What must the turns ratio of a transformer be to match a 2 ohm speaker to a 50 ohm source?

Answer 1

The turns ratio of a transformer is proportional to the voltages of the windings, not their impedances. To figure a transformer turns ratio based on the input and output impedances, you must calculate the ratio between the square roots of each of the two impedances.

For example, the turns ratio for this transformer would be 5:1 because it is the ratio of sqr(50) / sqr(2).

WK

Answer 2

For maximum power transfer, the load impedance should be equal to the source impedance. Since impedance varies with the square of the transformer turns ratio, the primary winding (connected to the source) should have 5 times the number of turns as the secondary winding (connected to the speaker).

Here's the math: The transformer has almost no power loss, so the power going into a transformer is essentially equal to the power going out of the transformer. The power going out of the transformer and into the speaker is:

Ps = (Vs^2) / Rs

where Vs is the secondary voltage (and the voltage on the speaker), and Rs is the speaker impedance.

Similarly, the power going into the transformer is

Pp = (Vp^2) / Rp

where Vp is the primary voltage and Rp is the apparent input impedance of the transformer that you want to be 50 ohms. Since the two powers are equal,

(Vp^2) / Rp = (Vs^2) / Rs

Rearranging,

(Vp/Vs)^2 = Rp/Rs

But the voltages on the primary and secondary of the transformer are in proportion to the turns ratio:

Vp/Vs = Np/Ns

Replacing turns ratio for voltage and taking the square root,

Np/Ns = (Rp/Rs)^0.5

For this problem,

Np/Ns = (50/2)^0.5 = (25)^0.5 = 5

or, the number of turns in the primary is 5 times the number in the secondary.

Answer 3

50 ohm / 2 ohm = 25
So it would be a 25:1 Ratio

Answer 4

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Answer 5

25:1

Answer 6

why on earth are you hooking up a speaker to a radio amplifier? it wont work.... AT ALL, but, take pictures with what you do. Im curious to see the hackjob...