Yamaha P-2200/2201 - Manual (Page 57)

NOTES:
"N
1
" is the number of turns on the primary side of
the transformer, " N 2 " is the number of turns on the
secondary side of the transformer.
"V
1
" is the voltage level on the primary side of the
transformer, " V 2 " is the voltage level on the secondary
side of the transformer.
"I 1 " is the current level on the primary side of the
transformer, " I
2
" is the current level on the secondary
side of the transformer.
"Z 1 " is the impedance of the circuit seen at the
primary side of the transformer, "Z
2
" is the impedance
seen at the secondary side of the transformer.
Equations:
1 . V 1 / V 2 = N 1 / N 2
2 . l / I
2
= N
2
/ N
1
3 . Z
1
/ Z
2
= [N
1
/N
2
]
2
Equation 1 shows that the voltage ratio between the
primary and secondary windings of a transformer is
directly proportional to the transformer's turns ratio.
This equation is applicable to voltage level matching
between two circuits.
Equation 2 shows that the current ratio between the
two windings of the transformer is inversely proportional
to the turns ratio.
Equation 3 describes the impedance matching action
of a transformer. Note that the impedance ratio between
the primary and secondary of the transformer is directly
proportional to the square of the turns ratio.
Often, the transformer spec sheet gives its impedance
ratio, but not its turns ratio. A simple manipulation of
Equation 3 solves the problem:
Consider the following example:
A transformer has a primary impedance of 15K-ohms,
and a secondary impedance of 600 ohms. If the input
(primary) voltage is -16dB (0.123 volts), what is the
output voltage?
From Equation 4 : N 1 / N 2 =
Since N
1
/ N
2
= V
1
/ V
2
(Equation 1 ) , then:
5 = ( 0 . 1 2 3 volts) / V
2 ,
o r V
2
= ( 0 . 1 2 3 volts) / 5
Answer: V 2 =24.6mV=-30dB
From this example, transforming a -16dB (0.123
volts) hi-fi output, with a source impedance of 15K-ohms,
to a professional input with an input impedance of
600-ohms also drops the level a full 14dB to -30dB
(24.6mV).
Fig. 84 - Typical Audio Transformer
OTHER CONSIDERATIONS
A transformer actually doesn't have any impedance
of its own. It merely transforms an impedance at its
primary (according to Equation 3) to a corresponding
impedance at its secondary. Thus, the transformer in the
above example has an impedance ratio of 15,000-to-
600 = 25-to-1. If a 150K-ohm circuit is connected to its
primary, the impedance seen at the secondary will be
150,000/25 = 6000 ohms. Since this impedance trans-
formation works in both directions, if a 6000-ohm
circuit is connected to the secondary of the transformer,
the impedance seen at the primary will be 150,000-
ohms. Voltage and current matching also work in both
directions.
However, a transformer that is specified as having an
impedance ratio of 15,000 ohms-to-600 ohms has been
manufactured specifically to transform those imped-
ances. If it is used with circuits having considerably
greater or smaller impedances, its frequency response
may be degraded, or it can "ring" (resonate). One way
to overcome this problem is to terminate the transformer
with its rated impedance as discussed on Page SIX 2.
It is also important to use a transformer at the
voltage and power level for which it was planned. For
example, a mic level transformer will probably saturate
(distort) if it is used for line level circuit matching. Also,
a line level transformer will not perform properly if it is
used for mic level circuit matching (the magnetic fields
are so weak that non-linearity occurs). Whenever possible,
pick a transformer for each use according to the voltage
levels, power levels, and the impedances of the circuits
under consideration.
One other significant use of audio transformers is to
isolate the ground wire of one circuit from another to
prevent ground loops and reduce hum. The discussion of
balanced lines on Page EIGHT 5, and the grounding dis-
cussion on Page SIX 13 expand this concept.
Speaker level transformers (70-volt transformers,
and auto-transformers) are discussed on Page SEVEN 6.