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For matching a circuit of output impedance 200 ohms with a load of 8 ohms, the turns ratio of the two winding of transformer should be
- a)25
- b)1/25
- c)1/5
- d)5
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
For matching a circuit of output impedance 200 ohms with a load of 8 o...
Concept:
Transformers are used for impedance matching applications. This is explained with the help of the following figure:
The load impedance reflected on the primary side is redrawn as shown:
For the load to match with the source resistance:
Calculation:
With RL = 8 Ω, and RS = 200 Ω, the transformation ratio will be:
Most Upvoted Answer
For matching a circuit of output impedance 200 ohms with a load of 8 o...
Matching a circuit of output impedance 200 ohms with a load of 8 ohms requires the use of a transformer. The turns ratio of the two windings of the transformer can be calculated using the impedance transformation formula.
The impedance transformation formula states that the ratio of the primary impedance (Zp) to the secondary impedance (Zs) is equal to the square of the turns ratio (Np/Ns) of the transformer.
The formula can be expressed as:
Zp / Zs = (Np / Ns)^2
In this case, the load impedance (Zs) is 8 ohms and the output impedance (Zp) is 200 ohms. We need to find the turns ratio (Np/Ns) that satisfies this equation.
First, let's rearrange the formula to solve for Np/Ns:
(Np / Ns)^2 = Zp / Zs
Taking the square root of both sides:
Np / Ns = sqrt(Zp / Zs)
Substituting the given values:
Np / Ns = sqrt(200 / 8)
Simplifying the expression:
Np / Ns = sqrt(25)
Taking the square root of 25:
Np / Ns = 5
Therefore, the turns ratio of the two windings of the transformer should be 5. This means that the primary winding should have 5 times more turns than the secondary winding.
The turns ratio of the transformer determines the voltage ratio between the primary and secondary windings. In this case, the voltage across the load will be 5 times lower than the voltage across the output impedance. This allows for efficient power transfer from the circuit to the load.
By choosing the appropriate turns ratio, we can match the output impedance of the circuit with the load impedance, ensuring maximum power transfer and minimizing reflection of power.
The impedance transformation formula states that the ratio of the primary impedance (Zp) to the secondary impedance (Zs) is equal to the square of the turns ratio (Np/Ns) of the transformer.
The formula can be expressed as:
Zp / Zs = (Np / Ns)^2
In this case, the load impedance (Zs) is 8 ohms and the output impedance (Zp) is 200 ohms. We need to find the turns ratio (Np/Ns) that satisfies this equation.
First, let's rearrange the formula to solve for Np/Ns:
(Np / Ns)^2 = Zp / Zs
Taking the square root of both sides:
Np / Ns = sqrt(Zp / Zs)
Substituting the given values:
Np / Ns = sqrt(200 / 8)
Simplifying the expression:
Np / Ns = sqrt(25)
Taking the square root of 25:
Np / Ns = 5
Therefore, the turns ratio of the two windings of the transformer should be 5. This means that the primary winding should have 5 times more turns than the secondary winding.
The turns ratio of the transformer determines the voltage ratio between the primary and secondary windings. In this case, the voltage across the load will be 5 times lower than the voltage across the output impedance. This allows for efficient power transfer from the circuit to the load.
By choosing the appropriate turns ratio, we can match the output impedance of the circuit with the load impedance, ensuring maximum power transfer and minimizing reflection of power.
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