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If we want to use a low impedance speaker or headphone in a crystal receiver, we need to use a audiotransformer.
The transformer converts a high input impedance (=primary impedance) to a low output impedance (=secondary impedance).

100 Volt line transformers which are used for 100 Volt loudspeakersystems are very suitable for this.
In 100 Volt loudspeakersystems the input of the transformer is connected to a audiosignal with a maximum amplitude of 100 Volt. The transformer converts this to a lower level, which drives the speaker.
Via several tap's on the transformer primary winding, you can select how much power the speaker gets.

The power of the tap determines the input impedance of this tap.
In the following table are some standard values for power and the corresponding input impedance.
We can calculate this with the formula: impedance = (100Volt x 100Volt) / power.

in Watt's
in k.Ohm
0.125 80
0.25 40
0.5 20
0.625 16
1.0 10
1.25 8
2.0 5
2.5 4
4.0 2.5
5 2
10 1.0
Left on this picture: audiotransformer brand: Visaton model: TR10.16
The input has tap's for 1, 2, 4, 8 and 16 k.Ohm.
The output has tap's for 4, 8 and 16 Ohm.

Right on this picture: audiotransformer brand: Adastra model: 952.431
The input has tap's for 5, 10, 20, 40 and 80 k.Ohm.
The output has tap's for 8 and 16 Ohm.


Schematic 1

Connection of a audiotransformer in a crystal receiver.
Capacitor C1 is for removing radio frequencies behind the diode
Toghether with the transformer primary impedance (Ztr), C1 forms a lowpassfilter with a frequency of f=1/ (2.pi.Ztr.C1).
This frequency must be minimal 4.5 kHz, than we have no reduction of audio quality.

The DC resistance of the transformer is much lower than the impedance for audio frequencies. That is why resistor R is added, the value of R must be about the transformer input impedance.
Capacitor C2 passes all audio currents, so there is no loss of audio signal across R. The full audio signal will stay across the transformer.
When R and C2 are not added, strong distortion can occur when receiving strong stations.

C2 and R form a highpassfilter with frequency f=1/(2.pi.R.C2)
This frequency must be lower than 50 Hz.

In the following table are some useable values for C1, R and C2 for a given transformer impedance.

impedance in k.Ohm.
C1 R C2
640 k.Ohm 47 pF 680 k.Ohm 10 nF
320 k.Ohm 100 pF 330 k.Ohm 22 nF
160 k.Ohm 220 pF 150 k.Ohm 47 nF
80 k.Ohm 390 pF 82 k.Ohm 100 nF
40 k.Ohm 820 pF 39 k.Ohm 220 nF
20 k.Ohm 1.5 nF 18 k.Ohm 470 nF
10 k.Ohm 3.3 nF 10 k.Ohm 1 uF

Series connection of primary windings.

Schematic 2 Schematic 3

If we need a higher input impedance, we can connect some transformers with the primary windings in series, the primary impedances can than be added.
The values of C1, R and C2 must correspond to the total input impedance.
In the schematic the black dots indicates the common connections of the transformers.

The secundary windings can be series connected like in schematic 2.
The secundary impedances can than be added, so two 8 Ohm winding become one 16 Ohm output.

The secundary windings can also be parallel connected (schematic 3).
The output impedance wil now be divided by 2.


Schematic 4.

4 trafo's in series.
The input impedance is 4 times the value of a single transformer.

The output windings are via a combination of series and parallel connection connected to the loudspeaker.
The output impedance is the same as a single transformer.


Transformer efficiency.

The power going into the primary winding must also come out of the secondary winding.
But in practice the transformer wil give some loss of power.

The transformer efficiency is equal to the output power divided by the input power.
In the ideal case the efficiency is 1.
Bigger transformers have in practice a better efficiency than smaller transformers.

For crystal receivers we need a efficiency of at least 0.60
The efficiency is sometimes also expressed as a loss in decibel (dB).

Loss (in dB) = 10 LOG efficiency.

The transformer 952.431 from Adastra has a efficiency of 0.79 which is a loss of 1 dB

Connecting the primary windings in series (schematic 2, 3 ,4) has no effect on the efficiency.

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