Transformer impedance is a critical parameter in electrical power systems, influencing power transfer, voltage regulation, and system stability.
In this blog post, we will delve into the intricacies of reflected impedance in transformers, exploring its mathematical formulation and practical implications.
What Is a Reflected Impedance
The reflected impedance refers to the impedance or resistance seen by the primary circuit when a load is connected to the secondary side.
When a load is connected to the secondary winding of a transformer, it creates a load impedance on the secondary side. This secondary load impedance is then “reflected” back to the primary side of the transformer, appearing as a different impedance value to the primary circuit.
Formula for Reflected Resistance
The reflected resistance, also known as the reflected impedance, is a key concept in understanding how transformers match impedances between circuits. In an ideal transformer, the impedance seen by the primary circuit is the load impedance connected to the secondary windings multiplied by the square of the transformer’s voltage ratio. This relationship is described by the following formula:
Reflected Resistance (Rr) = (Ns/Np)^2 × RL
Where:
- Rr is the reflected resistance seen by the primary circuit
- Ns is the number of turns in the secondary winding
- Np is the number of turns in the primary winding
- RL is the load resistance connected to the secondary circuit
This formula demonstrates that the impedance transformation ratio is equal to the square of the turns ratio (Ns/Np). For example, if a transformer has a turns ratio of 10:1 (Ns/Np = 10), and a 100 ohm load is connected to the secondary winding, the reflected resistance seen by the primary circuit would be:
Rr = (10)^2 × 100 ohms = 10,000 ohms
This means that the 100 ohm load connected to the secondary winding appears as a 10,000 ohm load to the primary circuit.
