.  Then make sure
there is minimal voltage between neutral and
ground.  Between outlets (using an extension
cord), measuring from hot to hot will yield 0V if
the outlets are on the same leg; 208V if they are
on different legs of a three-phase circuit; 240V for
different single-phase circuit.

Impedance

Impedance and signal level are two different
things.  Level is the voltage swing in a circuit; the
higher the level, the higher the voltage swings.
Impedance is the resistance to signal flow in a
circuit.  It is the amount of power needed to move
a signal around a circuit.

Connecting two devices and sending a signal be-
tween the two uses power.  The sending device
has to supply power in the form of a signal that
is sent to the receiving device.

To determine the impedance of cables and patch
cords, first, look at the spec for the cable.  On it
will be a value for capacitance per foot and in-
ductance per foot.  Using

  Z= L/C

where Z = the cable impedance in 

, L = the cable

inductance in Henrys and C = the cable capaci-
tance in Farads.  For example, for

C = 34pF,  L = .17µH,  Z 

 70

Professional line-level equipment designed to
drive low source impedances, e.g., 600

 loads,

tends to have source output impedances in the
range of 50

-600

.  There is no relationship be-

tween impedance and balanced circuits.  In prac-
tice, there are very few low source load imped-
ances: telephone lines and tube circuits.

Semi-professional equipment, designed to drive
loads of 10K

, tend to have source output im-

pedances in the range of 600

-2K

.

Devices that are designed to be connected as
bridging a 600

 source load impedance typically

have impedances of 5K

-10K

 or greater.

Microphone inputs typically have a load termina-
tion impedance of about 1.4K

 for low imped-

ance microphones (mics with a source output im-
pedance of 50

-600

), mid-range mics 1k

-4k

,

and high impedance mics above 25k

.  Low im-

pedance microphones are better as they allow for
long mic cables without noticeable hum or high-
frequency loss.

Home stereo equipment has source output im-
pedances between 1K

-10K

.  This is the actual

value inside the box at the circuit level; their load
termination impedance ranges from 50K

-

200K

.