Audio-frequency transformers are used mainly for matching impedances and transmitting audio frequencies. They also provide isolation from direct currents and present balanced impedances to lines or circuits.

**Types of Magnetic Cores**

The magnetic core for this type of transformer is usually an EI or EE type using either audio-grade silicon steel or nickel-alloy tape cores in toroidal form are used for extreme bandwidths. High permeability ferrite cores with highly polished mating surfaces are also used to obtain wide bandwidths.

If there is no direct current in the windings, it is possible to design a small, high quality audio transformer with a high permeability ferrite core. Material with initial permeability above 10 000 is available. To minimize the air gap in the assembled core, the mating surfaces are ground flat and polished to a mirror finish. Because of the small core volume, when these transformers are used at low frequencies care must be taken to avoid core saturation. The maximum flux density in a core is given by:

**B**

_{max }= (3.49 x 10^{6}) E/fNA_{c }
where,

B

_{max }= maximum flux density (gauss),
E = rms volts,

f = frequency (hertz),

N = number of winding turns,

A

_{c }= cross section of core (square inches)**Design of Audio-Frequency Transformers**

**Important parameters**- Important parameters are generator and load impedances, R

_{s}and R

_{l}, respectively; generator voltage ; frequency band to be transmitted; harmonic distortion; and operating voltages (for adequate insulation).

**Midband Frequencies**- The relative low- and high-frequency responses are taken with reference to midband frequencies where

**α E**

_{out}/E_{g}= [( 1 + R_{s}/R_{l}) + R_{l}/a^{2}R_{l}]^{-1}_{}**Low Frequencies**- At low frequencies, the equivalent unity-ratio network of a transformer becomes approximately as shown in Fig. 1.

Fig.1 Equivalent network of an audio frequency transformer at low frequencies |

Amplitude = [( 1 + (R'

_{par}/X_{m})^{2}]^{-1/2}
Phase angle = tan

^{-1}(R'_{par}/X_{m})
where,

R'

_{par }_{}= (R_{1}R_{2}a^{2}) / (R_{1}+ R_{2}a^{2})
R

_{1}= R_{g}+ R_{p}
R

_{2}= R_{l}+ R_{s}
X

_{m}= 2πfL_{p}
In a good output transformer, R

_{p}, R_{s}and R_{c }may be neglected. In input or interstage transformers, R_{c }may be omitted.**High Frequencies**- At high frequencies, neglecting the effect of winding and other capacitances, the equivalent unity-ratio network becomes approximately as in Fig. 2.

Fig.
2 Equivalent network of an audio frequency transformer at high
frequencies, neglecting the effect of the winding shunt capacitances |

Amplitude = [1 + (X

_{l}/R'_{se})]^{-1/2}
Phase angle = tan

^{-1}(X_{l}/R'_{se})
where,

R'

_{se }= R_{1}+ R_{2}a^{2},
X

_{l }= 2 πf l_{scp},
l

_{scp}= inductance measured across primary with secondary short-circuited = l_{p}+ a^{2}l_{s}.
The low- and high-frequency responses are shown by the curves of Fig. 3.

Fig. 3 Universal frequency and phase response characteristics of output transformers. |

If at high frequencies the effect of winding and other capacitances is appreciable, the equivalent network on a 1:1 turns-ratio basis becomes as shown in Fig. 4.

In a step-up transformer, C

Fig. 4 Equivalent network of a 1:1 turns ratio audio frequency transformer at high frequencies when effect of winding shunt capacitances is apprecaible |

In a step-up transformer, C

_{2}= equivalent shunt capacitances of both windings. In a step-down transformer, C_{2}shunts both leakage inductances and R_{2}. The relative high-frequency response of this network is given by
This high-frequency response is plotted in Fig. 5 for R

_{2}= R_{1}(matched impedances), based on simplified equivalent networks as indicated. At frequency f_{r}X_{l}= X_{c}and B = X_{c}/R_{l}.Fig. 5 Transformer characteristics at high frequencies for matched impedances |

**Harmonic Distortion**- Harmonic distortion requirements may a constitute a deciding factor in the design of transformers. Such distortion is causffed by either variations in load impedance or non linearity of magnetizing current. The percent harmonic voltage appearing in the output of a loaded transformer is given by

(Percent harmonics = 100E

_{h}/E_{f}= 100I_{h}/I_{f}( R'_{par}/X_{m}) [ 1 - (R'par/4X_{m}) ]
where 100I

_{h}/I_{f}= percent of harmonic current measured with a zero-impedance source (values in table 1 are for a 4-percent silicon-steel core).Table 1 Harmonics by various flux densities B_{m } in a 4-percent silicon-steel-core audio trasformer |

**Insertion Loss**- Insertion loss is the loss introduced into the circuit by addition of the transformer. At midband, the loss is caused by winding resistance and core loss. Frequency discrimination adds to this at low and high frequencies. Insertion loss is input divided by output expressed in decibels, or (in terms of measured voltages and imepdance)

(dB insertion loss) = 10 log [ (E

_{g}^{2}R_{1}) / (4E_{o}^{2}R_{g}) ]**Impedance Match**- For maximum power transfer, the reflected load impedance should equal the generator impedance. Winding resistance should be included in the is calculation: For matching

_{g}= a

^{2}( R

_{1 }+ R

_{s}) + R

_{p}

Also, in a properly matched transformer

R

where,_{g}= a^{2}R_{1 }= (Z_{oc}x Z_{sc})^{1/2}Z

_{oc}= transformer primary open-circuit impedance,

Z

_{sc }= transformer primary impedance with secondary winding short-circuited.

If more than one secondary is used, the turns ratio to match impedances properly depends on the power delivered from each winding.

N_{s}/N

_{p}= [ (R

_{a}/R

_{g}) (W

_{a}/W

_{p}) ]

^{1/2}

Example : Using Fig. 6

N

_{2}/N

_{p}= [(10/600)(10/16)]

^{1/2}= 0.102

N

_{3}/N

_{p}= [(50/600)(5/16)]

^{1/2}= 0.161

N

_{4}/N

_{p}= [ (100/600)(1/16)]

^{1/2}= 0.102

Fig. 6 Multisecodary audio trasformer |

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